On Apr 6, 5:30 pm, Yusuf B Gursey <ybg@theworld.com> wrote:
> this deserves a follow-up on the islamic lunar months, that according
> to one theory were once luni-solar. I might change the title and add
> soc.history.medieval and I might delete alt.usage.english .
Also I will discuss the Arabic pre-Islamic calendar and other aspects of calendar and timekeeping.

>
> On Feb 13, 6:16 pm, "Peter T. Daniels" <grammatim@verizon.net> wrote:
>
>
>
> > On Feb 13, 4:10 pm, Adam Funk <a24...@ducksburg.com> wrote:
>
> > > On 2010-02-10, Peter T. Daniels wrote:
>
> > > > If you _really_ want to distress Daniel, you could point out that
> > > > September through December are not the seventh through tenth months.
>
> > > A weird thought just occurred to me.  Are there any languages that
> > > have names o fmonths calqued from the "wrong" numbers?
>
> > > I don't mean copies and near-copies of the Latin words, like the
> > > English "December" and German "Dezember", but taking a language's
> > > existing word for "ten" and naming the 12th month after it, for
> > > example.
>
> > What names does Arabic use when talking about the Western calendar?
> > (Hebrew, too, for that matter, but calendars printed in Israel are
> > likely to simply be bilingual.)


BTW since the calendar is tied to religion, quotes from the Qur'an and pious traditions are for historical purposes only, the Qur'an is the only substantial document from the period (most now agree that it was compiled early, after a hiatus in which some put forward the possibility of a later compilation) for the area for that period in question, I do not intend to advocate any particular religious belief. The Qur'an is used to allude to the practices of the Arabs at the time of Muḥammad and what he instructed. It also does not intend to foster belief in any Biblical or other pious narrative prior. the Islamic pious traditions about Muḥammad ('aḥādī*th* أَحَادِيثُ , sing ḥadī*th* حَدِيثٌ ) are less reliable, many are clearly interpolations, nevertheless they are not all totally rejected, so they do enter into scholarly discussions. As will be shown conclusively the purely lunar calendar was instituted quite early.

Actually it is believed, at least by many, that the islamic (now) calendar was once luni-solar, as evidenced by the etymology of certain months names.
This post contains much UNICODE. There is some inconsistency in transliteration, sometimes I use extended roman UNICODE characters, sometimes I might use my own purely ASCII system with the emphatics put in capital letters and long vowels indicated by a colon. occassionally, when the discussion involves some well known names are left in conventional English forms, without any diacritics. <ẓ> i.e. <z.> represents an emphatic *dh* i.e. *DH*, <x> represents <*kh*>, <ḫ>, all the same phoneme. both <ḳ> and <q> represent the same phoneme. a" represents 'alif maqṣūra(t) in my transliterations, pronounced in later Classical Arabic as [ā]. I transliterate `ayn either as <`> or <3>. I transliterate tā' marbūṭa(t) as <(t)>. When I quote an article I keep the transliteration of the article. I am amply providing  the Arabic orthography of many names and words, frequently in fully vowelled form and with case endings (which don't appear in the romanization). in the transliterations there is some inconsisitency of whether to show the assimilation of the definite article with the sun letters and whether in definite constructs the case ending is included or not. sometimes some common words are not fully transliterated, when in an English text. the astronomer and polymath known with the surname (nisba) Biruni, Abu 'l-Rayḥān Muḥammad b. Aḥmad al-Bīrūnī أبو الريحان محمد بن أحمد البيرونيّ (Bērūnī), who wrote the work reffered to here c. 390 AH / 1000 CE  is al-Bīrūniyy (al-Bīrūnī), less commonly al-Bayrūniyy (al-Bayrūnī) in Arabic; from Bērūnī in Classical Persian, in which his name is: Abū Rayḥān Muḥammad b. Aḥmad Bērūnī ابوریحان محمد بن احمد بیرونی (not distinguished in writing from Bīrūnī) and in Indian Persian (in English works originating in India it is written Beruni) and Bērūnī / Bērōnī in Modern Dari in Afghanistan, where there is a Al Beroni or Al Beruni University, and Bīrūnī in Modern Farsi (of Iran). The old pronounciation of [ē] is attested (described in medieval sources), also Alberonius in Latin. It comes from the Bērūn "suburb" of  of Kāth, capital of Khwārizm (now disapeared; it was very near the city of Khīva, which survives; in the region of the Amū-Daryā delta, now the autonomous republic of Ḳaraḳalpaḳistan in Uzbekistan on the southern shores of the Aral Sea). The work refered to here is  Kitāb al-Āthār al-Bāḳiya `an al-Ḳurūn al-Khāliya (Chronologie orientalischer Völker, published by Edward Sachau, Leipzig 1878, reprinted by helioplan, Leipzig 1923; English translation entitled The Chronology of Ancient Nations, London 1879). It literally translates as "the book of the remaining signs from the past centuries" (so in Wikipedia: "The Remaining Signs of Past Centuries"). Tt is also known as "Vestiges of the Past". Bīrūnī himself was Khwārizmian and knew the Khwārizmian language - which was written in modified Arabic script those days but now extinct, though Arabic and Persian were the main literary languages of his region.
Since Muḥammad is mentioned, a comment will follow on whether or not Muḥammad is a historical person or not. The answer is yes. sceptics Michael Cook and Patricia Crone point out in their otherwise controversial and speculative book "Hagarism" that in "Doctrina Jacobi", a Byzantine polemic against Jews, it is mentioned that "a Saracen Prophet" bent on conquest has appeared and accuses the Jews of sympathizing with him. the manuscript is dated c. 640 CE,but seems to have been originally composed earlier, dealing with events 634 CE two years after Muḥammad's death according to Arab sources, and perhaps originally composed then. There is also the writing of Thomas the Presbyter mentioning Muḥammad c. 640 a Syriac source. Somewhat later Christian sources also give his name as Muḥammad, including Seboes, Armenian c. 660 with a brief biography.addition there is the curious undated graffito in the Ḥijāz with a list of names, the first an unknown person probably the scribe, the second being انا محمد بن عبدالله 'ana Muḥammad b. `Abdillāh, "I am Muḥammad son of Abdullāh", without any titles. the rest are similar, containing the names of people that Arab historiography says hunkered down at the site before a battle in c. 4 AH / c. 625 CE . The inscription has not been challenged on paleographic grounds. The opinion is that it is indeed a 1st. cent. A.H. inscription.
http://www.islamic-awareness.org/History/Islam/Inscriptions/hamid2.html

The calendrical terminology is yawm يَوْمٌ for day (nahār نَهَارٌ is daytime), 'usbū` أُسْبُوعٌ for week, šahr شَهْرٌ for month and sana(t) سَنَةٌ or `ām عَامٌ for year. the word for "week" comes from "seven", and the word for month oiginally meant "waxing crescent".
The Qur'an also on a few occasions uses حِجَّةٌ ḥijja(t) "pilgrimage" and حَوْلٌ ḥawl "turning around" for "year", but these are not normally used aso in Arabic.

A good bibliography on the Islamic calendar is found in:
http://www.staff.science.uu.nl/~gent0113/islam/bibl_cal.htm

The muslim lunar months are:
http://en.wikipedia.org/wiki/Islamic_calendar
previous version:
 <<
The Islamic months are named as follows:[3]
1.al-Muḥarram المحرّم (or Muḥarram al-Ḥarām)
2.Ṣafar صفر (or Ṣafar al-Muẓaffar)
3.Rabī` al-Awwal (Rabī` I) ربيع الأوّل
4.Rabī` al-Thānī (or Rabī` al-Ākhir) (Rabī` II) ربيع الآخر أو ربيع الثاني
5.Jumādā al-Ūlā (Jumādā I) جمادى الأولى
6.Jumādā al-Thāniya (or Jumādā al-Ākhira) (Jumādā II) جمادى الآخرة أو جمادى الثانية
7.Rajab رجب (or Rajab al-Murājab)
8.Sha`bān شعبان (or Sha`bān al-Muʿaẓẓam)
9.Ramaḍān رمضان (or Ramaḍān al-Mubārak)
10.Shawwāl شوّال (or Shawwāl al-Mukarram)
11.Dhū al-Qa`da ذو القعدة (or Dhū al-Qi`da)
12.Dhū al-Ḥijja ذو الحجّة (or Dhū al-Ḥajja)
 >>
A more recent version:

http://en.wikipedia.org/wiki/Islamic_calendar
 1.Muḥarram — المحرّم — means "forbidden" in Arabic, so called because it was unlawful to fight during this month. Muharram is the second most sacred Muslim month, and includes the Day of Ashura.
 2.Ṣafar — صفر — means "void" in Arabic, supposedly named because pagan Arabs looted during this month and left the houses empty.
 3.Rabī` I (Rabī` al-Awwal) — ربيع الأوّل — means "the first Spring" in Arabic.
 4.Rabī` II (Rabī` ath-Thānī or Rabīʿ al-Ākhir) — ربيع الآخر , ربيع الثاني — means "the second (or last) Spring" in Arabic.
 5.Jumādā I (Jumādā al-Ūlā) — جمادى الأولى — means "the first month of parched land" in Arabic.
 6.Jumādā II (Jumādā ath-Thāniya or Jumādā al-Ākhira) — جمادى الآخرة , جمادى الثانية — means "the second (or last) month of parched land" in Arabic.
 7.Rajab — رجب — means "respect" or "honor" in Arabic. Rajab is another of the sacred months in which fighting was traditionally forbidden.
 8.Sha`bān — شعبان — means "scattered" in Arabic, marking the time of year when Arab tribes dispersed to find water.
 9.Ramaḍān — رمضان — means "scorched" in Arabic. Ramadan is the most venerated month of the Hijri calendar, during which Muslims fast between dawn and sunset.
 10.Shawwāl — شوّال — means "raised" in Arabic, as she-camels begin to raise their tails during this time of year, after giving birth.
 11.Dhū al-Qa`da — ذو القعدة — means "the one of truce" in Arabic. Dhu al-Qa'da was another month during which war was banned.
 12.Dhū al-Ḥijja — ذو الحجّة — means "the one of pilgrimage" in Arabic, referring to the annual Muslim pilgrimage to Mecca, the Hajj


Muḥarram is more properly al-Muḥarram المحرّم and it could also be Muḥarram al-Ḥarām مُحَرَّمُ الْحَرَامِ (genitive construct) also al-Muḥarram al-Ḥarām اَلْمُحَرَّمُ الْحَرَامُ (adjectivial), some say (Enc. of Islam II), because there was a prefixed Ṣafar صفر , which was Ṣafar I, Ṣafar being then Ṣafar II. In languages other than Arabic, the article is usually omitted. The vowelings Dhū al-Qi`da ذُو الْقِعْدَةِ and Dhū al-Ḥajja ذُو الْحَجَّةِ are rare but attested Lane.
Sha`bān and Ramaḍān are diptote. Lane gives Rabī` as triptote but says diptote is permissible, many treat it as triptote, while some sources give it as diptote:  رَبِيعُ الثَّانِي rabī`u~*th**th*ānī (Haywood and Nahmad, Trtton). Sometimes the word šahr "month is prefixed before it, presumeably to avoid confusion with the season. šahru rabī`in~i*th**th*ānī شَهْرُ رَبِيعٍ الثَّانِي (Lane). I have seen Rajab treated as diptote as well.
The vowelled forms are 1. المُحَرَّمُ al-Muḥarram; 2. صَفَرٌ Ṣafar; 3. رَبِيعٌ الأَوَّلُ  Rabī` al-'Awwal; 4. رَبِيعٌ الثَّانِي Rabī` al-*Th*ānī, رَبِيعٌ الآخِرُ Rabī` al-'Āxir; 5. جُمَادَى الأُولَى Jumādā al-'Ūlā; 6. جُمَادَى الثَّانِيَةُ Jumādā al-*Th*āniya(t), جُمَادَى الآخِرَةُ Jumādā al-'Āxira(t); 7. رَجَبٌ Rajab; 8. شَعْبَانُ Ša`bān; 9. رَمَضَانُ Ramaḍān; 10. شَوَّالٌ Šawwāl; 11. ذُو القَعْدَةِ *Dh*ū al-Qa`da(t) (or ذُو الْقِعْدَةِ *Dh*ū al-Qi`da(t)); 12. ذُو الحِجَّةِ *Dh*ū al-Ḥijja(t) (or ذُو الْحَجَّةِ *Dh*ū al-Ḥajja(t)).

The use of ḏ- in Epigraphic South Arabian and Ḥimyarite month names (and common in place names and names of people) is found in all month names. it's Arabic cognate is ذو ḏū (*dh*ū) meaning "possesor of". Daniel Martin Varisco in "Medieval Agriculture and Islamic Science - the Almanac of a Yemeni Sultan" (1994) p. 65 comments that << This usage survives in the two Islamic month names Dhū al-Qa`da and Dhū al-Ḥijja. >> 

The month began with the sighting of the crescent, particularly the observance of Ramaḍān. a witness is required for the sighting of the crescent, but nevertheless, astronomers made calculations to predict it, and some found Qur'anic justification for this. acc. to Enc. of Islam II "Ru'yat al-Hilāl" ("sigthing of the crescent"): << The earliest Muslim astronomers adopted a simple Indian visibility condition, namely that the difference in setting times of the sun and moon be at least 12 equatorial degrees (or 48 minutes of time). >> another peculiarity of Ramaḍān is that it cannot last more than 30 days, even if the crescent is not sighted by a witness for some reason. this is probably because it involves fasting.
The traditional canonical method for determining for determining the start of a lunar month, according to "The Book of Calendars" is that two witnesses considered reliable go to the judge, الْقَاضِي al-qāḍī, that the crescent has been sighted, who then informs the mufti or interpreter of law الْمُفْتِي al-muftī, who then proclaims that a month has started. under adverse weather conditions, the algorithm of alternating months of 29 or 30 days is used. However muslims say that:
 <<
 
 One reliable witness, examined to determine that he is a muslim should he arrive after seeing the hilal {i.e. the crescent} en route to a place where it had not been seen, who testifies in the town, village, or encampment, after maghrib {sunset} and before 'Isha {evening prayer}, determines the month for everyone in that town, village, or encampment.  His testimony is sufficient to establish the month, without a qadi.
 If it is known from astronomical calculation, known with certainty to be reliable because ... {the Qur'an} says that the movement of celestial bodies is regular (and thus calculable), that the hilal {the crescent} could not have been seen by the witness, then his testimony is to be rejected.
 >>
In Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Culturees, "Calendars in Islam" Mohammad Ilyas reports that:
 <<
Based on scientific understanding, certain ground rules were laid down which form the part of sharī`ah (the Islamic legal system) governing the calendar.
Some of these were:
1. The length of a month should be 29 or 30 days.
2. The length of a year should be 354 or 355 days.
3. The maximum number of consecutive 30-day months is 4; the maximum number of consecutive 29-day months is 3.
4a. Each new month begins with the first light of the new crescent moon visible on the western horizon after sunset.
4b. One should try sighting the new moon on the 29th day of the month, but if it cannot be seen (even due to clouds), complete the month as of 30 days.
4c. The visual sighting report must be corroborated by a witness.
4d. The persons involved in the reporting must be reliable, adult, truthful, and sane, with good eyesight (implied). They are punished if proved to be purposely misleading.
4e. The visual sighting report should not conflict with basic scientific understanding and natural laws. Indeed, professional scientists' involvement is essential to ascertain the reliability of the reported sighting, and the scientific test would include a check on related parameters (e.g. the shape of the crescent, its position and altitude, time of observation, sky conditions).
4f. The sighting must be carried out in an organized way every month.
 >>
"The Book of Calendars" (1982) claims that <<It has become customary among Middle Eastern Muslims to accept the verdict of Cairo on when the month begins.>> this is not true for Turkey.
in contemporary Saudi Arabia, newspapers exhort the public to register their sighting of the waxing crescent at the end of each lunar month in courts. this however, is done in modern times only in Saudi Arabia.

Enc. of the Qur'ān "Moon" by Daniel Martin Varisco:

 <<
Each month began with the first sighting of the crescent moon, resulting in elaborate rules in legal texts for determining the beginning of the fasting month (see law and the qur'ān ). By the ninth century, al-Khwārizmī compiled a table showing lunar crescent visibility for the latitude of Baghdād. Despite such astronomical models for predicting the lunar crescent, religious law stipulated that the new moon be physically seen by a male Muslim of good standing.
 >>


When not determined by the sighting of the crescent or through astronomical calculation, the months are of 1. 30 days, 2. 29 days 3. 30 days, 4. 29 days, 5. 30 days, 6. 29 days, 7. 30 days, 8. 29 days, 9. 30 days, 10. 29 days, 11. 30 days, 12. 29 or 30 days.
Thus, in a normal year there are 354 days and so normally it moves back by 11 days for each solar year. A leap year is occassionally added to keep up with the phases of the Moon. usually the epoch is calculated from sunset June 16, 622 by the majority. A minority reckons it from midnight to midnight and uses July 15 as the epoch. periodically a leap year is added by adding an extra day to Dhū al-Ḥijja. for those using July 16, as the epoch. the leap day is added in the 2nd, 5th, 7th, 10th, 13th, 16th, 18th, 21th, 24th, 26th, and 29th years of a 30 year cycle. This is the system of Khwārazmī and of Yaḥyā b. Abī Manṣūr (also known as the Tabular Islamic Calendar or the Fatimid Calendar, acc. to Wikipedia, it was established in the first two centuries AH. It has an error of 1 day every 2500 years; it is most commonly used by historians) when the July 15 is used as an epoch the 15th rather than the 16th is used, the rest being the same. this is the algorithm usually used by historians and some muslim countries (this being somtimes called the "Astronomical Islamic Calendar"). See "The Book of Calendars" (F. Parise ed., 1987), section "the Islamic Calendar". Enc. Iranica "Calendars" gives a third system making the 3rd, 6th, 8th, 11th, 13th, 16th, 19th, 21th, 24th, 27th and 30th, though this is not generally followed by astronomers, acc. to the article. a refinement of the Tabular Islamic calendar is that << If leap days are added whenever the remainder equals or exceeds a half day, then all leap years are the same except 15 replaces 16 >> acc. to Wikipedia "Tabular Islamic calendar" {I haven't seen this mentioned elsewhere}. the Tabular Islamic calendar is a day short once every 2500 years and also deviates from observation for various reasons. recently Microsoft has introduced "the Kuwaiti algorithm", based on what are supposed to be patterns observed for Kuwait. The result is a version of the Tabular Islamic calendar with a 30 year cycle with leap years on the 2nd, 5th, 7th, 10th, 13th, 15th, 18th, 21th, 24th, 26th, 29th years. The Bohras (an Ismaili Muslim sect of about 1 million in India) use Thursday, July 15, 622 CE as their epoch and observe leap years 2nd, 5th, 8th, 10th, 13th, 16th, 19th, 21st, 24th, 27th and 29th. Bīrūnī's algorithm is described in "Al-Bīrūnī's International Lunar Calendar" by Saiyid Samad Husain Rizvi, Hamdard Islamicus, Vol. 29, No. 3 . the order of leap years is 2nd, 5th, 7th, 10th, 13th, 15th, 18th, 21st, 24th, 26th, 29th. starting Friday, July 16, 622 CE.

The differences in the epoches of the astronomical calendar (taking midnight as the start of the day) and the Tabular Islamic calendar are summarized thus:

http://www.al-islam.org/al-serat/hijrah.htm
 <<
Al-Serat  
The History of the Islamic Calendar in the Light of the Hijra

Hakim Muhammad Said
Vol X No. 1 , Spring 1984
Reprinted, by courtesy of the editor, from Hamdard Islamicus, vol. IV, no.3 {1981)


{diacritics are from the original}
...
Shams al-Dīn Muḥammad ibn `Abd al-Raḥmān al-Sakhāwī (d. 902) in his al-I`lān bi'l-Tawbīkh li-man dhamma ahl al-tawrīkh gives the following details about the origin of the Islamic calendar: 

... The Hijra took place on Tuesday the 8th of Rabī` I. The first of that year—that is, al-Muḥarram—fell on a Thursday according to the average (calculation). After this had become generally known, it was considered (the correct date). However, according to observation (of the new moon) and astronomical(?) calculation, the day fell on a Friday. The author of the Nihāyat al-idrāk said that (the Hijra) was used, and for all future times the era was counted from it. Agreement on this matter was reached in the year 17 of the Hijra, the fourth year of the caliphate of `Umar. Until then, each year (after the Hijra) was called after its main event, and this was used for dating purposes. The first year of the Prophet's residence in Medina was thus called: 'The permission to travel'. The second year was called: 'The year of the command to fight'. The third year: 'The year of the test', and so on. Afterwards, the custom of naming the year after the main events was abandoned. ...
...(F. Rosenthal, "A History of Muslim Historiography", second revised edition, Leiden 1968, p.384).

 >>
 al-I`lān bi'l-Tawbīkh li-man dhamma ahl al-tawrīkh الإِعْلانُ بِالتَّوْبِيخِ لِمَنْ ذَمَّ أَهْلَ التَّوْرِيخِ is translated by F. Rosenthal as (the book of) "The Open Denunciation {the publication of blameworthiness} of the Adverse Critics of Historians {"people of history / dating}". The book also appears under the title al-I`lān bi'l-Tawbīkh li-man dhamma al-ta'rīkh الإِعْلانُ بِالتَّوْبِيخِ لِمَنْ ذَمَّ التَّأْرِيخَ "The Open Denunciation {the publication of blameworthiness} of the Adverse Critics of History". The Arabic text does not have the word "astronomical". it says حساب الاجتماعات ḥisāb al-ijtimā`āt "calculation of the conjunctions".
This explanation is unsatisfactory to François de Blois the article "Ta'rīkh" in Enc. of Islam II << Some modern scholars have made a great fuss about this question and claim that the uncertainties involved in the conversion of Muslim dates result from the parallel use of a “scientific” and a “popular” era beginning on 15 and 16 July respectively, but this is without any foundation. >> the opinion given by M. Plessner in the article "Ta'rīkh" in Enc. of Islam I (Supplement) is that << The question on what day the 1st Muḥarram of the year I fell is not yet decided; nor does Buhl, Das Leben Muhammeds, transl. by H. H. Schaeder (1930), p. 196, contribute anything to its solution. J. Mayr, following Babinger, G. O. W. (cf. also M. 0. G., ii. 269), is of the opinion that July 15, 622 was originally the first day of the Muslim era. Difficulties emerged later on astronomical grounds and instead of establishing an extraordinary intercalary day to remove them the date was transferred to July 16. >> The same article continues by talking about the date used in the Ottoman Empire: << In a note Babinger gives his view that the 15th was accepted down to the time of Selīm I, as the "Thursday" in `Āshiḳpāshāzāde, p. 273, 9, shows. After the conquest of Egypt they reckoned from the 16th but there is no evidence of this. >> The Ottoman conquest of Egypt took place in 1517 CE / 923 AH. a generation later, the Ottoman Empire reached its maximum extent. at any rate, there was probably intercalation, and the date of the beginning of the era might be retrospective. nevertheless, the year of the era is historical, as will be shown later.
D.A.Hatcher in "Generalized Julian Day Numbers and Calendar Dates" in Q. Jl R. astr. Soc. (1985) 26, 151-155 says: 
 <<
The schematic Islamic calendars. The Islamic year has 12 lunar months each beginning with the sighting of the crescent moon (or after the 30th day of the last month); it is therefore local and uncomputable. Numerous schematic calendars exist, usually with 11 leap years in each 30-yr cycle, and with months of 30 and 29 days alternately, except in leap years when the last month has 30 days instead of 29. There are two epochs in the literature, Thursday July 15 and Friday July 16, AD 622. The first is the attested new year's day of the year of the Prophet's flight from Mecca to Medina (the Hejra); the second is a backreckoning from the date of the Prophet's arrival in Medina, Monday Rabî' I 8, schematic day 67.
The schematic year has 30 days in Muḥarram and 29 in Ṣafar; that local year must have had 30 days in both months. The variable E in Table I has the value zero for epoch Thursday, 1 for epoch Friday, which is the more widely used. The difference between the two epochs is often confused with the differences due to different leap year cycles. Each value of q (or of v, since q + v = 29) specifies a different pattern of leap years, and it is possible for dates to differ in all but the first 354 days of each cycle, although the calendars have the same epoch. Table I gives the values of q and v for the two most popular cycles, at least in western literature: the first has years 2, 5, 7, 10, 13, 16, 18, 21, 24,26 and 29 as leap years; the second differs only in having year 15 in place of year 16 as a leap year.
 >>
The Tabular Islamic Calendar was official during the Fatimids (10th - 12th cent. CE), it was developed by astronomers in 2nd cent AH / 8th cent. CE. The Fatimids were Ismaili Shia, who are most amenable to astronomical calculations for determining the lunar months.
Friday, 16 July 622 for 1 Muḥarram 1 AH is what is found using the Tabular Islamic Calendar, the Islamic day began at the preceding sunset on the evening of 15 July and this it seems is what later historians seemed to have done.

Previous to the establishment of the Islamic calendar 16 or 17 AH the years were named, according to Abū Rayḥān al-Bīrūnī, at the time of the Prophet:
1.The 1st year after the flight is "the year of permission." سَنَةُ الإذنِ sanatu~l-'iḏn
2.The 2nd year         "           "the year of the order of fighting." سَنَةُ الأَمْرِ بالقِتال sanatu~l-'amri bi~l-qitāl
3.The 3rd year         "           "the year of the trial." سَنَةُ التَّحْمِيص sanatu~l-taḥmīṣ
4.The 4th year         "           "the year of congratulation on marriage." سَنَةُ التَّرْفِئة sanatu~l-tarfi'a(t)
5.The 5th year         "           "the year of the earthquake." سَنَةُ الزَّلزال sanatu~l-zalzāl
6.The 6th year         "           "the year of enquiring." سَنَةُ الاسْتِئناس sanatu~l-isti'nās
7.The 7th year         "           "the year of gaining victory." سَنَةُ الاسْتِغْلاب sanatu~l-isti*gh*lāb
8.The 8th year         "           "the year of equality." سَنَةُ الاسْتِواء sanatu~l-istiwā'
9.The 9th year         "           "the year of exemption." سَنَةُ البَراءة sanatu~l-barā'a(t)
10.The 10th year       "           "the year of farewell." سَنَةُ الوَداع sanatu~l-wadā`


For other methods and algorthms see:
http://en.wikipedia.org/wiki/Islamic_calendar
and its links. Fortunately for historians, it was common to mention the day of the week as well. since this agrees with non-Islamic calendars, it provides a guide if the sighting of the crescent was used instead of the tabulated calendars.
One recent method is the "Umm al-Qura" ( 'umm al-qurā أُمُّ القُرَى litt. Mother of the Villages, an epithet of Makkah) calendar, which is based on astronomical calculations of the appearance of the crescent in Makkah, which is used as the official civil calendar in Saudi Arabia. Since 17 April 1999 (1420 AH) the following rule has been used: on the 29th of an Islamic month, if the sun sets before the moon, the next day is the first of a new month; and if the moon sets before the sun, the next day is the last (30th) of the current month (the times for the setting of the sun and the moon are based upon the coordinates of Mecca). However for religious purposes, witnesses of the sighting of the crescent is used. the details are found in:
http://www.phys.uu.nl/~vgent/islam/ummalqura.htm
Acc. to ENCYCLOPEDIA OF MODERN ASIA, "CALENDARS—WEST ASIA" - "Islamic Calendar"
 <<
Most Muslims depend on a local sighting of the moon, but some follow an authoritative declaration made somewhere else in the Muslim world. Both are deemed valid in Islam, although they often lead to different starting days for the months.
 >>
This has led to the use of the Umm al-Qura calendar to be used frequently in recent times by muslim communities in the west and in computer software. But this has been criticized by other Muslim communities who use the actual sighting of the crescent.
Similar to the Umm al-Qura in principle is the system used in Malaysia, Indonesia and Egypt. In Malaysia, Indonesia, and a few others begin each month at sunset on the first day that the moon sets after the sun (moonset after sunset). in Egypt, the month begins at sunset on the first day that the moon sets at least five minutes after the sun. The Islamic calendar used in Turkey is based (partially) on the results of the Conference for Determining the beginnings of Lunar Months which was held in Istanbul, on 28 November 1978, and which set forth 3 astronomical criteria for the prediction of lunar visibility: (1) Sunset should occur after conjunction (ie. the New Moon), (2) an angular distance between the moon and the sun of at least 8 degrees, and (3) an angular distance of the moon from the horizon that should not be less than 5 degrees. In principle, these criteria were to be used by all the following countries, Bangladesh, Algeria, Indonesia, Iraq, Qatar, Kuwait, Egypt, Saudi Arabia, Tunisia, but in practice, nowadays, only Turkey follows these criteria. In other words, the lunar month is assumed to begin on the evening when, within some inhabited region of the terrestrial globe, the computed centre of the lunar crescent at local sunset is more than 5° above the local horizon and more than 8° from the Sun. The aim of this was to provide uniformity throughout the world. during the last decades of the Ottoman Empire, the Tabular Islamic Calendar was used. in 1925 it was modified somewhat. Qatar, Kuwait, UAE and Yemen use the Umm al-Qura calendar.
A list of countries with a method of calculation of the Islamic Calendar is given in (that Turkey follows Saudi Arabia is not consistent with the information I have from Turkey, Turkey still follows the principles laid out in the conference mentioned before) :
http://www.moonsighting.com/methods.html

For Turkey:
http://www.phys.uu.nl/~vgent/islam/diyanetcalendar.htm

In the USA the following astronomical principles are invovled:

http://www.icbwayland.org/include/MoonsightingDecisionWeb.pdf
 <<
THE FIQH COUNCIL OF NORTH AMERICA:
...
September 7th, 2007
...
1. It is decided to use astronomical calculation to determine the beginning of the Islamic lunar months with the consideration of the sightability of the crescent anywhere on the globe.
2. To determine a lunar Islamic calendar, a conventional point of reference must be used. The International Date Line (IDL) or the Greenwich Mean Time (GMT) may be used.
3. The new Islamic Lunar month begins at sunset of the day when the conjunction occurs before 12:00 Noon GMT. If the conjunction occurs after 12:00 UT, then the month begins at sunset of the next day.
Western Europe also use astronomical calculations:
 <<
In 2007, the Islamic Society of North America, the Fiqh Council of North America and the European Council for Fatwa and Research announced that they will henceforth use a calendar based on calculations, using the same parameters as the Umm al-Qura calendar, to determine (well in advance) the beginning of all lunar months (and therefore the days associated with all religious observances). This was intended as a first step on the way to unify Muslims' calendars throughout the world, in some future time. But, despite this stated objective, they will continue to differ, on this point, from Saudi Arabia's officially stated, but hard to verify policy of relying exclusively on sighting to determine the dates of religious observances
 >>
However, ethnic groups tend to follw the calendar of their countries of origin.
The month of Dhū al-Ḥijja nowadays tends to depend on the reckoning of Saudi Arabia, as it involves the time of pilgrimage to Mecca (starting on the 7th).

Acc. to Enc. of Islam II "Hilāl" {Cresent} by J. Schacht, calculation was justified as follows:
 <<
The Ḳur'ān refers to the new moon in sūra II, 189 (a verse of indeterminate date; Gesch. des Qor. , i, 181): “They ask thee about the new moons; say: 'They are fixed times (mawāḳīt) for the people and for the pilgrimage.'” Another relevant passage is sūra II, 183 f. (to be dated shortly before the Ramaḍān of the year 2; Gesch. des Qor. , i, 178): “O ye who believe, fasting is prescribed for you as it was prescribed for those before you—maybe ye will show piety—during a certain number of days (ayyām(an) ma`dūdāt).” As the observation of the new moon even in a clear sky is subject to chance, as described, for instance, by Ibn Djubayr (162), whereas the terms mawāḳīt and ma`dūdāt in the Ḳur'ān seem to refer to an exactly determined date or period, it seemed indicated that the beginning of the month should be determined by calculation, and several systems of calculation came into being. An argument in favour of calculation ( ḥisāb ) was also drawn from sūra X, 5 (belonging to the third Meccan period; Gesch. des Qor. , i, 158) which reads: “He it is who has made the sun a glow and the moon a light, and has given it determined stations (wa-ḳaddarahū manāzil ), that ye may know the number of the years and the reckoning ( ḥisāb ) [of time].”
 >>

Nevertheless, all schools of Islam except the Ismailis rejected calculation. Nevertheless, some sort of calculation was put into effect when the crescent was not visible due to weather conditions. The details of this is found in the article. particularly the verse refering to the obsevance of fast of Ramaḍān being ma`dūdāt "a certain counted" (number of days) (Q 2:184) , and thus being limited to 30 days.
Al-Baqara
(Fast) a certain number of days ... (184)
سُوۡرَةُ البَقَرَة
... أَيَّامً۬ا مَّعۡدُودَٲتٍ۬‌ۚ
(١٨٤)

Another algorithm for the Islamic calendar was proposed during the Ottoman Empire and had an eight year cycle. this is described by F. K. Ginzel, Handbuch der mathematischen und technischen Chronologie, das Zeitrechnungswesen der Völker (1906), the passage translated for this post from the German by Peter T. Daniels:
 <<
In their Rûz-nâme (perpetual calendars) the Turks use an eight-year leaping-cycle. This is put together out of 5 years of 354 days = 1770 days and 3 leap years of 355 days = 1065 days, thus containing 2835 days or 405 weeks. The cycle is less precise than the 30-year one (see p. 64), since 8 astronomical month-years comprise only 2834 d 22 h 28,8 m (the difference adds up in just about 126 years to a day), but it has the advantage that it contains a full 405 weeks and as a result can be used as the basis of a perpetual calendar. Leap years are the 2nd, 5th, and 7th year of the cycle. The founder of the calculation using an 8-year cycle is probably Darendeli Mehmed Effendi, who is also named elsewhere in the history of the Turkish calendar as a reformer.
 >>
See:
http://tinyurl.com/ruzname

 <<
Calendar scroll (Ruzname)
...
A ruzname (book of days) is a pocket size, portable type of reference calendar in the rotulus or scroll format. These calendar scrolls became popular in the Ottoman Empire from the 17th century onward and were made of vellum or watermarked European paper. Although their sizes vary, they are usually around 100 cm in length and 8-9 cm in width with a leather flap at the top followed by a decorative headpiece (serlevha). Various grids make up the majority of these works, usually accompanied by explanatory text in Ottoman Turkish alongside the grids in the margins. A man by the name of Darendeli Mehmed Efendi is commonly associated with the founding of this form and its widespread popularity in later Ottoman times.
 >>
rûznâme "book of days" is from Persian, روزنامه rūznāma < rōznāma, rūz < rōz "day" and nāma "book" (in modern Persian rūznāma means "newspaper"). Darendeli Mehmed Efendi died 1739. the details are found in: Navoni, J.B.: Rouz-name ou Calendrier perpetuel desTurcs, avec des remarques et des exemples sur la manière de compter les lunaisons, et avec des tables pour trouver la correspondance des dates entre l'èreturque et l'ère vulgaire. Fundgruben des Orients (Wien) 4. 1814. pp. 38-67; 127-153; 253-277; 10 pis. (Appended: Tables pour trouver la correspondance des dates entre les années juliennes et les années de l'Hégire from Fundgruben des Orients 1. 1809). reprinted in: Islamic Mathematics and Astronomy Volume 64 Calendars and Chronology in the Islamic World, Texts and Studies I, Collected and reprinted by Fuat Sezgin in collaboration with Mazen Amawi, Carl Ehrig-Eggert, Eckhard Neubauer.

The etymologies of the lunar month names have to do with the seasons:
Rabī` has to do with herbage, rains, Spring (and formerly early Fall). Lane says that properly it should be  شَهْرُ رَبِيعٍ šahru Rabī`in "the month of Rabī`" in order to distinguish it from rabī`"Spring"(though this frequently comes with the definite article). Ramaḍān has to do with رَمَضٌ ramaḍ "scorching heat". Jumādā جُمَادَى posses a problem, as some lexicographers and Chronologists associated it with جَمْدٌ jamd "freezing", yet it is only two month appart from Ramaḍān . This problem is pointed out by de Blois. however it becomes solved (see Lane, quoting Caussin de Perceval, 1843) if one derives it from jamād جَمَادٌ "a thing which does not grow or increase", "(dry) land upon which no rain has fallen", "sterile, barren or unfruitful land" "ground which was not watered or a rainless year" etc.. jumādā جُمَادَى itself "a dry eye, a tearless eye" in other words it denotes the cessation of rains, appropriately coming after the rainy months. besises, "freezing cold" is not appropriate for Arabia. OTOH the medieval lexicographers do have jumādā جُمَادَى as "freezing cold", "freezing of water" so al-Bīrūnī, or as a synonym for winter (Lane). Maybe this was due to false etymology later by others when the month had shifted through the seasons due to poor intercalation. These etymologies are accepted by those who believe there was once intercalation of a month, until the Qur'an forbade it.

Others relate to activities: Dhū al-Qa`da "rest" (or according to Enc. of Islam I, "Owner of the Truce"), Dhū al-Ḥijja "pilgrimage" (lit. "Owner of the Pilgrimage'), (al-)Muḥarram "sanctity", though apparently in pre-Islamic times it was called Ṣafar I, then Ṣafar al-Muḥarram, "the sacred Ṣafar:, then just al-Muḥarram. That's why it has a definite article, as it was originally just an adjective (Enc. of Islam II "(al-)Muḥarram". Ṣafar II became simply Ṣafar. According to Enc. of Islam I and II "Ṣafar" by A.J. Wensinck << According to Wellhausen, in the old Arabian year, Ṣafar comprised a period of two months in which al-Muḥarram (which name, according to this scholar is a Muslim innovation) was included. As a matter of fact, tradition reports that the early Arabians called al-Muḥarram Ṣafar and considered an `umra during the months of the Ḥadjdj as a practice of an extremely reprehensible nature. They embodied this view in the following saying: Idhā bara'ā 'l-dabar wa-`afā 'l-athar wa 'nsalakha Ṣafar ḥallati 'l-`umra li-man i`tamar, i.e. “When the wounded backs of camels are healed and the vestiges [of the pilgrims] are obliterated and Ṣafar has passed, then the `Umra is allowed for those who undertake it.” >> `Umra is the lesser pilgrimage, Ḥajj (lit. "pilgrimage") is the main pilgrimage. The Arabic of the phrase is إِذَا بَرَأَ الدَّبَرُ وَعَفَا الأَثَرُ وَانْسَلَخَ صَفَرٌ حَلَّتِ الْعُمْرَةُ لِمَنِ اعْتَمَرَ (should be bara'a not bara'ā as in Enc. of Islam II, see Lane, dabar دَبَرٌ ). Also Enc. of Islam II "al-Muḥarram" by M. Plessner << The name is originally not a proper name but an adjective, as the article shows, qualifying Ṣafar. In the pre-Islamic period, the first two months of the old Meccan year were Ṣafar [q.v.] I and II, which is reflected in the dual a potiori of al-Ṣafarān for al-Muḥarram and Ṣafar; in the old Arab year, the first half year consisted of “three months of two months each” (Wellhausen), as the two Ṣafars were followed by two Rabīʿs and two Djumādās. The first of the two Ṣafars, as the one that belonged to the sacred months, was given the adjectival epithet al-muḥarram which gradually became the name of the month itself. As Dhu 'l-Ḥidjdja also belonged to the sacred months, three of the four sacred months came together except in leap year. The month intercalated to equate the year to the solar year was inserted after Dhu 'l-Ḥidjdja and was not sacred. >> Rajab "expresses ideas of fear and respect" acc. to Caussin de Perceval, as one can understand from Lane. Perhaps relating to it being a sacred month in pre-Islamic times. In pre-Islamic times it was Rajab that was sometimes called al-Muḥarram.
The other etymologies are given in Lane: Ṣafar conveys ideas of being vacant. According to the Arab traditions given in Lane Ṣafar was so named because that was the time the granaries became empty, or that people left for expeditions. Shawwāl comes from the verb "to rise or become elevated". According to Arab tradition when the she-camels raised their tails, or that it means "lift or carry", because the she-camels were carrying a fetus at that time. Sha`bān from ša`aba شَعَبَ "to disperse"(it also has the opposite meaning of "to assemble", because the Arabs dispersed for search of water (Lane). acc. to Enc. of Islam II it may have meant "interval", Wikipedia previosly had "seperation" for the reason of dispersal given previously. admittedly, some of these etymologies sound fanciful, but they suggest a tradition connecting them to the seasons. Lane says that the names of the month were given by an ancestor of Muḥammad,  كِلابُ بْنُ مُرَّةَ  Kilāb b. Murra(t), some two centuries before Islam, and were intercalated by a month called النَّسِيءُ al-nasī', though not everyone accepts this, as will be discussed further.

The etymologies summarized from Lane can be found in this reference:
Time-Reckoning During the Islamic Period
Dr. Reza Abdollahy
Gahname Fachzeitschrift des VINI 239
Nr. 7/2004
http://www.vini.de/Gahname/Gahname7/Gahname7-Time-Rekoning%20Islamic%20Periode.pdf
 <<
1. Moharram forbidden (for war), sacred
2. Safar emptiness (of granaries)
3. Rabī' I (awwal) rains (beginning)
4. Rabī' II (āḵer) rains (ending)
5. Jomādā I (ūlā) dry (beginning)2)
6. Jomādā II (āḵera) dry (ending)2)
7. Rajab forbidden (for war)
8. Ša`bān Separation (to search for water)
9. Ramazān extreme heat
10. Šawwāl raising the tail (of camels, to give birth)
11. Ḏu’l-qa`da sitting, breaking in young camels
12. Ḏu’l-hejja pilgrimage
1) Definitions are taken from E. W. Lane, An Arabic-English Lexicon, London, 1863; reprint Beirut, 1968, s.v.
2) According to some medieval sources, the name Jomādā was derived from “freezing of water” and the two months of that name originally fell in winter, an interpretation that would seem reasonable in more northern climates. For these sources and the opinion that in Arabia the two months originally fell in a dry period of late spring, see Lane, s.v. Jomādā .
 >>
(The author uses a persian-type transcription; the same table appears by the same author in Enc. Iranica "Calendars"). I corrected Jomādā II as (āḵera), in the feminine, as it appears correctly in Enc. Iranica.

Daniel Martin Varisco "Islamic Folk Astronomy" in "Astronomy Across Cultures - The History of Non-Western Astronomy" (2000; H. Selin ed.) gives a summary of the etymologies given by Bīrūnī:
1. One of the four sacred months known as { حُرُمٌ } ḥurum. 2. People procure their provisions for going out. 3. and 4. falling of rain and dew and the appearance fo plants. 5. and 6. water froze { جَمَدَ } (jamada) 7. People formed the intention of travel because it was safe. 8. Tribes were dispersed. 9. Stones roasted by heat. 10. increase then decrease of heat. 11. People stayed in their homes. 12. People performed the pilgrimage.
As said previously, it is dificult to accept 5. and 6. on seasonal grounds, too close to 9. Varisco notes that these are connected with the activities and life of the Bedouin.

Lane's Arabic-English Lexicon (his own editions are 1863 - 1872) accepts the traditions collected by Caussin de Perceval and his theory (see below). Lane gives a three year intercalation, with Muḥarram falling on late November.
One theory and tradition is that there was intercalation, but even before that, roughly 200 years before it was prohibited there was no intercalation. The proponent of the intercalary month theory was A. M. Caussin de Perceval, "Mémoire Sur Le Calendrier Arabe Avant l'Islamisme"; J. Asiatique, April 1843. translated into English as "Notes on the Arab Calendar Before Islam" in "Islamic Culture" vol 21, April 1947 (p. 135 - 153). Opposing him was Maḥmūd Efendi, an Egyptian astronomer, Mahmoud Efendi (later he became Maḥmūd Pasha, also refered to as Maḥmūd Pasha al-Falakī i.e the Astronomer or simply as to as Mahmud i.e. Maḥmūd, in later literature) is a title: Mahmoud Effendi, Mémoire Sur le Calendrier Arabe Avant l'Islamisme et sur la Naissance et l'Âge du Prophète Mohammad; J. Asiatique February - March 1858. It was made into a pamphlet of the same title, Paris, "Imprimerie Impériale," 1858. these were followed by denying intercalary months by A. Sprenger, "Über den Kalender der Araber vor Muhammad," ZDMG 13 (1859), 139-59 Lane (c. 1870) supports intercalation) and  supporting intercalation, A. Moberg, An-nasī' in der islamischen Tradition, Lund 1931 (his article in Enc. of Islam II is quoted here). "The Concept of Time in Islam" by Gerhard Böwering in Proceedings of the American Philosophical Society, Vol. 141, No. 1 (Mar., 1997), pp. 55-66, supports it without going into details, as does F.E. Peters "Muhammad and the Origins of Islam" (1994). Finally F. de Blois in the article "Ta'rīkh" in Enc. of Islam II (quoted below) does not, but modifies his view in a later article. Enc. of Islam I "Zamān" by Willy Hartner says there was intercalation until the year 10 AH. A. Moberg writing Enc. of Islam I and Enc. of Islam II "Nasī'" support and believe to prove intercalation. Daniel Martin Varisco "Islamic Folk Astronomy" in "Astronomy Across Cultures - The History of Non-Western Astronomy" (2000; H. Selin ed.) accepts the reconstruction of Caussin de Perceval. Enc. Iranica "Calendars" by Reza Abdollahy believes in intercalation with a qualification << The lunar Hejrī calendar was based on the synodic month, reckoned from one sighting of the new moon to the next. The root meanings of the month names, many of which refer to climatic conditions (see Table 34), indicate that in pre-Islamic Arabia lunar months had customarily been brought into line with the seasons through recurrent insertion of an intercalary month and thus that a sort of lunisolar calendar was in use. There is, however, a great deal of evidence to suggest that no such intercalation took place in the territory under the Prophet’s rule during the first decade after the hejra (Nallino, pp. 108ff.; Beeston, pp. 15-25; Nilsson, pp. 251-55; see also Abdollahy, 1987, pp. 29-30). The lunar Hejrī calendar used by Muslims today for the timing of religious observances still follows the same pattern as in those first Hejrī years; it consists of lunar years and months with no intercalations. >>. M. Hamidullah, in "The Nasi', the Hijrah Calendar and the Need of Preparing a New Concordance for the Hijrah and the Gregorian Years", Journal of the Pakistan Historical Society Vol XVI, Part 1, January 1968 (with a follow up  has his own reconstruction of the intercalation, and also in "The Concordance of the Hijrah and Christian Eras for the Lifetime of the Prophet", Journal of the Pakistan Historical Society Vol XVI, Part 4, October, 1968, also thinks that there was no intercalation in Medina during Muhammad's stay there. Another with a similar view is F.A. Shamsi who believes there was intercalation, but at some point Muhammad abolished intercalation while the pagans continued to practice it.

I disagree that "no such intercalation took place in the territory under the Prophet’s rule during the first decade after the hejra", as the Muslims and the Idolaters seem to have agreed on the Forbidden Months, and it was only after the Farewell Pilgrimage that the Pilgrimage was to be performed seperately, acc. to the accepted traditions, and passages from the Qur'an. Here is evidence that the Pagans and Muslims agreed on the timing of the sacred (or forbidden) months and had agreed that there would be no warfare at that time from Qur'an 9:5. Therefore the two sides agreed on whatever form of nasī' took place:

http://www.quranexplorer.com/quran/

all translations are from Dr. Pickthall

 <<

Al-Tawba

Then, when the sacred months have passed, slay the idolaters wherever ye find them, and take them (captive), and besiege them, and prepare for them each ambush. But if they repent and establish worship and pay the poor-due, then leave their way free. Lo! Allah is Forgiving, Merciful. (5)

سُوۡرَةُ التّوبَة
فَإِذَا ٱنسَلَخَ ٱلۡأَشۡہُرُ ٱلۡحُرُمُ فَٱقۡتُلُواْ ٱلۡمُشۡرِكِينَ حَيۡثُ وَجَدتُّمُوهُمۡ وَخُذُوهُمۡ وَٱحۡصُرُوهُمۡ وَٱقۡعُدُواْ لَهُمۡ ڪُلَّ مَرۡصَدٍ۬‌ۚ فَإِن تَابُواْ وَأَقَامُواْ ٱلصَّلَوٰةَ وَءَاتَوُاْ ٱلزَّڪَوٰةَ فَخَلُّواْ سَبِيلَهُمۡ‌ۚ إِنَّ ٱللَّهَ غَفُورٌ۬ رَّحِيمٌ۬
(٥)

However, M. Hamidullah, in "The Nasi', the Hijrah Calendar and the Need of Preparing a New Concordance for the Hijrah and the Gregorian Years", Journal of the Pakistan Historical Society Vol XVI, Part 1, January 1968 finds a discrepancy in the year 6 AH:
 <<
8. The migration of the Prophet to Madīnah complicated the situation. Cut off from Makkah and the pilgrimage, the Muslim masses could not follow when intercalation was to be made. We have clear references to it. We know that the truce of al-Ḥudaybyīah was concluded in the 11th month of the calendar (Dhu al-Qa`dah) of 6 H.2 Yet Abū Yūsuf3 says that the Prophet set out from Madīnah for al-Ḥudaybyīah in Ramaḍān which is the 9th month. Ibn Kathīr4 reports : "the truce of al-Ḥudaybyīah took place in Dhu al-Qa`dah (the 11th month of the year), yet according to `Urwah it took place in Shawwāl which is the 10th month, and that is very strange from `Urwa." But it will not at all look strange If we take into consideration that, with usual intercalations, the llth month of the Makkans was in fact the 9th month in the year 6 H., the year of the truce. An intercalation was practised at the end of the year 6 H., and yet another at the end of the year 9 H. So that when the Prophet went on pilgrimage in. 10 H., months had returned to their original position, and the difference of 2 months existing in 6 H. had vanished, and the Prophet could without the least complication abolish the nasī', saying1 in his celebrated oration : "The time has now returned to the position it was when God had created the heavens, and the earth with a year of 12 months".
9. Makkah was already conquered in 8 H., yet the Prophet did not interfere with the intercalation in 9 H., but waited2 and abolished; it only in 10 H., when the months of both the intercalated and non-intercalated computations had coincided. ...
2 "And waited" ( وانتظر ), these are the words used by Bīrūnī, Āthār, p. 63.
 >>

The context of Qur'an, al-Tawba 9:5 ("the Sword Verse") is the Battle of (or Raid on) Tabūk (NW Arabia), which took place on 9 AH. Muḥammad was in Madīnah but Makkah had already been conquered. Yet, that year, according to Hamidullah, the Pagan's and Muslim's calendars had not coincided.
Incidentally, the Prophet did not make contact with hostile forces at Tabūk, but received the submission of some local chiefs of the region and the Gulf of `Aqaba-Red Sea coastal region.
Also as an aside, according to Qur'an, al-Baqara, 2:21 defence of the faith takes preference over the sacred month.
 << 

Al-Baqara
They question thee (O Muhammad) with regard to warfare in the sacred month. Say: Warfare therein is a great (transgression), but to turn (men) from the way of Allah, and to disbelieve in Him and in the Inviolable Place of Worship, and to expel His people thence, is a greater with Allah; for persecution is worse than killing. And they will not cease from fighting against you till they have made you renegades from your religion, if they can. And whoso becometh a renegade and dieth in his disbelief: such are they whose works have fallen both in the world and the Hereafter. Such are rightful owners of the Fire: they will abide therein. (217)
سُوۡرَةُ البَقَرَة
يَسۡـَٔلُونَكَ عَنِ ٱلشَّہۡرِ ٱلۡحَرَامِ قِتَالٍ۬ فِيهِ‌ۖ قُلۡ قِتَالٌ۬ فِيهِ كَبِيرٌ۬‌ۖ وَصَدٌّ عَن سَبِيلِ ٱللَّهِ وَڪُفۡرُۢ بِهِۦ وَٱلۡمَسۡجِدِ ٱلۡحَرَامِ وَإِخۡرَاجُ أَهۡلِهِۦ مِنۡهُ أَكۡبَرُ عِندَ ٱللَّهِ‌ۚ وَٱلۡفِتۡنَةُ أَڪۡبَرُ مِنَ ٱلۡقَتۡلِ‌ۗ وَلَا يَزَالُونَ يُقَـٰتِلُونَكُمۡ حَتَّىٰ يَرُدُّوكُمۡ عَن دِينِڪُمۡ إِنِ ٱسۡتَطَـٰعُواْ‌ۚ وَمَن يَرۡتَدِدۡ مِنكُمۡ عَن دِينِهِۦ فَيَمُتۡ وَهُوَ ڪَافِرٌ۬ فَأُوْلَـٰٓٮِٕكَ حَبِطَتۡ أَعۡمَـٰلُهُمۡ فِى ٱلدُّنۡيَا وَٱلۡأَخِرَةِ‌ۖ وَأُوْلَـٰٓٮِٕكَ أَصۡحَـٰبُ ٱلنَّارِ‌ۖ هُمۡ فِيهَا خَـٰلِدُونَ
(٢١٧)
 >>

(Acc. to Enc. of Islam I "Muḥarram" the Qur'an always speaks only of the sacred month (ii. 194, 217; v. 2, 97); only in Sura ix. 36 in laying down the method of reckoning time does it speak of four sacred months; OTOH it speaks of "months" - more than two - in 9:5)

Hamidullah believes that there was intercalation every three years but after the 30th year there was an intercalation in the 31st year and then there was an intercalation in the 33th year. This reconciles traditions that there was an intercalation every two years with those that say there was intercalation every three years. Ibn Iṣḥāq also mentions an intercalation every year. Hamidullah concludes that <<each narrator had observed the practice only once, and generalised it and did not know that the system was much more complicated. >>

In support of his reconstruction Hamidullah quotes Maqrīzī:
 <<
The 13th month was intercalated sometimes every two years and sometimes every three years according to the requirements of the time calculation, cf. Bīrūnī, al-Āthār al-Bāqiyah, p. 62, Maqrīzī, Imtā` al-Asmā'. (MS Koprülü 1004), p.-1727. As this part of Maqrīzī's work is not yet printed, I quote him textually by, translation :
"...
... After all this, if they observed that a (whole) month is in advance of any of the four seasons (of the year) due to the accumulation of the fractions of the solar year and the rest of the difference between it and the lunar year which they tried to equalize with the solar year they proceeded to an additional intercalation".
...
فإن ظهر لهم مع ذلك تقوم شهر عن فصل من فصول الأرربعة لما يجتمع من كسور سنة الشمس وبقيت فصل ما بينها وبين سنة القمر الذي الحقوه به كبسوا كبسًا جديدًا  ...

The last sentence of this citation is particularly interesting,' and it says that, in addition to the normal intercalation every third year, they were obliged to have recourse to a supplementary intercalation, and this whenever a whole month was necessary to have a given season in a given month. Naturally this can occur once every 30 years.
 >>

Hamidullah claims that this was the type of intercalation of months practiced in Babylonia at the time of Hammurabi, but also with the addition of leap years with an intercalation of a day, to keep up with the phases of the Moon, as mentioned by Bīrūnī.
However, it seems that by the time of Muḥammad the months had moved from the seasons they had originally designated. So according to most views, and that of Caussin de Perceval, Bīrūnī and Maqrīzī were using a system they figured out would work.

The English translation of de Perceval's article may be found online at:
http://tinyurl.com/ArabCalPerceval
One can search for the old issues of Journal Asiatique at:
http://gallica.bnf.fr/ark:/12148/cb34348774p/date.r=journal+asiatique.langEN

Here is a source that says they were two kinds of nasī':

http://www.al-inaam.com/library/calendar2.htm
 <<
INTERCALATION
Syed Khalid Shaukat
Every calendar except one, at any time in the entire history of the world, has had to make corrections by either adding or subtracting time. The Jewish, Chinese, or Hindu calendars add a thirteenth month periodically, to bring the lunar calendar in line with the solar calendar. This is called "intercalation" or "Nasee” (in Arabic). Two kinds of Nasee' were in practice at the time of Prophet Muhammad, sallallahu alayhi wasallam. One was inserting a thirteenth month, and the other was transposing a sacred month with another for certain social or political needs and advantages. During the Prophet's farewell message, two revelations regarding the Islamic calendar were given to humankind, Allah says, "The number of months in the sight of Allah is twelve (in a year). So ordained by Him, the day He created the heavens and the earth. Verily the transposition (of a prohibited month or intercalation) is an addition to disbelief." [9:36-37)
 >>
{the website is otherwise polemical, claiming that even an intercalation of a day is prohibited, whereas, algorithmic Islamic calendars do in fact do that.}
Caussin de Perceval says:
 <<
 Thus the nas'āt, according to Muḥammad Jarkasī, were invested with two functions intimately connected and even fusing one into the other, under a certain aspect. For whether after several lunar years, they intercalated one month between Dhu'l-Ḥijja and Muḥarram, or, during a series of lunar years without embolism, they transferred the privilage of Muḥarram to Ṣafar, they too were making a nasi, a postponment of a holy month to a later date: 29 or 30 days later. All are agreed that nasi means retardation تاخير . If we concede to Jawharī, Bayḍāwī, etc. that the word nasi was more specially used to designate the postponing of the observance of Muḥarram, by the transfer of the inviolable character of this month, we readily realize, however, that the same word meant the embolism, considered as retardation in the observance of Muḥarram by the intercalation of a lunar month immediately before.
 >>
{nas'āt is an error for nasa'a(t)}

This is summarized by Burnaby thus:

 <<
... He maintains that the privilege of transposing the sacred character of Muḥarram to Ṣafar, when the warlike tendencies of the Arab tribes made the change expedient, was entrusted to the Nasa'a or Ḳalâmis ; and, that the declaration that this exchange between the two months might be effected, was proclaimed at the same time as the Nasî, or intercalation of a month, namely, at the close of the Pilgrimage when the pilgrims were about to quit Mecca.
Thus the office of the Nasa'a had a double character, partly civil or political, partly religious. They were invested with two functions which were very closely connected, and which, under a certain point of view, might -be resolved into one. For, suppose that they intercalated a month at the end of three Lunar years, that is, immediately before the commencement of the sacred month Muḥarram in the fourth year ; there would be a postponement of Muḥarram ; only two sacred months would come together consecutively. Suppose again that on some occasion during the course of the three Lunar years, of which the last was Embolismic, they had transferred the sacred character of Muḥarram to Ṣafar; this would equally make a postponement ; the arrival of the sacred month would be retarded by twenty-nine or thirty days. Hence this transfer was called by the same name as the Intercalation Nasî.
 >>


So de Perceval also recognizes that nasī' sometimes meant just a change in the sanctity of the months, without intercalation. (nas'āt) seems to be a typo, should be nasa'a(t)).
See also:
http://www.sizes.com/time/cal_islam.htm
But the quotation from Bīrūnī is truncated and not very literal in some points.
 <<
In pagan times the Arabs dealt with their months as the Moslems do now, and their pilgrimage moved through all the four seasons of the year. Then, however, they decided to fix their pilgrimage at a time when their wares, hides and fruits were ready for market; so they tried to make it immovable, to have it always in the most abundant season. So 200 years before the Hegira they learned intercalation from the Jews and, using the same method the Jews did, added the difference between their year and the solar year to the months of the year, whenever the difference had increased to a month. Then at the end of the pilgrimage ceremonies the Kalammas (the Sheiks of a certain tribe, in charge of this task) would come forward, speak to the people, and intercalate a month by giving the next month the name of the present one. People expressed their approval of the Kalammas' decision by applauding. This procedure they called Nasi, that is, shifting, because every second or third year the beginning of the year was shifted.....They could determine the right time [for Nasi] by the risings and settings of the menazil. Thus it remained up to the flight of the Prophet from Mecca to Medina.
[quoted in Ginzel, page 245]

 >>

That does not mean that Bīrūnī had the last word on the method of intercalation (if there was one), and was probably incorrect (see later). Bīrūnī here gives the strange method of intercalation, by renaming months, first appearing from Abū Ma`shar al-Balkhī, discussed later. it is quoted by Mahmoud Effendi in his article, the only published version of it. Abū Ma`shar al-Balkhī seems to favor an intercalation of one month every two years. He also mentions that some sources report an intercalation of 9 months every 24 years.
al-Mas`ūdī says intercalation was accomplished by adding a month called al-nasī'
See also:
http://www.al-islam.org/al-serat/hijrah.htm
 <<
Al-Serat  
The History of the Islamic Calendar in the Light of the Hijra

Hakim Muhammad Said
Vol X No. 1 , Spring 1984
Reprinted, by courtesy of the editor, from Hamdard Islamicus, vol. IV, no.3 {1981)
 >>
(diacritics from the original) here is what he has to say about intercalation (kabīsa(t) كَبِيسَةٌ )
  <<
...

... The Arabs were seized by the fatal malady of idolatry three hundred years before the advent of the Prophet, the Ḥajj for them was nothing more than a big festival. Their calendar being lunar, this feast was sometimes held in seasons when the crops had not been harvested and were not yet ready for sale. They, therefore, devised the method of kabīsa, according to which a year sometimes consisted of 13 months. The period of the Ḥajj was also not specified. The responsibility for announcing the date of the Ḥajj was entrusted to a man from Banū Kināna named Qalammas, who was to announce on the occasion of the Ḥajj when the next pilgrimage was to be performed, and which month the thirteenth month was to follow. The first Qalammas was an individual, but then the name became specific to the announcer. We thus see a sizeable number of the Qalammasa. The Qalammasī calendar was based upon lunar computation, and another link in the historical chain is provided by the fact that among the Arabs the months of Rajab, Dhū'l-Qa`da, Dhū'l-Ḥijja, and Muḥarram were regarded as the months of peace and sanctity. But, with this calendar, these months also began to undergo changes, and it was one of the responsibilities of the Qalammasa to announce as to what months would be the sacred months in the following year. They are called al-nasī' in Arabic. 
The custom of kabīsa was current among the Beduins but not among the townsmen. The Arabs had, therefore, two calendars: one was with the kabīsa, the other without it. The Prophet in his address, to which we have referred, announced the abrogation of both - i.e. the kabīsa and nasī'. Thus the time for the pilgrimage was fixed and the lunar calendar was to be enforced without the kabīsa. 

 >>

The claim that there were two different calendars amongst the Arabs does not ring true, as this would have caused confusion concerning the pilgrimage and the ban on fighting. Also not ringing true was that the period of the pilgrimage not being specified, and that it was merely a big feast. Also Qalammas was not a proper name.

Enc. of Islam II "al- Muḥarram" by M. Plessner explains how the misconception of renaming months came about:
 <<
al- Muḥarram  (a.), the first month of the Muslim year. The name is originally not a proper name but an adjective, as the article shows, qualifying Ṣafar. In the pre-Islamic period, the first two months of the old Meccan year were Ṣafar [q.v.] I and II, which is reflected in the dual a potiori of al-Ṣafarān for al-Muḥarram and Ṣafar; in the old Arab year, the first half year consisted of “three months of two months each” (Wellhausen), as the two Ṣafars were followed by two Rabīʿs and two Dj̲umādās. The first of the two Ṣafars, as the one that belonged to the sacred months, was given the adjectival epithet al-muḥarram which gradually became the name of the month itself. As Dhu 'l-Ḥidjdja also belonged to the sacred months, three of the four sacred months came together except in leap year. The month intercalated to equate the year to the solar year was inserted after Dhu 'l-Ḥidjdja and was not sacred. The month intercalated to equate the year to the solar year was inserted after Dhu 'l-Ḥidjdja and was not sacred. It thus came about that learned Muslims described the intercalation as renaming the Muḥarram concerned as Ṣafar, i.e. as making Muḥarram not sacred; they meant that the month after the pilgrimage, which they consider as al-Muḥarram, following the custom, is not sacred, i.e. is Ṣafar , and the second month, i.e. in their view Ṣafar, is al-Muḥarram . In doing this they of course overlook the fact that Ṣafar proper now only comes third; but when the intercalary month was abolished in Islam, the proper conception of the state of affairs was lost [see nasī' ].
 >>

Enc. of the Qur'ān "Moon" by Daniel Martin Varisco also agrees that there was once intercalation of a month.
 <<
Of the twelve lunar months, only Ramaḍān is mentioned by name in the Qur'ān ( q 2:185). In pre-Islamic Arabia an intercalary month (nasī') was added to bring the shorter lunar calendar of 354 days into alignment with the seasons (q.v.), but this was expressly forbidden in the Qur'ān ( q 9:37) and in statements of Muḥammad (see pre-islamic arabia and the qurʾān ). The rationale ordinarily given for this ban is that holy months, such as Ramaḍān, could then be confused with ordinary months.
 >>
The fact that only Ramaḍān is mentioned by name in the Qur'ān is not a problem, since there are Islamic papyri and inscriptions older than the compilation of the Qur'ān that attest to their names.
There are reports of older month names.

These names are given in Lane under the entry šahr شَهْرٌ and are ascribed to the mythical (?) tribe of `Ād, as are many things "ancient" in Arab tradition (`Ād is described in the Qur'an as one of the three tribes that were obliterated by God for having disobeyed the prophet sent to them, the other two, Thamūd and Madyan are historical. There are some attempts to identify the `Ād and the city associated with them, 'Iram; `Ād may just come from a common noun meaning "old" acc to Enc. of Islam II "`Ād"):
1. مُؤْتَمِرٌ  mu'tamir
2. نَاجِرٌ   nājir
3. خَوَّانٌ   xawwān
4. بُصَّانٌ   buṣṣa:n
5.  رُبَّى   rubba"
6.  حَنِينٌ   ḥanīn 
7.  اَلأَصَمُّ  al-'aṣamm
8.  عَاذِلٌ  `ā*dh*il
9.  نَاتِقٌ   nātiq
10. وَعْلٌ   wa`l
11. وَرْنَةُ   warna(t)
12. بُرَكٌ or بُرَكُ  ? burak
5 is indeclinable, 11 is diptote, 12 triptote or perhaps there is a diptote variant. the rest are triptote. 1 has a version with the definite article المُؤْتَمِرُ al-mu'tamir. 5 rubba" is sometimes pointed as رُنَّى runna". also some authorities give a slightly different order. all in all, these month names came to be quite forgotten in medieval times. 6. has the versions: الحَنِينُ al-ḥanīn, حِنِّينٌ ḥinnīn, الحِنِّينُ al-ḥinnīn, حُنَيْنٌ ḥunayn. 7 has the dialectical version al-'aṣabb الأصبّ (Lane), perhaps due to a sound change, but traditionally explained as << “the pouring” because the unbelievers of Mecca used to say that the mercy is pouring forth in this month.>> acc. to Enc. of Islam II, "Radjab" by M.J. Kister. also it was sometimes qualified by  المُحَرَّمُ al-muḥarram, even sometimes just called  المُحَرَّمُ al-muḥarram because it was holy, it corresponds to رَجَبٌ rajab, which was also holy and the first two names remained as by-names of Rajab.

Mahmoud Effendi concludes from dictionaries that 1.مؤتمر mu'tamir ("moutamer", corresponds to Muḥarram); 2.ناجر nājir ("nadjir"); 3. خوّان xawwān ("khawan") 4. صوّان ṣawwān ("ssawan"); 5. حِنِّين ḥinnīn or رُبَّى rubba" ; 6. رُنَّى ? runna"? ("ronna") or بائدة bā'ida(t) ("baïdah"); 7. الأص al-'aṣamm  (assamm); 8. واغل wā*gh*il or وَعِل wa`il or عاذل `ā*dh*il ("adhel") or عادل `ādil; 9. ناتق nātiq ("natik") or ناطل ? nāṭil ? ("nattel"); 10. وعل wu`l / (wu`ul?) ("wool) or وغل wu*gh*l (woghl); 11. هواع hiwā' ("hewa") or رنّة ranna(t) ("rannah"); 12. برك barak ("barak").

Mahmoud Effendi collects some variants: from al-Bīrūnī ( 973? - 1048; "al-'Āthār al-Bāqiyyah" 1000 CE, (I checked Bīrūnī and I will give Bīrūnī's voweling in the published version of Sachau, 1878), 1. المُؤْتَمِرُ al-mu'tamir ("moutamer"); 2. نَاجِرٌ nājir ("nadjir"); 3. خَوَّانٌ xawwān ("khawan"); 4. صُوَانٌ ṣuwān (Bīrūnī is quite clear on this) but M.E. has صوّان  ṣawwān ("ssawan"); 5. حَنْتَمٌ ḥantam (Sachau) but M.E. has حِنِّين ḥinnīn ("hennin"); 6. زَبَّاءُ zabbā' (Sachau) but M.E. has   رُنَّا ـ  رُنَّى runnā, runna" ("ronna"); 7. الأَصَمُّ al-'aṣamm ("assamm"); 8. عَادِلٌ `ādil ("adel"); 9. نَاتِقٌ nātiq ("natik"), 10. وَاغِلٌ wā*gh*il ("waghel"); 11. هِوَاعٌ huwā` ("hewwah"); 12. بُرَكٌ burak but M.E. برك barak ("barak").

Bīrūnī comments that "The forms as well as the order of these names sometimes differ from what we have given." and presents another set from a poem (for some reason many appear in the feminine in the poem):
1. مُؤْتَمِرٌ mu'tamir ("moutamer"); 2. نَاجِرَةٌ nājira(t) ("nadjer"); 3. الخَوَّانُ al-xawwān ("kawan"); 4. الصُّوَانُ al-ṣuwān ("ssawan"); 5. Sachau: الزَّبَّاءُ al-zabbā' but M.E. الرُّبَّا al-rubbā ("robba"); 6. بَائِدَةٌ  bā'ida(t) ("baïdah"); 7. أَصَمُّ 'aṣamm ("assam"); 8. وَاغِلَةٌ wā*gh*ila(t) ("waghel") 9. نَاطِلةٌ nāṭila(t) ("natel"); 10. عَادِلَةٌ `ādila(t) (or M.E. عَاذِل `ā*dh*il ?) ("adhel"); 11. رَنَّةُ ranna(t) ("rannah"); 12. بُرَكٌ burak ("barack").
The poem says that: يَعودُ أَصَمُّ صَمَّ بِه الشَّنانُ ya`ūdu 'aṣammu ṣamma bihi ~š-šanānu (M.E. السنان ~s-sinānu); ṣamma means "to be deaf"; شَنَانٌ šanān means "to attack", سِنَانٌ sinān means a "spearhead". Sachau, 1879 (English by W.H. Allen & Co.) translates the passage as "Then comes the turn of 'AṢamm, in which hatred was deaf". M.E. says "dans laquelle on n'entend point le bruit des armes" and includes al-rubbā' and bā'ida(t) in this as well.
Also Sachau "And Wâghila, Nâṭila and `Âdila all three are noble and beautiful. ( غُرَرٌ حِسانُ "*gh*urar-un ḥisānu - the nunation is ommited because of versification). M.E. "qui sont brillants et beaux". Sachau is more literal.
(There is a problem: the feminine months except 11 are given as triptote, so I reproduced them that way, but they should be diptote according to Arabic grammar, as proper names ending with the feminine ending are always diptote; also for some reason they appear in the feminine in the poem, whereas elswhere they appear as masculine, without the feminine ending; M.E. transcribes them in the masculine, but again in the Arabic text they are feminine.)
Bīrūnī then gives the following etymologies (Sachau et al.):
 <<
 Almu'tamir { المُؤْتَمِرُ } means that it "obeys" all the decrees of fortune, which the year is going to bring.
 Nâjir { ناجِرٌ } is derived from najr { النَجْر }, which means "intense heat," ... {verse follows}
 Khawwân { خَوَّانٌ } is the form فَعَّال {fa``āl} of the verb to decieve," and Ṣuwân { صُوانٌ } is the form فُعال {fu`āl} of the verb "to preserve, to take care." And these significations agreed with the natures of the months at the time when they were first employed as names for them.
 Zabbâ {text: الزَّبَّاءُ al-zabbā'} means "a great and frequently occurring calamity." The month was so called because in it there was much and frequent fighting.
 Bâ'id {text: البائِدُ al-bā'id}, too, recieved its name from the fighting in it, for many people used to "perish" in it. This circumstance is expressed by the following proverb "All that is portentous happens between Jumâdâ and Rajab. "for in this month people were in great haste and eagerness to carry out whatever blood revenge or warlike expeditions they were upon, before the month of Rajab came in.
 'A
Ṣamm {text: اَلأَصَمُّ al-'a
Ṣamm} was called so, because in it people abstained from fighting, so the clash of weapons was not heard.
 Wâghil {text: الواغِلُ al-wā*gh*il} means "one who comes to a drinking party without having been invited." This month was so called because it suddenly comes in after Ramaḍân, and because in Ramaḍân there was much wine-drinking, on account of the next following months being the months of pilgrimage.
 Nâṭil { نَاطِلٌ } means means "a measure, a pot of wine." The month was called so, because in it people indulged in drinking debauches, and frequently used that pot.
 `Âdil {text: العادِلُ al-`ādil} is derived from "`adl { العَدْل al-`adl}" (which means either "to be just" or "to turn aside"). The month was called so, because it was one of the months of pilgrimage, when they used to abstain from the use of the Nâṭil, i.e. the wine pot.
 Ranna {text: الرَّنَّةُ al-ranna(t)} was called so, because the sheep were "crying" on account the drawing near of the time they were to be killed.
 Burak { بُرَكٌ burak} was called so, because of the kneeling down of the camels on being led to the slaughtering-place.
 >>

Bīrūnī recognizes the problem of having two entirely different months, Nâjir, the 2nd and Ramaḍān, the 9th having both the meanings of "heat". I think some of the etymologies that are given are fanciful.
Bīrūnī then gives another poem, not given by Mahmoud Effendi, listing the months, which Bīrūnī considers better:
1. مُؤْتَمِرٌ mu'tamir; 2. نَاجِرٌ nājir; 3. خَوَّانُ xawwān; 4. صُوَانُ ṣuwān; 5. حَنِينٌ ḥُanīn; 6. زَبَّا zabbā ; 7. اَلأَصَمُّ al-'aṣamm; 8. عَادِلٌ  `ādil; 9. نَافِقُ nāfiq; 10. وَغْلٌ wa*gh*l; 11. رَنَّةُ ranna(t) 12. بُرَك burak
2,3,4,11 are given as diptote.
Bīrūnī gives a final list (Sachau):
1. لمُؤْتَمِرُ al-mu'tamir; 2. نَاجِرٌ nājir; 3. خَوَّانٌ xawwān; 4. بُصَّانٌ buṣṣān; 5. *حنتم  *ḥantam (text: خنتم <xntm>); 6. * زَبَّاءُ *zabba:' text: زُبَّى zubba"; 7. الأَصَمّ al-'aṣamm; 8. عَادِل `ādil; 9. نَافِقٌ nāfiq; 10. وَغْلٌ wa*gh*l; 11. هُوَاعٌ huwā`; 12. بُرك burak
Enc. of Islam I "Zamān" reads 5 as Ḥantam or Ḥanam and says its vocalization is uncertain. it reads 6 as zubbī which might be an error on the part of the author. the article also says that at least some of the name of these months were used as epithets for the later, current, ones. it says Rajab was called al-'aṣamm and `ādil for Sha`bān.

Christian Ludwig Ideler in "Über die Zeitrechnung der Araber", Abbhandlungen der historisch-philolgischen Klasse der Königlich-Preßischen Akademie der Weissenschaften aus den Jahren 1812-1813. Berlin 1816 pp. 97-120, has (referencing Nuwayrī):
1. مُؤْتَمِرٌ mu'tamir (actually he gives مُوتَمِرٌ mūtamir {Mûtemer}); 2. نَاجِرٌ nājir {Nâdschir}; 3. خَوَانٌ xawān {Chawân}; 4. صَوَانٌ ṣawān {Sawâ}; 5. رِتْمَا ritmā {Ritma} ; 6. إِيدَةُ  'īda(t) {Ida}; 7. أَصَمُّ 'aṣamm {Assam}; 8. عَاذِلٌ `ā*dh*il {Adsil}; 9. نَاطِلٌ nāṭil {Nâtil}; 10. وَاعِلٌ wā`il {Wâïl}; 11. وَرْنَةُ warna(t) {Warna}; 12. بُرَك burak {Burek}. 
All seem to agree that مُؤْتَمِرٌ mu'tamir (corresponding to al-Muḥarram) was the first month and that الأَصَمُّ al-'aṣamm corresponded to Rajab and was a holy month of not fighting as well, and  that  بُرَكٌ  burak was the last month.
Bīrūnī gives a poem of month names attributed to the Thamūd, not given by Mahmoud Effendi:
1. مُوجِبٌ mūjib; 2. مُوجِرُ mūjir; 3. مُورِدُ mūrid; 4. مُلْزِمُ mulzim; 5. مُصْدِرٌ muṣdir; 6. هَوْبَرُ hawbar; 7. هَوْبَلٌ hawbal; 8. هَوْهَاءُ hawhā'; 9.  دَيْمُرٌ daymur; 10. دَابِرٌ dābir; 11. حَيْفَلٌ ḥayfal; 12. مُسْبِلُ musbil.
Of these 2,3,4,6,12 are given as diptote. possibly 5 and 9 as well.
In the list most are triptote:
1. مُوجِبٌ mūjib; 2. مُوجِرٌ mūjir; 3. مُوجِدٌ mūrid; 4. مُلْزِمٌ mulzim; 5. مُصْدِرٌ muṣdir; 6. هَوْبَرٌ hawbar; 7. هَوْبَلٌ hawbal; 8. هَوْهَاءُ hawhā'; 9.  دَبْمُرٌ dabmur; 10. دَابِرٌ dābir; 11. حَيْفَلٌ ḥayfal; 12. مُسْبِلٌ musbil.
all of these are triptote except 8 . 11 (corresponding to  حَيْفَلٌ ḥayfal) has the scribal variant حَيْقَلٌ ḥayqal
The relevant passages of Bīrūnī (from the English translation of Sachau) can be found in Google Books, p. 70 - 83:
http://books.google.com/books?id=kUpmAAAAMAAJ&printsec=frontcover#v=onepage&q&f=false

Yet previously Mahmoud Effendi had given other orders and names from al-Mas`ūdī (d. 956?) "Murūj al-Dhahab". I use the published edition Shārl Pillā, as well as what M.E. gives. evidently there are quite a variation among the manuscripts.
From al-Mas`ūdī: 1. ناتق nātiq ("natik") mss. variant: داتق dātiq; 2. تقيل taqīl or ثقيل *th*aqīl ("thakil"); 3. طاليق ṭālīq or طليق ṭalīq ("talik"); 4. ناجر nājir ("nadjir"); 5. أسلخ 'aslax (S.P., M.E.) or ابتلج <'btlj>, S.P. or أسلح 'aslaḥ (M.E.) or سماخ samāx (M.E.) or سماح samāḥ (M.E. "asmakh" or "asmâkh" {this form does not appear on the arabic script version M.E. gives, there seems to be a typo somewhere, the variations has to do with the manuscripts); 6. اميح 'amyaḥ (S.P.) or افلح 'aflaḥ (S.P.) or أمنح 'amnaḥ (M.E."amnah"); 7. أحلك 'aḥlak ("ahlak"); 8. كسع  kasa` ("kasa"); 9. زاهر zāhir ("zâher"); 10. بُرَك burak (S.P.) or بوط būṭ (S.P.)or برط barṭ (M.E. "bart") or مرط marṭ (M.E. "mart"); 11. حرف ḥarf (S.P., ME. "harf") or نعيس na`īs ("na-ïs"); 12. نعس na`as (S.P., ME. "naas", in some sources na`s) or مريس mirīs (M.E. "meris").


Nevertheless, the Arabs also determined the seasons by the rising of certain stars ('anwā' أَنْوَاءٌ , the singular naw' نَوْءٌ denoting a period of time ) and the lunar mansions ("stations") manāzil مَنَازِلُ in this specific sense with the definite article al-manāzil المَنَازِلُ  or manāzil al-qamar مَنَازِلُ القَمَرِ "mansions/stations of the moon" ; singular, manzil مَنْزِلٌ . the system of lunar mansions is said to be of Indian origin. the same stars are used for 'anwā' as for al-manāzil. 'anwā' gives the seasons and al-manāzil the day of the lunar month. the 'anwā' are not quite solar but stellar, being in very long periods subject to the precession of the Earth. There are 28 lunar mantions (or "stations") because the orbital period of the Moon around the Earth is 27 1/3 days (explained in detail later). The method of lunar mansions has Qur'anic sanction Q 10:5:

http://www.quranexplorer.com/quran/
Dr. Pickthall
Yunus
He it is Who appointed the sun a splendour and the moon a light, and measured for her stages, that ye might know the number of the years, and the reckoning. Allah created not (all) that save in truth. He detaileth the revelations for people who have knowledge. (5)
سُوۡرَةُ یُونس
هُوَ ٱلَّذِى جَعَلَ ٱلشَّمۡسَ ضِيَآءً۬ وَٱلۡقَمَرَ نُورً۬ا وَقَدَّرَهُ ۥ مَنَازِلَ لِتَعۡلَمُواْ عَدَدَ ٱلسِّنِينَ وَٱلۡحِسَابَ‌ۚ مَا خَلَقَ ٱللَّهُ ذَٲلِكَ إِلَّا بِٱلۡحَقِّ‌ۚ يُفَصِّلُ ٱلۡأَيَـٰتِ لِقَوۡمٍ۬ يَعۡلَمُونَ
(٥)

The moon, sun and stars as regulating the affairs of men are referred to, in addition to the ones mentioned here, in 14:33 (Sun and Moon), 16:12 (Sun, Moon and Stars), 3:29 (Sun and Moon; 36:40 lunar mansions again) and 39:5 (Sun and Moon). So the calendar was definitely lunar.
I think 10:5 may refer to an embolismic calendar, and was "revealed" before the ban on embolism was "revealed", as the manāzil stars (which determine the day of the lunar month) and the 'anwā'stars are the same. the verse says it determines the number of years, so the number of years in the lunar calendar were not far off from the number of years of the calendar using the 'anwā'. Hence I think this refers to an embolismic calendar, which was "abrogated" (using islamic terminology) by the verse that says the number of months is twelve. IMO. This is consistent with Bīrūnī's view or statement that the right time for nasī' was determined by the manāzil (see Ginzburg's translation and quote, mentioned before). This is the opinion of F.A Shamsi "The 'Year' in the Qur'ān" Studies, Vol. 25, No. 3 (Autumn 1986), pp. 305-324 http://www.jstor.org/stable/20839778 :

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Thus the Arabs could do one of two things: (1) determine the number of years by the number of helical settings of a lunar mansion, or (2) determine the number of years by taking, say, twelve lunar revolutions around the mansions as constituting the period of a year. In the former case the year would constitute a natural unit and it would be correct to say that the number of years was learned from the lunar mansions. In the latter case the year would constitute a conventional period and it would be more appropriate to say that the number of lunar revolutions through the lunar mansions determines the number of years.
Thus it seems that the verse favours the luni-solar view although it does not rule out the vaguely lunar view.

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It is also pointed out by Shamsi that "the reckoning" اَلْحِسَابُ al-ḥisāb also "calculation" seems to refer to the intercalation. he says:
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In fine, these verses, though not sufficient by themselves to reject the vaguely lunar view, lend so great a support to the luni-solar view as to make it almost certain.
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Enc. of Islam II "Manāzil" by P. Kunitzsch:
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al- Manāzil  (A.) or more fully manāzil al-ḳamar , the lunar mansions, or stations of the moon (sing. manzil or manzila), a system of 28 stars, groups of stars, or spots in the sky near which the moon is found in each of the 28 nights of her monthly revolution.
The system seems to be of Indian origin (see Scherer; Pingree [1] and [2]; Billard). Babylonian origin has sometimes been suggested (cf. Hommel), but could never be established from the documents. The “stars in the moon's path”, in the mulAPIN text (cf. van der Waerden [1], 77; recently re-dated to 2300 B.C., cf. van der Waerden [2]) are 17 or 18 in number and rather represent an early stage in the development of the zodiac. The system of the lunar mansions was adopted by the Arabs, through channels as yet unknown, some time in the pre-Islamic period, since the term manāzil is already mentioned in the Ḳur'ān (X, 5; XXXVI,39). To the single mansions, the Arabs applied names already found with them previously, and originally used to designate their anwā' [see anwā' ]. ...
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But the accepted intepretation was that the manāzil mentioned in the Qur'an are strictly for determining the lunar phases. Enc. of the Qur'ān "Calendar" by A. Dallal:
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There is no reference in the Qur'ān to the pre-Islamic system of anwā' (see pre-islamic arabia and the qur'ān ), which was used by the Arabs to estimate the passage of time and to predict the state of the weather (q.v.). In this system, the year is divided into precise periods on the basis of the rising and setting of certain stars (see cosmology in the qur'ān ). According to tradition, this system was considered anathema in Islam. The most relevant qur'ānic allusion to calendar-related computation is the phases of the moon ( manāzil al-qamar, q 10:5; 36:39). q 10:5 reads: “It is he who gave the sun (q.v.) its radiance, the moon (q.v.) its luster, and determined its phases so that you may compute years and numbers…” Qur'ānic exegesis as well as the exact scientific computations of calendars identify 28 such phases. The definition of these phases, however, is based on a combination of the pre-Islamic system of anwā' with the system of lunar phases. Thus the solar zodiac is divided into 28 equal parts defined by the rising and setting of certain stars or constellations. Each of these parts is a station, or phase, and in rough measure the moon occupies one of these stations each day of the lunar month. At the end of a lunar month, the moon would have traveled through all 28 stations; in other words, the moon would have completed one revolution along the solar zodiac (Qurṭubī, Jāmi`, viii, 310; xv, 29-30).

The official Islamic calendar is lunar with year one coinciding with the year 622 c.e., the date of Muḥammad's emigration ( hijra, q.v.) from Mecca (q.v.) to Medina (q.v.). This calendar was adopted during the reign of the second caliph `Umar (q.v.; r. 13-23/634-44). Later sources, however, suggest that the use of the lunar calendar is already prescribed in the qur'ānic references to the phases of the moon. For example, in the commentary on q 10:5 mentioned above, al-Qurṭubī (d. 671/1272; Jāmi`, viii, 310) maintains that after mentioning the light of the sun and the moon, the Qur'ān uses the singular (qaddarahu, not qaddarahumā). This is taken to indicate that only the lunar calendar is meant to serve as the basis for computing the official months or “new moons” (ahilla, q 2:189) and for determining the dates for important religious activities such as fasting (q.v.) and pilgrimage (q.v.). Unless otherwise specified, time stipulations in legal contracts and documents are based on the hijra lunar calendar (see law and the qur'ān ).

...

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Also Enc. of the Qur'ān "Months" by  Alexander Knysh:

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q 10:5 and 36:39 give us an insight into how pre-Islamic Arabs and the first Muslims reckoned their time. These verses refer to the system of twenty-eight lunar mansions (manāzil), i.e. stars, groups of stars or spots on the sky in which the moon “is located on each successive night of the sidereal (not the synodic) month” (de Blois, Ta'rīkh, 260; see stars and planets ). Whereas later Muslim astronomers abandoned this system in favor of more precise astronomical calculations, it has survived until today and lies at the foundation of agricultural calendars in many Arab countries and their neighboring areas.
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Daniel Martin Varisco in "The Origin of the anwā' in Arab Tradition", Studia Islamica, No. 74 (1991), pp. 5-28
expresses some doubts as to whether the manāzil represents the stations rather than the phases of the moon:
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In Islamic astronomy one of the standard methods of dividing the heavens into discrete reckoning units is the concept of twenty eight lunar stations (manāzil al-qamar).(1) This constitutes a lunar zodiac, the round of stars in which the moon stations (yanzilu) each night of its sidereal revolution around the earth. Since this revolution takes about 27 1/3 days, the selection of twenty-eight asterisms provides a rough guide for charting the nightly course of the moon. However, the sidereal revolution is not equivalent to a lunation, the time between phases of the moon, so this method was not applicable to the Islamic lunar calendar. The lunar stations could be used as an approximate sky clock on any given night, but the primary importance of the concept was in astrology. ...
...
Anwā' as Manāzil al-Qamar: The Evidence
 
 The belief that the anwā' were equivalent to the lunar stations was taken as a universal truth by early Muslim scholars. This is nowhere more apparent than in interpretation of two Quranic passages describing the moon and the manāzil. The first reference is in surah Yūnus (10: 6), which has been rendered as follows: "He
it is Who has made the sun a source of light and the moon shedding lustre, and ordained for it stages (manāzil), that you might learn the method of calculating the years and determining time".(33) The second reference is in surah Yā Sīn (36: 39): "We have appointed stages (manāzil) for the moon, till it wanes into
the shape of an old dry branch of a palm tree". The authors of the anwā' genre and most Quranic commentators take thereference to manāzil, translated above as stages, as meaning the twenty-eight lunar stations, which are equivalent to the anwā' of pre-Islamic Arabia.(34)
 A close reading of the two passages, however, brings into question the identification with the formal lunar zodiac. Ibn Kathīr, in his commentary, differed from the standard interpretation by referring to the manāzil here as phases of the moon in its waxing and waning.(35) The passage in surah Yā Sīn seems better suited to the moon's phases in its description of the moon coming to the shape of a dried-up, old palm branch (`urjūn). The reference in surah Yūnus to the function of time keeping is also more appropriate for the phases of the moon, because these formed the basis of the Muslim lunar calendar rather than the lunar
stations. The Quranic usage should thus be seen as an echo of the biblical tradition (e.g., Genesis 1:14, Psalm 104:19), where God is said to have appointed the sun and moon for marking the seasons.
...
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The passage refered to 36:39 is:
Ya-Seen
And for the moon We have appointed mansions till she return like an old shrivelled palm-leaf. (39)

سُوۡرَةُ یسٓ
وَٱلۡقَمَرَ قَدَّرۡنَـٰهُ مَنَازِلَ حَتَّىٰ عَادَ كَٱلۡعُرۡجُونِ ٱلۡقَدِيمِ
(٣٩)


In Enc. of Islam II "Anwā'" by Ch. Pellat we have the following:

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Anwā'  (a.), a system of computation among the early Arabs. The singular naw' , connected with the root nā'a “to rise with difficulty, to lean, to support a load with difficulty” (cf. Ḳur'ān, xxviii, 76), denotes the acronychal setting of a star or constellation and heliacal rising of its opposite ( raḳīb ); by extension, it is applied to a period of time and, in the language of the later Middle Ages and the modern era, it has come to mean “cloud, rain, storm, tempest” (see Dozy, Suppl., s.v.; Beaussier, s.v.; H. Wehr, Arab. Wörterbuch, s.v.), on account of the pluvial role ascribed to the stars contemplated. In the plural, anwā' denotes the whole system based on the acronychal setting and helical rising of a series of stars or constellations; it also appears in the title of a number of works which constitute a separate class of their own.
 The system of the anwā' .

To estimate the passage of time, the early Arabs possessed a primitive system—perhaps already influenced by the “Calendar of the Pleiades” (cf. J. Henninger, Sternkunde, 114 and references quoted)—which can be summarized as follows:—(a) on the one hand, the acronychal setting of a series of stars or constellations marked the beginning of periods called naw' , but within which the duration of the naw' proper was from 1-7 days. The stars themselves were responsible for rain and were invoked during the istisḳā' [q.v.]; knowledge of these anwā' enabled Bedouin trained in this science to foresee the state of the weather during a given period; (b) on the other hand, the helical rising of the same series of stars or constellations, at six monthly intervals, marked out the solar year by fixing a number of periods probably about 28. Such maxims as have survived suggest that this was the very basis of the calendar.
Some time before Islam (cf. Ḳur'ān x, 5; xxxvi, 39) the Arabs learnt from the Indians to distinguish the “stations” or “mansions” (manzila), pl. manāzil [q.v.]) of the moon, numbering 28. Perceiving that the list of these mansions corresponded grosso modo with their own list of anwā' , they proceeded to combine the two ideas and to adjust their anwā' to make them coincide with the manāzil, by dividing the solar zodiac into 28 equal parts of approx. 12° 50'; thus the 28 anwā' identified with the 28 manāẓil (see list in the article manāzil ) are determined by 28 stars or constellations constituting 14 pairs (the acronychal setting of the one corresponding to the heliacal rising of the other) and marking the beginning of 27 periods of 13 days and one of 14. These modifications, the date of which cannot be fixed accurately, were definitely completed after Islam, the passage from one system to the other being favoured by the development of astronomy, and by the anathema hurled by the Prophet against the anwā' , which are not mentioned in the Ḳur'ān. The old system, however, still survived, on the one hand empirically among the Bedouin tribes (cf. for example the nūwa, pl. nwāwi of the Marāzīg of southern Tunisia in G. Boris, Documents linguistiques …, Paris 1951, 208-11), on the other hand traditionally, and with complete identification of the anwā' with the mansions, in the specialised works which have perpetuated it among certain rural populations (see Ed. Westermarck, Ritual and Belief in Morocco, London 1926, ii, 177, and Wit and Wisdom in Morocco, London 1930, 313-17).

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{manāẓil is a typo, should be manāzil}

Enc. of Islam III (online) "Anwa'" by D. M. Varisco gives more information:
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Anwā'
The formal star calendar consists of 28 asterisms along the zodiacal belt, starting with Sharaṭān (β γ Arietis). The term naw' (pl. anwā') among astronomers refers to the setting of one of these asterisms in the west at dawn and the simultaneous rising of another opposite it in the east. During a solar year each naw' period consists of 13 days except for one (usually Jabha) of 14 days. A distinct lexical genre evolved on the anwā', notably the texts of Ibn Qutayba (d. 276/889), Abū Isḥāq al-Zajjāj (d. after 377/987), and Quṭrub (d. 206/821). These texts provide, for each period, relevant seasonal information on rain, wind, periods of heat and cold, animals and plants, pastoral and agricultural activities, and cultural events. Many texts include a set of rhymed proverbs on the anwā', with considerable variation among the texts.
There is no evidence that Arab tribes used the formal model of 28 asterisms before Islam. Abū Zayd (d. 214 or 215/830–1) and Quṭrub, two of the earliest sources, record a different system among the Qushayriyyūn, in which rainy seasons of varying lengths are marked by some of the anwā', but they include the non-zodiacal Nasrān (Altair and Vega). Ibn Qutayba noted that there was no pre-Islamic poetry for some of the anwā'.
The etymology of naw' is widely debated in the early sources. The term appears to originate in pre-Islamic rain divination. Ibn al-A`rābī (d. c. 231/846) claimed there could be no naw' without rain. In a ḥadīth Muḥammad condemned those who said  they were rained upon by the naw' of the Pleiades rather than God. Al-Zamakhsharī (d. 538/1144) suggested that the name of the goddess Manāt (Q 53:21) may be related to the same root as naw', so named because of her role in rainmaking. Ibn Kunāsa (d. c. 207/823) and al-Bīrūnī (d. after 442/1050) defined naw' with reference to the influence of the star rather than as a setting or rising. The term naw' does not appear in the Qur'ān. Many commentators link references to stations (manāzil) of the moon in Q 10:6 and 36:39 to the 28 asterisms of the anwā', but Ibn Kathīr (d. 774/1373) reads this as a reference to the stages of the moon in the Islamic lunar calendar. For astronomers and astrologers the manāzil meant the 28 asterisms that the moon regularly conjoined each night of its sidereal revolution of about 27 and 1/3 days. Prognosticative predictions based on which asterism the moon conjoined led to an astrological tradition merged with lore from India and transmitted through Arabic sources to mediaeval Latin texts such as the Picatrix. Borrowing the idea of a lunar zodiac from India, Islamic astronomers equated each asterism with an arc of 12° 51' minutes (360 degrees divided by 28). The division of the solar year into 28 equal naw' units is an arbitrary application of these 28 asterisms rather than being based on actual seasonal events or an observable calendar. It may represent an attempt to salvage the timekeeping function of the star calendar from its pre-Islamic divinatory practices.
D. M. Varisco
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Also acc. to Enc. of the Qur'ān "Moon" by Daniel Martin Varisco:
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An alternative lunar calendar was provided by charting the nightly progression of the moon vis-à-vis the stars for a full lunation, a period of about twenty-seven and one-third days. This system of twenty-eight lunar stations ( manāzil al-qamar) is elaborated in Islamic astronomical and astrological texts, but is not specifically mentioned in the Qur'ān. Another pre-Islamic calendar plotted months by noting the number of days after the crescent moon until the moon conjoined with the Pleiades (thurayyā). While commentators often associate Sūrat al-Najm ("The Star," q 53), with the Pleiades, there is no specific mention of this conjunction calendar in the Qur'ān or ḥadīth (see ḥadīth and the qur'ān ).
Although Muḥammad condemned the use of stars for prediction (see foretelling; divination; planets and stars ) — an interdiction against the so-called anwā', which Arab scholars linked to the lunar stations — and worship of the sun or moon is forbidden in the Qur'ān ( q 41:37; see idols and images; south arabia, religion in pre-islamic ), the moon has a variety of symbolic associations in Islamic esoterica and mysticism. ...
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I think the above verse does have something to do with the system mentioned in the article, otherwise it would not mention "counting of the years" for the manāzil, it would have said "counting the days of the month". but that is just my opinion. this is also the opinion of F.A. Shamsi "The 'Year' in the Qur'an" Islamic Studies, Vol. 25, No. 3 (Autumn 1986), pp. 305-324.In my opinion  this is consistent with Bīrūnī's statement that the intercalation was done through the manāzil. However, it is not certain that this was done accurately. 
According to "The Rain Periods in Pre-Islamic Arabia" by Daniel Martin Varisco, Arabica, T. 34, Fasc. 2 (Jul., 1987), pp. 251-266 :

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 The term naw' (plural, anwā') is generally defined as the dawn setting of a star or asterism in the west at the same time as an opposite star rises with the sun in the east. There is some disagreement over whether the naw' refers to the setting or the rising6. The verbal root clearly indicates a rising (nuhūḍ), but the Arabs are said to have used the opposite meaning of setting (suqūṭ) for those stars which mark times of rain, wind, heat or cold. This shift in meaning may simply reflect the idea that the concomitant rising and setting were one event in which only the setting star would be visible. While the literatures suggests that the setting of the star was the marker for rain, virtually all of the sayings recorded by Ibn Qutayba and others mention only the risings.
  Ibn al-A`rābī claimed that there could only be a naw' when rain occurred. In contemporary Arabic dialects naw' often becomes a term for rain or a rain period8. In the pre-Islamic poetry cited by Ibn Qutayba the naw' is always linked to stars known to mark periods of rain. This sense is also implied in a tradition of the prophet Muḥammad, who condemned the pre-Islamic practice of invoking rain from stars rather than from God9. Certain idols had been erected at the Ka`ba and were prayed to for rain. In his commentary on sūra 53:19-23, al-Zamaḫšarī10 suggested that naw' was related to the goddess Manāt, who was worshipped by certain tribes and invoked for rain. All of this suggests that the meaning of naw' has more to do with the occurrence of rain than the setting (or rising) of a star per se.
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(I think there is a bit of folk etymology there)
Daniel Martin Varisco "Islamic Folk Astronomy" in "Astronomy Across Cultures - The History of Non-Western Astronomy" (2000, H. Selin ed.) says:
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 The earliest Islamic texts uniformly claim a pre-Islamic origin for the stations from the weather lore associated with the asterisms known as anwā' (naw', singular) in Arabic. The term naw' well attested in the earliest lexical sources and defines a distinct genre of anwā' texts cosmical setting of one of the twenty-eight lunar stations. Ibn Qutayba (1956: 6) amplified this as follows: the setting of an asterism from the lunar stations to the west at dawn and simultaneous rising of another opposite it to the east (suqūṭ al-najm minhā fī al-maghrib ma`a al-fajr wa-ṭulū` ākhar yuqābiluh min sā`atih fī al-mashriq). The sense here is said to be for one star setting as its opposite in the sky rises. Fahd (1966: 413) believes the opposition is common to the root meaning in earlier Akkadian and Hebrew.
 There is confusion in the medieval lexicons regarding how this meaning of a setting could have arisen from a root (n-w-') that refers to rising (nuhūḍ or ṭulū`). Abū `Ubayd (quoted in Lisān al-`Arab, article n-w-') argued that this sense of setting only applied to naw' with regard to the lunar stations, because it is said that the Arabs linked the coming of rain. wind, heat or cold to the influence of a setting star. Ironically, in the surviving poetry and sayings on these anwā' indicate the opposite - that the rising of the star was the important reference. It is interesting to note that in the Indian Vedic texts the dawn setting of a lunar station marked the timing of certain religious acts (Kane, 1948: 5: 510).
 Ibn Qutayba (1956: 7-8) recorded both senses, setting and rising, for naw', but prefered the idea of setting because of the usage of the verbal form in surah al-Qaṣaṣ (28:76) of the Quran. ...
... It should be noted that a number of prominant stars known as markers of rain (e.g. Canopus, Orion, Spica, Arcturus) are not considered anwā', while Sirius is considered a naw' in the poetry even though it does not figure in the lunar zodiac.
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The arabic phrase is:
سُقُوطُ النَّجْمِ مِنْهَا فِي الْمَغْرِبِ مَعَ الْفَجْرِ وَطُلُوعُ آخَرَ يُقَابِلُهُ مِنْ سَاعَتِهِ فِي الْمَشْرِقِ

The Qur'anic passage is: (Pickthall's translation)
Al-Qasas
Now Korah was of Moses' folk, but he oppressed them; and We gave him so much treasure that the stores thereof would verily have been a burden for a troop of mighty men. When his own folk said unto him: Exult not; lo! Allah loveth not the exultant; (76)

سُوۡرَةُ القَصَص
۞ إِنَّ قَـٰرُونَ ڪَانَ مِن قَوۡمِ مُوسَىٰ فَبَغَىٰ عَلَيۡهِمۡ‌ۖ وَءَاتَيۡنَـٰهُ مِنَ ٱلۡكُنُوزِ مَآ إِنَّ مَفَاتِحَهُ ۥ لَتَنُوٓأُ بِٱلۡعُصۡبَةِ أُوْلِى ٱلۡقُوَّةِ إِذۡ قَالَ لَهُ ۥ قَوۡمُهُ ۥ لَا تَفۡرَحۡ‌ۖ إِنَّ ٱللَّهَ لَا يُحِبُّ ٱلۡفَرِحِينَ
(٧٦)
Specifically the part:
 verily have been a burden for a troop of mighty men.
 إِنَّ مَفَاتِحَهُ ۥ لَتَنُوٓأُ بِٱلۡعُصۡبَةِ أُوْلِى ٱلۡقُوَّةِ 
 'inna mafātiḥahu latanū'u bil-`uṣbati 'ūlī~l-quwwati
Lane, gives نَاءَ nā'a from root <nw'> meaning "to rise with difficulty". Penriss, who deals with Qur'anic meanings  "to rise with difficulty", "to weigh down a load (with بِ bi of person)" the last one the meaning in the Qur'an. Lane says this as that نَاءَ بِحَمْلِهِ nā'a bi-ḥamlihi as meaning "he rose with his burden with effort and difficulty (or oppressed with its weight). Lane confirms that most dictionaries and authorities say it signifies the setting of a star, some the setting and simultaneous rising of another, a minority the rising of a star. But Lane concludes from the proverbs concerning the stars that the primary meaning is rising.

The 'anwā' stars and the manāzil stars were the same (though some non-Zodiacal stars were added to the 'anwā'). They are, according to Enc. of Islam II "al-Manāzil" by P. Kunitzsch:

1. al-sharaṭān  الشَّرَطَانِ (also: al-naṭḥ النَّطْحُ ), βγ, or βα Arietis. 2. al-buṭayn البُطَيْن , εδρ Arietis. 3. al-thurayyā الثُّرَيَّا , the Pleiades. 4. al-dabarān الدَّبَرَانُ , α Tauri. 5. al-haḳ`a  الهَقْعَةُ , λφ 1,2 Orionis (according to the Almagest , one nebulous object, the first star of Orion; but registered as three individual stars by al-Bīrūnī [3]). Alternatively also, al-maysān المَيْسَانُ , which properly would be one of the two stars of no. 6. 6. al-han`a  الهَنْعَةُ , γξ Geminorum; also al-taḥāyī التَّحَايِي , ημν Geminorum (either separately, or together with γξ Geminorum). Al-Bīrūnī [3] has it νγξ Geminorum. 7. al-dhirā`  الذِّرَاعُ , αβ Geminorum. There is confusion in the sources as to whether this dhirā` is al-dhirā` al- maḳbūḍa  الذِّرَاعُ المَقْبُوضَةُ or al-dhirā` al-mabsūṭa الذِّرَاعُ المَبْسُوطَةُ and 8. al-nathra  النَّثْرَةُ , ε Cancri, or εγδ Cancri (Ibn Ḳutayba, and al-Bīrūnī [3]). 9. al-ṭarf الطَّرْفُ , κ Cancri + λ Leonis. 10. al-djabha الجَبْهَةُ , ζγηα Leonis (included with this station is the star α Leonis, “Regulus”, which had no individual name in the classical Arabic star lore). 11. al-zubra الزُّبْرَةُ (also: al-kharātān الخَرَاتَانِ ), δθ Leonis. 12. al-ṣarfa الصَّرْفَةُ , β Leonis. 13. al-`awwā' العَوَّاءُ , βηγε Virginis, sometimes δ Virginis is also added to these. 14. al-simāk السِّماكُ (i.e. al-simāk al-a`zal السِّمَاكُ الأَعْزَلُ ), α Virginis. 15. al-ghafr الغَفْرُ , ικλ Virginis (al-Bīrūnī [3] has ικ only). 16. al-zubānā الزُّبَانَى , αβ Librae. 17. al-iklīl الإِكْلِيلُ , βδπ Scorpii. 18. al-ḳalb القَلْبُ , α Scorpii. 19. al-shawla الشَّوْلَةُ , λυ Scorpii. Sometimes, al-ibra الإِبْرَةُ , or ibrat al-`aḳrab إِبْرَةُ العَقْرَبِ , is given as an alternative designation, but some authors refer this name to a different object, viz. the nebulous cluster following behind al-shawla الشَّوْلَةُ , i.e. M 7 Scorpii. 20. al-na`ā'im  النَّعَائِمُ , the two groups of four stars each, γδεη + σφτζ Sagittarii; alternatively, al-waṣl الوَصْلُ , the space between these two groups. 21. al-balda البَلْدَةُ , a region void of stars, between stations nos. 20 and 22. 22. sa`d al-dhābiḥ الذَّابِحُ , α 1,2 νβ Capricorni. 23. sa`d bula`  سَعْدُ البُلَعِ , με Aquarii, to which some authors add Fl. 7, or ω Aquarii, as a third star. 24. sa`d al-su`ūd سَعْدُ السُّعُودِ , βξ Aquarii + c1 Capricorni. 25. sa`d al-akhbiya سَعْدُ الأَخْبِيَةُ , γπζη Aquarii. 26. al-fargh al-muḳaddam الفَرْغُ المُقَدَّمُ (also al-fargh al-'awwal الفَرْغُ الأَوَّلُ), αβ Pegasi. 27. al-fargh al-mu'akhkhar الفَرْغُ المُؤَخَّرُ (also al-fargh al- thānī الفَرْغُ الثَّانِي ), γ Pegasi + α Andromedae. 28. baṭn al-ḥūt بَطْنُ الحُوتِ (also al-rishā' الرِّشَاءُ ). β Andromedae.
Ch. Pellat gives π Sagittarii for 21. Yampolsky says it is the space bounded by it.

Lane under naw' نَوْءٌ singular of 'anwā' أَنْوَاءٌ says al-naw' (with the article is especially applied to 3. the Pleiades al-thurayyā الثُّرَيّ ; which is also known as النَّجْمُ al-najm "the Star"). Lane  notes the occasional use of 1. as al-sharaṭ  الشَّرَطُ (perhaps βγ Arietis); β Arietis (acc. to Lane, some consider γ the other horn) which is  al-naṭḥ النَّطْحُ and αβ (according to Lane, modern European terminology has βγ Arietis as Sharatan) Arietis as al-sharaṭān الشَّرَطَانِ and βγα Arietis as  الأَشْرَاطُ  al-ashrāṭ (plural), but the dual being more common; النَّاطِحُ al-nāṭiḥ is α Arietis, but elswhere Lane says the reverse. Wehr and other modern sources have Lane have α Arietis as  النَّاطِحُ al-nāṭiḥ. Lane has 14. as just as al-'a`zal الأَعْزَلُ or سَاقُ الأَسَدِ sāq al-'asad "the leg (or thigh) of the Lion" and 15. as al-raqīb الرَّقِيبُ (though this is a nickname for various stars that are in opposition, i.e. one sets and the other one rises); and 27 is sometimes called al-`arquwatān al-mu'akhkharatān  العَرْقُوَتَانِ المُؤَخَّرَتَانِ and 26. being called al-`arquwatān al-'ūliyān العَرْقُوَتَانِ الأُولِيَانِ . elsewhere Lane gives حُمَةُ العَقْرَبِ  ḥumat al-`aqrab as an alternative name for 19. for 6.  al-taḥāyī التَّحَايِي or al-taḥā'ī  التَّحَائِي Lane says that sometimes this is given to as seperate asterism that the Moon deviates to, or it is a synonym of al-han`a  الهَنْعَةُ . Lane also includes and al-nasrān ("the two vultures") النَّسْرَانِ with one being al-nasr al-wāqi` النَّسْرُ الوَاقِعُ "the swooping vulture" α Lyrae for 18 and the other being al-nasr al-ṭā'ir النَّسْرُ الطَّائِرُ "the flying vulture" α Aquilae among the 'anwā'. These are non-zodiacal and part of an older system. they set aurorally on 24 July O.S. in the period in question and marked the rains (not season) of الخَرِيفُ al-xarīf, a period of little rain. some Arabs included for 7 Sirius, α Canis Maioris, الشِّعْرَى al-shi`rā, more  precisely الشِّعْرَى اليَمَانِيَّةُ al-shi`rā al-yamāniyya ("the Southern al-shi`rā"), as part of the 'anwā but not of the manāzil. { الشِّعْرَى الشَّامِيَّةُ al-shi`rā al-shāmiyya or الشِّعْرَى الشّْآمِيَّةُ al-shi`rā al-sha'āmiyya "the northern shi`rā" being Procyon, α Canis Minoris; in the dual, الشِّعْرَيَانِ al-shi`rayān designated the two stars Sirius, α Canis Maioris, and Procyon, α Canis Minoris, together. according to Enc. of Islam II there is likely no relation between the Arabic name الشِّعْرَى al-shi`rā "the hairy one" and the Greek name Σείριος Seirios "scorcher" Old Arabic shīn was a lateral and I find it unlikley that it would render Greek sigma}. It rose aurorally 13 July O.S. at the time of the Hijra (622 CE) and it was associated with a time of intense heat. Enc. of Islam II says that in the 'anwā' books it was included "in the zodiacal sign of { الجَوْزَاءُ } al-jawzā' = Gemini", this became the conventional name of Gemini but this was also older name for Orion as well, in which case Gemini was called التَّوْءَمَانِ (sometimes spelt التَّوْأَمَانِ ) al-taw'amān "the twins", so IMO Orion is meant; but not in Greek based scientific works, where it was included in Canis Maior, in Arabic   كَلْبُ الجَبَّارِ kalb al-jabbār "Orion's dog"; Orion being called الجَبَّارُ al-jabbār "the giant" , Canis Maior also being called more literally الكَلْبُ الأَكْبَرُ al-kalb al'akbar. Among the other Arabic names for Sirius are العَبُورُ al-`abūr (the crosser of the galaxy) or الشِّعْرَى العَبُورُ al-shi`rā al-`abūr and بَرَاقِشُ barāqish (the one of many colors). while Procyon was sometimes called  الغُمَيْصَاءُ al-ghumayṣā' or الشِّعْرَى الغُمَيْصَاءُ al-shi`rā al-ghumayṣā'.  غُمَيْصَاءُ ghumayṣā' means "almost blind", i.e. relatively dim. the legend goes like this acc. to Enc. of the Qur'an "Sirius" by Bassel A. Reyahi  << ...  Sirius and Procyon, which are, in Arabic star-lore, both sisters of Suhayl (Canopus), and resided in the northern sky. After a failed courtship attempt, Suhayl had to flee to the southern sky (i.e. with respect to the Milky Way) and only one sister — the brighter Sirius — could follow. The other (Procyon) remained and cried until she became almost blind ( ghumayṣā — hence her relative dimness).>>  also sometimes included among the 'anwā' was non-Zodiacal Canopus, سُهَيْلٌ suhayl α Carinae. it is visible south of 37°N. Lat. and visible in the "land of the Arabs".  سُهَيْلٌ suhayl is the diminutive of سَهْلٌ sahl which denotes ease, also acc. to the Arabic Wikipedia, equilibrium, graceful, noble, shining, etc. Lane has al-dhirā` al-mabsūṭa الذِّرَاعُ المَبْسُوطَةُ for 7.  αβ Geminorum, "the outstreached arm (or paw, of the Lion)". Lane has  al-dhirā` al- maḳbūḍa  الذِّرَاعُ المَقْبُوضَةُ "the clenched arm (or paw, of the Lion)" for αβ Canis Minor.
NB from the above names, English Aldebaran (α Tauri), Altair (α Aquilae) and Vega (α Lyrae) come from Arabic. al-dabarān الدَّبَرَانُ is "the follower",according to some implies the back-side, i.e the hump (of the Bull) it is also named التَّابِعُ al-tābi` or تَابِعُ النَّجْمِ tābi` al-nadjm, follower of the Star (the Pleiades) or التُّوَيْبِعُ al-tuwaybi` "the follower" presumably because this bright star appears to follow the Pleiades}. Lane says it may apply to the Hyades as well.
Enc. of Islam I "Manāzil al-Qamar" gives the meanings of the names in the first list. it is also given in "The Origin of the Twenty-Eight Lunar Mansions" Philip Yampolsky, Osiris, Vol. 9 (1950), pp. 62-83. I have added my own notes.
1. al-sharaṭān الشَّرَطَانِ "the two signs" also الأَشْرَاطُ al-'ashrāṭ "the signs" (probably because they once marked the Vernal Equinox. 2. al-buṭayn  البُطَيْنُ "the little paunch" (paunch of the Ram) {i.e. the little belly} 3. al-thurayyā الثُّرَيَّا , the Pleiades "the little thick set group" {Lane derives it from the diminutive of *th*arwa(t) ثَرْوَةٌ meaning "many, of a great number" (later also "richness"), Bīrūnī also derives it from *th*arwa" ثَرْوَى meaning "abundance", which he relates to the former word, because it is a great number of things, i.e. stars, but he also says that some derive it from this word 'because of the plenty produced in the pastures and crops by the attendant rains '. Clinton Bailey in Bedouin Star-Lore in Sinai and the Negev BSOAS Vol. 37,No. 3 (1974), pp. 580-596 derives it from *th*ara"(n) ثَرًى "moisture" (so in Lane), from the moisture, i.e. rains associated with it, also, popularly, probably later, "the chandelier". there are two roots <*th*rw> "many" <*th*ry> moisture} 4. al-dabarān الدَّبَرَانُ Aldebaran (with the Hyades), "the follower" {also "the hump"}  5. al-haḳ`a االهَقْعَةُ , "the horse-mark"  6.  al-han`a  الهَنْعَةُ, γξ Geminorum "the pile"; the stars al-zirr الزِّرُّ "the button" and al- maysān المَيْسَانُ {walker with a proud gait, a lion or wolf that so walks};   al-taḥāyī التَّحَايِي  is plural of التَّحْيَاةُ al-taḥyā(t) which is a verabl noun which means "to make to live long" or to "to greet". 7. al-dhirā`  الذِّرَاعُ "the Lion's paw", Castor and Polllux,  8. al-nathra  النَّثْرَةُ "the nostril" of the Lion, 9. al-ṭarf الطَّرْفُ "the look" for طَرْفُ الأَسَدِ  ṭarf al-'asad "the eye" of the Lion. 10. al-djabha الجَبْهَةُ , "the forehead" (of the Lion). 11. al-zubra الزُّبْرَةُ for زُبْرَةُ الأَسَدِ for zubrat al-'asad "the mane" of the Lion.the etymology of الخَرَاتَانِ al-kharātān, is the dual of الخَرَاةُ al-kharāt acc. to some philologists, but no meaning is given. 12. al-ṣarfa الصَّرْفَةُ ,"the weathercock", "the turn". 13. al-`awwā' العَوَّاءُ , {EI1 al-sawwā' السَّوَّاءُ seems to be typo} "the barker" i.e. the barking Dog. 14. al-simāk السِّماكُ "the prominant" also al-simāk al-a`zal السِّمَاكُ الأَعْزَلُ  "the unarmed" (also "the seperate" or "cut off") simāk", Spica, because there are no bright stars next to it. 15. al-ghafr الغَفْرُ , "the cover". 16. al-zubānā الزُّبَانَى , for زُبَانَى العَقْرَبِ "the claw" of the Scorpion; EI1 has الزُّبَانَةُ al-zubāna(t). 17. al-iklīl الإِكْلِيلُ , "the crown" {more precisely "the diadem"} i.e. the head of the Scorpion. 18. al-ḳalb القَلْبُ , "the heart" of the Scorpion, Antares. 19. al-shawla الشَّوْلَةُ , "the sting", "the part of tail of the scorpion that rises", al-ibra الإِبْرَةُ , or ibrat al-`aḳrab إِبْرَةُ العَقْرَبِ , the "needle" of the Scorpion. حُمَةُ العَقْرَبِ ḥumat al-`aqrab means "stinger of the scorpion". 20. al-na`ā'im  النَّعَائِمُ , "the ostriches". 21. al-balda البَلْدَةُ , "the town". 22. sa`d al-dhābiḥ الذَّابِحُ , "the luck of the slayer" or sacrificer. 23. sa`d bula`  سَعْدُ البُلَعِ , "the luck of devourer", EI1 has μν Aquarii. 24. sa`d al-su`ūd سَعْدُ السُّعُودِ , "the greatest luck" {"the luck of lucks"}. 25. sa`d al-akhbiya سَعْدُ الأَخْبِيَةُ , "the luck of the tents". 26. al-fargh al-muḳaddam الفَرْغُ المُقَدَّمُ (also al-fargh al-'awwal الفَرْغُ الأَوَّلُ), "the fore socket" {i.e. outlet} on the pail.  27. al-fargh al-mu'akhkhar الفَرْغُ المُؤَخَّرُ (also al-fargh al-thānī الفَرْغُ الثَّانِي ) "the hinder socket" {i.e outlet} on the pail. 28. baṭn al-ḥūt بَطْنُ الحُوتِ , "the fish belly"; { al-rishā' الرِّشَاءُ means "the well-rope"} Lane also gives it as قَلْبُ الحُوتِ "the heart of the Fish". 1, 2 and 3 are usually identified as the horns, the belly and fat tail أَلْيَةٌ alya of the Ram. 1. is called al-naṭḥ النَّطْحُ "the smitting with a horn" (particularly of rams), more speicifically α Arietis (acc. to Lane), while النَّاطِحُ al-nāṭiḥ "the smitter with a horn (particularly of rams)" is identified by Lane as β Arietis (Lane identifies α and β Arietis as the horns, though some modern illustrations have γ Arietis as the other horn) but elswhere gives the reverse.  Wehr and other modern sources have Lane have  α Arietis as  النَّاطِحُ al-nāṭiḥ. together they are called  النَّطْحُ وَالنَّاطِحُ al-naṭḥ wa-l-nāṭiḥ. the auroral rising of al-naṭḥ النَّطْحُ is considered an ill omen, but weatherwise it is considered a good time to sit on the house top in the evening. they were associated with the beginning of spring. in the timeof the Hijra it set aurorally on 17th Oct. in astronomy Aries is called الحَمَلُ al-ḥamal "the lamb", but some have argued that it should be called الكَبْشُ al-kabsh "the ram". 13. al-simāk al-a`zal السِّمَاكُ الأَعْزَلُ "the unarmed" simāk contrasts with al-simāk al-rāmiḥ السِّمَاكُ الرَّامِحُ "the simāk with a spear", which is Arcturus, α Boötis (not of the 'anwā'), η Boötis being "the spear of the simāk" رُمْحُ السِّمَاكِ rumḥ al-simāk or simply الرُّمْحُ al-rumḥ "the spear". السِّمَاكُ al-simāk by itself denotes Spica, but together with Arcturus they are known as  السِّمَاكَانِ al-simākān, "the two simāk". Spica is also known as سَاقُ الأَسَدِ sāq al-'asad "the thigh or the (hind) shank) of the Lion" and Spica and Arcturus are also known as  رِجْلا الأَسَدِ "the two (hind) legs of the Lion". al-`arquwatān al-mu'akhkharatān  العَرْقُوَتَانِ المُؤَخَّرَتَانِ means "the later two pieces of wood that are put athwart the leathern bucket { دَلْوٌ dalw} to keep it from collapsing for the purpose of attaching the well-rope". al-`arquwatān al-'ūliyān العَرْقُوَتَانِ الأُولِيَانِ means "the first two `arquwa". 13. is acc. to Lane also known as al-`urqūb al-'asad عُرْقُوبُ الأَسَدِ "the hock-tendon of the Lion". the hock-tendon corresponds to the heel tendon or Achilles tendon of humans. sometimes al-zubānā الزُّبَانَى "the claw" was put into the dual الزُّبَانَيَانِ al-zubānayān, "the two claws".
There is a typo in EI1 as it defines 17. as βδπ Librae, which is clearly wrong.

Tt should be noted that traditional Arab constellations are different from the Greek ones, which were adopted by the Arabs when Greek works, particularly the Almagest was translated. some are similar, Scorpio and Leo, but cover a wider area. in Enc. of Islam II "Minṭaḳat al- Burūdj" { مِنْطَقَةُ البُرُوجِ } the belt (or "circle", later "zone"). of the Constellations," i.e. the Zodiac, also the ecliptic itself}, (W. Hartner [P. Kunitzsch]) suggests that  al-zubānā الزُّبَانَى , for زُبَانَى العَقْرَبِ zubānā al-`aqrab "the claw" of the Scorpion, αβ Librae, is really a false etymology for Babylonian zibānītu (“balance”) and was equally understood as the “horns” of Scorpius. Lane says that الجَوْزَاءُ al-jawzā' as "Gemini" was called so because it it is said to cross the جَوْزٌ jawz or "middle" of the sky. I think this etymology was originally for Orion. my theory as to why Geminii was called الجَوْزَاءُ al-jawzā' is that it is from colloquial Arabic جَوْز jawz "couple" which comes from classical Arabic زَوْجٌ zawj which means "one of a pair", "mate (husband)" or "couple" (in Moroccan Colloquial Arabic zōj or jōj means "two"). but Enc. of Islam II labels the etymology as unknown. Enc. of Islam II sees in الجَبّارُ al-jabbār "Orion," meaning in Arabic "the Giant" an older Syriac desgnation gabbārā . some of the constellations are similar, the Lion, the Scorpion, but their limits are different. the Lion in particular is very large. Enc. of Islam II "Minṭaḳat al- Burūdj" { مِنْطَقَةُ البُرُوجِ } says: << Not less than eight (or even nine) lunar mansions (nos. 7 to 14, or 15) have been related to asad which, therefore, in modern research literature, became famous as “the huge Arabic Lion”. It is to be noted that the indigenous Arabic Lion figure, in location, is again different from the Greek tradition in that it stretches from αβ Geminorum to α or even ικλ Virginis. >>. the labeling of Aries as the first of the 'anwā' or manāzil shows Babylonian influence, according to the studies on the subject.

Yampolsky says a similar system of 28 Lunar Mansions were employed by the Chinese and Indians, and he compares the names and the asterisms used. as stated before the Arabs seem to have acquired it from India. it is not clear whether the system originated in China or India, and even Babylonia is given as a candidate. Enc. of Islam II "Manāzil" by P. Kunitzsch disagrees about the Babylonian influence (see quoted passage above), as does Daniel Martin Varisco "Islamic Folk Astronomy" in "Astronomy Across Cultures - The History of Non-Western Astronomy" (2000, H. Selin ed.): << The origin of the twenty-eight lunar stations is not clear. A spirited debate arose in the 19th century over whether the original lunar zodiac evolved in China or India before diffusing to the Middle East. There is no evidence for this lunar zodiac in Babylonian astronomy or in classical Greek science. Despite wild claims to the contrary, such a system can not be found in found in the Biblical records. The idea seems to have been borrowed by early Islamic scholars from India, probably via Sassanian Iran. Welhausen's (1987: 210, note 4) suggestion that the twenty-eight stations were borrowed from India and merged with Arab star lore still holds. >> OTOH he continues as << The earliest Islamic texts uniformly claim a pre-Islamic origin for the sations from the weather lore associated with the asterisms known as anwā' (naw', singular) in Arabic. >>
5 and 6 were frequently combined into الجَوْزَاءُ al-jawzā' "Gemini", even though 5 is part of Orion, which as stated below once had that name.
See also "Dictons rimés, anwā' et mansions lunaires chez les Arabes", Ch. Pellat, Arabica, T. 2, Fasc. 1 (Jan., 1955), pp. 17-41. it also cites a poem with the Manāzil and 'anwā' names, according which:
3. rises helicaly 6 {18} May; 4. 19 {31} May; 5. 1 {13} June; 6. 14 {26} June, also corresponding to Gemini  الجَوْزَاءُ al-jawzā'; together with what is called العُذْرَةُ al-`u*dh*ra(t); 7. 27 {9 July} June, the same time as الشِّعْرَى al-shi`rā ; 8. 10 {22} July ; 9. 23 July {4 August}; 10. 5 {17} August, incl. سُهَيْلٌ suhayl (Canopus, α Carinae) between 5 and 18 August; 11. 19 / 17 {31} August; 12. 1 {13} September; 13. 14 {26} September; 14. 27 September {9 October}; 15. 10 {22} October; 16. 23 October {4 November}; 17. 5 {17} November; 18.  الهَرَّارَانِ al-harrārān, together with al-ḳalb القَلْبُ , and al-nasr al-wāqi` النَّسْرُ الوَاقِعُ  rising 18 {30} November; 19. العَقْرَبُ al-`aqrab (Scorpio) 1 {13} December; 20. 14 {26} December 21. 27  December {8 January};22. 9 {21} January; 23. 22 January {3 February}; 24. 4 {16} February; 25. 17  February {1 March} 26. & 27. الدَّلْوُ al-dalw "the bucket", between 2 {14} March (26.) and 15 {27} March (27.); 28. الحُوتُ al-ḥūt ("the Fish") 28 March {9 april}; 1. 10 {22} April; 2. 23 April {5 May}.
The dates given are the average dates calculated by Bīrūnī for previous authors, {...} are the dates for 1040.
Ch. Pellat transliterates الخَرَاتَانِ al-xarātān as al-xarāṯān (al-xarā*th*ān), this may be a scribal error of his source.
The 'anwā' almanacs were (and still are) siderial. i.e. the they are concerned with the rising and setting of the stars or asterisms in the actual time they are written, they change because of precession, and do not remain frozen at a particular time as the astrological zodiac calendars. However, it is remarked that this is not always so in folklore, as some associate 1. with the first point of Aries, the spring equinox. Lane quotes the saying إِذَ طَلَعَ الشَّرَطَان  \  اِسْتَوَى الزَّمَان 'i*dh*ā ṭala`a ~š-šaraṭān / istawa(:) ~z-zamān . which is given the meaning "when al-sharaṭān rises the weather becomes temperate" or when al-sharaṭān rises the night and day become equal". The second is more literal, as it literally means "time becomes equal". Lane concludes that this might imply that the lunar stations go back to 12th cent. BCE, Babylonian times.
The arab - muslim navigators of the Indian Ocean before the Portuguese used a calendar based on the rising of 17. al-iklīl الإِكْلِيلُ , "the Diadem", according to "Encyclopedia of the History of the Arabic Sciences" Vol. 1 "Arabic Nautical Science" by Henri Grosset-Grange (in collaboration with Henri Rouquette). the rising of Diadem at 15º declination marked the beginning of the year (of fixed 365 days). The beginning of the year was called nawrūz نَوْرُوزٌ or nayrūz نَيْرُوزٌ sometimes vocalized as nīrūz نِيرُوزٌ , a usual word for "New year's Day" for solar calendars in Arabic, by the navigator اِبْنُ مَاجِدٍ Ibn Mājid who piloted in part Vasco da Gama's expedition, from a certain point on. nawrūz نَوْرُوزٌ is Persian nawrūz نَوْرُوزْ , Classical Persian [nawrōz], lit. "new day" (naw is cognate with "new" and rōz "day" is cognate with "light" and in Old Iranian originally meant so, PIE *leuk-), "new year's day", nayrūz نَيْرُوزٌ is influenced by Coptic feast of Ni-Yarouou (the feast of the rivers), which they call the new year's celebrations. This was taken as 20 November. I looked at the facsimile of the text of Kitāb al-Fawā'id fī uṣūl `ilm baḥr wa 'l-ḳawā`id (Book of Useful Information on the Principles and Rules of Navigation" dated 895 AH /1490 CE), and it is unvocalized, so probably [nayrūz] is meant. it also says that it is the "Indian Nayrūz" النيروز الهندي  al-nayrūz al-hindiyy (with the definite article). this is explained as the Sasanian Persian vague year of 365 days with no leap years, the Yazdigerd (the last Sasanian Shah) era, but with the New year's day two days later by Daniel Martin Varisco in "Medieval Agriculture and Islamic Science - the Almanac of a Yemeni Sultan" (1994). It had shifted into November in that era. Also the encylcopedia identifies 'Diadem' with α Librae, which does not correspond to rising in 20 November and belongs to the previous asterism, al-zubānā, "the Claw". another problem with this calendar is that these seafarers were operating near the Equator, while the astronomical tables for the rising of the stars were given for above 25° N latitude.
27. الدَّلْوُ al-dalw "the pail", does not refer Aquarius, which came to be later known by that name, but to the old Arab constellation of that name. as is evident from the above, it consisted of the four bright stars that form a square in Pegasus.  similarly, 28. clearly refers to  baṭn al-ḥūt بَطْنُ الحُوتِ , "the fish belly",  β Andromedae; i.e the Old Arabic constellation know as  الحُوتُ al-ḥūt ("the Fish"), not the Greek constellation Pisces, later also known as  الحُوتُ al-ḥūt ("the Fish", not the use of the singular, not he dual). I couldn't find anything on what is called الهَرَّارَانِ al-harrārān ("the two barkers"). it is not clear what is meant by  العُذْرَةُ al-`u*dh*ra(t). according to Lane it can be five stars at the extremity of the Milky Way, or one below Sirius, also called العَذَارَى al-`a*dh*ārā (its pural, ε Canis Maior (called adar or adard in western astronomy), or η Canis Maior, which rises in the latter part of July O.S. between Sirius and Canopus (this does not fit the description of what is involved above), known in the West as aludra. عُذْرَةٌ `u*dh*ra(t) means "a sign, mark or token that is tied to the forelock of a horse and outstrips, [as preservative] against the [evil] eye {Lane}. also a small quantity of haor or the forelock of a horse.  according to Lane, Canopus,  سُهَيْلٌ suhayl α Carinae rose aurorally 4. August on the year of the Hijra (622 CE). Sirius, α Canis Maioris, الشِّعْرَى al-shi`rā rose aurorally 13 June on the year of the Hijra and is associated with a time of intense heat. the rising of Antares, al-qalb القَلْبُ , α Scorpii is associated with intense cold. the rising of canopus on 4 August at the time of the Hijra is said to have marked the end of  القَيْظُ al-qayẓ or time of intense heat (see below). 3. the Pleiades set aurorally on 12. Nov. O.S. on the time of the Hijra, and those was judged to be most beneficial to the weather.

Lane's Arabic-English Lexicon (his own editions are 1863 - 1872) accepts the traditions collected by Caussin de Perceval and his theory (see below). Lane gives a three year intercalation, with Muḥarram falling on late November. months 11, 12, 1, 2, 3, 4 being the periods of rain اَلرَّبِيعُ al-rabī`(here as a synonym for "winter" as a half year, acc. to Lane), the two Jumādā's (5, 6) being called اَلصَّيْفُ al-Ṣayf ("Spring / Summer" in Old Classical Arabic; March - May), 7, 8, , 10 being "mostly dry". al-rabī` was further divided into الوَسْمِيُّ al-wasmiyy (11, 1, 2; Sept. - Dec.), then الشَّتَوِيُّ al-šatawiyy ("wintery";2, 3, 4; Dec. - Feb.) and finally الدَّفَئِيُّ al-dafa'iyy (starting with end of 3. basically just 4.; Feb. - March). the "mostly dry" periods were divided into the rains الحَمِيمُ al-ḥamīm ("hot" 7, 8; May - July ) and الخَرِيفُ al-xarīf ("fresh ripe dates", also meaning "autumn"; 9, 10; July - Sept.) in other words, starting with 11 one has الوَسْمِيُّ al- wasmiyy, الشَّتَوِيُّ al-šatawiyy, الدَّفَئِيُّ al-dafa'iyy, all under اَلرَّبِيعُ al-rabī`; then اَلصَّيْفُ al-Ṣayf, الحَمِيمُ al-ḥamīm and then الخَرِيفُ al-xarīf. dafa'iyy دَفَئِيٌّ comes from دَفْءٌ daf' "warmth, heat", and means "the rain that falls after the heat has gained strength", acc. to Lane. it has a rare variant دَثَئِيٌّ da*th*a'iyy that on the basis of Sabaic and Safaitic seems to be older. الوَسْمِيُّ al-wasmiyy refers to a rain which literally marks ( يَسِمُ yasimu) the ground with vegetation. the wasmiyy rain was generally considered the first rain of the year because it was long anticipated after the hot days of summer, according to "The Rain Periods in Pre-Islamic Arabia" by Daniel Martin Varisco, Arabica, T. 34, Fasc. 2 (Jul., 1987), pp. 251-266. the above are those given for pre-Islamic Arabia, South Arabia, Yemen, had different orders and names, and this is true currently in the folklore of modern times, where the names and timings of the rains are different for different localities.

J. Wellhausen in "Reste arabischen heidentums" (1897), p. 96- claims an orginal division of the year into three: the period of rain  اَلرَّبِيعُ al-rabī`, the period of drought  اَلصَّيْفُ al-Ṣayf ? and the period of heat  الحَمِيمُ al-ḥamīm. he does not name them but he references Lane.

The first rain (see above for rains) is called  الوَسْمِيُّ al-wasmiyy starting with 27. set aurorally 21 Sept. Old Style (calculated for the Hijra, 622 CE).  الشَّتَوِيُّ al-šatawiyy came with 5. setting aurorally 8 Dec. .  الدَّفَئِيُّ al-dafa'iyy began with the auroral setting of 10. on 11 Feb. . اَلصَّيْفُ al-Ṣayf began with the auroral setting of 14. on 4 April.  الحَمِيمُ al-ḥamīm at the auroral rising of 4. ( al-dabarān الدَّبَرَانُ / Aldebaran) on 20 May (on 1 AH / 622 CE).  الخَرِيفُ al-xarīf came with the auroral setting of 18. i.e. al-nasrān ("the two vultures") النَّسْرَانِ with one being al-nasr al-wāqi` النَّسْرُ الوَاقِعُ α Lyrae, the other, al-nasr al-ṭā'ir النَّسْرُ الطَّائِرُ α Aquilae, on 24 July. the rain  اَلصَّيْفُ al-Ṣayf is also called اَلصَّيْفِيُّ al-Ṣayfiyy acc. to Lane.

Lane under صفر <Ṣfr> gives some variations:
These are: صَفَرِيٌّ ṣafariyy صَفَرِيِّةٌ ṣafariyya(t) or الصَفَرِيِّةُ al-ṣafariyya(t) (either with the rising of Canopus on 4 August O.S. during the Hijra, to the rising of Mansion 14. 4 October O.S. whenthere are forty nights of alternating heat and cold, the increase of offspring of sheep and goats, or the setting of Mansion 7. 3 January O.S. at the Hijra; the time when their breeding is approved,), the first increase of sheep and goats is صَقَعِيّ ṣaqa`iyy (when the Sun smites تَصَقَّعَ taṣaqa``a the heads of the young ones), sometimes called شَمْسِيٌّ šamsiyy (from the word for "Sun"; according to some ṣafariyy comes afterwards) or قَيْظِيٌّ qayẓiyy, at the end of this season called قَيْظٌ qayẓ the rain خَرَفِيٌّ xarafiyy from the autumnal season الخَرِيفُ al-xarīf.      
Daniel Martin Varisco in "Medieval Agriculture and Islamic Science - the Almanac of a Yemeni Sultan" (1994) gives rain names for Yemen. also dealt with for Arabia as well, by the same author in, "The Rain Periods in Pre-Islamic Arabia" Arabica, T. 34, Fasc. 2 (Jul., 1987), pp. 251-266 where deviations from the classical model are given.
xarf خَرْفٌ is given in the medieval Yemeni literature as an Indian term for light percipitation or mist which occurs in Dhofar on the coast of southwestern Yemen. in the Mahri dialect it survives as the term for the summer monsoon. It's actually related to Arabic خَرِيفٌ xarīf. رَمَضٌ ramaḍ (intensity of heat) or رَمَضِيٌّ ramaḍiyy , the last one meaning either clouds or rain at the end of summer ( قَيْظٌ qayẓ) and beginning of autumn ( خَرِيفٌ xarīf). synonymous with this is شَمْسِيٌّ šamsiyy or شَمْسِيِّةٌ šamsiyya(t) (from the word for "Sun"). the  قَيْظٌ qayẓ rain in Yemen is in June. صَيْفٌ ṣayf or صَيِّفٌ ṣayyif is the word for summer, although in Yemen this would be in spring. شَتِيٌّ šatiyy or شَتَوِيٌّ šatawiyy comes from شِتَاءٌ šitā' or winter, sometimes associated with drought ( قَحْطٌ qaḥṭ) because there is no rain in winter. sometimes شِتَاءٌ šitā' is used for the rain period itself. the Rwala ( الرُوَالَّةُ Ruwālla(t) or الرُوَيْلَةُ Ruwayla) Bedouin (N. Arabia, desert areas of the Levant) recognize a šitwī rain after the autumn وَسْمٌ wasm rain. a وَلِيٌّ waliyy rain is a rain which follows a rain, hence its name. it usually means a rain following a وَسْمِيٌّ wasmiyy rain, considered most important. the Yemeni ruler and scholar al-Malik al-'Ashraf claims that the rain falling in the month of July, تَمُّوزٌ Tammūz could be called by the month name. It was not regarded as beneficial as to the intense heat during that month. There is doubt that it was actually used, and if so, in a pastoral setting. a ثَوْرٌ thawr rain is associated with the evening rising of the constellation Taurus, hence its name, around May 19. this is a local rain documented only in Yemeni almanacs.
Finally, Yemen had its own tradition of marker stars for agricultural almanacs, mostly independent of the 'anwā' stars. These are discussed by Daniel Martin Varisco in "The Agricultural Marker Stars in Yemeni Folklore", Asian Folklore Studies, Vol. 52, No. 1 (1993), pp. 119-142.

Originally the seasons were six (two solar months each), starting with the beginning of autumn, الخَرِيفُ al-xarīf, then الشِّتَاءُ al-šitā',then اَلرَّبِيعُ الأَوَّلُ al-rabī` al-'awwal, i.e. al-rabī` I or less commonly رَبِيعُ الكَلأِ rabī`u~l-kala'(i) "rabī`of herbage", then "early spring" اَلصَّيْفُ al-Ṣayf, القَيْظُ al-qayẓ, then اَلرَّبِيعُ الثَّانِي al-rabī` al-*th*ānī i.e. al-rabī` II, or less commonly رَبِيعُ الثِّمَارِ rabī`u~l-*th*imār(i) "rabī` of fruits". under رَبِيعٌ rabī`, however, Lane says that اَلرَّبِيعُ الثَّانِي al-rabī` al-*th*ānī commences at the autumnal equinox, making a different order: اَلرَّبِيعُ الثَّانِي al-rabī` al-*th*ānī or less commonly رَبِيعُ الكَلأِ rabī`u~l-kala'(i) "rabī`of herbage", الخَرِيفُ al-xarīf, then الشِّتَاءُ al-šitā',then اَلرَّبِيعُ الأَوَّلُ al-rabī` al-'awwal, i.e. al-rabī` I or (less commonly رَبِيعُ الكَلأِ rabī`u~l-kala'(i) "rabī` of herbage", then "early spring" اَلصَّيْفُ al-Ṣayf, القَيْظُ al-qayẓ, making al-šitā' colder and القَيْظُ al-qayẓ (defined as the hottest part of summer) hotter. In the Ḥimyarite system qyẓ comes in June in accordance with Yemeni weather and xrf comes in August in agreement with the first order. also Lane says that the numbering of the two rabī`'s was sometimes transposed. Also they were sometimes given longer names. perhaps there was also a second order, but most agree on the first. popularly, the year was divided into two, between شِتَاءٌ šitā'"winter", starting with the autumnal equinox, and صَيْفٌ Ṣayf "summer" (so in Q 106:2), starting with the vernal equinox. Sometimes صَيْفٌ Ṣayf was taken as feminine. these seasonal names are attested in Ancient North Arabian, with cognates in Sabaic. قَيْظٌ qayẓ is also attested in an Ancient North Arabian inscription with the variant <'yẓ>, with the pronounciation of /q/ as a glottal stop found in some modern colloquials. xarīf خَرِيفٌ also means "fruits, gathered and plucked". As stated previously rabī` رَبِيعٌ has to do with herbage, rains or according to one source "plenteous herbage resulting from rain at any season."

Later, the Arabs adopted the conventional four season system. Two different nomenclatures emerged. The first were associated with the Bedouin. the second with the people of `Irāq and also the Persians and was regarded as "vulgar". Modern Standard Arabic adopted the second system. The first system is: اَلرَّبِيعُ al-rabī` (autumn), الشِّتَاءُ al-šitā'(winter), اَلصَّيْفُ al-Ṣayf (spring), القَيْظُ al-qayẓ (summer). the second and current system is: الخَرِيفُ al-xarīf (autumn), الشِّتَاءُ al-šitā'(winter), اَلرَّبِيعُ al-rabī` (spring), اَلصَّيْفُ al-Ṣayf (summer). the traditonal way of reckoning the seasons (Bīrūnī says the first set was forgotten in his time), by lunar mansions or the position of the Sun in the sky, was as follows: autumn started 3rd 'aylūl (September), winter: 3rd kānūn I (December), spring: 5th 'ā*dh*ār (March) and summer: 4th Ḥazīrān (June). This would be the Julian dates of his time.

In "The Seasons and Transhumance in the Safaitic Inscriptions", Journal of the Royal Asiatic Society, Third Series, Vol. 2, No. 1 (Apr., 1992), pp. 1-11, by M. C. A. MacDonald, the seasons of the North Arabian bedouin (referencing the Rwala from A. Musil, The Manners and Customs of the Rwala Bedouins, Oriental Explorations and Studies, 6 (1928)), in Colloquial Arabic are mentioned and their parallels in Safaitic inscriptions are discussed. The modern ones are:
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AṢ-ṢFERI (al-ṣafariyy): Al-wasm (or aṣ-ṣferi) rains
sheyl (Suhayl, Canopus): early October-mid November: 40 nights
ṯrayya (Pleiades): mid November-early December: 25 nights
ğawza' (Gemini): early December-early January: 25 nights
AŠ-ŠTA' (al-šitā'): as-šitwi rains
aš-ša`era (Sirius): early January-mid February: 40 nights
AS-SMĀK (al-simāk al-ramīḥ): as-smāk rains
as-smāk (Arcturus): mid February-mid April: 50 nights
[The first part of as-smāk (i.e. late February-early March) is also known as "the second part of aš-šta'" and corresponds to the period of the dafa'iyy rains.5]
AṢ-ṢEYF: aṣ-ṣeyfi rains:
mid April-early June
[This season and the next are not ruled by stars.]
AL-QĒẒ (al-qayẓ): no rains:
early June to early October.
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The article continues with Safaitic:
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So far, the names of only four seasons have been found in Safaitic: s2t', dṯ', ṣyf, and qyẓ. Of these, three clearly correspond to the bedouin šta (winter), ṣeyf (early summer) and qēẓ (the hot, dry season). Ṣferi, the first season of the bedouin year, does not appear to be attested in Safaitic, though it is possible that the star associated with the rains marking its beginning, al-Suhayl (Canopus) is mentioned in LP 736. Littmann read l N w nfr h s1hl s1l and translated "and there rushed forth a torrent in this plain", despite the fact that, as he noted, "there is no large plain here". However,it seems possible that this expression should be compared to the saying quoted by Musil ilya ṭala`at as-sheyl lā tāmen as-seyl "when Canopus rises, trust not the creek".6 I would therefore suggest reading wa-naffarahu suhayl(an) sayl(un) "and a torrent made him flee in [the season of] Suhayl".7 It will also be noted that Safaitic has no equivalent to Smāk,8 but that, on the other hand, it has a season, dṯ' not recorded among the modern bedouin. The translation of Safaitic dṯ' as "spring" or "to spend the spring" appears to go back to Littmann who, however, gave no justification for it.9 Dussaud10 compared it with Sabaic and Minaic dṯ' whichclearly refers to the season of the northeast monsoon (November to April) which brings the the lesser of the two rainy seasons in South Arabia.11 However, it is doubtful whether the names of seasons used in South Arabia, with a weather pattern governed by the monsoons, can be assumed, without further justification, to have the same meaning in the very different climates of southern Syria and northern Arabia.12
 Some of the Arabic lexica regard the word daṯa'iyy as a variant of dafa'iyy13 which Lane says is used of "the rain that falls after the heat has acquired strength... when the earth has put... forth the kama' or truffles... when the sharpness of winter is broken, and the trees put forth their leaves" (p. 889b). This is neatly paralleled by three Safaitic inscriptions in which this season is associated with the gathering of truffles. WH 1232 and JaS 61 have w dṯ' w km' 14 ("and he spent the df' [here] and fed on truffles") and Ms 4 has w dṯ' h rḥbt w km' ("and he spent the df' on this raḥaba15 and fed on truffles").
  It is clear from the Arabic lexica that the season called *df'/dṯ'6 occurs between al-šitā' and al-ṣayf and almost certainly corresponds to the "period sometimes called the second part of aš-šta'", beginning in late February and ending in early March.17 This is within the period known to the modern bedouin as al-smāk, see above.
 Thus the traditional translation of Safaitic dṯ' places it at the right time of year. Unfortunately, however, the word "spring" carries misleading nuances for it suggests the beginning of a period of fertility, whereas dṯ' marks the transition from the seasons of rain and abundance (aṣ-ṣferi and aš-šta') to those of heat and dearth (aṣ-ṣeyf and al-qēẓ). I would therefore suggest "the season of the later rains" as a less misleading translation. ...
15 A raḥaba is an area of flat, low ground where water collects and which produces abundant herbage. See Lane p. 1052a and NAEN I, 1.

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The “Calendar of the Pleiades” is explained by Daniel Martin Varisco "Islamic Folk Astronomy" in "Astronomy Across Cultures - The History of Non-Western Astronomy" (2000; H. Selin ed.):

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 In much of the Middle East the Pleiades appears to disapear from view under the rays of the sun for about 40-50 days in early May. This is refered to by several terms dufūn, ghāsiq, ghurūb and istisrār. In Egypt this time marks the Forty Days of Summer (arba`īn al-ṣayf) or period of the khamsīn winds (Klunzinger 1878: 301). The Rwala Bedouins have a proverb that says plants dry up due to the heat at its disappearance (Musil, 1928: 17). ... According to al-Bīrūnī (1879: 251) a pre-Islamic fair was held at Dair `Ayyūb when the Pleiades reappeared after their forty days' absence. ...
...
 One of the indigenous calendars from the Arabian Peninsula is based on the monthly conjunction of the Pleiades with the moon. The moon conjuncts with the Pleiades about once every 27 1/3 days. This conjunction was visible monthly from autumn through spring and occured about the same time each year; thus it coincided with the main parts of the pastoral cycle on much of the Arabian Peninsula. ...
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{khamsīn means "fifty"; in the oblique case, used for the nominative as well in the colloquials}

This calendar reflects the true period of the orbital motion of the Moon around the Earth, not involving lunations which involve the rotation around the Sun as well.

http://www-istp.gsfc.nasa.gov/stargaze/Lcalend.htm

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-- What is the basic unit of lunar calendars and how is it defined?
The basic unit is the "lunar" month: the time from one "new moon" to the next.

-- How long is that?
The "lunar" month is 29.53 days.

--Is that the orbital period of the Moon? If not, why the difference?
The "new Moon" is when the Moon overtakes the Sun. For the next "new Moon," the Sun has moved about 1/12 of the distance around the sky, and the Moon needs 2 extra days to catch up. Therefore the time for its full circuit around the Earth is about 2 days shorter than a lunar month

--What is the Moon's orbital period?
The orbital period of the Moon is 27.32 days.

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All these aids aside, the calendar used for dating purposes was that of lunations. the Islamic Calendar uses the period of twelve lunations. The  question how it was in pre-Islamic times.

http://en.wikipedia.org/wiki/Islamic_calendar#Pre-Islamic_calendar
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History
Pre-Islamic calendar
Some scholars, both Muslim[5][6] and Western,[7] think that the pre-Islamic calendar of central Arabia was a purely lunar calendar similar to the modern Islamic calendar, differing only when the sanctity of the four holy months were postponed by one month from time to time.
Other scholars, both Muslim[8][9] and Western,[10][11] concur that it was originally a lunar calendar, but about 200 years before the Hijra it was transformed into a lunisolar calendar containing an intercalary month added from time to time to keep the pilgrimage within the season of the year when merchandise was most abundant for Bedouin buyers. This intercalation was administered by the Nasa'a of the tribe Kinana, known as the Qalāmis, the plural of Qalammas, who learned of it from Jews. The process was called Nasi or postponement because every third year the beginning of the year was postponed by one month. The intercalation doubled the month of the pilgrimage, that is, the month of the pilgrimage and the following month were given the same name, postponing the names and the sanctity of all subsequent months in the year by one. The first intercalation doubled the first month Muharram, then three years later the second month Safar was doubled, continuing until the intercalation had passed through all twelve months of the year and returned to Muharram, when it was repeated. Support for this view is provided by inscriptions from the south Arabian pre-Islamic kingdoms of Qataban (Kataban) and Sheba (Saba) (both in modern Yemen), whose lunisolar calendars featured an intercalary month obtained by repeating a normal month. The prohibition of Nasi was revealed when the intercalated month had returned to its position just before Nasi began.
If Nasi meant intercalation, then the number and the position of the intercalary months between 1 AH and 10 AH are uncertain, western calendar dates commonly cited for key events in early Islam such as the Hijra, the Battle of Badr, the Battle of Uhud and the Battle of the Trench, should be viewed with caution as they might be in error by one, two or even three lunar months.
Prohibiting Nasi
In the tenth year of the Hijra, as documented in the Qur'an (sura 9:36-37), Muslims believe God (Allah) revealed the prohibition of the Nasi.
The number of months with Allah has been twelve months by Allah's ordinance since the day He created the heavens and the earth. Of these four are known as forbidden [to fight in]; That is the straight usage, so do not wrong yourselves therein, and fight those who go astray. But know that Allah is with those who restrain themselves.
Verily the transposing (of a prohibited month) is an addition to Unbelief: The Unbelievers are led to wrong thereby: for they make it lawful one year, and forbidden another year, of months forbidden by Allah and make such forbidden ones lawful. The evil of their course seems pleasing to them. But Allah guideth not those who reject Faith.

... This prohibition was repeated by Muhammad during the farewell sermon which was delivered on 9 Dhu al-Hijja 10 AH on Mount Arafat during the farewell pilgrimage to Mecca.
Certainly the Nasi is an impious addition, which has led the infidels into error. One year they authorise the Nasi, another year they forbid it. They observe the divine precept with respect to the number of the sacred months, but in fact they profane that which God has declared to be inviolable, and sanctify that which God has declared to be profane. Assuredly time, in its revolution, has returned to such as it was at the creation of the heavens and the earth. In the eyes of God the number of the months is twelve. Among these twelve months four are sacred, namely, Rajab, which stands alone, and three others which are consecutive.
—translated by Sherrard Beaumont Burnaby[13]
...
5.^ Mahmud Effendi (1858), as discussed by Burnaby, pages 460–470.
6.^ According to "Tradition", repeatedly cited by F.C. De Blois.
7.^ F.C. De Blois, "TA'RIKH": I.1.iv. "Pre-Islamic and agricultural calendars of the Arabian peninsula", The Encyclopaedia of Islam X:260.
8.^ al-Biruni, "Intercalation of the Ancient Arabs", The Chronology of Ancient Nations, tr. C. Edward Sachau, (London: William H. Allen, 1000/1879) 13–14, 73–74.
9.^ Abu Ma'shar al-Balkhi (787–886), Kitab al-Uluf, Journal Asiatique, series 5, xi (1858) 168+. (French) (Arabic)
10.^ A. Moberg, "NASI'", The Encyclopaedia of Islam VII:977.
11.^ A. Moberg, "NASI'", E.J. Brill's first encyclopaedia of Islam
12.^ From an illustrated manuscript of Al-Biruni's 11th c. Vestiges of the Past (Bibliothèque Nationale, Paris, Arabe 1489 fol. 5v. (Bibliothèque Nationale on-line catalog Mandragore
13.^ Sherrard Beaumont Burnaby, Elements of the Jewish and Muhammadan calendars (London: 1901) 370.

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The arabic of the verses (9:36-37), in Sūrat Al-Tawba. cited:
http://www.quranexplorer.com/quran/

سُوۡرَةُ التّوبَة
إِنَّ عِدَّةَ ٱلشُّہُورِ عِندَ ٱللَّهِ ٱثۡنَا عَشَرَ شَہۡرً۬ا فِى ڪِتَـٰبِ ٱللَّهِ يَوۡمَ خَلَقَ ٱلسَّمَـٰوَٲتِ وَٱلۡأَرۡضَ مِنۡہَآ أَرۡبَعَةٌ حُرُمٌ۬‌ۚ ذَٲلِكَ ٱلدِّينُ ٱلۡقَيِّمُ‌ۚ فَلَا تَظۡلِمُواْ فِيہِنَّ أَنفُسَڪُمۡ‌ۚ وَقَـٰتِلُواْ ٱلۡمُشۡرِڪِينَ كَآفَّةً۬ ڪَمَا يُقَـٰتِلُونَكُمۡ ڪَآفَّةً۬‌ۚ وَٱعۡلَمُوٓاْ أَنَّ ٱللَّهَ مَعَ ٱلۡمُتَّقِينَ
(٣٦)
إِنَّمَا ٱلنَّسِىٓءُ زِيَادَةٌ۬ فِى ٱلۡڪُفۡرِ‌ۖ يُضَلُّ بِهِ ٱلَّذِينَ كَفَرُواْ يُحِلُّونَهُ ۥ عَامً۬ا وَيُحَرِّمُونَهُ ۥ عَامً۬ا لِّيُوَاطِـُٔواْ عِدَّةَ مَا حَرَّمَ ٱللَّهُ فَيُحِلُّواْ مَا حَرَّمَ ٱللَّهُ‌ۚ زُيِّنَ لَهُمۡ سُوٓءُ أَعۡمَـٰلِهِمۡ‌ۗ وَٱللَّهُ لَا يَهۡدِى ٱلۡقَوۡمَ ٱلۡڪَـٰفِرِينَ
(٣٧)
Al-Tawba
Lo! the number of the months with Allah is twelve months by Allah's ordinance in the day that He created the heavens and the earth. Four of them are sacred: that is the right religion. So wrong not yourselves in them. And wage war on all of the idolaters as they are waging war on all of you. And know that Allah is with those who keep their duty (unto Him). (36)
 Postponement (of a sacred month) is only an excess of disbelief whereby those who disbelieve are misled; they allow it one year and forbid it (another) year, that they may make up the number of the months which Allah hath hallowed, so that they allow that which Allah hath forbidden. The evil of their deeds is made fair-seeming unto them. Allah guideth not the disbelieving folk. (37)

The Farewell Sermon says:
http://sirah.al-islam.com/Page.aspx?pageid=204&BookID=160&TOCID=764
أيها الناس إن النسيء زيادة في الكفر يضل به الذين كفروا ، يحلونه عاما ويحرمونه عاما ، ليواطئوا عدة ما حرم الله فيحلوا ما حرم الله ويحرموا ما أحل الله . إن الزمان قد استدار كهيئته يوم خلق الله السموات والأرض وإن عدة الشهور عند الله اثنا عشر
شهرا ، منها أربعة حرم ثلاثة متوالية ورجب مضر ، الذي بين جمادى وشعبان

From A. Guillaume's translation:
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"Postponement of a sacred month is only an excess of disbelief whereby those who disbelieve are msiled; they allow it one year and forbid it another year that they may make up the number of months that which God has hallowed, so that they permit what God has forbidden and forbid what God has allowed"1 Time has completed its cycle and is as it was when God created the heavens and the earth. The number of months with God is twelve; four of them are sacred, three consecutive and Rajab is between Jumādā and Sha`bān. ...
1. Sūrah 9.37
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In this usual version there is the explanatory note that adds: "which {Rajab} is between Jumādā and Sha`bān"
Rajab is called "Rajab of {the tribe of} Muḍar", which has been transmitted by Ibn Iṣḥāq in Ibn Hishām's version. Burnaby evidently paraphrased it by saying that "Rajab which stands alone"

Here is an excerpt from F. de Blois's article in Enc. of Islam II "Ta'rīkh" saying that it was not intercalation (or rather embolism, intercalating a lunar month) that nasī' refered to:
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Ḳur'ān IX, 36 says that the months are twelve, of which four are “forbidden”, and the next verse states that postponement ( nasī' ) “is an increase in unbelief, in which are led astray those who disbelieved, in that they declare it permissible one year, and declare it forbidden one year, so as to equalise the number of what God has forbidden, and so they declare permissible what God has forbidden”. Muslim authors have disagreed over the interpretation of this difficult verse. Some maintain that nasī' was a procedure by which an official (the nāsi') connected with the Ka`ba cult at Mecca altered the distribution of “forbidden” and “permitted” months within a given year (or within two successive years), but say nothing to imply that this involved actual manipulation of the calendar. Others claim that the “postponement" of the forbidden months was the result of the fact that the pagan Arabs intercalated a thirteenth month every two years; nasī' is thus in effect the old Arabic word for “intercalation” (kabīsa), a practice which was abolished with the revelation of the above-cited verse. The latter interpretation has generally been accepted by Muslim astronomers (first, it seems, by the astrologer and charlatan Abū Ma`shar al-Balkhī) and has been favoured by modern scholars since Moberg (who summarises his views above, s.v. nasī' ), but it is doubtful whether it reflects anything more than learned speculation by the `Abbāsid authors. The former (non-calendrical) interpretation was accepted, and the “evidence” for intercalation rejected, with arguments that still seem largely valid, by Mahmoud Effendi and Sprenger, and it is in our opinion supported by an early Sabaic inscription from Haram (CIH 547), not precisely datable, but surely from well before the Christian era. Here the authors offer their excuses to the god Ḥlfn for the fact that they had not performed a certain ritual in the month  ḏmwṣbm, when war had forced them to flee their country, but “postponed” (ns1'w) it until the month ḏ`ṯṯr. As a result of this impiety, the god withheld the waters during the winter and summer growing seasons, whereupon the authors promised not to repeat their transgression in future. It is quite clear from the context that in Haram, at least, the verb ns1' has nothing to do with intercalation, but only with the moving of cultic occurrences within the calendar itself. The rather striking similarity between the religious conceptions in this ancient inscription and in Ḳur'ān IX, 37 (“postponement” is in both cases something of which the deity disapproves) makes it seem likely that this is also the meaning of Ḳur'ānic nasī'.

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François de Blois in "Qur'ān 9:37 and CIH 547", "Procceedings of the Seminar for Arabian Studies" 34 (2004) modifies his views and admits << I should like to stress - and this is a modification of my argument in Encyclopaedia of Islam (de Blois 1998) - that it is very likely that the inhabitants of Central Arabia did practice intercalation and that this practice was subsequently abolished by Islam. It is also possible that the intercalation of a thirteenth month did disturb the distribution of sacred and profane months in the sense that, if an intercalary month was inserted after one of the sacred months, the sanctity of that month was "postponed" to the intercalary month. I would however, still maintain that the primary meaning of nasī' is not "intercalation" but "postponment", Qur'ān 9:37 is not directed against intercalation, but only against the redistribution of sacred and profane months. >> OTOH, IMHO, Qur'ān 9:36 with its mention of twelve months, is against intercalation of a month.
Here is the translation of CIH 547:
1. [The cla]n `Amīrum and the clan `Athtaru
2. [confes]sed and did penance to (the god) Ḥalfān
3. because they did not grant to him his miṭradu
4. in (the month) Dhū Mawṣabim, when they decamped
5. to Yathilu in the war of Ḥaḍramōt,
6. and they performed the pilgrimage (ḥaggaw) in (the month) Dhū Shamawayi in Yathilu and
7. they postponed {nas1a'aw) the miṭradu until (the month) Dhū `Athtari.
8. He did not grant them the *inundation
9. of their watercourse in spring and autumn (= late summer)
10. on account of *exceedingly little water,
11. that they might be wary of the like
12. in the future. May (the god) Ḥalfān recompense
13. them with the reward that he bestows because of
14. the confession. At the time of (the month) Dhū Makhẓadim
15. the former this confession took place
16. by command of (the god) Ḥalfān
de Blois concludes:
Our inscription is far removed in time and place from the Qur'ān, but it is evident that the two texts refer to a similar situation. In Haram, the tribesmen post- poned (nas1a'w) a, cultic event by two months and were subsequently punished by the god to whom that event is sacred. In the Qur'ān, Allāh expresses his vehement disapproval of a postponement (nas') which results in a disturbance of the preordained distribution of sacred and profane months. In both documents "postponement" is a religious technical term for the observation of cultic events at the wrong time of the year

And here is part of Moberg's article in Enc. of Islam II "Nasī'" favoring intercalation (embolism):
(it seems nearly identical with the Enc. of Islam I article, which can be found online without a subscription):
http://books.google.com/books?id=9JQ3AAAAIAAJ&printsec=frontcover#v=onepage&q&f=false
 <<

Nasī'  (a.), intercalary month , intercalation, or person (pl. nasa'a) charged with the duty of deciding on intercalation. The word occurs in Ḳur'ān, IX, 37, and in Muḥammad's sermon at the Farewell Pilgrimage (Ibn Hishām, 968; see ḥadjdj ). Nasiyy, nasy and nas' are variants and the word is connected with nasa'a to “postpone” or “add” or with nasiya to “forget”. In any case, it is given in Islamic tradition a meaning which brings it into connection with the method of reckoning time among the pagan Arabs. The Ḳur'ānic verse describes nasī' as “a further expression of unbelief” and it is therefore forbidden to the believers.
The context of the above-mentioned passages, where sometimes the number of months in the year is put at twelve and sometimes the number of “holy” months at four, allows us to connect nasī' with the calendar. Ḳur'ānic exegesis as a rule connects nasī' with the “holy” months and explains it sometimes, it is true, as the postponement of the pilgrimage from the month fixed by God for it, but sometimes, and preferably, as “transference of the sanctity of one holy month to another, in itself not holy”. The expositors are also able to give the reasons for such a postponement in full detail. As a rule, however, these are pure inventions in which suggestions and perhaps memories of old traditions are freely expanded. A collection of such expositions in the form of regular ḥadīths is given in al-Ṭabarī, Tafsīr , 2nd ed., x, 91-3.
The critical examination of these explanations reveals, however, traces of an older conception not quite unknown to Tradition, even in the form in which we have it, according to which nasī' denotes neither the intercalation of an intercalary month nor the month itself. This interpretation of the word is the only one really acceptable in the circumstances. The association of the pre-Islamic pilgrimage with annual markets made it necessary to fix the ḥadjdj in a suitable season of the year. For that purpose, a prolongation of the lunar year in some way was necessary, and nothing contradicts that older tradition according to which it was obtained by the intercalation of an intercalary month. The lunar month was the only unit of time available for the purpose because it was the only one which the Bedouins, the customers at the markets, could observe directly. Thus one had only to let them know at the ḥadjdj of a year whether they had to reckon to the next ḥadjdj twelve or thirteen months.
Definite evidence of this intercalation of a month is found in the astronomer Abū Ma`shar al-Balkhī (d. 272/886 [q.v.]) in his Kitāb al-Ulūf (see JA , ser. 5, xi [1858], 168 ff.), and, following him, in al-Bīrūnī, who also deals at length with this intercalation in his Chronology (ed. Sachau, 11-12, 62-3). According to him, the Arabs took this intercalation from the Jews. How much in what these scholars tell us is really historical knowledge, and how much intelligent reconstruction, can hardly be decided. It is remarkable, however, that al-Bīrūnī when dealing fully with the Jewish intercalation (op. cit., 52, l. 17) connects the Hebrew word for intercalary year, `ibbūr, with me`ubbäräth “pregnant woman” and observes: “they compare the addition of a superfluous month to the year to the woman carrying something which does not belong to her body”. In this connection we may recall that al-Ṭabarī (op. cit., 91, l. 6) explains the Arabic nasī' as nasū' “pregnant woman”, among other interpretations, saying nusi'at al-mar'a “on account of the increase which the child in her means”. This agreement in the two explanations, which can hardly be accidental, might really indicate that nasī' in the sense of intercalation or intercalary month is modelled on the Hebrew word `ibbūr and thus support al-Bīrūnī's statement which is in itself not impossible. Caussin de Perceval ( JA , ser. 4, i, 349) even quotes the Hebrew nāsī (prince) as a title of honour of the leader of the Sanhedrin, to whom fell the duty of dealing with the intercalation (cf. Bab. Talmud, Sanhedrin, 11a: “the intercalation of the year may only be done with the approval of the nāsī”). According to one of the meanings of the Arabic nasī' given in Tradition, it was really the “name of a man”, a meaning which is all the more remarkable in this connection as it does not suit the Ḳur'ānic passage. There is a definite agreement on the fact that in the Jewish intercalation only the month following Adar was an intercalary month while in the Arab system, as the critical examination of Tradition — contradicting the literal interpretation of its text—shows, only the month following Dhu 'l-Ḥidjdja, i.e. the intercalated month, in both cases was inserted between the normally last month and the normally first one of the year, Nisān (or, amongst the Arabs, al-Muḥarram).

...
A. Moberg
 
 >>

The man in charge of the nasī' was called a نَاسِئٌ nāsi', plural نَسَأَةٌ nasa'a(t) (uncommonly, acc. to Lane, also نَاسِئُونَ nāsi'ūn, also known as a قَلَمَّسٌ qalammas, plural قَلامِسُ qalāmis. But this was normally a title with the definite article القَلَمَّسُ al-qalammas and the plural with the definite article القَلامِسُ al-qalāmis refered to the family holding the position. etymologically, as a common noun قَلَمَّسٌ qalammas meant "sea, copious well" and by extention a "generous, able man", acc. Enc. of Islam II quoting Lisān al-`Arab. Some suggest a relation between qāmūs (okeanus) or perhaps calendas. the trouble with equating Hebrew nāsī (prince) with Arabic  نَاسِئٌ nāsi'is that in Hebrew it is nāśī' נָשִׂיא with Hebrew שׂ śīn which gives ﺵ šīn in Arabic cognates not Arabic ﺱ sīn, and correpsonds to Sabaic s2 whereas the verb in Sabaic is with s1. This is pointed out by François de Blois in "Qur'ān 9:37 and CIH 547", Procceedings of the Seminar for Arabian Studies 34 (2004). he says that Ṭabarī divided the traditions about 9:37 into two. those who said there was no intercalation one or more of the prohibited months were deprived of their sacred character and the Arabs were allowed to engage in warfare. this was compensated in the next year by having more than four sacred months. the other group said there was intercalation say that nasī' was what the scentific authors call kabīsah كَبِيسَةٌ (a loanword from Aramaic, still used for "intercalary," or "intercalated", i.e. sana(t) kabīsa(t) means سَنَةٌ كَبِيسَةٌ "leap year") and that the ancient Arabs normally had twelve months in a year but in certain years they inserted a thirteenth month.

Ibn Isḥāq (sīrat rasūl Allāh سيرة رسول الله ; died 767, or 761; known from the edition of Ibn Hishām, died 833. This is sort of regared as the canonical biography of Muhammad by muslims) does not describe nasī' as intercalation, although its most well known English translation "The Life of Muhammad" by A. Guillaume translates nasī' as "intercalation" p. 21-22 (the context is the alledged reasons of the expedition of the Ethiopian king of Yemen, Abraha, for more details of this see towards the end of the post):
 <<
... When the Arabs were talking about this letter of his {Abraha} one of the calendar intercalators {al-nasa'a(t) النّسأة } was enraged. ... The intercalators { النّسأة } are those who used to adjust the months for the Arabs in the time of ignorance. They would make one of the profane months holy to balance the calendar. It was about this that God sent down 'Postponment {al-nasī' النَّسِيء } (of a sacred month) is but added infidelity by which those who disbelieve are misled. They make it (the month) profane one year and make it sacred the next year, that they may make up the number of months which God has made sacred .'1
 The first to impose this system of intercalation {man nasa'a al-šuhūr من نسأ الشهور } on the Arabs was al-Qalammas Ḥudhayafa b. `Abd b ...; his son followed him ... and Abū Thumāma Junāda b. `Auf who was the last of them, for he was overtaken by Islam. When the Arabs had finished the pigrimage, it used to be their practice to gather round him and he would declare the four sacred months Rajab, Dhū'l-Qa`da, Dhū'l-Ḥijja and al-Muḥarram. If he wanted to free a period he would free al-Muḥarram and they would declare it free and ban Ṣafar in its place to make up the number of the four sacred months. When they wanted to return from Mecca,2 he got up and said: 'O God, I have made one of the Ṣafars free for them, and I have postponed the other till next year.'
1 Sūra 9. 37.
2 If by this time a sacred month was due, raiding and blood-revenge would be taboo; hence the need to declare the month profane
 >>
There does not seem to be a mention of an intercalary month by Ibn Isḥāq and he does not deal with the previous verse about twelve months, though he mentions it later when reporting the Farwell Sermon.
acc. to Burnaby:
 <<
Five different systems for their Calendar have been suggested :
1. That 9 months were intercalated in the course of every 24 years
2. That 7    "           "                  "        "    19  "
3. That 1 month was      "                  "        "    3   "
4. That 1    "   "       "                  "        "    2   "
5. That the system employed was purely Lunar ; that is, no intercalation was ever made.
 >>
Also some modern authors suggest that the intercalation was irregular.
An irregular intercalation, based on observation of the drift, would actually keep up with the seasons eventually, so would 1 and 2 which would work well. but we know that the months had drifted from the seasons they were originally based on by etymological considerations, to their position during Muhammad's lifetime. 4 is just too bad. that leaves 3 or 5 as the leading candidates.

 >>
Also is the account of Abū Ma`shar al-Balkhī, described by de Blois as "a prolific writer on astrology and other pseudo-sciences" in his lost work Kitābu l-'ulūf, lost but quoted later. this is described by François de Blois in "Qur'ān 9:37 and CIH 547", "Procceedings of the Seminar for Arabian Studies" 34 (2004) as follows:
 <<
... According to this account the ancient Arabs copied the practice of the Jews but did not understand it correctly. Thus, whereas the Jews add a thirteenth month every two or three years based on the Metonic cycle, the Arabs added an extra month every two years precisely, with the result that their months did not keep up with the seasons. Abū Ma`shar then adds a very confusing account of how the extra month was added each time at a different point in the year and that the names of the months were shifted, that is postponed, so that every month had in effect two names, its real name and its shifted name. This chaotic situation continued until the time of Muḥammad, who abolished intercalation altogether. ...
 >>
F. de Blois blames this on polemics between Persians and Arabs: << the ancient Arabs were stupid and did not know how to use the calendar properly.>> F. de Blois says that the description of the ancient Arab calendar are only found in scientific and pseudo-scientific authors and not in specialist writings on Arab antiquities, therefore they only tried to make sense of the Qur'anic verses and thus have no value as antiquarian information. IMHO Mas`ūdī's three year intercalation does not fit into these categories.

The meaning of nasī was discussed, I believe wrongly, in view of the findings of F. de Blois by F.A. Shamsi
"the Meaning of Nasi': An Intepretaionof Verse 9:37" in Islamic Studies, Vol. 26, No. 2 (Summer 1987), pp. 143-164. he says:
  <<

To summarise our discussion, we may point out that the word al-nasī as it occurs in verse 9:37,
(i) cannot mean
 (a) the system or practice of postponement of the sacredness of a month to another month, or,
 (b) a month shorn of its sacredness;

(ii) cannot have been the name or epithet of a (regular) pagan month;
(iii) might have been the name or epithet of the intercalary month, but, if so, the intercalary month either used not to be the thirteenth month always or the ḥajj used not to be invariably made in the intercalary month; and that,
(iv) in all probability, primarily signified the progression of a calendar year over the solar year, and was the name or epithet of those days in the beginning of the first month of the calendar year which used to perform the function of lengthening the previous calendar year for certain religious purposes and thus of postponing (relatively to the given calendar year) the dates of various occasions whose observance used to be a religious duty for the pagan Arabs, inasmuch as this as this view of al-Nasī
  (a) enables a coherent construction of the various clauses of Verse 9:37,
  (b) is compatible with, and throws much light upon, all the meanings the word nasī' bears, to postpone, delay, put back, forget, omit, prolong, extend, increase,- be pregnant, be mixed up with, etc.,
 
  (c) is compatible with, and makes intelligible, all the reports about the Arabian calendar and the meaning of Verse 9:37,

  (d) alone harmonizes with the report that intercalations used to be made after Dhū al-Ḥijjah and the ḥajj used to be made in the intercalary month, and,
  (e) yields an insight into the working of the Arabian calendar and its intimate bond with Arabian religion.
 
  >>

In light of what F. de Blois later says (i) is clearly wrong.



That the Arab calendar was based on the sighting of the crescent there is no doubt (and the Qur'an says so). The word šahr "month" meant "waxing crescent" in South Arabian, and this meaning was known to the philologists. Lane under šahr شَهْرٌ says << "The new moon, when it appears, so called because of its conspicousness" - You say رَأَيْتُ الشَّهْرَ  {ra'aytu~š-šahra; "I saw the šahr"} Hence there is a trad. صُومُوا الشَّهْرَ {șūmu(:)~š-šahra} Fast ye the first day of the month. And hence the trad., إِنَّمَا الشَّهْرُ تِسْعٌ وَعِشْرُونَ {'innama(:)~š-šahru tis3un wa3išrūna} The utility of watching for the new moon is on the nine and twentieth night [Or the meaning is, that the lunar month is nine and twenty nights.] >>. and IMO šahr is used in the meaning of "waxing crescent" in the Qur'an when talking about the observance of the fast of Ramadan in Qur'an 2:185, although this is not the usually accepted meaning of the verse.
http://www.quranbrowser.com/cgi/bin/get.cgi?version=pickthall+yusufali+khan+shakir+sherali+khalifa+arberry+palmer+rodwell+sale+transliterated&layout=auto&searchstring=002:185
http://tinyurl.com/y9uvtnw

The part is, with the usual translation:
http://www.quranexplorer.com/quran/
Dr. Pickthall

And whosoever of you is present, let him fast the month, and whosoever of you is sick or on a journey, (let him fast the same) number of other days.
وَٱلۡفُرۡقَانِ‌ۚ فَمَن شَہِدَ مِنكُمُ ٱلشَّہۡرَ فَلۡيَصُمۡهُ‌ۖ وَمَن ڪَانَ مَرِيضًا أَوۡ عَلَىٰ سَفَرٍ۬ فَعِدَّةٌ۬ مِّنۡ أَيَّامٍ أُخَرَ‌ۗ
but I think in the phrase

<<... fa-man šahida minkum-u~š-šahra ...>>
فَمَن شَہِدَ مِنكُمُ ٱلشَّہۡرَ

 šahida شَہِدَ usually means "witnessed", but it could also mean "be present". the usual exegisis of that part of the verse usually adds "at home" being implied for this particular instance.
... so whoever among you witnessed the šahr ...

 šahr originally meant "waxing crescent" and I would translate it as "whoever witnessed the waxing crescent"
cf. Rodwell who translates it as << as soon as any one of you observeth the moon >>. according to Hashim Amir-Ali "The 'Month' in the Qur'ān" Islamic Culture vol. 60, no. 1, January. 1977 p. 21-30, exegets and then translators were split as to whether it should be intepreted as "month" or "moon."
 <<
As to the month Ramadhan in which the Koran was sent down to be man's guidance, and an explanation of that guidance, and of that illumination, as soon as any one of you observeth the moon, let him set about the fast; but he who is sick, or upon a journey, shall fast a like number of other days.
 >>
Enc. of the Qur'ān "Months" by  Alexander Knysh, agrees:
 <<

A review of Qur'ānic passages that contain the word “month” reveals that it is often linked to the lunar calendar. Thus, in q 2:185, the word shahr seems to denote the new moon that signals the beginning of a new calendar month. This usage is richly attested by Arab lexicographers who trace the etymology of the word to the root sh-h-r, “to be apparent,” or “to manifest one/itself” (Lisān al-`Arab, iv, 431-3; cf. Ṭabarī, Tafsīr, i, 552). This meaning is further confirmed by epigraphic evidence from south Arabia, where sh-h-r was “a synonym for the first day of the calendar-month” (Beeston, Epigraphic, 8; see epigraphy of the qurʾān; arabic script ). In many verses, the new moon is expressly described as the measurement of time par excellence. A typical example is q 2:189: “They will question you concerning the new moons (al-ahilla). Say: ‘They are appointed times for the people, and the pilgrimage.’” This and other similar verses indicate that the beginning of the month or of the year must be established by an actual observation of the new moon ( q 10:5; cf. 71:16). According to Ibn `Abbās (d. 69/688), the meaning of this verse is that “by means of it (i.e. the new moon) [the people] determine the affairs of their religion, the waiting periods of their wives, the time of their pilgrimage and the due dates for their debts” (Ṭabarī, Tafsīr, i, 580; see debt; waiting period; marriage and divorce ). This commentary conveniently demarcates the spheres of human activities that are to be regulated by lunation. In another exegetical statement “the affairs of their religion” are specified as “the periods of fasting and of breaking the fast.” They are to be determined by the “observation of [the moon's] waning and waxing” (ibid., 581; cf. Ibn Kathīr, Tafsīr, i, 503).

 >>

(However šahida شَہِدَ  could also mean "to present"; so the verse is often translated as "whoever is present (at home) in the month")

François de Blois in "The month and its divisions in ancient South Arabia", Procceedings of the Seminar for Arabian Studies" 28 (1998) also sees in the expression šahru ramaḍān شَهْرُ رَمَضَانَ for the crescent which marks the beginning of the month of fasting.
I think that the verse is consistent with the practice that a "witness" to the new crescent is needed especially for the religious observance of Ramadan, not an algorithm or calculation}.
Enc. of the Qur'ān "Months" by  Alexander Knysh, agrees:

 <<
One consequence of the Qur'ānic injunction to use the moon for keeping time is the practice of watching for the new crescent to determine the beginning and the end of Ramaḍān. Of all Muslim schools of law (see law and the qur'ān ) and sects (see theology and the qur'ān ) only the Ismā`īlīs (see shī`ism and the qur'ān ) rely on mathematics to calculate the length of their months (see science and the qur'ān; measurement ). All other Muslim communities insist that the beginning and end of the new month, especially of Ramaḍān, be determined by the sighting of the new crescent. The importance of Ramaḍān for the Muslim ritual is attested by the fact that it is the only month of the calendar that is explicitly mentioned in the Qur'ān ( q 2:185; see festivals and commemorative days; ritual and the qur'ān ). ...
 >>

Also that the crescents al-'ahilla(t) (only) mark time in 2:189 (so the calendar is based on the moon). there are other verses that establish a lunar (with or without intercalation of a month at that particular time) calendar:
http://www.quranexplorer.com/quran/
Dr. Pickthall

Al-Baqara

They ask thee, (O Muhammad), of new moons, say: They are fixed seasons {mawāqīt, or appointed times} for mankind and for the pilgrimage. ...

سُوۡرَةُ البَقَرَة
 يَسۡـَٔلُونَكَ عَنِ ٱلۡأَهِلَّةِ‌ۖ قُلۡ هِىَ مَوَٲقِيتُ لِلنَّاسِ وَٱلۡحَجِّ‌ۗ
(١٨٩) ...
also 6:96
Al-An`am
He is the Cleaver of the Daybreak, and He hath appointed the night for stillness, and the sun and the moon for reckoning. That is the measuring of the Mighty, the Wise. (96)
سُوۡرَةُ الاٴنعَام
فَالِقُ ٱلۡإِصۡبَاحِ وَجَعَلَ ٱلَّيۡلَ سَكَنً۬ا وَٱلشَّمۡسَ وَٱلۡقَمَرَ حُسۡبَانً۬ا‌ۚ ذَٲلِكَ تَقۡدِيرُ ٱلۡعَزِيزِ ٱلۡعَلِيمِ
(٩٦)


So the sun determines the length of the day (the day begins at sunset) and the moon that of the month. that the day begins at sunset is tied with the month beginning with the observation of the waxing crescent, as this occurs at sunset. Old Arabs divided daylight into 8 equal seasonal hours and gave names for them. some of these names are preserved in the names of the prayer times. the early Arabs then only had sundials (I had seen a crude Nabataean sundial in the Istanbul Archaeology Musueum), although in medieval times the Islamic World became famous for its water-clocks. some of the water-clocks were adjustable to the seasonal hours. Incidentally the inscription on the Nabataean sundial gives a Jewish sounding name << "Menashā bar Nathan Shelam." This may have been the name of the craftsman who set up the sundial, or possibly that of the astronomer >>. the sundial, at al-Ḥijr (near modern Madā'in Ṣāliḥ), is estimated to belong to the 1st cent. BCE. it was in the medieval period that the Arabs became adept with waterclocks. A seasonal hour was called ساعة زمانيّة sā`a(t) zamāniyya(t), while the one with fixed 24 hours was called ساعة فلكيّة sā`a(t) falakiyya(t) "astronomical time". de Perceval gives eight of the seasonal hours (he claimed that was all, but eventually the number was brought up to 24, the principle ones remained at eight):

al-Fajr الفجر "day break"; Shurūq ash-Shams شروق الشمس "Sunrise"; aḑ-Ḑuḥā الضحى "forenoon"; aẓ-Ẓuhr الظهر "noon"; al-`Aṣr  العصرا"afternoon"; al-*Gh*urūb الغروب {al-Maghrib المغرب } "sunset"; al-`ishā' العشاء "night"; Niṣf-al-Layl نصف الليل "midnight"
de Perceval claims these are the ones only known to the ancient Arabs, and remained the principle "moments: of the day, but de Blois says that at some time the Arabs became familiar with the division of the day into 24 hours, and the additional seasonal hours are found in medieval almanacs by dividing the above seasonal hours further into like "the false daybreak", "the true daybreak" etc.. these are mentioned in some medieval astronomical tables. large mosques had a "timekeeper" called a مُوَقِّتٌ muwaqqit responsible for communicating the correct time for the caller to the prayer or مُؤَذِّنٌ mu'a*dh**dh*in (English muezzin, cf. Turkish müezzin) to make the call to prayer. recently, Cairo adopted a decision, well recieved in Turkey, to send the call to prayer electronicaly simultaneously to all mosques in order to avoid cacophony as slightly different times are reckoned for by each mosque. The problem is finding employment for the muezzins.
Incidentally, a solar calendrical day, 24 hours, from noon to noon, does not purely reflect the rotation of the Earth, as the Earth revolves around the Sun, so the apparent motion of the Sun moves as well:

http://www-istp.gsfc.nasa.gov/stargaze/Lcalend.htm
 <<
-- How is "one day" usually defined??
A day is usually defined by the position of the Sun, as the time from one noon to the next.

-- How would you define noon for this purpose?
The time when the Sun is exactly to the south--for points north of the equator.
(For points south of the equator, the time when the Sun passes exactly to the north.)
   Actually the time from noon to noon varies slightly, because of the uneven motion of Earth in its orbit. What clocks measure is the average day.

...

-- The "average solar day" of 24 hours is not exactly the duration of one full rotation of the Earth. Why the difference?
24 hours is the average time from noon to noon: but in that time the Sun's position in the sky also changes! The Earth needs to rotate a little more to bring the Sun to the same place in the sky, so 24 hours is a little more than a full rotation period.
...
-- What is the rotation period of the Earth?
The rotation period of the Earth is about 4 minutes (or about 1/365th of the day) short of 24 hours. A full year contains about 365.25 days, but 366.25 rotations of the Earth.


 >>




It is pointed out in Enc. of Islam II "Layl and Nahār" by Ch. Pellat that the relative closeness of Arabia to the equator mitigated the differences in the seasonal hours and astronomical time.

Acc. to Enc. of the Qur'ān "Day and Night" by A. Dallal:
 <<
... Two systems were used for measuring the length of the hours of the night and day. In the system of equal hours, one daylight hour is equal in length to one night hour and the whole day is divided into twenty-four equal parts. In the system of unequal hours, however, the arc of daylight and the arc of the night are each divided into twelve equal parts; thus, one daylight hour generally differs from a night hour while the total number of each of the daylight hours and the night hours is always twelve. 
 >>
Some of the seasonal hours mentioned in the Qur'an are dealt with in Enc. of the Qur'ān "Day, Times of" by Sebastian Günther
 <<
... Five sūras are named for times of day or daily natural phenomena: “The Dawn” (al-Fajr, q 89); “The Night” (al-Layl, q 92); “The Forenoon” (al-Ḍuḥā, q 93); “The (late) Afternoon” (al-`Aṣr, q 103) and “The Daybreak” (al-Falaq, q 113).

 ...
The times of the day in chronological order
The “night”  ( layl, 93 times; layla, 8 times; pl. layāl, 4 times) is the first, dark half of the full day. It starts with the “evening twilight”  ( shafaq, q 84:16; defined as “the first moment of the night,”  li-awwal sā`a min al-layl [Hamadhānī, Alfāẓ, 287]; cf. Pellat, Layl and nahār, 709). Furthermore, the beginning of the night is described as “a darkening [at the beginning] of the night”  ( ghasaq al-layl, q 17:78) or the “nigh of the night”  ( zulafan min al-layl, q 11:114; see day and night ).
The “late, dark evening”  (`ashī, `ashiyya) corresponds to the period “from the time when the sun starts to disappear until it completely sets”  (Qurṭubī, Jāmi`, vi, 82, ad q 3:41). It marks the “end of the bright day”  (Jalālayn, 54, ad q 3:41). It occurs as `ashiyyatan ( q 79:46); bi-l-`ashī ( q 38:31); bi-l-`ashī wa-l-ibkār ( q 3:41; 40:55); bi-l-`ashī wa-l-ishrāq ( q 38:18); `ashiyyan wa-ḥīna tuẓhirūna ( q 30:18); `ashiyyatan aw ḍuḥāhā ( q 79:46); and, in a different sequence, bi-l-ghadāti wa-l-`ashī ( q 6:52; 18:28); ghuduwwan wa-`ashiyyan ( q 40:46); bukratan wa-`ashiyyan ( q 19:11, 62). The term `ishā', however, is used both as a synonym for `ashī and in designation of a time following it (Hamadhānī, Alfāẓ, 287). It foreshadows the beginning of darkness (q.v.); see `ishā'an ( q 12:16) and ṣalāt al-`ishā' ( q 24:58).
...
Morning, conversely, implies freshness and pristineness (e.g. the root b-k-r from which is derived not only early morning [bukra], but also virgins [abkār], q 56:36; 66:5). At this time, the normal work of the day is described as beginning ( q 68:21-2, 25) and important events such as battles ( q 3:121) are prepared.
 >>

Enc. of Islam II "Layl and Nahār" by Ch. Pellat gives information on the divisions of the night:

 <<
 
... Although we know of a considerable number of terms designating any part of the night (see Mukhaṣṣaṣ, ix, 45), only a few words seem to be at all precise, in spite of differences in interpretation; thus, `ashwa, si`w, had' and variants = 1/4 of the night; ḳiṭ`a and variants = 1/3; dhuhl and variants = 1/3 or 1/2; hitā', hazī`, thabadj, mawhin and variants = 1/2 approximately. The middle of the night was called djawz, usṭumm, djarsh, but astronomers rendered “midnight” simply by niṣf al-layl (in the same way they called “midday” niṣf al-nahār ) and the modern language uses the expression muntaṣaf al-layl. The `as`asa precedes the third third, the saḥar or saḥr, which matches the ghasaḳ and is immediately followed by the morning twilight, the fadjr ; for the Muslim astronomers, this twilight begins at the moment that the sun is 19° below the horizon, but the real duration of it is indicated, as has been seen above, in the calendars. It is during this final part of the night that the morning prayer ( fadjr or ṣubḥ ) is performed. Since their territory did not extend as far as latitude 48°, the Arabs did not know that at the summer solstice there is no complete night (the layl alyal of the astronomers) at this latitude.
 >>

It is said that a man in Central Asia who reported the "white nights" of northerly latitudes almost got his head cut off for balsphemy when he reported it to a local sultan, but the intervention as to the veracity of his report by a man trusted by the sultan saved him. muslims first encountered the problem of prayer times at such latitudes when the Volga Bulghars adopted Islam in the beginning of the 10th century. Ibn Faḍlān, who visited the place reports of the adjustements the muslims made for their observances. the modern town of Bolgar (renamed so fairly recently), just slightly north of historical Bulghar, is at latitude 54° 58′ 27″ N.
During the Middle Ages, there were Arab water clocks that could be adjusted for the seasonal hours. During the Ottoman Empire, European clocks (or local versions of them) were used. But the clock (or later, watch) was set to 12:00 at each sunset to mark the beginning of the new calendar day. Enc. of Islam II calls this "Ottoman time". "Encyclopedia of the History of the Arabic Sciences" Vol. 1, "Astronomy and Islamic Society" by David A. King, "Timekeeping in Ottoman Turkey" says << A feature distinguishing some of these Ottoman tables from the earlier Egyptian and Syrian tables is that the values of the time of day are based on the convention that sunset is 12 o'clock. This convention, inspired by fact that the Islamic day begins at sunset (because the calendar is lunar and the months begin with sighting of the crescent shortly after sunset), has the disadvantage that clocks registering 'Turkish' time need to be adjusted by a few minutes every few days. >> it was gradually discontinued by the end of the 19th cent. and during the Young Turk period (after 1911, circa 1912-1914 when Western conventions were made official. in Decemeber 1925 under the Republic the 24 hour clock was made the sole official time keeping system) Western style time was in general use. in the article "The Clock, the Calendar and the Koran" by S. M. Zwemer, The Moslem World Volume 3, Issue 3, pages 262–274, July 1913, << Persia, Turkey {Ottoman Emire}, Arabia, Morocco, Afghanistan, and the rest of the Moslem world generally >> are listed as those using "Moslem time" while << Egypt, India, Algeria and Malaysia most Moslems >> use Western time "because of the influence of European governments". Modern Islamic almanacs still frequently show this system in addition to regular time for the prayer times, as a deference to tradition, but it is not used officially or for practical purposes in any country since the end of the Ottoman Empire. 


Abbreviations were used for the months by the Ottomans, mainly in fiscal matters. Frequently Siyaqat script was employed.

1. م
2. ص
3. را
4. ر
5. جا
6. ج
7. ب
8. ش
9. ن
10. ل
11. ذا
12. ذ


Prior to 1839 (after which fiscal matters were handled by a solar calendar), the Ottomans for certain fiscal matters divided the lunar year into four periods of three months each, and named these periods by making acronyms out of the abbreviations (the Turkish pronounciations are given as well as the equivalent in phonemic Arabic).

1. 1,2,3 masar /maSar/  مَصَر
2. 4,,5,6 recec /rajaj/ رَجَج
3. 7,8,9 reşen /rašan/ رَشَن but not *beşen  */bašan/  *بَشَن
4. 10,11,12 lezez /laδaδ/ لَذَذ


The days of the week are:

Days of the week
يَوْمُ الأَحَدِ - Yawmul 'Aḥad - Sunday
يَوْمُ الاِثْنَيْنِ - Yawmul I*th*nayn - Monday
يَوْمُ الثُّلاَثَاءِ - Yawmu*th* *Th*ulāthā' - Tuesday (also يَوْمُ الثَّلاَثَاءِ Yawmu*th* *Th*alāthā')
يَوْمُ الأَرْبِعَاءِ - Yawmul 'Arbi`ā' - Wednesday (also يَوْمُ الأَرْبَعَاءِ Yawmul 'Arba`ā' AFAIK more common)
يَوْمُ الْخَمِيْسِ - Yawmul *Kh*amīs - Thursday
يَوْمُ الْجُمْعَةِ - Yawmul Jum`a(t) - Friday (in the Qur'ān يَوْمُ الْجُمُعَةِ Yawmul Jumu`a(t))
يَوْمُ السَّبْتِ - Yawmus Sabt - Saturday

1-5 are derived from numbers, they resemble (old) Aramaic forms. Friday comes from "gathering" (see below). Saturday is from Aramaic שַׁבְּתָא šabbəṯā (*sh*abb&*th*a:) ( ܫܒܬܐ šabbəṯā i.e. *sh*abb&*th*a: > šabbṯā i.e. *sh*abb*th*a:) i.e. Hebrew  שַׁבָּת šabbA*th* "Sabbath", Jeffrey "The Foreign Vocabulary of the Qur'an" has "Jewish {Aramaic} שַׁבְתָּא {šavtā}". the form given by Jeffrey is unattested in Jasrow's "Dictionary of Targumim, Talmud and Midrashic litterature" nor in Levy's "Chaldäisches Wörterbuch über die Targumim : und einen grossen Theil des rabbinischen Schriftthums". it seems to be an error on the part of Jeffrey. a religious Sabbath is not observed in Islam (the Qur'anic injunction is just against work during the Friday noon prayer), but in Arab countries, during the Ottoman Empire and Iran Friday is a day off; the first day of work varies, but it tends to be a single day weekend with Friday off, those with two days off the first workday tends to be Sunday. Maltese has the same names, with phonetic changes, even for "Friday", il-Ġimgħa. the arabic word for "Friday" has been borrowed into the languages of Muslim peoples, but in Persian the former Ādīna آدینه still has currency, so in the Farsi Wikipedia entry.
OTOH Toufic Fahd, an expert in pre-Islamic Arab religion speculates jum` جُمْعٌ with the name of Friday, although he puts a question mark to that.

The Qur'an mentions the Sabbath as a rule imposed on God for the Jews (only). Although it mentions a six day Creation, it rejects the idea that God rested in the seventh day Q 50:38 (Qaf) "Weariness did not touch us". So exegetes restricted the meaning of the verb sabata سَبَتَ to "to cease" or "being still", without the idea of "resting". so according to traditions, the early Companions of the Prophet objected to taking a holiday on Friday, finding this an imitation of Jewish and Christian practices. nevertheless Friday as a day off from work was practiced in medieval times, acc. to Enc. Of Islam II  "Djum`a".
http://www.quranexplorer.com/quran/
Dr. Pickthall
Qaf
And verily We created the heavens and the earth, and all that is between them, in six Days, and naught of weariness touched Us. (38)
سُوۡرَةُ قٓ
وَلَقَدۡ خَلَقۡنَا ٱلسَّمَـٰوَٲتِ وَٱلۡأَرۡضَ وَمَا بَيۡنَهُمَا فِى سِتَّةِ أَيَّامٍ۬ وَمَا مَسَّنَا مِن لُّغُوبٍ۬
(٣٨)
Also for Muslims being exempt from Sabbath observances 16:124:
An-Nahl
The Sabbath was appointed only for those who differed concerning it, and lo! thy Lord will judge between them on the Day of Resurrection concerning that wherein they used to differ. (124)

سُوۡرَةُ النّحل
إِنَّمَا جُعِلَ ٱلسَّبۡتُ عَلَى ٱلَّذِينَ ٱخۡتَلَفُواْ فِيهِ‌ۚ وَإِنَّ رَبَّكَ لَيَحۡكُمُ بَيۡنَہُمۡ يَوۡمَ ٱلۡقِيَـٰمَةِ فِيمَا ڪَانُواْ فِيهِ يَخۡتَلِفُونَ
(١٢٤)

Nevertheless, gradually a belief in the sanctity of Friday and various pious traditions in the degree of مُتَوَاتِرٌ mutawātir to this effect were put in the mouth of the Prophet.
See:
http://en.wikipedia.org/wiki/Friday
 <<
In many countries, and recently (2013) in Saudi and Iran, Friday is the first day of the weekend, and Sunday is the first workday. In Bahrain, the United Arab Emirates (U.A.E.) and Kuwait, Friday was also formerly the last day of the weekend while Saturday was the first workday. However, this was changed in Bahrain and the U.A.E. on 1 September 2006[1] to Friday as the first day of the weekend and Sunday as the beginning of the workday, with Kuwait following on 1 September 2007.[2]
...
In some Islamic countries, the week begins on Sunday and ends on Saturday, just like the Jewish week and the week in some Christian countries. In most other Islamic countries, such as Saudi Arabia and Iran, the week begins on Saturday and ends on Friday
 >>

Many secular muslim countries, i.e. Turkey (after the law of 1935), ex-Communist countries, Indonesia, as well as in more Islamic Malaysia (except in some states),  Brunei, but also Pakistan (although in addition Friday is half a day off, this may have changed), Muslim African countries have a Sunday (and Saturday) weekend. in Turkey, a few decades ago, Saturday was half a day off, and schools had half a day off in Wednesday as well. in Turkey many shops remain open on Sunday.

In the Ottoman Empire, Friday was a holiday.
Friday-Saturday weekend: Bahrain, Qatar, Jordan, Syria, Egypt, UAE, Libya, Iraq, Mauritania, Algeria and Kuwait (recently)
Thursday-Friday weekend (mainly Friday): Saudi Arabia, Oman, Yemen, Somalia.
Djibouti (member of the Arab league with an Arab minority) has a Friday - Saturday weekend.
The Sudan has a Friday - Saturday weekend (in the Southern States, in what has become South Sudan, it was Sunday)
Bangladesh has a Friday - Saturday weekend.
Iran and Afghanistan have a Friday weekend.

In Palestine the official weeekend is Friday - Saturday, but some firms give Sunday off, while others give Friday off, which is the government holiday.

Lebanon has a Saturday-Sunday weekend. some businesses may observe it on Friday.
Morocco and Tunisia have a Saturday - Sunday weekend
The Comoro Islands, a non-Arab member of the Arab League, has a Saturday - Sunday weekend.
In Syria, Christian school districts observe a Saturday - Sunday weekend.
Malaysia has a Saturday - Sunday weekend (except the states of Kelantan, Terengganu and Kedah in the North, which have a Friday - Saturday weekend)

In Pakistan the situation is complicated:
http://blogs.msdn.com/michkap/archive/2005/09/20/471605.aspx
 <<
How many days in a weekend?
...
# re: How many days in a weekend?
Sunday, December 30, 2007 11:24 AM by Tanveer Badar

... In Pakistan weekend has shifted back and forth between Friday and Sunday at least half a dozen times. We even had two day long weekend in the 90s. This would make weekend 2.5 days long because of the half day on Friday and holidays on Saturday and Sunday. ...
 >>
also
http://en.wikipedia.org/wiki/Workweek_and_weekend
 <<
Muslim countries
Indonesia, the largest muslim country in the world, has a work week of Monday through Friday, with Saturday and Sunday as the weekend[1]. Other Muslim-majority countries differ, with Friday a day of prayer, so the working week may adjust to allow people time to attend prayer. The legal work week in the Middle East is typically either Saturday through Wednesday (Saudi Arabia[2]), Saturday through Thursday (as in Iran[3] [4]) or Sunday through Thursday as in Egypt, Iraq[5], Jordan, and Syria[6]. A working week of Sunday through Thursday, with Friday and Saturday as the weekend, is becoming more common, with Qatar shifting to this model in 2003, Bahrain and the United Arab Emirates[7] in 2006, Kuwait in 2007, Oman in 2008, and Algeria in 2009[8]
In 2009, formal proposals are also being discussed in Yemen and Saudia Arabia to shift to a Saturday to Thursday work week. This trend is to allow for respect of Fridays as the day for Jummah prayers in Muslim countries while also having more working days to overlap with international financial markets.

...
In secular Turkey, the workweek is Monday through Friday, as in European countries. However, most shops are open on Saturday and Sunday.


 >>


also Arabic Wikipedia:
http://ar.wikipedia.org/wiki/%D8%AC%D9%85%D8%B9%D8%A9
and
http://fulbrighter-in-kuwait.blogspot.com/2007/05/kuwait-changes-to-friday-saturday.html
 <<
Kuwait Changes to Friday-Saturday Weekend

The Kuwaiti government recently announced that it will change the official weekend from the current Thursday-Friday to Friday-Saturday starting Sept 1 of this year. Friday is the day of worship to Muslims equivalent to Sunday for Christians. In Egypt and the Levantine countries (Lebanon, Syria,and Jordan), the weekend has long been on Friday and Saturday. However, the Persian Gulf countries followed a Thursday-Friday weekend. Yet, as the economies of these countries grow and businesses become more interrelated with their trading partners in Europe and the United States, the fact that the Thursday-Friday weekend meant there were only three shared business days between East and West became a hindrance to doing business. Thus, it is all the more economically feasible solution to institute a Friday-Saturday weekend and private business were the first to follow suit. ...
 >>
Lebanon has a Saturday - Sunday weekend, but some bussinesses observe it on Friday.

For "Friday"
Lane also gives the Classical dialectical reading of Eastern Arabia as  يَوْمُ الْجُمَعَةِ yawmu~l-juma`a(t); OTOH جُمْعَةٌ jum`a(t) would be the more common verbal noun form, as a common noun.
(For the days, commonly the yawmu "day of" part is omitted). Enc. of Islam II "Djum`a" by S. D. Goitein explains the name preceded the establishment of the Friday Sermon (for which there is a gathering):
 <<
DJum`a  (Yawm al-), the weekly day of communal worship in Islam. The only reference to it in the Ḳur'ān, LXII, 9-11, clearly indicates that the term is pre-Islamic, for v. 9 says: “When you are called to prayer on the day of the assembly”, and not “to the Prayer of the Assembly”. The decisive proof for the correctness of this interpretation is the fact that Ibn Ubayy read yawm al-`arūba al-kubrā for yawm al-djum`a, the former being another pre-Islamic name for Friday, meaning eve of the Sabbath, cf. A. Jeffery, Text of the Qur'ān, 1937, 170; R. Blachère, Le Coran , 1950, 825.
The expression yawm al-djum`a, “the day when people come together”, an exact equivalent of Hebrew (and Aramaic) yōm hak-kenīsa, designated the market day, which was held in the oasis of al-Madīna on Friday,“ when the Jews bought their provisions for the Sabbath”, cf. Kāshānī, Badā'i` al-ṣanā'i`, Cairo 1327/8, i, 268 and Ibn Sa`d iii, 1, 83, where t*dj*hz (tadjahhazu) is to be read for y*dj*hr, as in Kāshānī. It is natural that the day preceding the weekly holiday of the Jews should have been chosen as the market day in a place like Medina, which had a large Jewish population. Similarly, in Islam, Thursday served as a weekly market day all over Arabia, cf. H.St. J. Philby, Arabian Highlands, 1952, 36, 130, 233, 274-5, 387, 485-7, 597. Friday as market day is well attested in pre-Islamic Jewish literature, cf. S. Krauss, Talmudische Archaeologie, Leipzig 1911, ii, 690, note 340.
According to the unanimous testimony of the ancient Muslim sources, no Friday service was held in Mecca, cf., e.g., al-Ṭabarī, i, 1256. However, even before Muḥammad arrived in Medina, the Muslims convened there for public worship, but it was Muḥammad who ordered that it should be observed regularly on “the day when the Jews prepared for their Sabbath”, cf. Ibn Sa`d, quoted above, and parallel sources. The Jewish and Christian institutions of a weekly day of public worship might have served as an example in general, as suggested by al-Ḳasṭallānī, ii, 176. However, the reference to the Jews in the ancient account of the inauguration of the Friday service betrays no particular dependence on Judaism, nor a polemical tendency against the older religions—two assumptions in vogue in modern research on the subject, cf. D. S. Margoliouth, Mohammed, 1905, 248-9, M. Gaudefroy-Demombynes, Mahomet 1957, 522, and the works of Wensinck, Buhl and Watt quoted in the bibliography. It was Muḥammad's practical wisdom, which decided for Friday, as in any case on that day the people of the widely dispersed oasis dwellings of Medina gathered regularly for their weekly market.
This origin of the Friday service explains one of its most puzzling aspects: It is held at noon, a very inconvenient time in a hot climate. The market is dissolved early in the afternoon, see, for Arabia, e.g., Philby, Arabian Highlands 234. In classical times, ἀγορῆς διάλυσις, the breaking up of the market, was a term designating the early afternoon, Liddell and Scott s.v. Thus noon was the reasonable time for the public prayer.
The admonition of the Ḳur'ān, not to leave the prayer and to run after business and amusement, LXII, 11, is to be understood against this background. The people of Medina were farmers, not business men; but Friday was their market day, on which also, as everywhere at fairs, amusements were provided. 
...
 >>
Goitein says in an article that according to Jeffreys, in an inscription dating to Umayyad times, يوم العروبة الكبرى yawm al-`arūba(t) al-kubrā was written for the verse in question, so the tradition about Ibn Ubayy's codex is authentic.
Also there is 62:9.
62:9 is:
http://www.quranexplorer.com/quran/
Dr. Pickthall
 <<

Al-Jumua
O ye who believe! When the call is heard for the prayer of the day of congregation, haste unto remembrance of Allah and leave your trading. That is better for you if ye did but know. (9)

سُوۡرَةُ الجُمُعَة
يَـٰٓأَيُّہَا ٱلَّذِينَ ءَامَنُوٓاْ إِذَا نُودِىَ لِلصَّلَوٰةِ مِن يَوۡمِ ٱلۡجُمُعَةِ فَٱسۡعَوۡاْ إِلَىٰ ذِكۡرِ ٱللَّهِ وَذَرُواْ ٱلۡبَيۡعَ‌ۚ ذَٲلِكُمۡ خَيۡرٌ۬ لَّكُمۡ إِن كُنتُمۡ تَعۡلَمُونَ
(٩)
 >>
62:10 and 62:11 is
 <<
Al-Jumua
And when the prayer is ended, then disperse in the land and seek of Allah's bounty, and remember Allah much, that ye may be successful. (10) But when they spy some merchandise or pastime they break away to it and leave thee standing. Say: That which Allah hath is better than pastime and than merchandise, and Allah is the best of providers. (11)

سُوۡرَةُ الجُمُعَة
فَإِذَا قُضِيَتِ ٱلصَّلَوٰةُ فَٱنتَشِرُواْ فِى ٱلۡأَرۡضِ وَٱبۡتَغُواْ مِن فَضۡلِ ٱللَّهِ وَٱذۡكُرُواْ ٱللَّهَ كَثِيرً۬ا لَّعَلَّكُمۡ تُفۡلِحُونَ
(١٠)
 وَإِذَا رَأَوۡاْ تِجَـٰرَةً أَوۡ لَهۡوًا ٱنفَضُّوٓاْ إِلَيۡہَا وَتَرَكُوكَ قَآٮِٕمً۬ا‌ۚ قُلۡ مَا عِندَ ٱللَّهِ خَيۡرٌ۬ مِّنَ ٱللَّهۡوِ وَمِنَ ٱلتِّجَـٰرَةِ‌ۚ وَٱللَّهُ خَيۡرُ ٱلرَّٲزِقِينَ
(١١)


Acc. to Burnaby, Monday, Wednesday, Thursday, and Friday are considered to be fortunate days. Tuesday, Saturday, and Sunday are unfortunate and evil days. But Lane says that Wednesday was a day of ill-luck. in Turkey, I know that Tuesday is considered an inauspicious day.

Mahmoud Effendi gives pre-islamic names for the days starting from Sunday (I took the voweling from Wikipedia, Bīrūnī and Lane, who agree and are more reliable and Gernot Rotter "Der veneris dies im vorislamischen Mekka ..." Der Islam, 70 Heft 1 (1993) p.112-132): 1. أَوَّلُ 'awwal ("awal") 2. أَهْوَنُ. 'ahwan ("ahwan") variant (Wikipedia, Tāj al-`Arūs): أَهْوَدُ 'ahwad also  أَوْهَدُ 'awhad (Rotter); 3.جُبَارٌ jubār (Lane, Wikipedia, Rotter) (or M.E. jabār "djabar"); 4. دُبَارٌ dubār (Lane, Rotter, Wikipedia) (or ME dabār "dabar"); 5. مُؤْنِسٌ mu'nis (Lane, Wikipedia, Rotter) (or M.E. and in a passage by Mas`ūdī مونس "mounis"); 6. عَرُوبَةُ `arūba(t) ("aroubah"); 7. شِيَارٌ šiyār (Lane, Wikipedia, Rotter) or  شَيَارٌ šayār (Wikipedia) or شبار šabār (M.E. "chabar"; this is the dotting given in a passage by Mas`ūdī, in the main passage concerning these names Mas`ūdī gives  شِيَارٌ šiyār ; it is manuscript error) also  سِبَار sibār (Rotter).
One tradition has  أَهْوَدُ 'ahwad as alternative for Sunday in which case  أَهْوَنُ. 'ahwan becomes Monday.
1,2,6 are diptote (1,2 are unattested in Lane, are diptote in Bīrūnī, the triptote form of 6 in Bīrūnī must be a scribal error or typo, in the poem it is correctly diptote), 3,4,5,7 are triptote. 1,2,3 are not found in Lane, but 2. is found in Lisān al-`Arab and Tāj al-`Arūs; 4. may appear as diptote in poetry and  دِبَارٌ dibār is given as an alternative. 5. may also appear as diptote in poetry.
The details are given by A. Fischer "Die altarabischen Namen der sieben Wochentage" in Zeitschrift der Deutschen Morgenländischen Gesellschaft (ZDMG) Bd. 50 (1896) p. 220-226

6. "Friday" عَرُوبَةُ `arūba(t) has a variant with the definite article العَرُوبَةُ al-`arūba(t), and also there is  يَومُ العَرُوبَةِ yawmu~l-`arūba(t), and also with the epithet "great" (see above; "great" qualifies `arūba(t), not "day") يَومُ العَرُوبَةِ الكُبْرَى yawmu~l-`arūbati~l-kubra" . it comes from Aramaic / Syriac ܥܪܘܒܬܐ `ərūḇtā ( > `rūḇtā) i.e. `&rūvtā > `rūvtā <3rwbt'> (in Syriac the feminine t is sometimes spirantized). this was recognized by the Arabic lexicographers who mistook the "Nabataean" (meaning Aramaic) name as أرُبَا 'arubā (acc. to Lane), others took it to mean "the manifest, the magnified". it is related to Aramaic עַרְבָּא `arbā "eve, day preceding" (Sokoloff, "A Dictionary of Jewish Babylonian Aramaic"), and used in reference to the eve of the Sabbath; and Hebrew עֶרֶב `ereḇ, `erev "evening, eve" (of the Sabbath) relating to the root to set (of the sun), related to Arabic غَرَبَ *gh*araba of the same meaning. see Enc. of Islam I "`Arūba": << ... Doubtless it is the `ereb of the Hebrews, having reference to the festival of the Sabbath customary among many Arabian tribes. ... >>. but Toufic Fahd "Le panthéon de l'Arabie centrale a la veille de l'Hégire" considers it to be from "gathering"
 <<
 ... du syriaque `arûbtô dont l'arabe ǧumu`a peut être la traduction;  car `arûbô désigne l'arabe al-ǧam` << la foule >>...
  >>
Rotter points out to  عَرُوبَةٌ `arūba(t) or  عَرُوبٌ `arūb "a woman who loves her husband passionately" and tries to associate the word with attributes of Venus.
Rotter also speculates a connection between  عَرُوبَةُ `arūba(t) and Europa, which has been speculated by others.
According to Rotter, the "Nabataeans" (which in medieval Arabic discourse means Aramaic speakers) used * ā*dh*īnā (cf. Persian ādīna) for Friday. Rotter toys with the idea as to a relation with Athena (I think he wants a Hellenistic interpretation of everything).

The etymology of  أَوْهَدُ 'awhad comes from وَهْدَةٌ wahda(t) "depression", i.e. the declining of the number from the first to the second, acc. Lisān al-`Arab, mentioned in Wikipedia. so, in Tāj al-`Arūs, where it is attributed to the (mythical?) tribe of `Ād. It is diptote. the variant  أَهْوَنُ 'ahwan means "easy, comfortable, lesser". Rotter tries to associate أَهْوَدُ 'ahwad with the lunar deity وَدٌّ Wadd, thus in his efforts to connect it with the planetary week.
Lane gives  دِبَارٌ dibār as "the last of, the following". Hashim Amir Ali finds a resemblance with al-dabarān الدَّبَرَانُ Aldebaran (with the Hyades)
According to Lane Arab tradition holds that مُؤْنِسٌ mu'nis was so named because the Arabs inclined towards pleasure during Thursday  ( لِأَنَّهُمْ يَمِيلُونَ فِيهِ إِلَى الْمَلَاذِّ li'annahum yamīlūna fīhi 'ila(:)~l-malāḏḏ). litteraly it would mean that which gives cheer. it also means "friend".
According to Rotter شِيَارٌ šiyār means "decoration, beauty"
Rotter speculates a relation with جُبَارٌ jubār and جَبَّارٌ jabbār which he notes as a divine epithet (also meaning "giant"), actually meaning "one who magnifies himself" and Syriac gabrō "man" and claims these are words related to Mars. others note its relation to  الجَبّارُ al-jabbār "Orion" Lane gives جُبَارٌ jubār as meaning "a thing of which no account or retaliation is taken".   
Rotter goes to lengths to show that these names are derived from the attributes of the deities asscoiated with the planetary week.
I find Rotter's speculations very doubtful.
"Sunday" أَوَّلُ 'awwal means "first"
All are mentioned in a pre-islamic poem (except the variant 'awhad which is mentioned in a different variant) given in Bīrūnī, Mas`ūdī, Wikipedia and by Mahmoud Effendi. Mas`ūdī attributes the poet to the tribe of Thamūd (see above).
These and the poem is given in Arabic Wikipedia:
http://ar.wikipedia.org/wiki/%D8%B4%D9%8A%D8%A7%D8%B1
Mahmoud Effendi and a passage in Mas`ūdī give مونس mūnis ("mounis") for 5. I don't think these are reliable on the details of pronounciation as these are scribal errors.

Ff these the name for "Friday" عَرُوبَةُ `arūba(t) is well known. See the above extract from Enc. of II. It's mentioned in Lane (the rest are not).

Christian Ludwig Ideler in "Über die Zeitrechnung der Araber", Abbhandlungen der historisch-philolgischen Klasse der Königlich-Preßischen Akademie der Weissenschaften aus den Jahren 1812-1813. Berlin 1816 pp. 97-120, has alternative بَاهُونٌ bāhūn for 2. (Monday)
The same author mentions that the mnemonics of the first six Abjad groups (those in common with the Aramaic alphabet) were names of the week. these are given as 1. أَبُجَد 'abujad {Abudsched; Sunday}; 2. هَوَز hawaz {Hawas};  3. حُطِي ḥuṭī {Hoti}; 4. كَلَمُن kalamun {kelamun}; 5. سَعْفَص sa`faṣ {Safas}; 6. قُرِشَت qurišat {korischat}. according to this tradition, Friday was known as  عَرُوبَةُ `arūba(t) not ثَخَذ *th*axa*dh*.
Besides sounding fanciful, the older abjad order deferred in the case of 5. and 6., preserved in the Maghribi order. 
Enc. of Islam II "Abdjad" by (G. Weil [G.S. Colin*]) says:
 <<

All that they had to say on this head, however interesting, is but a fable. According to one version, six kings of Madyan arranged the Arabic letters after their own names; according to another tradition, the first six groups are the names of six demons; a third tradition explains them as the names of the days of the week. Sylvestre de Sacy has noted the fact that in these traditions only the first six words are used, and that, e.g., Friday is not called thakhadh, but `urūba ; yet it is not admissible to base on such vague traditions the conclusion that the Arabic alphabet had originally only twenty-two letters (J. A. Sylvestre de Sacy, Grammaire arabe 2, ii, par. 9). In fact, even among the Arabs there were some more enlightened grammarians, such as al-Mubarrad and al-Sīrāfī, who, not satisfied with the legendary explanations of abdjad, straightforwardly declared that these mnemotechnic words were of foreign origin.
 >>
Incidentally, no word for "week" nor weekday names are attested in Epigraphic South Arabian, though Jews and Christians among them must have known the seven day week.
In addition to the seven day week, the Arabs had special names for the *nights* of a month, unlike the Persians who gave special names for the days. the nights were given names for three days each of a month, a total of ten. the names are given by al-Bīrūnī, with his etymologies, in the English translation of Sachau p. 74-75, p/ 63-64 of the published Arabic; [ ... ] are alternatves given in Enc. of Islam II "Layl and Nahār":
I. 1-3 *gh*urar غُرَرٌ (pl. of *gh*urra(t) غُرَّةٌ triptote or غُرَّةُ - diptote, because it is a feminine proper name) meaning the first of everything, or refering to the blaze on the horse, because the crescent is seen on them {Sachau didn't translate the last phrase}. [ *gh*urr غُرٌّ , qurḥ قُرْحٌ ]
II. 4-5 nufal  نُفَلٌ etymologically from tanaffala تَنَفَّلَ "beginning to make present without any necessity". also called šuhb شُهْبٌ refering to "white nights" {actually from "gray"}. [j̲uhar جُهَرٌ ]
III. 7-9 tusa` تُسَعٌ because the ninth is the last of them. also {al-}buhr البُهْرُ because the darkness is particularly "thick". [buhr بُهْرٌ , zuhr زُهْرٌ ]
IV. 10-12 `ušar عُشَرٌ because the tenth night is the first of them.
V. 13-15 bīḍ بِيضٌ because they are white by the shining of the moon.
VI. 16th-18th dura` دُرَعٌ because they blask in the beginning and are like a sheep with a black head and a white body. originally refering to a coat of mail which is of a different color than the body. [ dur` دُرْعٌ ]
VII. 19th-21th ẓulam ظُلَمٌ because they were usually dark.
VIII. 22th-24th ḥanādis حَنَادِسُ (plural of حِنْدِسٌ ḥindis "extremely dark") or duhm دُهْمٌ on account of them being dark.
[nuḥs نُحْسٌ ]
IX. (25th-27th) da'ādi' دَآدِئُ because they are remainders. also derived from the gait of the camel, stretching forth one foot, to which the other is quickly following. [quḥam قُحَمٌ ]
X. (28th-30th) miḥāq مِحَاقٌ on account of the waning of the moon. [maḥāq مَحَاقٌ , muḥāq مُحَاقٌ ]

VIII. and IX. are diptote, the rest are triptote, except when a feminine is used as a proper name.


Alternate scheme acc. to Ch. Pellat:
13th to the 21th bear the same names but:
 1-3: hilāl هِلالٌ ; then 4-6: qamar قَمَرٌ ; then 7-12: nufal نُفَلٌ  ;{previous scheme}; 22-27: ḥanādis  حَنَادِسُ then 28-29: daʾādiʾatān(i)  دَآدِئَتَانِ  ; then 30 miḥāq مِحَاقٌ , maḥāq مَحَاقٌ , muḥāq مُحَاقٌ  .
hilāl هِلالٌ means "crescent"; qamar قَمَرٌ means "moon".

Also some special nights:
The last night is called {al-}sirār السِّرَارُ on account of the waning of the moon because in it the moon "hides" herself. also called {al-}faḥama(t) الفَحَمَةُ because there is no light in it. and also {al-}barā' البَرْآةُ {aloofness} because the sun has nothing to do with it (or as Varisco puts it "because the moon is clear of all sunlight").

The last day of the month is {al-}naḥīr النَّحِيرُ , because it is the naḥr نَحْرٌ or throat of the month.
The 13th night is called {al-}sawā' السَّوَاءُ .
The 14th night is called {al-}badr البَدْرُ because the moon is full and its light "complete". {badr is a well known word for full-moon}.
Acc. to Ch. Pellat in Enc. of Islam II:
Three last nights were qualified with, respectively, da`jā'دَعْجَاءُ , dahmā' دَهْمَاءُ and laylā' لَيْلاءُ , but the 30th also bore the names sirār سِرَارٌ , sarār سَرَارٌ , sarar سَرَرٌ , naḥīra نَحِيرَةُ or نَحِيرَةٌ , da'da' دَأْدَأٌ , falta فَلْتَةُ or فَلْتَةٌ  .
Lane gives details: falta  فَلْتَةٌ as a common noun means a sudden or unexpected event. falta فَلْتَةُ or فَلْتَةٌ means "the last night of any of the sacred months, of which people differ as to whether it be lawful to war therein or not" or "the last day night of any month", or "the last day of a month after which there is a sacred month". laylatu fatratin لَيْلَةُ فَلْتَةٍ or laylatu~l-fatrati لَيْلَةُ الفَلْتَةِ is "the night by [the deducting of which] the month becomes deficient, and by [the addition of] the month becomes complete", "because some see the new moon and others do not ...". naḥru~-l-šahri  نَحْرُ الشَّهْرِ or naḥīratuhu (its naḥīra) نَحِيرَتُهُ or al-nāḥir النَّاحِرُ is the last night of the month but sometimes applied to the first. there are variants sarāru l-šahri سَرَارُ الشَّهْرِ , sirāruhu (its sirār) سِرَارُهُ  (the latter not aprroved usage), sararuhu سَرَرُهُ , siraruhu سِرَرُهُ , laylatu l-sirār {night of the sirār} لَيْلَةُ السِّرَارِ are variants. da'da' دَأْدَأٌ is from an encroachment or alternate meaning of set IX.

The first and the last days of the month, in historical works and correspondence, are also designated by terms connected with the moon: *gh*urra  غُرَّةُ for the first and munsalax مُنْسَلَخٌ or salx سَلْخٌ {"stripped off"} or sarār سَرَارٌ for the last. acc. to Ch. Pellat.


François de Blois in "The month and its divisions in ancient South Arabia", Procceedings of the Seminar for Arabian Studies, 28 (1998) also says that there was a tradition (occassionally applied) among the Arabs, like the South Arabians of dividing the lunar month into three, ten nights each. They were called acc. de Blois, al-`ašru l-'uwal العَشْرُ الأُوَلُ (or in the singular al-`ašru l-'ūlā العَشْرُ الأُولَى ), al-`ašru l-wusaṭ العَشْرُ الوُسَطُ (or in the singular al-`ašru l-wusṭā العَشْرُ الوُسْطَى ), al-`ašru l-'uxar العَشْرُ الأُخَرُ (or in the singular al-`ašru l-'uxrā العَشْرُ الأُخْرَى ). meaning respctively, the fist ten, the middle ten, the last (lit. "the other") ten. these are found in Lane as well. since the month, from one sighting of the crescent to the next could normally be either 29 or 30 nights later, the Muslims distinguish between "complete months" شُهُورٌ طَامَّةٌ šuhūr ṭāmma(t) and "defective months" شُهُورٌ نَاقِصَةٌ šuhūr nāqiṣa(t). thus sometimes the last "decade" of the month had only 9 nights each. a similar system was used by the Ancient Greeks in regards to days.

There was also a  tradition of dividing the month into periods of ten days but not specifying a day of the month and this continued ocassionally.

Instead the following were put into constructs with the name of the month.

Days 1-10 'awā'ilu (...) أَوَئِلُ the first (days) (of ...)
     11-20 'awāsiTu (...) أَوَاسِطُ the middle (days) (of ...)
     21-40 'awāxiru (...) أَوَاخِرُ the last (days) (of ...)

The first day was called *gh*urra(t)  غُرَّة
The last day was called salx سَلْخ

Months are normally counted from the beginning of the month, certainly always so in later and modern Arabic, but earlier there was a different scheme described by F. de Blois in Enc. of Islam II "Ta'rīkh":
 <<
The days (or nights) of the month can be counted consecutively from the first to the last, but in the second half of the month the Muslims (like the ancient Greeks and Romans) also counted backwards, dating events by the number of nights supposedly remaining in the month. Thus, assuming a “complete” 30-day month, typical dating formulae might be:
1st: li-ghurrati Radjab
2nd: li-laylatayni khalatā min Radjab
3rd: li-thalāthi layālin khalat (or khalawna) min Radjab (etc.)
15th: li 'l-niṣfi min Radjab
16th: li-arba`a `ashrata laylatan baḳiyat (or baḳīna) min Radjab
17th: li-thalātha `ashrata laylatan baḳiyat (or baḳīna) min Radjab
18th: li-’thnatay `ashrata laylatan baḳiyat (or baḳīna) min Radjab
19th: li-iḥdā `ashrata laylatan baḳiyat (or baḳīna) min Radjab
20th: li-`ashri layālin baḳiyat (or baḳīna) min Radjab
21st: li-tis`i layālin baḳiyat (or baḳīna) min Radjab
22nd: li-thamānī layālin baḳiyat (or baḳīna) min Radjab
23rd: li-sab`i layālin baḳiyat (or baḳīna) min Radjab
24th: li-sitti layālin baḳiyat (or baḳīna)min Radjab
25th: li-khamsi layālin baḳiyat (or baḳīna) min Radjab
26th: li-arba`i layālin baḳiyat (or baḳīna) min Radjab
27th: li-thalāthi layālin baḳiyat (or baḳīna) min Radjab
28th: li-laylatayni baḳiyatā min Radjab
29th: li-laylatin baḳiyat (or baḳīna) min Radjab
30th: li-salkhi Radjab
But since it is not actually known in advance how many nights the current month will have, this backward-dating is purely conventional. This is noted quite clearly by mediaeval authors, for example by al-Ṣūlī ( Adab al-kuttāb , Cairo 1341/1922-3, 183), when he writes that “careful people” avoid dating in this way “because they do not know how many nights remain, owing to the fact that the month can be either defective or complete”, i.e. it can have either 29 or 30 days. See also al-Ḳalḳashandī, Ṣubḥ al-a`shā , vi, 237-8, who says that some authorities forbid backward-dating, while others permit it only on the assumption that it implies the unspoken proviso “if the month be complete”. In other words, salkh always means “the thirtieth day”; if the crescent is sighted after 29 days, then the day “when one night remains” is followed immediately by the first of the next month. It must be stressed again that with backward-dating, as with forward-dating, a precise conversion of Muslim dates is normally only possible if the day of the week is indicated in the source.
 >>

The verbs in paranthesis are in the old agreement rule (in terms of number and gender), but they were used in later as well.
Also for evidence of a lunar (with an intercalary month or not) calendar, ta'rīx  تَأْرِيخٌ "specification a date" (also later, "history"), plural tawārīx تَوَارِيخُ , is a back formation from its plural (F. de Blois) and warraxa  وَرَّخَ / tawrīx تَوْرِيخٌ  "specification of a date" is attested in old classical arabic (Lane), though the lexicographers considers this an error without realizing it was an archaicism. it comes from (de Blois) South Arabian "moon" *warx, Mehri warx, Ethiopic wärx, Sabiac <wrx> "month". this is cognate with Hebrew yArǝḥ (yArǝ(a)ḥ) יָרְחַ "moon" and Hebrew yeraḥ יֶרַח "month".al-Sakhāwī uses the word tawrīx in the title of his book and says it is in the dialect of the tribe of Tamīm (E. Arabia) while ta'rīx is in the dialect of Qays.
Also the Islamic era and Calendar are on good historical footing (except before intercalation was forbidden by the Qur'an). It seems though that the early chroniclers of Muhammad's life seem to have established the corresponding dates on different calendars as if there had never been intercalation. the eras before the establishment of the Islamic era were done in Central Arabia according to some important event. The firm footing of the Islamic era is based on a 22 AH manuscript with the Byzantine era and Coptic months. It establishes that indeed something momentous for muslims occured on 622 CE, it is near enough for there to have been plenty of witnesses that the incident is not fabricated. It is also the earliest dated manuscript with some dots on the arabic letters, and is therefore of interest to the study of writting systems as well. It is also about an inoccuous incident, so it cannot be a forgery. the evidence supports Arab traditional chroniclers who credit the Caliph `Umar (in power: 13AH - 23AH) with the institution of the era in 16 AH (traditionally, according to Donner "Narratives ...", p. 237 or 17 AH according to some sources). The earliest "firm numismatic evidence" of the use of the era is on a coin of 23 AH, with possible 21 AH and 22 AH dates. The earliest monumental attestation on a tombstone 31 AH (see Donner, "Narratives of Islamic Origins: ..." p. 237) but Cook and Crone in "Hagarism" cite a year 17 on a coin from Damascus. So the numismatic evidence supports the establishment of the era during 16 / 17 AH. According to one tradition, the year of the Birth of the Prophet was rejected because there was disagreement about it, and  that informally there had already been a tradition of dating from the Hijra (some say Muhammad used it). For the papyrus and the article see: 
http://www.islamic-awareness.org/History/Islam/Papyri/PERF558.html
"The Dotting Of A Script And The Dating Of An Era: The Strange Neglect Of PERF 558" Alan Jones, Islamic Culture, 1998, Volume LXXII, No. 4, pp. 95-103.


http://www.islamic-awareness.org/History/Islam/Papyri/jones.html
 <<
The Dotting Of A Script And The Dating Of An Era: The Strange Neglect Of PERF 558
Alan Jones
Islamic Culture, 1998, Volume LXXII, No. 4, pp. 95-103.

....

 The subject of the texts of the papyrus is mundane. It is simply the acknowledgement of the requisition of sixty-five sheep from Herakleopolis by the forces led by `Abd-Allâh b. Jâbir,** to be set off against the year's taxes. It has been suggested that the Greek version was written first, but this is by no means certain. The Greek occupies lines 1-3 and half of line 5 (5a) on the recto, and there is also a line on the verso. The Arabic occupies line 4, half of line 5 (5b) and lines 6-8 on the recto. The Arabic is not a direct translation of the Greek, but the core of the contents is the same in both versions. The Greek version refers to the Arab invaders as magaritai (i.e., muhâjirûn).[10]

...

In the name of the Merciful, Compassionate God. These are the animals for slaughtering that `Abd-Allâh ibn Jâbir and his companions took from Ihnâs:§ we took from the representatives of Theodor[akios],á the elder son of Abû Qîr, and from the representative of [Chr ]istofor[ os ],á the younger son of Abû Qîr, fifty sheep from the animals for slaughter and fifteen other sheep, which were butchered for the men on his ships,∞ his cavalry and his infantry in the month Jumâdâ I of the year Twenty-Two. The scribe was Ibn Ḥadîd.§§
Though the main contents of the document cannot be described as vital, except to the sheep and the expeditionary force, the Arabic version contains two features that are of outstanding significance. The first is the script that is used; the second is that the date is given as the year A.H. 22.
The year 22 is the first Islamic year for which any dated documents written in Arabic survive, and there are only two of those: P Berol 15002,[11] which is unfortunately fragmentary, and PERF 558, the first complete Arabic document of the Muslim era.

...

This combination of date and script would be remarkable enough in itself, but the papyrus has yet another nugget of priceless information. The Greek version has its own Byzantine date[13] in line 5a of the recto of the papyrus. This has the form: "30 Pharmouthi of the indiction year 1". Such dates are commonly found in Greek papyri, and indeed there are half a dozen other documents in the Erzherzog Rainer Papyrus group that have indiction dates for the period A.D. 642-43.[14] The only problem is that the indiction cycle is a relatively short one of fifteen years, and thus great care is needed in working out the appropriate date in the Christian era. Grohmann worked out "30 Pharmouthi of the indiction year 1" to be 25th April, 643 A.D.
The date fits with two of the most commonly available conversion tables: those of Caetani[15] and of Freeman-Grenville.¥¥ They make the last day of Jumâdâ I equate with 26th April, 643 A.D. Given the virtual inevitability of imprecisions of dating at the period, the fit is remarkably good. ¤¤
¤¤ Whilst such tables as those produced by Caetani and Freeman-Grenville and others may have a spurious certainty (and this is perhaps even more so with recent versions on CD-ROM), it would appear that they are not likely to be far out.
...
§ Literally "This is what `Abd-Allâh ibn Jâbir and his companions took from Ihnâs from the animals for slaughtering."
á The translation gives the name forms recoverable from the Greek version, which may be translated as:
Recto
1. In the name of God. [From the] Amîr `Abd-Allâh to you Christophor[os and] Theodor[akios], pagarchs of Herakle[opolis],
2. I have taken from you for the purpose of feeding the Saracens who are with me in Herakle[opolis] 65 sheep (sixty-
3. five and no more); and I have had the present document written to make this clear .
5a Written by me, Ionnes, no[tary] and off[icial], 30th day of the month of Pharmouthi of the ind[iction year] 1.
Verso
1. Document about sheep given to the muhâjirûn (Greek magaritai) and other [new] arrivals, towards the payment of the taxes of the Ind[iction year] 1.
∞ Literally "which the men on his ships. . . had butchered."
§§ The name Ibn Ḥadîd is followed by a further waw, the import of which is not clear, though there are parallels in the Safaitic inscriptions.


 >>
The name of the era, however, is not mentioned until much later. Many East Syriac texts mention the "year ... of the rule of the Arabs" (Hoyland, "Seeing Islam as others saw it" p.547). There is a papyrus dated 42 AH that uses the formula "sanat qaḍā' al-mu'minīn سنة قضاء المؤمنين " (p. 690) "the year of the dispensation of the believers". There is a report of a lost inscription in Cyprus dated 29 "lilhijra(t)" للهجرة "of the Hijra" but this is probably an interpolation by the medieval reporter. (Donner, p. 88)
Incidentally, there is another manuscript dated 22 AH that shows dotting of nūn, /n/ < ن > as it is dotted later,
http://www.islamic-awareness.org/History/Islam/Papyri/PBerol.html
And an inscription 24 AH with some modern dots (including dotting <f> in the eastern fashion), mentioning the death of `Umar, establishing him as a historical figure (though this is done by an Armenian source around his time as well) and confirming the traditions concerning his death.
http://www.islamic-awareness.org/History/Islam/Inscriptions/kuficsaud.html

The formula "sanat qaḍā' al-mu'minīn سنة قضاء المؤمنين " "the year of the dispensation (or jurisdiction) of the believers" is found in two payri from Egypt one dated 42 the other 57.


http://www.islamic-awareness.org/History/Islam/Papyri/PVindobA1119.htm

http://www.islamic-awareness.org/History/Islam/Papyri/PLouvre.html


Yusuf Ragib in "Une ère Inconnue D'Égypte musulmane: l'ère de la juridiction des croyants", Annales Islamologiques, 2007,
Volume "41, pp. 187-207 argues that this era refers to a solar calendar on the Coptic model but harmonized with the Islamic era. Both papyri refer to debt setlements.

The crucial phrase in P. Louvre Inv. J. David-Weill 20 is

 قضا المـ]و[منـ]ـين شـ[ـهـ]ـد عقيب ابن عمرن وحى ابن سعد وكتب]

 الى مل الغيل الى مل اثنان واربعين [[....]]

قضا ا]لمومنـ[ـين] شهد عريب ابن ينة و... ابن تفضل وكتب]



1. [In the jurisdiction of b]el[iev]ers. Testified ʿUqayb b. ʿImran and Ḥayy b. Sʿad. Wrote
2. [[............]] until refilling the tanks the end of (year) forty-two
3. In the jurisdiction of believers. ʿArib b. Yanah and ... b. Tafaddul (?)... and wrote

The last day of 42 AH falls on 14 April 663 CE but the Coptic year ends at 28 August 663 and the filling of the tanks / bassins by the Nile would be accomplished soon after. It would be impossible for April.

Thus the "Year of the Jurisdiction of the Believers" is a Solar Coptic calendar with the Islamic era. Evidently this is an early example of using a solar calendar for financial purposes.


The traditions concerning `Umar and the foundation of the Islamic era can be found in Ṭabarī:

 <<
Muḥammad b. Ismā`īl—Qutaybah b. Sa`īd—Khālid b. Ḥayyān Abū Yazīd al-Kharrāz—Furāt b. Salmān—Maymūn b. Mihrān: A money order was brought before `Umar which fell due in (the month of) Sha`ban. 'Umar said, "Which Sha`ban? The one which is coming or the one we are in now?" Then he said to the Messenger of God's Companions, "Contrive something for the people which they can recognize." Some said, "Write according to the chronology of the Greeks; it is said that they date their letters from the time of Alexander, but that was a long time ago." Others said, "Write according to the chronology of the Persians; it is said that whenever a king rises up amongst them he discards the era of his predecessors." In the end they agreed that they should see how long the Messenger of God had remained in al-Madīnah. They found this to be ten years, and the era was reckoned from the Messenger of God's emigration. Then they said, "From which month shall we begin?" They said, "Ramaḍān," and then they said, "al-Muḥarram, for that is the month when people depart from their pilgrimage, and it is a sacred month." So they agreed upon al-Muḥarram.

...
Muḥammad b. Ismā`īl—Qutaybah b. Sa'īd—Nūḥ b. Qays al-Tāḥī—`Uthmān b. Miḥsan: concerning the Qur'ānic verses "By the dawn, and ten nights,"241 Ibn `Abbās used to say, "The dawn is al-Muḥarram, the dawn of the year."
Muḥammad b. Ismā`īl—Abū Nu`aym al-Faḍl b. Dukayn—Yūnus b. Abī Isḥāq—Abū Isḥāq—al-Aswad b. Yazīd—`Ubayd b.
`Umayr: Al-Muḥarram is God's month, and it is the beginning (that is the first month) of the year. In it, the Ka`bah is clothed dating commences, and silver is struck. In it is a day upon which people repented, and God forgave them.
 >>

Also:
http://en.wikipedia.org/wiki/Hijri_year
 {diacritics and some details of transcription of Arabic names mine}

 <<
“ Some time in [CE 638], Abū Mūsā Ash`arī, the Governor of Basra wrote:
"Amīr-ul-Mu'minīn, we receive instructions from you every now and then, but as the letters are undated, and some times the contents of the letters differ, it becomes difficult to ascertain as to which instructions are to be followed."
That set `Umar thinking. In the meantime, he received from Yemen a draft for some money which was encashable in Sha`bān. `Umar thought that the practice of merely mentioning the month in such cases was defective for one could not be sure whether the month referred to was of the current or the following year.
`Umar convened an assembly to consider the question of calendar reform.
Some one suggested that the Roman calendar should be adopted. After discussion the proposal was rejected as the Roman calendar dated from too remote an era and was cumbersome.
It was next considered whether the Persian calendar might be adopted. Hurmuzān explained the salient features of the Persian calendar called 'Māhrōz'. The consensus of opinion was that such a calendar would not be suitable for the Muslims.
The general opinion was that instead of adopting any alien calendar, the Muslims should have a calendar of their own. This was agreed to, and the point next considered was from when should such an era begin?
Some one suggested that the era should begin from the date of birth of the Holy Prophet. Some suggested that it should begin from the death of the Holy Prophet. `Alī suggested that it should begin from the date the Muslims migrated from Mecca to Madīna. After discussion, `Alī's suggestion was agreed to.
The Holy Prophet had migrated in the month of Rabī`-ulAwwal, when the year had already run two months and eight days. Next the question arose from which month should the new era start.
Some one suggested that the calendar should start with the month of Rajab as in the pre-Islamic period this month was held sacred. Some one proposed that the first month should be Ramaḍān as that is a sacred month for the Muslims. Another proposal was that the first month should be Dhū 'l-Ḥijja as that is the month of the pilgrimage.
`Uthmān suggested that as in Arabia the year started with Muḥarram the new era should also start with Muḥarram. This suggestion was accepted. The date was accordingly pushed back by two months and eight days, and the new Hijri calendar began with the first day of Muḥarram in the year of migration rather than from the actual date of migration.
`Umar accordingly issued instructions to all concerned regarding the enforcement of the Hijri calendar[1]
1^ Umar bin Al-Khattab (2002). "Islamic Actions and Social Mandates: The Hijri Calendar". witness-pioneer.org. http://www.witness-pioneer.org/vil/Articles/companion/14_umar_bin_al_khattab.htm#The%20Hijri%20Calendar. Retrieved 2006-12-16. 

 >>
Shams al-Dīn Muḥammad ibn `Abd al-Raḥmān al-Sakhāwī (d. 902) in his al-I`lān bi'l-Tawbīkh li-man dhamma ahl al-tawrīkh gives the following details about the origin of the Islamic calendar and repeats traditions similar to the one above:

 <<
A certain scholar showed the propriety of starting with the hijrah. There are four events in the life of Muḥammad which might be used as epoch years of the era: His birth, (the year) when the first call came to him, the hijrah and his death. There are diffferences of opinion with regard to the exact year of his birth as well as the year when the first call came to him. The year of his death was rejected because of its associations. The choice, thus, was restricted to the hijrah. ...  
...
 The first to institute the (Muslim) era is said to be Ya`lâ b. Umayyah when he was in the Yemen. he wrote to `Umar a letter that was dated (mu'arraḫ). `Umar liked it. and the Muslim era was instituted. ...
...
 It was reported by Aḥmad (b. Ḥanbal) ... that the letter said: "An I.O.U. payable in Ša`bân was presented to `Umar. `Umar said: Which Ša`bân, last Ša`bân, or this one or the coming one? Give the people something they can understand." ...
...
Al-Ḥâkim reported that Sa`îd b. al-Musayyab said: "`Umar called the people together-that is the emigrants and the others-and asked them which day they should choose as the beginning of the (Muslim) era. `Alî suggested the day of Muḥammad's departure from Mecca, the territory of polytheism-that is, his departure for Medina. `Umar followed `Alî's suggestion." 
 Ibn Abî Ḫayṯamah reported, through Muḥammad b. Sîrin that the latter said: "Someone arrived from the Yemen that he had seen there something which was called by the Yemenites ta'rîḫ and used by them (to date) documents from a certain year and month. Whereupon `Umar said: 'This is fine. Let us institute an era (arriḫû).' When this was agreed to someone suggested the year of Muḥammad's birth as the epoch of the era. Others suggested the year when the call came first to him, or the year when he emigrated (from Mecca to Medina), or the year of his death. `Umar decided to use the year when Muḥammad left Mecca for Medina as the epoch year of the era."
 Then, (`Umar) asked 'With which month shall we begin?' Some people suggested Rajab, and someone Ramaḍân. `Umar said 'Let us use al-Muḥarram as the beginning of the era. Al-Muḥarram is a sacred month. It is the beginning of the year and the month in which the people return from the pilgrimage.' This happened on Rabî` I of the year 17/ 638.
 We learn from these combined reports that al-Muḥarram (as the first month of the Muslim era) was indicated by `Umar, `Uṯmân and `Alî.
...
 Sa`d b. Abî suggested to `Umar the year of the death of the Prophet as the epoch of the era. `Alî however, suggested the hijrah, because has seperated truth from falsehood  and given victory to Islam. The Muslims, (consequently), generally agreed to the use the year of the hijrah as the beginning of the of the era, since it was the year in which Islam and the Muslims (first) showed their strength.

 Then there was disagreement with regard to the month. `Abd-ar-Raḥmân b. `Awf suggested Rajab, because it was the first of the sacred months. `Alî, however, suggested al-Muḥarram because it was the first month of the year and one of the sacred months. `Umar followed `Alî's suggestion, and this usage spread to all Muslim territories.
 A report on the authority of Ibn Abbâs states that there existed no era in Medina when the Prophet arrived. People there came to use an era a month or two after his arrival. This continued until Muḥammad's death, Then the era was discontinued, and there was none during the caliphate of Abû Bakr and the first four years of the caliphate of `Umar. Then, the (Muslim) era was established.
 `Umar is reported to have said to the assembled dignitaries among the men around Muḥammad: "The income is considerable. What we have distributed has been without fixed dates. How can we remedy that?". One answer came from al-Hurmuzân. He had been king of al-Ahwâz. After his capture he became a Muslim. He said the Persians had (a method) of calculation called Mâhrôz and which they ascribed to their Sassanian rulers. The word mâhrôz was arabicized as mu'arraḫ, and the infinitive ta'rîḫ was formed from it. It was used in all other forms. Al-Hurmuzân then explained to them how to use it. `Umar (however,) said" "Give the people an era in which they can use in business and which permits an exact indication of the date in their mutual dealings." A Jewish convert said: "We (Jews) have a similar calculation which we ascribe to Alexander." The others however, did not like that era, because it is too remote. Some were for the adoption the Persian era. It was however, objected that the Persian era had no fixed epoch and always started anew with the ascension (to the throne) of each new king. An agreement was reached to institute the era of the rule of Islam, beginning with the hijrah of the Prophet from Mecca to Medina. There are no differences of opinion with regard to the date of the hijrah as there are with regard to the time when the call first came to Muḥammad and with regard to the day and year of his birth. And although the date of his death is fixed, it is no pleasant thought to use (such a sad event) as the beginning of the era. The hijrah, moreover, coincided with the success of the religion (millah) of Islam, the frequent arrival of embassies and the Muslim ascent to power. ...   
...
... Those of the children of Ismâ`îl who remained in the Tihâmah used an era which covered which the period of the exodus of the Banû Zayd, Sa`d, Fahd and Juhaynah from the Tihâmah to the death of Ka`b b. Lu'ayy. Then they introduced an era which covered the period from (the Year of) the Elephant to `Umar's introduction of the era of the hijrah. This took place in the year 16, 17 or 18/637 - 639.
 Another (story about the pre-Islamic era) states that the Ḥimyarites used the reigns of the Tubba`s as the epoch years of their era; the Ġassânids (the break of) the Dam (of Ma'rib); and the inhabitants of Ṣan`â' (first) the victory over the Yemen by the Abbysinians and later on the Persian conquest (of the Yemen). The Arabs then used the famous battle days, such as the war of al-Basûs, Dâḥis, and al-Ġabrâ' the day of Ḏû Qâr, al-Fijâr, and so on. Between the war of al-Basûs and the year the call came to the Prophet, there was an interval of sixty years. This story was told by Muḥammad b. Sa`d, on the authority of Ibn al-Kalbî.
...
Ibn al-Aṯîr said: "Each Arab (Bedouin) group had their most famous event as the epoch of an era. They had no common era. This is shown by the verse of a certain (ancient Arab poet):
...
and by the verse of another:
...
 Each of these poets used a famous event as the epoch of his particular era. If there had been a common era, they would not have used different ones."
 >>

From F. Rosenthal, "A History of Muslim Historiography", second revised edition, Leiden 1968, p.380-388.).
Tihâmah is the area where Mecca is situated.
These traditions support the consensus that al-Muḥarram was the first month of the pre-Islamic calendar.
Deriving from māhrōz ماهروز is indeed folk eymology, while the tradition that ta'rīx came from Yemen recalls the South Arabian origins of the term. It also points out that the Yemenis before Islam had the Late Sabaean era, which was continuous, while. The Byzantines had their cycle of indictions and the Sasanid Persians dated the era from each successive king. māh ماه in Persian means "moon, month" and rōz (> rūz) روز means "day". Steingass has māhrōza ماهروزه meaning "an almanac, ephemeris; date, day of the month". In Persian /z/ sometimes alternates with /x/. the past stem of some verbs ending in -x have present stems ending in -z. Yemen used the Sabaean era, at least until the end of Ethiopian rule, at which point Sabaic inscriptions cease. It has been finally determined that it was a luni-solar calendar. Beeston and Kister give 552 CE for Abraha's expedition against Arabia, which is dated 662. giving 110 BCE for the beginning of the Sabaean era. it certainly cannot be later than 554 CE because it mentions a certain Lakhmid king al-Mundhir III who was assasinated that year, putting a limit for the beginning of the Sabaean era. Other events are used to calibrate it against mostly Byzantine sources. acc. to F. de Blois in Enc. of Islam II "Ta'rīkh" << In early South Arabian texts, years are not counted according to an era, but rather each year bears the name of a specifically appointed official (eponym); but from the later periods several different eras are attested, the best known of which is the so-called Ḥimyarite era, with a nominal epoch (according to the short chronology proposed by present author) in the spring of 110 B.C., though some have favoured a long chronology with an epoch in 115 B.C. >>. C. Robin also favors 110 BCE as the beginning of the Himyarite era. Beeston in "Epigraphic South Arabian Calendars and Dating" says that this era was not used until the 3rd cent. CE, and for a while competed with another era. the use in Yemen of dating from the reigns of the kings (called in the singular tubba` by the Arabs, although epigraphically this is attested in Sabaic as the name of an individual king, and not used for "king" in Sabaic. Enc. of Islam I "Ḥimyar" derives it from the Yemeni family bata`) , as mentioned by al-Sakhāwī, prior to the use of the Late Sabaean era (the Ḥimyarite era) is correct (though the "first Tubba`" according to Arabic sources occurs quite late). In reality, the era was done according to the officeholders with the title of "kabir" the Ḥimyarite month names have been delt with in previous posts, they in survived in Arabized from in a medieval Arabic manuscript from a Yemeni on agriculture, and survive to some extent in Yemeni colloquals. The Ghassānids used the era of Bostra (see next), for they were in southern Greater Syria during the collapse of the Ma'rib dam, which was in Yemen, although the Ghassanids are said to be of Yemeni origin. The passage also vindicates that the date of birth of Muhammad was not precisely known, a subject that will be dealt with later. that the Jews used at times the Seleucid era is correct (see Encyclopaedia Judaica "Chronology"). al-Sakhāwī later says that the Jews dated from the destruction of the (Second) Temple, which is also correct, this is also mentioned among the eras used by Jews, mentioned in the same entry. The prominant role of `Alī in these traditions binds the Shiites to the Muslim calendar as well.
The pre-Islamic Arabs of Greater Syria used a solar calendar using the era of boṣrā (Latin Bostra) since the annexation of the city of that name by the Romans at 105 CE; Palmyrene (Aramaic) בּצרא  < bṣr'> "fortress" in Arabic the city is known as بُصْرَى buṣrā. Medieval Arabs when refering to the solar calendar, frequently, but not always, used the Seleucid era. The era dates from the return of Seleucus I Nicator to Babylon in 311 BCE after his exile in Ptolemaic Egypt, considered by Seleucus and his court to mark the founding of the Seleucid Empire. This was the practice of the Eastern Christians who counted years according to the Seleucid era, in the East generally, but wrongly, called the “Era of Alexander” (Arabic: تَأْرِيخُ  ذِي القَرْنَيْنِ  ta'rīx *Dh*i ’l-Ḳarnayn ( ذُو القَرْنَيْنِ *Dh*u ’l-Ḳarnayn (nominative) "Possesor of Two Horns" is the Qur'anic name of Alexander), with an epoch of 1 October 312 BCE (acc. to Enc. of Islam II; 311 acc. to Wikipedia). In Egypt and North Africa, years were often reckoned according to the Byzantine fifteen-year cycle of indictions, the “first indiction” beginning in (for example) A.D. 612, 627, 642, etc.. The Byzantine indictions begin on 1 September, but the cycle is used also in connection with other methods of determining the New Year. In al-Andalus there was the Spanish era ( تَأْرِيخُ الصُّفْرِ ta'rīx al-ṣufr; presumably from أَصْفَرُ aṣfar "yellow" or by extention "light colored," a name applied to Greeks and later Europeans), with its epoch on 1 January 38 BCE. Probably the date of a new tax imposed by the Roman Republic on the subdued population of Iberia. whatever the case, the date signifies the beginning of the Pax Romana in Hispania. The so-called Christian era of Western Europe was unknown both to Christians and Muslims in the medieval Near East. The months in the East were Syrian based (see previous post in sci.lang) and in the West, names based on North African Romance (see previous post in sci.lang) were used. nowadays, except for Saudi Arabia and formerly Libya under Gaddafi these two sets of month names with the Common Era calendar is used. In Egypt, the Coptic calendar is also used, though the Gregorian calendar is used more often. Libya, under the Gaddafi regime, used a solar calendar with its own newly invented month names, based on an era on the traditional birth of Muhammad, while it used the lunar calendar with the traditional month names, but an era based on the death of Muhammad.
It is attested that the Arabs after Islam and other Muslim people always used a solar era alongside the Islamic calendar, as agricultural taxes had to be in step with the seasons. The only time a lunar-solar calendar was used alongside the purely lunar Islamic calendar was under the Ilkhanid Mongols in Persia, even after they converted to Islam, in which case the Chinese style Turco-Mongol calendar continued to be used in addition to the Islamic one. the Seljuks in Iran reformed the solar Persian calendar, under the direction of Omar Khayyam, who devised an algorithm even more accurate than the Gregorian calendar. what was adopted was a system in which the vernal equinox was determined by astronomical calculation. "Various Eras and Calendars Used in the Countries of Islam (Continued)" by S. H. Taqizadeh in Bulletin of the School of Oriental Studies Vol. 10, No. 1 (1939) describes it thus: << The New Year's Day, however, was always the day at the midday of which the sun was already in Aries, or in other words the day on which the equinox occurred before its noon and after that of the preceding day. It follows that each time the equinox happened after noon (provided that it had occurred before noon in the preceding year),3 that day was a leap day and the year just coming to a close a leap year (of 366 days). Therefore no rule for the periodical readjustment of the year by the intercalation of a supplementary day was necessary nor was it provided. The same system is adopted now in Iran and consequently the question of finding the leap years according to a conventional rule never arises ... >>. this calendar first started with the reign of Sultan Malikšāh, and was known as the Jalālī calendar, from his epithet Jalāl al-Dawla ("glory (jalāl) of the state"). the era began on 15th March, A.D. 1079 then there was the Mongol interlude. the dynasties in Iran afterwards used this solar calendar but with the Hijri era. the Asian 12 year animal cycle of naming years lingered on in Iran after the Mongols until the takeover of the Pahlavi dynasty (the last dynasty of Iran). a frequent ruse in using the solar Hijri era was the practice of skipping years to keep it in step with the Hijri lunar calendar. this was the case with the Ottoman Fiscal Calendar, the practice being known as sıvış or siviş "slipping away or disapearing" in Turkish, and a year skipped was called a siviş yılı "a siviş year". this was discussed in a previous post. earlier, such a practice was known during the Abbasids. in 1871 CE / 1288 AH, the practice was dropped as a result of a clerical error. during the Abbasids the practice of skipping a taxational, خَرَاجِيٌّ xarājiyy year was called تَحْوِيلٌ taḥwīl (“changing” one tax year to another). this happens when the lunar year finishes its cycle before the start of the solar year, or if the solar year falls within 11 days of the start of the lunar year. this happens every 33 year lunar years and 4 months. during the reform of Pope Gregory, the Middle East (with the exception of Iranian domains whose solar calendar maintained the principles of the was under that of the Jalālī calendar mentioned previously) was under the domination of the Ottoman Empire, whose solar calendar maintained the Julian system (with leap years the same as that of the Christian Julian calendar) until 1 March 1917 NS, and began its next New Year's Day on 1 January 1918 NS, while previously the New Year had started in March. The Coptic calendar, which still has a Julian type system, has an official status in Egypt, along with the Common Era calendar and the Islamic Calendar.

As mentioned before, Spain used it's own era dating to Roman times, the Byzantines the Indiction cycle, the Syrians, the Seleucid Era, the Copts the Coptic Era (that of Diolectian). So medieval Arabs did not have much encounter with Christians using the birth of Christ. But nowadays, the Common Era is used, called مِيلَادِيٌّ  mīlādiyy, "concernign the birthday", distinguishing مِيلَادٌ mīlād for Jesus from مَوْلِدٌ mawlid or مَوْلُودٌ mawlūd for Muhammad. Transjordan (Jordan) under the British mandate was the first Muslim country (unless one discounts the short lived independence of Azerbaijan after the war) to officially use this era, followed by Republican Turkey in 1926.

I found the only mention of the Christian Era in a garbled form in al-Sakhāwī in the previously mentioned work, << (Ibn al-Kalbî) said: ... The Christians used an era which began with the ascension of `Îsâ the Messiah >> F. Rosenthal, "A History of Muslim Historiography", second revised edition, Leiden 1968, p.386.
`Îsâ عِيسَى is the Qur'anic name for Jesus (so used in Arabic, except by Christians in liturgy). Obviously there is confusion between Christmas and Easter. perhaps because Easter is more important in Orthodox Churches, it was assumed that the Christian era dated from the Resurection ("ascension" - raf` - is used instead of "resurection" because Muslims believe Jesus did not die, and hence was not resurected, but ascended to Heaven directly - he will return, die a natural death and be resurected in the general resurection, according to Muslim belief; the Qur'an entitles Jesus as "the Messiah" but without its Christian or Jewish significance). The Arabic texts says  واما النصارى فبرفع عيسى المسيح عليه السلام wa-'ammā l-naṣārā fa-bi-raf`i `īsā~l-masīḥi `alayhi~l-salām "and as for the Christians {they date} by the ascension of Jesus the Messiah, peace be upon him".

Incidentally, Islam knows no New Years festival, at least traditionally. The Islamic New Year nowadays however, is a public holiday in Egypt, Lebanon, Jordan, Palestine, Syria, Iraq, Sudan, Morocco, Western Sahara, Mauritania, Yemen, Tunisia, Oman, Qatar, United Arab Emirates, Libya, Kuwait; among the non-Arab countries Djibouti (member of the Arab League), Iran, Senegal, Brunei and Indonisia. However, especially the Shiites gave the solar نوروز nawrōz >  nawrūz > navrūz , nowrūz (Iranian / Zoroastrian) at the spring equinox an Islamic coloration. It is also celebrated by current Turkic people (except in Turkey) and in Albania. Iraq, due to its Kurdish population, celebrates it as an official holiday in the Kurdish region, where it also has a national significance for the Kurds. it was also celebrated during Abbassid times, though marred by the collection of taxes. the Birth of the Prophet, مَوْلِدُ النَّبِيِّ mawlid al-nabiyy or مَوْلُودُ النَّبِيِّ mawlūd al-nabiyy is also a public holiday in many Islamic countries, Algeria, Morocco, Western Sahara, Mauritania, Yemen, Oman, Bahrain, Kuwait, United Arab Emirates, Libya, Tunisia, Sudan, Lebanon, Egypt, Jordan, Palestine, Syria and Iraq, and among the non-Arab countries Afghanistan, Iran (on a differnet day) Pakistan, Eritrea, Djibouti (member of the Arab League), Somalia (member of the Arab League), Mali, Niger, Nigeria, Senegal, Chad (Arabic an official language), Indonesia, Malaysia, and Brunei although some Islamic jurists have disapproved of it. In the Islamic legal code, Sharia, the only required days off from work are the Festival of Breaking the Fast عِيدُ الْفِطْرِ `īd al-fiṭr, after Ramaḍān, on 1 Shawwāl for three days and the Festival of Sacrifice عِيدُ الأَضْحَى `īd al-'aḍḥā on 10 Dhu ’l-Ḥijja for four days. These are the only holidays celebrated in Saudi Arabia, in addition to a solar National Day, which doubles as the New Year of its solar fiscal calendar. the Shia take a day off on 9 and 10 Muḥarram, though these are days of mourning. they also observe other holidays in connection with the Alids. 10 Muḥarram `āšūrā' عَاشُورَاءُ  is a holiday in Iran (Shia), Afghanistan, Algeria, Iraq (partly Shia), Lebanon (partly Shia), Libya, Bahrain (partly Shia), Somalia. It is mentioned in the Qur'an, and was a religious day before it became a day of mourning for al-Ḥusayn b. `Alī.
There is a tradition that the pagan Arabs had two days that were festivals, but no details are given. see "Muslim Festivals" by Hava Lazarus-Yafeh Numen, Vol. 25, Fasc. 1 (Apr., 1978), pp. 52-64. Stable URL: http://www.jstor.org/stable/3269678 

I think there was intercalation in pre-Islamic times and during much of the life of Muḥammad, and it was prohibited (but proabably there was a parallel practice of simply not declaring a month not sacred on occassion for practicle reasons, and both may have been known by the same name, as stated by one tradition) otherwise the Qur'anic statement that the year consists of 12 months does not make sense, i.e. there was an intercalary month. the Qur'an seems to imply that it was done one year and not another, but this phrase should not be taken too litteraly. From some traditions and a 19th cent. reconstruction, the intercalation seems to have been done every three years, apparently an obsolete Jewish custom, and this is supported by an extensive 19th cent. work on the subject. "Memoire Sur Le Calendrier Arabe Avant l'Islamisme" by A.M. Caussin de Perceval; J. Asiatique, April 1843. Translated into English as "Notes on the Arab Calendar Before Islam" in "Islamic Culture" vol 21, April 1947 (p. 135 - 153). He repeats his views in in his " Essai sur L'Histoire des Arabes avant L'Islamisme," tom. i. pp. 241-248 and 413-417. Paris, 1847.
The South Arabian calendars had an intercalated month and were proabably lunar, though scholars took some time to accept this.

M. Hamidullah in "The Nasi', the Hijrah Calendar and the Need of Preparing a New Concordance for the Hijrah and the Gregorian Years", Journal of the Pakistan Historical Society Vol XVI, Part 1, January 1968 says that there was intercalation of a month before the time given of the qalāmis, the "institution of the Nasī'" by the Kinānah tribe. this is based on al-'Azraqī. the Kindites had briefly formed a unified kingdom throughout much of Arabia. The transfer of the function was transfered to the qalāmis of the Kinānah is explained by al-'Azraqī, according to Hamidullah, by the marriage of Mālik Ibn Kinānah with the daughter of
Mu`āwiyah Ibn Thawr al-Kindī.

Caussin de Perceval points out that in South Arabia a luni-solar calendar was used. he points out that if a purely lunar calendar was in use by the tribes of the North and Central Peninsula, it would make a conflict of sacred months that one would be untenable, since the southern and northern tribes would be prevented from fighting at different times, leading to an untenable situation. that's persuasive, but not conclusive.
Caussin de Perceval takes a 3 year intercalation of a month (so in Mas`ūdī, Murūj al-Dhahab, Ch. 59, #1302):
 <<
... But the Jews adopted the 19 year cycle towards the end of the 4th century of the Christian era. That method was still new to them when, at the beginning of the 5th century after Christ, the embolismic system was introduced among the Arabs. Were the Medina Jews who had taught them and, being less advanced than those of Palestine, were accustomed like the other Jewish communities living away from Jerusalem to recieve from the doctors of that town the indication of the years when embolism was to be made, were those Jews then acquainted with 19 year theory and were able to communicate it to the Arabs together with the practice of intercalation? This is rather doubtful. ...
 This method must be the one pointed out by Abu'l-Fidā and Mas`ūdī, the first of Arab authors to treat this matter; I mean the addition of one month at the end of every third lunar year. This small cycle was one of those tried by the Greeks and the Jews. Its very imperfection gives a certain traditional touch to the evidence of Mas`ūdī and Abu'l-Fidā, for it can easily be seen that these historians took no trouble to verify its soundness: they seem to have naively accepted whatever tradition handed to them.
 >>

And he assumes that the 10 AH (the year it intercalation of a month was abolished) was to be an embolismic year. He also takes up the tradition that this was the 220th year since the institution of the Nasi:
 <<
 The year of the pilgrimage during which Muḥammad abolished the nasi, 10th year of the Hijra, is a starting point from which anterior Arab years can be determined. Muḥammad Jarkasī, al-Bīrūnī and Maqrīzī state that this 10th year of the Hijra was the 220th since the institution of the nasi. It does not seem likely that the 9th or 8th were embolismic years. Muḥammad having become Master of Mecca  in the year VIII maintained the functions called Ḥijāba and Siqāya and abolished all other functions of pagan origin, consequently that of the nasa'at. I believe, at all events, that the 10th of the Hijra should have been an embolismic year, but for Muḥammad's express interdiction. ...
 >>

Working back, he concludes that when the Nasi was instituted, 1 Muḥarram fell on Nov. 21, 412 CE. The pilgrimage season fell on Oct. 21, in the heart of autumn, what was considered the optimal time for it, as provisions were plentiful. de Perceval then compares the etymology of the months and finds it compatible with the climate of Makkah. But as the years progressed, the bad intercalation caused the meanings to be obsolete. Here is his reconstruction for the original year when the embolismic calendar was instituted:
 <<
Muḥarram                  from Nov. 21, 412 A.D. to December 21
Ṣafar                     from Dec. 21 412 A.D.  to Jan. 19, 413 A.D. 
Rabī` I (month of rain)   from Jan. 19.          to Feb. 18
Rabī` II (rain and        from Feb. 18           to March 19
 vegetation)                
Jumāda I (rain stops      from March 18          to April 18
 or becomes rare)             
Burckhardt1 states that the last showers in the Hijāz fell at the beginning of April, so the designations must have had a close connection with the climate of the Hijāz whence they were derived.
Jumāda II                 from April 18          to May 17             
Rajab                      "   May 17             " June 16
Sha`bān                    "   JUne 16            " July 15                 
Ramaḍān                    "   July 15            "  Aug. 14
Shawwāl                    "   Aug 14             " Sept. 12
Dhu'l-Qa`da                "   Sept. 12           " Oct. 12
Dhu'l-Ḥijja (month of      "   Oct. 12            " Nov. 10
 pilgrimage)
 The pilgrimage festival fell on Oct. 21, in the heart of autumn.
 This relation between the two calendars went on diverging year after year. However, for about 30 years, that is the space of one generation the divergence was not so wide as to render ridiculous the designation of the months with respect to the seasons. In the 34th year of the nasi when Muḥarram began on Oct. 18, 445 A.D. the two Rabī`, included within between Dec. 16 and Feb. 13, were always rainy months. Jumāda I (Feb. 13 to March 15) already began to part company with its own designation ; but Jumāda II (March 15 to April 13) still coincided with the tail-end of the rainy season ; and Ramaḍān (June 11 to July 11) was still a very hot month.
 Finally the connection between the months and the seasons ceased to exist. ...
 The date of the pilgrimage festival maintained itself rather longer within reasonable limits. In the 51st year of the nasi it fell very near autumn at the beginning of September, which is the fruit season in Arabia. The object in view had thus been attained during at least half a century. ...
1 Travels in Arabia, translated by Eyries, Vol II, p. 152
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thus Burnaby concludes:
 <<
Although the error, which amounted to 3d. 2h. 20m. 15s. at the end of every triennial period, caused the coincidence between the months and the seasons to grow less and less every year till at last such coincidence ceased to exist, yet the names of the months derived from the seasons were retained when the system of Intercalation was abolished by Muḥammad, and have, in fact, been retained to the present time.
 >>


The relevant passage in Mas`ūdī (d. 956 CE), Murūj al-Dhahab (947 CE), Ch. 59, #1302 is:
 <<
وقد كانت العرب في الجاهلية تكبس في كلّ ثلاث سنين شهرًا وتسمّيه النسيء وهو التأخير
Avant l'Islam, les Arabes intercalant un mois supplémentaire tous les 3 ans; s'est ce qu'ils nommaient nasî' ou le retardement.
 >>

wa-qad kānati~l-`arabu fi(:)~l-jāhiliyyati takbisu fī kulli *th*alā*th*i sinīna šahran wa-tusammīhi~n-nasī'a wa-huwa~t-ta'xīru
My translation:
And the Arabs, in the Time of Ignorance {Jāhiliyya}, intercalated a month every three years and they called it al-nasī', that is, retardation {al-ta'xīr}


The relevant passage in Abū-l-Fidā' (d. 1331 CE), Syrian prince, historian, and geographer, of the family of the Ayyūbids (Kurdish origin) is in his Al-Mukhtaṣar fī ta'rīkh al-bashar also known as Ta'rīkh Abī-l-Fidā', Ch. 5 section "Dhikr 'umam al-`arab wa-'aḥwālihim qabla-l-'islām" p. 154 of the Beirut 1997 edition:
وكانوا يكبسون في كل ثلاثة أعوام شهرًا
My translation:
and they {the Arab Nations before Islam} used to intercalate {yakbisūna} a month every three years
Daniel Martin Varisco "Islamic Folk Astronomy" in "Astronomy Across Cultures - The History of Non-Western Astronomy" (H. Selin ed.) accepts this. for the "Islamic Lunar Calendar" he says:
 <<
 The month names are derived from a Pre-Islamic Arabic Calendar, which added an intercalary month called nasī' every third year to bring the months in line with the seasons. This intercalation, which was supposedly derived from the Jewish calendar, was forbidden in Quran (9:37). The standard etymologies reflect Bedouin seasonal interests, ...
 The Arabs began their lunar calendar in anticipation of the autumn rain rather than according to a specific astronomical event such as the equinox. ...
 >>
A. M. Caussin de Perceval constructs a table of the ancient Arab Calendar based on his conclusions. he then looks at some events in history and tradition to see if it is compatible with his reconstruction. one particular instance he looks at is a passage in Procopius," De Bello Persico," lib. ii. cap. xvi. In that year Belisarius was sent to defend the eastern portion of the Roman Empire against the attacks of Chosroes (or Nushirvan), King of Persia. He was encamped with his army beyond the Euphrates, within six miles of the City of Nisibis.
 <<
 Procopius who tells us1 at a meeting of the Roman Generals convened at Dara by Belisarius, at 541 A.D., to discuss a plan of campaign, two officers who commanded a corps formed of Syrian troops declared that they could not march with the main army against the town of Nisibius, alleging that their abscence would leave Syria and Phoenicia an easy prey to the raids of the Almondar Arabs (al-Mundhir III). Belisarius showed these two officers that their fears were groundless, because they were nearing the summer solstice, a time when the pagan Arabs used to devote to the practice of their religion, abstaining from any bellicose act whatsoever.
 Evidently this refers to the time of pilgrimage, for it was the only time of the year when the Arabs had two consecutive holy months ; in fact there may have been three: Dhu'l-Qa`da, Dhu'l-Ḥijja and Muḥarram. The pilgrimage held in the 129th year of the nasi (according to the above table) fell in fact, on June 22, 451 A.D., precisely at the summer solstice.
 So we are in the possession of three quasi-certain data : the pilgrimage was timed to take place in autumn, about 413 A.D.; at the summer solstice, in 541 ; at the beginning of spring in 632. These data concur exactly with the hypothesis of the constant and regular use of triennial embolism, as shown in the table ; this opinion appears highly probable and conformable to reality. As a consequence some change must be made concerning the calculation, up to now considered as purely lunar years. However, this change implies a difference of a few months and concerns only the first 7 years. I have already stated why I think that intercalation, expressly abolished in the 10th year, was praciced neither in the 9th nor in the 8th.
 To verify my conjectures and check my table of correspondence, I have looked up among Arab historical documents, especially during the first 7 years of the Hijra, those containing any mention of temperature, together with the date and month (Arab). I found only two of the kind.
 In the very year of the Hijra, Muḥammad arrived at Medina in the middle of Rabī` I ; the heat was then *very inconvenient*.2 From the table, the middle of Rabī` I coincides with the first days in July.
 In the 5th year of the Hijra, an army of allied tribes was beseaging Madina in the month of Shawwāl had much to endure from the cold and the inclemency of the weather.3 From the table, that month of Shawwāl covers the period from Jan. 23 to Feb. 22.
 Thus the historical evidence confirms the new concordance which I am putting forward between the first years of the Hijra and the Christian Era. In conclusion I shall now give a brief summary of these notes on the Arab calendar.
 The present names of the Arab months were adopted more than two centuries before the Hijra, along with the triennial embolismic system aiming at maintaining the pilgrimage in autumn. This aim was frustrated by the incorrect method of calculation used. When no embolism was resorted to, the pagan Arabs to avoid having two consecutive holy months, sometimes transferred the privilage of Muḥarram to Ṣafar. The word nasi, whose proper meaning is retardation, also meant the intercalary month and the retardation of Muḥarram, either through embolism or the postponment of the observance of that month to the following month. Muḥammad abolished both these practices in 632 A.D., the 10th year of the Hijra.
 One can easily imagine that since the pilgrimage no longer coincided with the season originally selected as the most favorable for that purpose, embolism was but a vain and useless practice that Muhammad could well abolish without let or hinderance.
1. De bells Persico, lib II, cap. XVI.
2. Sīrat ar-Rasūl, fol. 84
3. Ibid., fol. 179
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[The English text contains typos, it's 541 AD not 451, it's De bello Persico not De bells Persico etc.}
Acc. to "The Islamic Jewish Calendar" By Ben Abrahamson and Joseph Katz (this article goes too far, and assigns a Jewish origin for many Islamic observances)
http://www.alsadiqin.org/history/The%20Islamic%20Jewish%20Calendar.pdf
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 The summer solstice June 21, 541 CE would have fallen on 10th of Jumaada al-Thaani according to the strictly Lunar Calendar now in Islamic use, six months too early for the Hajj pilgrimage. This means that intercalation must have been in use in the years before the Prophet. If we assume the Jewish intercalation currently used, the solstice would have fallen on Dhu al-Qa'dah (Tammuz) – the first of the "two months". If we assume a simple 3 year intercalation the solstice would have fallen on 10th of Dhu al-Hijjah, the correct date.
 >>
Caussin de Perceval takes the summer solstice for that time as June 22, Mahmoud Effendi takes it as June 10, (which would be the astronomical summer solstice for the 19th century in the Julian calendar) and hence concluded that this was an error. those who argue for no intercalation argue that the Lakhmids of southern Iraq had different dates for holy months. Mahmoud argues that it was the month of Rajab that was refered to, and that "2 months" was an error for "1 month". but then again, he is off somewhat, for it does not fall on the summer solstice. some argue that "two months" meant that the abstention from fighting was for a lunar month overlaping two solar months. for the arguments, see "Elements of the Jewish and Muhammadan calendars : with rules and tables and explanatory notes on the Julian and Gregorian calendars" (1901), by Rev. Sherrard Beaumont Burnaby. the whole book is archived on the net, a very big download:
http://www.archive.org/details/elementsofjewish00burnuoft
Caussin de Perceval calculates 1 Muḥrram 1AH to be Monday, April 10, 622
OTOH Mahmoud endeavours to fix the Julian dates of the death of Ibrahim, the infant son of the Prophet ; the day of Muhammad's entry into Medina after the flight from Mecca ; the date of his birth ; and the Arabian dates corresponding to those of the Lunar Eclipse which occurred on November 20, A.D. 625, and of the Summer Solstice, June 20, A.D. 541. He thus brings up to five the number of epochs upon which he grounds his researches.

One bone of contention between de Perceval and Mahmoud is the arrival of Muhammad in Madina. Mahmoud goes to the traditions that place the arrival of Muhammad to Madina on the day of Jewish fasting, identified by most as Yom Kippur. There is the tradition of the fast of 3āšūrā' عَاشُورَاءُ on the 10th of Muḥarram (in the Qur'an, before it became associated with the Shiite day of mourning). It is an arabized version of Hebrew עָשׂוֹר i.e. 3Aśōr (with the correct etymologization to Arabic šin, ś was pronounced [s] at the time) "tenth" (Lev.16:29) with the Aramaic determinative -ā . It suggests the day of Yom Kippur, though there is still doubt that the days were in synch with the calendar used by the Jews (but the Jews of Medina may have used a poorly intercalated calendar similar to that of the other Arabs). Biruni says that when the Arabs saw a fast of the Jews in their tenth of the first month, the Arabs chose fast in theirs. the islamic traditions link it to Muhammad's arrival in Medina, but scholars, western and some muslims doubt it, as it may not coincide in any way with the traditions about the dates of Muhammad's arrival in Medina. there are also Islamic traditions linking Ashura to the Jews, and even a tradition linking it to the forgiveness of sins. OTOH the tradition linking Ashura to the Jews says that it was the day the Children of Israel were saved from their enemies, suggesting to some to speculate to link it with Passover, though most sources regard it as refering to Yom Kippur. here are the two traditions:
http://www.usc.edu/schools/college/crcc/engagement/resources/texts/muslim/hadith/bukhari/031.sbt.html#003.031.222
http://tinyurl.com/yb842k9
Bukhari:

Volume 3, Book 31, Number 222:

Narrated Ibn 'Abbas:
The Prophet came to Medina and saw the Jews fasting on the day of Ashura. He asked them about that. They replied, "This is a good day, the day on which Allah rescued Bani Israel from their enemy. So, Moses fasted this day." The Prophet said, "We have more claim over Moses than you." So, the Prophet fasted on that day and ordered (the Muslims) to fast (on that day).
http://www.usc.edu/schools/college/crcc/engagement/resources/texts/muslim/hadith/muslim/006.smt.html
http://tinyurl.com/ye8lg5m

Muslim:
Book 006, Number 2602:
Abu Qatada reported that a person came to the Apostle of Allah (may peace be upon him) and said: How do you observe fast? ... and I seek from Allah that fasting on the day of Ashura may atone for the sins of the preceding year.

http://www.forsanelhaq.com/en/showthread.php?t=88603
The Prophet (peace and blessings be upon him) said, "Fasting the day of `Ashura' (is of great merits), I hope that Allah will accept it as an expiation for (the sins committed in) the previous year" (Muslim). 

Bīrūnī mentions the possibilty of the connection between Yom Kippur and Ashura.

Also according to Enc. of Islam II "`Āshūrā"
 <<
Presumably for the sake of distinguishing themselves from the Jews some fixed the 9th Muḥarram either along with or in place of the tenth as a fast day with the name Tāsū`ā'.
 >>
{i.e. تَاسُوعَاءُ }.
Using a non-intercalated calendar, Mahmoud concludes from that tradition that it was 8th Rabī` al-'Awwal because this was a Monday (other dates are found in other traditions), as tradition says. and this did indeed corresponds to 10th Tishri (based on astronomical calculations). but Bīrūnī says this tradition is not sound, as it describes a different Jewish holy day, that of Moses being saved. so the tradition about Muhammad entering Madina on Yom Kippur is flawed, and hence may have been fabricated later, those who support an embolism for the pre-Islamic calendar argue. It may be that those who wrote the biography of Muhammad much later, may have doctored the dates to fit a non-embolismic calendar. a comment about temperature, on the other hand, may have escaped them. at any rate, the Arabs did not use the Jewish calendar, and traditions assert that the covering of the Ka`ba was changed on that day, the day being determined by a Jew. Then it seems that the Muslims fixed `Āshūrā' on the 10th of their own first month, i.e. 10th of al-Muḥarram. IMO if one is to accept de Perceval, one could argue that the setting of Muhammad's arrival in Medina on Yom Kippur is a rhetorical device, it was just one of the things that was impressive during his early months. as J. McKeithen points out in his doctoral thesis on Ibn Faḍlān's travelogue to Volga Bulgharia, he places the observation of the short winter days in the first and second days of his stay, even though he arrived there in May. The footnote #283 on p. 97 based on Czegledy's comments that he is employing a narrative device whereby he situates the most important points in a convenient spot in the story.
Mahmoud considers the fact that `Āshūrā' was not fixed in the Arab calendar (else why would Muhammad ask what day it was? plus the fact that the covering of the Ka`bah was determined by a Jew) as evidence that the Jewish calendar was luni-solar and that the Arab calendar purely lunar. But this could also result from the fact that the Arab calendar had a different (and faulty) method of intercalation.
Ibn 'Iṣḥāq and Ṭabarī place Muḥammad's arrival in Madīnah at 12 Rabī` al-'Awwal 1 AH on a Monday, whereas that day was a Friday  (24 Sept. 622 CE) if there was no intercalation. in the scheme of intercalation proposed by M. Hamidullah, in "The Nasi', the Hijrah Calendar and the Need of Preparing a New Concordance for the Hijrah and the Gregorian Years", Journal of the Pakistan Historical Society Vol XVI, Part 1, January 1968, 12 Rabī` al-'Awwal 1 AH falls on a Monday (31 May 622). his proposed intercaltion is an accurate one, every three years, but on occassion a supplementary intercalation.
12 Rabī` al-'Awwal on a Monday is given as the Prophet's death and his birth as well, so I am suspicous of it. however, it must be said that in Hamidullah's calculations, all do in fact fallon a Monday, provided that the year of his birth is taken as 569 CE. Hamidullah claims to have matched the days of the week to all traditional sources (although they do not always agree). of course, the sources may have been a reworking just acoording to this scheme, which was that of al-Bīrūnī. however, the arivval of Muhammad in Medina would not correspond to Jewish Yom Kippur.


The problem of the date of the Hijrah is discussed in detail in two articles:
F.A. Shamsi "The Date of Hijrah" Islamic Studies, Vol. 23, No. 3 (Autumn 1984), pp. 189-224
and a follow up
F.A. Shamsi "The Date of Hijrah" Islamic Studies, Vol. 23, No. 4 (Winter 1984), pp. 289-323
also
F.A. Shamsi "Three Proposed Arabian Calendars with Special Reference to the date of the Hijrah"  The Islamic Quarterly Vol 32, Third Quarter 1988 p. 139-172

F.A. Shamsi concludes:
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It may here be mentioned that if we accept that 12 Rabi' al-Awwal 1 A.H. was a Monday, this incompatibility between the reported day of the week and the date would not be a unique instance regarding events in the life of the Prophet. Days and dates reported of such important events as the Battle of Badr (Friday 17 Ramadan 2 A.H.), the Battle of Uhud (Saturday 11 or 15 Shawwal 3 A.H.), and the Conquest of Mecca (Friday 20 Ramadan 8 A.H.) are incompatible with each other in the Hijrah Calendar.5 And this is not the only kind of chronological problem infesting reports regarding dates of events in the life of the Prophet.6 Hence, scholars have come to assume that many of the reported dates belong to a luni-solar calendar then in vogue in Arabia, for, we have considerable evidence to show that the Arabs used to have a luni-solar calendar. It will involve a great digression to go into this question. Hence, we shall content ourselves here with stating that, according to one view (originated probably by Silvestre de Sacy7 and accepted by Winckler8 and Moulvi Ishaq al-Nabi9), at the time of Hijrah and till 9. A.H. the Arabs used to have two calenders, a purely lunar one (among the Meccans according to de Sacy and among the Medinese Arabs accordings to Moulvi Ishaq al Nabi) and a luni-solar one (among the Medinese according to de Sacy, and among the Meccans and other Arabs according to Moulvi Ishaq al-Nabi), and, according to another view, viz., that of Dr. Hashim Amir Ali, the pre-Islamic Arabs used to have a luni-solar calendar which continued to be in use during the lifetime of the Prophet, and that during the caliphate of Hazrat 'Umar, in 17 or 18 A.H., when the Hijrah era was adopted, it was further decided to take the lunar calendar backwards to the year of Hijrah by removing those intercalary months from the pre-Islamic calendar which had been intercalated after the migration of the Prophet.10 I regard Dr. Hashim Amir Ali's view as the correct one, except that I believe that when the pre-Islamic Arabian Calendar was abolished in (what be came) Ramadan 8.A.H. in pursuance of the command contained in Verses 9 : 36-37, the pre-Islamic Arabian calendar was recast into the lunar mould ab initio.
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Since nasī' turns out to mean retardation or postponemnet, I doubt that Muhammad would have rearranged the months. I also doubt that the Meccan calendar and the Medinan one would have been different as the calendar was meant to regulate intertribal activity such as months of truce and a collective pilgrimage.

As regards to the Battle of Uhud in Shawwāl, placed in winter by Perceval, Shamsi cites poem that the battle took place under the sign of Aries (where jamal "camel" is emended to Ḥamal). of course, the poem could be a later interpolation.
one tradition that Mahmoud Effendi relates is to the death of Muhammad's infant son Ibrahim in 10 AH. but that year no embolism took place, according to the view of de Perceval. So that tradition does not deny
or confirm the existence of an embolism. there was  solar eclipse when Ibrahim died, acc. to tradition. this occured on Jan. 27, 632 CE. and it was on 29 Shawwāl 10 AH, but this is dependent on the age of Ibrahim when he died, which is disputed by the traditonal accounts. the the others concern the reports about the birth of Muhammad, Mahmoud calculating 571 CE, based on the tradition that it occured after a conjunction of Jupiter and Saturn in Scorpio, in Mahmoud's calculations, March 29th or 30th, 571 CE and Muhammad was born on a Monday in Rabī` al-'Awwal. so according to Mahmoud, Muhammad was born on 9 Rabī` al-'Awwal, corresponding to April 20  CE. but it is not clear that this is the conjunction reffered to, acc. to some sources. but this might be a fabrication to give Muhammad's birth astrological significance, IMHO. instead the traditional date is Monday, August 20, 570 CE; so (assuming no intercalation). Muhammad's Birthday is traditionally celebrated on 12 Rabī` al-'Awwal; on the 17th by Shia's, harmonizing it with that of Imam Ja`far (so celebrated in Iran; Iraq uses the Sunni date). but these are not reliable, as there are many traditions concerning this. in fact, some well known conservative religious muslim scholars condemned the pratice of celebrating the birth of Muhammad (Mawlid). from Conrad:

"Abraha and Muḥammad: Some Observations Apropos of Chronology and Literary "topoi" in the Early Arabic Historical Tradition" by Lawrence I. Conrad, Bulletin of the School of Oriental and African Studies, University of London, Vol. 50, No. 2 (1987), pp. 225-240
Stable URL: http://www.jstor.org/stable/617116

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  Various aspects of this material, to which I shall return below, are debatable; but in general it does not seem possible to uphold against it any argument placing Abraha's expedition in A.D. 570. This traditional and still very widespread view is further undermined by another consideration of some importance. While it is true that medieval Islam soon came to regard the birth of the Prophet Muḥammad in the Year of the Elephant as having occurred forty years before the beginning of his mission, and to compute dates and ages at various other points in his biography accordingly,20 it is not likely that the earlier authorities following his activities had such chronological precision in mind. The Arabian society in which Islam arose had only a vague and often confused notion of time. Chronology was reckoned according to a great event of the recent past: when that event was overshadowed by another, the old chronology was abandoned and a new one begun.21 It was, in other words, difficult to maintain any continuous system of reference to time. The South Arabian kingdoms did establish their own continuous dating systems, but modern investigations demonstrate that even there a great deal of ambiguity and imprecision prevailed.22
...
  The same ambiguity applied to the ages of individuals, which were known only in a very general sense. Birth dates in particular were almost never fixed with any accuracy, largely because so little attention was paid to them. One's date of birth was an insignificant and difficult to determine item of information, and was so lacking in social relevance that most individuals had only a vague idea of when they had been born. Even later, when the Hijra calendar made continuous uniform dating possible, birth dates for even eminent persons remained for the most part unknown.25 This situation did change with the passage of time,26 but it is worth noting that the umma for centuries even resisted the tendency to regard the date of the Prophet's birth as an occasion for special commemoration. The mawlid al-nabī festival evolved only in later medieval times, and among conservative `ulamā' it was still then staunchly opposed. The Ḥanbalite Ibn Taymīya (d. 728/1328), for example, condemned the mawlid on the grounds that authorities disagreed on the date of the Prophet's birth, that the festival was an imitation of the Christians' Christmas, and that the early Muslims (al-salaf) neither commended nor observed it.27
21 See A. A. Duri, The rise of historical writing among the Arabs, ed. and tr. Lawrence I. Conrad
(Princeton, 1983), 14-20.
22 See Beeston, Epigraphic South Arabian calendars and dating.

27 Ibn Taymīya, Majmū`a fatāwā...Ibn Taymīya (Cairo, A.H. 1326-29), I, 312: 1-10, no. 230; idem, Kitāb iqtiḍā' al-Ṣirāt al-mustaqīm mukhālafat aṢḥāb al-jahīm (Cairo, 1325/1907), 141: 1-142: 4. Cf. also the study of Eugen Mittwoch, 'Muḥammeds Geburts- und Todestag', Islamica, 2, 1926, 397-401. This was of course not the prevailing attitude at this time. Muḥammad ibn Muḥammad al-Jazarī (d. 833/1429), for example, came to Mecca on pilgrimage in 792/1390 and found the mawlid to be the town's most lavishly celebrated festival. See his `Urf al-ta`rīf bi-'l-mawlid al-sharīf, Al-Maktaba al-Khālidīya (Jerusalem), unnumbered MS, fol. 6v: 3-6.
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Kister's article may be found in:
http://www.kister.huji.ac.il/sites/default/files/Huluban_0.pdf
It should be noted that Muhammad's traditional birthday is the same as his death, 12 Rabī` al-Awwal 11 AH, a Monday (though this does not figure as a Monday in all the algorthms). It is also said that he was born on a Monday as well. traditions say that the time of his death was known, so it is likely that his birthday was fabricated according to this. It should be noted that Shiah sources place his death on 28th Ṣafar 11 AH (25th May 632 CE).

from Burnaby, quoting Mahmoud Effendi:
 <<
In the first volume of "al-Sîrat-al-ḥalabîyah,* we read as follows: "Kotâdah states that the prophet said,' Monday is the day on which I was born.' Ibn-Bakkâr and Ibn-'Asâkir say that the birth took place at the break of day. Sa`îd ibn Musaiyib reports that the prophet was born in the middle of the day. This day was the twelfth of Rabî`u-1-avval, and was in the spring-time. The night before the twelfth is adopted generally in the cities, and at Mecca in particular, especially when the people wish to visit the place of his birth. Others say that he was born on the tenth of the month, and Historians assert that it was on the eighth."
According to these three opinions Muḥammad was born on the 8th, 10th, or 12th of Rabî`u-1-avval.
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al-Ṭabarī admits various traditons as to the age of Muḥammad at the time of his death.
also:
Henri Lammens, L'Âge de Mahomet et la chronologie de la sīra', Journal Asiatique, 10th Series, 17, 1911, 209-50.

Translation as it appears in "the Quest for the Historical Muhammad" by Ibn Warraq
Henri Lammens "The Age of Muhammad and the Chronology of the Sira" Journal Asiatique (March - April 1911), p. 209-250)

 <<
 To add to the confusion, tradition hesitates when it dares to specify the exact relation between the date of the Elephant and the birth of Muhammad. An anonymous synopsis of the sira sums up the diverse opinions thus: "The Prophet is supposed to have been born that very year, fifty days or two months after the departure of the Elephant, or even ten, fifteen, or even twenty years later." Fayyumi also mentions an opinion that admits of a ten-year interval between the two events. That gives us considerable latitude.
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Here is what Enc. of Islam II "Muḥammad" says:
 <<
 Muḥammad , the Prophet of Islam .
...
B. Muḥammad in Mecca
1. His early life
The very first question a biographer has to ask, namely when the person was born, cannot be answered precisely for Muḥammad. We have no certain chronological data for the Meccan period of his life. His activity in Medina covered approximately ten years, from the Hidjra [q.v.] in 622 A.D. until his death in 632. Most of the sources say his activity as a prophet in Mecca also lasted ten years, but there is considerable difference of opinion on this question. A statement in a poem ascribed sometimes to Abū Ḳays b. Abī Anas and sometimes to Ḥassān b. Thābit (ed. Hirschfeld, no. 19) says that his prophetic activity in Mecca lasted “ten and some years”. Muḥammad's biographers usually make him 40 or sometimes 43 years old at the time of his call to be a prophet, which, taken with the statements on the length of the Meccan and Medinan periods of his prophetic activity and his age at the time of his death, would put the year of his birth at about 570 A.D. When, however, tradition says that he was born in the “Year of the Elephant” (alluded to in sūra CV) this cannot be accepted, since Abraha's attack on Mecca must have taken place considerably before 570. There is better reason to believe that he may have been born later in the 570s. Since the traditional accounts differ widely and also contain elements that are clearly based on later legend, it is best to leave open the question of the year of Muḥammad's birth. For the period of his life before he came forth as a religious reformer the Ḳur'ān has only the indefinite expression `umr, in sūra X, 16: “I lived among you an `umr before it”, where the term is usually interpreted “a lifetime” and could just as well mean 35 as 40 or 43 years.

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http://www.quranexplorer.com/quran
Dr. Pickthall
Yunus
Say: If Allah had so willed I should not have recited it to you nor would He have made it known to you. I dwelt among you a whole lifetime before it (came to me). Have ye then no sense? (16)
سُوۡرَةُ یُونس
قُل لَّوۡ شَآءَ ٱللَّهُ مَا تَلَوۡتُهُ ۥ عَلَيۡڪُمۡ وَلَآ أَدۡرَٮٰكُم بِهِۦ‌ۖ فَقَدۡ لَبِثۡتُ فِيڪُمۡ عُمُرً۬ا مِّن قَبۡلِهِۦۤ‌ۚ أَفَلَا تَعۡقِلُونَ
(١٦)

The Meccans used to count the era from momentous events, in this case the "Year of the Elephant" عَامُ الفِيلِ `Āmu~l-Fīl, an expedition of Abraha, an Ethiopian ruler of Yemen, who waged an unsuccesful campaign against Makkah, according to traditon using an elephant (tradionally this provides the background for surah 105, "Surah of the Elephant" سُورَةُ الفِيلِ  al-Fīl, where a disaster befell from God to the "Companions of the Elephant أصحاب الفيل 'aṣḥāb al-Fīl). Traditionally Muhammad was born on the Year of the Elephant, but there are other traditions placing it various years after this era, including one by Ibn al-Kalbī (737 AD - 819 AD/204 AH) that says it is 23 years (apparently related also independently by Shu`ayb ibn Isḥāq (d. 189/805)). A Sabaic inscription in the "Well of Murayghan", Bi'r Muray*gh*ān بئر مريغان (Ry 506) (see: "The campaign of Ḥulubān - A New Light on the Expedition of Abraha" M.J. Kister, Le Muséon, LXXVIII, no. 3-4, p. 423-436) (1965)) discussing a campaign to the direction of Makkah has been found and dated to 552 CE. Makkah is not mentioned by name in the inscription, but it merely says that one branch of the returned with success. maybe the Meccans considered this a victory. it is summarised by Conrad thus: << The Murayghan inscription discovered by Ryckmans describes a campaign in which a part of the army of Abraha operating in the Hijaz defeated the confederation of the `Āmir ibn Ṣa`ṣa`a at Turaba, only 100 km. east of al-Ṭā'if >>. Turaba تربة is given as <trbn> *turabān (-(ā)n being the Sabaic definite article). al-Ṭā'if الطائف is another 100 km (60 miles) SE of Makkah مكّة . Unlike the traditional account of "the Elephant" Abraha did not command this branch of the campaign himself. the inscription cannot be later than 554 CE, as it mentions the Arab Lakhmid (S. Iraq) king al-Mundhir III (mentioned by Procopius above) who died at 554 CE. Kister mentions Ḥulubān being involved in Abraha's campaign that led to the Year of Elephant. It could be that in this campaign there was an attempt to capture Makkah which was unsuccesful and hence was not mentioned in the inscription.
The inscription is found in:
http://www.mnh.si.edu/EPIGRAPHY/e_pre-islamic/fig04_sabaean_img.htm
Finally Conrad, quoting from Kister give the following tradition, from Ibn Shihāb al-Zuhrī, d. 742 CE, a significant Muslim traditionalist, which involves minor personages and thus is less likely to be fabricated (fīl فيل means "elephant", as it is alledged that Abraha had an elephant in his expedition, `ām عام is "year", ḥarb حرب is "battle, war", sīra سيرة is "biography", lit. "way of going", here, that of Muḥammad, mab`ath مبعث is "awakening", "sending" i.e. Muḥammad's "call" to prophethood, 'ayyām أيّام is "days"; short for 'ayyām al`arab أيّام العرب "the Days of the Arabs", the account of pre-Islamic battles of the Arabs amongst themselves, each battle being designated "the day of ..."). from Conrad:

 <<

For the study of the sīra and early Islamic history, dating the Expedition of the Elephant to 552 clearly has important implications. These merit further consideration but can be mentioned only briefly here. Pushing `Ām al-fīl back two decades would obviously mean that if it can yet be demonstrated that Muḥammad was born in that year, then he was already close to 60 years old at the time of the first revelations in Mecca, and hence far older at the time of his death in 11/632 than is stated in the traditional accounts, most of which hinge on the literal interpretation of the symbolic age of forty for the beginning of his career. This cannot be dismissed as impossible, but seems unlikely in light of the numerous reports, collected by Lammens, indicating that Muḥammad died at an age considerably younger, not older, than the traditional chronology allows.90 Hence it would be useful to investigate further the accounts providing other alternatives for the birth date of Muḥammad.
  Such an investigation may not, however, do more than demonstrate that the enormously complex undertaking of sorting out pre-Hijra sīra chronology is an impossible task. The extent and depth of our uncertainty can be discerned even in the apparently well-founded dating, based upon the investigations of Beeston and Kister, of the Expedition of the Elephant. Here we must look more closely at the evidence adduced by Kister, a report transmitted on the authority of the renowned early traditionist and historian al-Zuhri.91 The text is as follows: 92

Quraysh counted, before the chronology of the Prophet, from the time of the Elephant. Between the Elephant and the (battle of the) Fijār they counted 40 years. Between the Fijār and the death of Hishām ibn al-Mughīra they counted six years. Between the death of Hishām and the building of the Ka`ba they counted nine years. Between the building of the Ka`ba and the departure of the Prophet for Medīna (i.e., the Hijra-K.) they counted 15 years; he stayed five years ( of these 15) not receiving the revelation. Then the counting (of the usual chronology) was as follows.

  The problem is clear: what are we to make of the '40 years' between the Expedition of the Elephant and the Ḥarb al-Fijār-accept it as proper chronological evidence, or dismiss it as a topos?
  In many such cases no answer can be given. But here we are more fortunate. As Kister observes, this report passes over in silence the question of Muḥammad's birth date. This suggests that it predates this issue's rise to prominence, and hence that it is very early. Such a conclusion is further reinforced by the fact that the report appears to predate the emergence of another early and important question-that of the Prophet's participation in the Ḥarb al-Fijār. The extant sīra and ayyām sources show a special concern for the time of this conflict, which is usually said to have occurred when Muḥammad was 14 years old,although 15, 20, and 28 are also ages given.93 But this is all embellishment that calculates on the basis of the topos of 'forty' for the Prophet's age at the mab`ath. ...
90 See Lammens, 'L'Âge de Mahomet', pp. 231-9. It is at least worth noting that according to the thirteenth-century Byzantine polemist Bartholomaios of Edessa, Muḥammad was 32 at the time of the first revelations and spent 15 years preaching the new faith before his death: i.e., he died at the age of 47. See his Elegchos Agafenou, ed. J.-P. Migne in his Patrologia Graeca, CIV (Paris, 1860), col. 1388 A-B, D. It is unfortunately impossible to determine whether these statements are based on reliable early sources, on the one hand, or baseless anti-Islamic slander, on the other.
91 See Duri, Historical writing, 27-30, 95-121, and the further works cited therein.
92 Kister's translation and glosses. See his ' The campaign of Ḥulubān ', 427.
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The Arabic of the quote is as follows:
حَدَّثَنَا الزُّبَيْرُ قَالَ : وَحَدَّثَنِي عُمَرُ بْنُ أَبِي بَكْرٍ الْمُؤَمِّلِيُّ عَنْ زَكَرِيَّا بْنِ أَبِي عِيسَى عَنِ ابْنِ شِهابٍ أَنَّ قُرَيْشًا كَانَتْ تَعُدُّ قَبْلَ رَسُولِ اللهِ صلعم مِنْ زَمَنِ الْفِيلِ. كَانُوا يَعُدُّونَ بَيْنَ الْفِيلَ وَبَيْنَ الْفِجَارِ أَرْبَعِينَ سَنَةً. وَكَانُوا يَعُدُّونَ بَيْنَ وَفَاةِ هِشَامِ بْنِ الْمُغِيرَةِ سِتَّ سِنِينَ . وَكَانُوا يَعُدُّونَ بَيْنَ بُنْيَانِ الْكَعْبَةِ وَبَيْنَ أَنْ خَرَجَ رَسُولِ اللهِ  صلعم إِلَى الْمَدِينَةِ خَمْسَ عَشْرَةَ سَنَةً. ثُمَّ كَانَ الْعَدَدُ يُعَدُّ

It is recorded by al-Zubayr b. Bakkār in his "Nasab Quraysh" and is quoted by Ibn `Asākir's "Ta'rikh madīnat Dimashq", in the last one without the chain of authorities.

Fijār فِجَارٌ  means (along with some other meanings) "sacrilege" and it refers to the war fought in the forbidden months, when fighting was forbidden. taking the Hijra as 622 CE (established by the papyrus) one gets 552 CE for the Year of the Elephant, exactly as the inscription is dated. That leads credence to the tradition that Muḥammad was born 23 years after this, at 575 CE, or to the tradition cited by Lammens that places it 20 years after, making it 572 CE. It discredits the statement that Muḥammad recieved the revelation at forty, but this, as Conrad shows, was a topos, a rhetorical convention or formula. "forty" was used in place of "many"and the age of forty was considered the ideal age of maturity (so in the Qur'ān 46:15, in al'aḥqāf). the Battle of Fijār, حَرْبُ الفِجَارِ  ḥarb al-Fijār is another event the Meccans used to date from. Conrad is even suspicious of the statement that there was forty years between the Year of the elephant and the battle of the Fijār. Abraha is reckoned to have died soon after 553 CE. the Murayghan inscription is one of the last; after it comes an inscription dated 553 CE concerning repairwork of the Ma'rib dam, with Abraha mentioned, and hence it is difficult to place a second expedition around 570 CE, when Yemeni power in general declined. nevertheless many contemporary muslim historians refuse to accept that the campaign described in the inscription refers to the "Year of the Elephant". But Ethiopian rule in Yemen came to an end around 570 CE, so maybe that's the confusion. I noticed that Bīrūnī says that Muḥammad was born 50 years after the invasion of the Abyssinians. "Events in Arabia in the 6th Century A. D." Sidney Smith, BSOAS Vol. 16, No. 3 (1954) says that << The year the nagaši invaded and defeated Dhu Nuwās is known from Syriac texts, 525.>> Dhū Nuwās was a Ḥimyarite king of Yemen, the nagaši are the Ethiopians, so that also puts Muḥammad's birth at 575. OTOH there are many traditions that put his birth at 571 or 572. accepting both an early date for the Year of Elpehant and accepting Muḥammad's birth as in the Year of the Elephant is problematical from a muslim theological viewpoint as it would make Muḥammad's participation in the sacrilegious war when he was a fully mature adult.
The traditionally accepted chronology is given by al-Ṭabarī, The History of al-al-Ṭabarī = Ta'rīkh al-rusul wa’l-mulūk {History of Prophets and Kings} v. 6 (SUNY series in Near Eastern studies) (Bibliotheca Persica) translated and annotated by W. Montgomery Watt and M. V. McDonald:
 <<
 As for the Quraysh among the Arabs, the latest epoch which I have been able to establish as being used by them in computing dates before the emigration of the Prophet from Mecca to al-Madīnah is that of the Year of the Elephant, which is the year in which the Messenger of God was born. There were twenty years between the Year of the Elephant and the Sacrilegious War, fifteen years between the Sacrilegious War and the rebuilding of the Ka`bah, and five years between the rebuilding of the Ka`bah and the beginning of the Prophet's mission.
 >>
there is a difference of twenty years between al-Zuhrī's account of the interval between the Year of the Elephant and the the Sacrilegious War (ḥarb al-Fijār) and al-Ṭabarī's account. 
an article in arabic opposing the identification of the inscription with the Year of the Elephant is:
http://www.kau.edu.sa/centers/spc/jkau/Data2/Review_Artical.aspx?No=1734
"The Murayghan Inscription Ascribed to Abraha, Does it Record the Expedition of the Elephant?", ABDUL MONEM ABDUL HALEEM SAYED, Journal of King Abdul Aziz University. Arts and Humanities . Volume No : 3 , Issue 1 , 1990 .
he aslo wrote an article in "Procceeding of the Seminar for Arabian Studies" Vol 18 (1988)
"Emendations to the Bir Murayghan Inscription Ry 506 and a New Minor Inscription There"
http://www.jstor.org/stable/41223072
basically his argument is traditional. the inscription describes a victory, not a defeat, Muḥammad was born in the Year of the Elephant etc..This is in accord with the observations of C. Robin. It does give some information on the tribes mentioned and as I understand does some minor emendations on the reading. he calls the language "Ḥimyari" (as was traditional among medieval arabs; though it is correct that the population and previous dynasty was Ḥimyari, the language of the inscription is Sabaic), not Sabaic etc.. he identifies the main theater of operations, Ḥulubān / Ḥalibān حلبان , Sabaic <Ḥlbn> in Central Arabia (as do most proponents of the theory that it represents the Year of the Elephant), not in the Yemen. this town or region exists in the works of medieval geographers, though about 276 miles north of the well is a small town, Ḥalibān, which is identified as the theater of operations by Sidney Smith in "Events in Arabia in the 6th Century A. D." Bulletin of the School of Oriental and African Studies, University of London, Vol. 16, No. 3 (1954), pp. 425-468 . Turaba still exists and is on most maps. Some dispute the identification of <trbn> with Turaba and identifiy it instead with Ṭarbān طَرْبَان further away and say there were no two theaters of operations. there is also Irfan Shahid's article in the Encyclopaedia of the Qur'ān, "the People of the Elephant" (who concedes that in 570 CE it may not have been Abraha that was involved):
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Attempts to invoke the epigraphic evidence from south Arabia to shed light on the People of the Elephant have failed. The Murayghān inscription commemorated a victory, not a defeat, for the Ethiopians and the site of the battle was very far from Mecca. Additionally, these attempts have been gratuitously plagued by the involvement of the Prophet's birth date — traditionally considered 570 c.e. — with the date of the expedition, mounted by the People of the Elephant. An alternative approach towards negotiating the imprecision of the sūra, namely, the exegesis of the Qur'ān by the Qur'ān ( tafsīr al-Qur'ān bi-l-Qur'ān), has been more fruitful and successful. Accepting the unity of the two sūras al-Fīl and Quraysh, and setting them against the background of the history of western Arabia in the sixth century, based on authentic contemporary sources, yield the following conclusions on the People of the Elephant and their expedition:
They were Abyssinians, not Arabs, the fīl being an African not an Arabian animal; their leader was either Abraha or one of his two sons who succeeded him, Yaksūm or Masrūq; the destination no doubt was Mecca and the Ka`ba, referred to in verse q 106:3; the destruction of the Ethiopian host may be attributed to the outbreak of an epidemic or the smallpox. Its destruction was Mecca's commercial opportunity in international trade, now that it could safely conduct the two journeys (see caravan; journey ): the winter journey to Yemen and the summer one to Syria (q.v.; bilād al-shām ); let the Meccans, therefore, worship the lord of the “house” (the Ka`ba; see house, domestic and divine ), who made all this possible ( q 106:3-4). The true motives behind the expedition remain shrouded in obscurity but they must be either or both of the following: (1) Retaliation for the desecration of the cathedral/church, built by Abraha in Ṣan`ā'; or (2) the elimination of Mecca as an important caravan city on the main artery of trade in western Arabia.
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According to Encyclopaedia Islamica "Abraha", some argue that the object of this attack was merely to prepare the ground for an attack on the northern areas of the peninsula, but that it came to an end at Mecca. so perhaps the expedition tried to reach closer to Makkah but failed to do so, and this part was not mentioned in the inscription. I favor Kister's arguments. very often, when an engagement is made the stuff of legend, one side presents as a victory as a defeat and vice versa.

However, a new inscription found at the same place makes the original Bir Murayghan inscription Ry 506 unlikely  to represent the "Year of the Elephant." The undated inscription lists territoris under Abraha's authority had conquered and includes Yathrib (Madinah) nd most of Arabia. Robin thinks it is unlikely to predate Ry 506. Since Abraha went as far as Madinah, it would be unlikely that he was defeated at Makkah. C. Robin thinks that there might have been a defeat of Abraha at Makkah, unrecorded, between 555 and 565 CE. Abraha is last recorded in an inscription dated November 558. It seems that the chronicler putting the Year of the Elephant at 552 confused it with the beginning of hostilities.

Furthermore, 3 panels of rock engravings were found in Novemebr 2014 90 km 90 NE of Najran depicting elephants with their handlers. Their is no mention of Perisans bringing elephants into the area, so they are no doubt brought their by Abyssinians. The Abyssinians were known through Byzanitine sources to use elephants in royal ceremonies and probably the elephant mentioned in Arab tradition was for a similar purpose and not for combat.

see:

Robin Christian Julien, « L’Arabie dans le Coran. Réexamen de quelques termes à la lumière des inscriptions préislamiques ».. p. 27-74 in "Les origines du Coran,le Coran des origines" Académie des Inscriptions et Belles-Lettres Paris 2015

Also quoted by Peters in connection with intercalation and the chronology given by the early Arab historians is Hashim Amir Ali "The First Decade in Islam. A Fresh Approach to the Calendrical Study of Early Islam" Muslim World 44, 1954 p. 126-138. Ali argues (p. 136) that `Umar also introduced a standard lunar calendar for the events of 622 - 632 CE, a chronology "that ousted to some extent the older chronology involving intercalation and ... naturally found its way into the chronicles of many historians of that period." the logic of Ali was as follows:

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If intercalation was forbidden to the Muslims and the new Muslim calendar is to be assumed to have commenced ten years prior to the cessation of intercalation, how could intercalation be incorporated in the calendar of these first ten years? It is only logical to assume that they decided to extend the purely lunar calendar with retrospective effect. Whether there had been intercalation or not, the Muslim calendar, commencing from the year of the Hijrah, should be regarded as if there had been no intercalation. And since this involved going back only a hundred and odd months parallel to the Jewish calendar, it is not inconceivable that a standard calendar, like a standard version of the Qur'ān, was prepared on this assumption for the purpose of
serving as an official chronology of events pertaining to the Prophet and this most important period of Islam. This hypothetical chronology seems to have served its purpose so well as to have ousted to some extent the older chronology involving intercalation and, naturally it found its way into the chronicles of many historians of the period. It is evidently this reckoning on which the arguments of Maḥmūd Effendi and many others are based. Is it a wonder that he could submit arithmetical proofs for a reckoning which had itself been worked out on a simple arithmetical basis-but twenty years later?

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Another possible date for the Murayghan Inscripton is 547 CE (the era might start either in 110 BCE or 115 BCE or some suspect there were two different eras involved).in which case Muhammad being born 23 years after the Year of the Elephant would restore the traditional date of his birth as 570 CE. 
Also:
Henri Lammens, L'Âge de Mahomet et la chronologie de la sīra', Journal Asiatique, 10th Series, 17, 1911, 209-50.

Translation as it appears in "the Quest for the Historical Muhammad" by Ibn Warraq
Henri Lammens "The Age of Muhammad and the Chronology of the Sira" Journal Asiatique (March - April 1911), p. 209-250)
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 The Muslim scholars, like us, did not know when Muhammad suppressed the nasi, or intercalary month. This lack of certainty did not prevent the authors of the sira from adopting a fixed chronology. The months which elapsed before this were denominated as if the suppression had already occured, 184 and so introduced a new cause for confusion.
184 Snouk op. cit. 65
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 {Snouk Hurgronje, Het Mekkaansche Feest}

One may conclude that the traditions Mahmoud chooses are not that reliable, and that there may have been tampering. OTOH there is the thesis of Hāshīm Amīr `Alī, that the entrance of Muhammad to Medina did occur as Mahmoud says on the 8th of Rabī` al-'Awwal corresponding to Monday September 20, 622 and this indeed corresponded to 10th of Teshri of the Jewish calendar, but the 8th of Rabī` al-'Awwal was not as the calendar was used at the time, but according to the reworked calendar of `Umar with no intercalation. this may be correct. but `Ali also believes the intercalated calendar used by the Arabs was intercalated like the Jewish calendar. the Jews began to use, according to de Perceval, a 19 year year intercaltion on the end of the 4th cent. and may have communicated this to the Arabs at the beginning of the 5th century, the beginning of the Nasi, as the they were less advanced than the Jews of Palestine. the shift from an autumn pilgrimage to a spring pilgrimage, as the traditions relate to Muhammad's Last Pilgrimage attest (which was in the spring and coincided with Passover), was not due to bad intercalation but due to a shift in custom from an autumn pilgrimage to a spring one. Ali goes into this in more detail in "Must the Hajj Rotate Through the Seasons - Is the Qur'an Opposed to a Solar Calendar?" in The Islamic Review March 1956 Woking, England. originally Rajab was the month of the "lesser pilgrimage" الحَاجُّ الأَصْغَرُ al-ḥājj al-'aṣ*gh*ar or the `umra العُمْرَةُ according to Muslim sources, which in the beginning of the Nasi occured in spring . Ali thinks this season lasted due to a 19 month intercalation, and that the pilgimages mentioned in the biography of Muhammad were these, including the Last Pilgimage. he believes these were reworked as the regular Ḥājj (or the greater pilgrimage, الحَاجُّ الأَكْبَرُ al-ḥājj al-'akbar) and reintepreted as occurring in Dhu'l-Ḥijja after Muḥammad. the `umra was then moved, to be performed at any time, as all tradions agree. Ali deals with Procopius's report in, Hashim Amir Ali "Fresh Observations on Perceval’s 100 Year Old Notes on the Arab Calendar Before Islam," Islamic Culture, Hyderabad, India, Vol. XXII No. 2 April 1948 p. 174-180. he says that "two whole months" should not be taken literally because the lunar months may overlap the solar Roman ones. he believes at the time the Ḥajj came at autumn at that year, but Rajab correponded with the summer solstice that year. He also contends that the absence of the mention of a pilgrimage but merely the absence of fighting, confirms that it was Rajab that Procopius was talking about. I think `Ali seems right about the reworking of the chronology, but I don't think that the Arab calendar was intercalated exactly like the Jewish one, except that the intercalary month occured in autumn, after Dhu'l-Ḥijja, whereas the Jewish intercalation occurs in the spring, after Adar. but he thinks both the Arab intercalation and the Jewish intercalation occured in the same year. a similar solution is advocated by F.A. Shamsi, that will be explained later. he also thinks there was a shift form an autumn pilgrimage to a spring one, but only by Muhammad, i.e. that the last pilgrimage occured in Rajab of the pagan calendar, which Muhammad named Dhu'l-Ḥijja 
Here are some more mainstream western scholarship veiw of the `umra, from Enc. of Islam II "`Umra" (R. Paret-[E. Chaumont])

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If the pre-Islamic `umra was annually performed in Radjab, and also if the calculation is correct which places Radjab originally in the spring, its similarity with the Jewish Passover strikes one at once. The animals which are sacrificed at it were perhaps, as in the Jewish ceremony, originally first-borns (cf. Wellhausen, Reste, 98-9; W. Robertson Smith, Lectures on the religion of the Semites 3, 227-8, 464). In Muḥammad’s time, however, the original significance of the `umra seems to have been practically forgotten and it no longer fell in the spring.

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Hashim Amir Ali was very interested in calendar reform, and he believed, giving mainly hs own theological arguments (not based on any Islamic tradition), that Muḥammad intended a solar calendar and that he died shortly after, leading to confusion. he also believed that a solar calendar was compatible with the Qur'an (he does not go into the verses citing that the moon determines time). I think this is impossible, given the short time between Muḥammad's death and the institution of the Islamic calendar, and that a purely lunar calendar would be of no use except for theological reasons. However, I think that his point of later historians making a purely lunar chronology of events of the first decade of Islam sound correct. The `umra in Islam is not tied to any particular time, it can be performed at any time of the year, and as it involves slightly different rituals, it may even be performed in conjunction with the Pilgrimage proper, the Ḥajj.

One problem with de Perceval's reconstruction according to Ali in his article "Fresh Observations on Perceval’s 100 Year Old Notes on the Arab Calendar Before Islam," Islamic Culture, Hyderabad, India, Vol. XXII No. 2 April 1948 p. 174-180, is the Battle of Badr.

The Battle of Badr is described by Enc. of Islam II "Badr" by W. Montgomery Watt
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...
Here occurred on 17 (or 19 or 21) Ramaḍān, 2 A.H. (= 13 or 15 or 17 March, 624) the first great battle of Muḥammad's career. Though there is a wealth of detail in the early sources, it is difficult to give a clear account of the battle and the events which led up to it. It is generally held that the earliest and most reliable version is that contained in a letter from `Urwa b. al-Zubayr to the caliph `Abd al-Malik (preserved in al-Ṭabarī, i, 1284 ff.), though even this has some material which seems to be legendary. Muḥammad received information that a rich caravan was returning from Syria to Mecca, led by Abū Ṣufyān b. Ḥarb, chief of the clan of Umayya. He collected a force of slightly over 300 men (about 80 Emigrants, the rest Anṣār), and marched to the neighbourhood of Badr in hopes of intercepting the caravan. Abū ufyān on his side had sent a request to Mecca for a force to protect the caravan while it traversed the region easily accessible from Medina. ..

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The Qur'an tells of winter and summer caravans. from Hashim Amir Ali "Fresh Observations on Perceval's 100 Year Old Notes on the Arab Calendar Before Islam," Islamic Culture, Hyderabad, India, Vol. XXII No. 2 April 1948 p. 177
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... Take for example the Battle of Badr. The references in the Qur'ān as well as the Ḥadīth make this out to have occured at a very hot season. But according to Perceval's calendar, this falls in January. We know that it was the *summer* caravan which went to the cooler climates of the North and it the *winter* caravan which went south to Yemen. How was the northern caravan returning in January?
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I don't see the problem. it was a returning caravan in winter (January) going south. the reference in the Qur'ān to the weather is in al-'Anfāl 8:11 that it rained. it seems copiously, since it says "to cleanse you" so it was in a season that it did rain, which fits January. I guess that Hashim Amir Ali means that the Quraysh, Abū Ṣufyān b. Ḥarb would have been in Mecca not Syria at the time.

... and sent down water from the sky upon you, that thereby He might purify you ...
... وَيُنَزِّلُ عَلَيۡكُم مِّنَ ٱلسَّمَآءِ مَآءً۬ لِّيُطَهِّرَكُم بِهِۦ ...
also in the Sīrat Rasūl Allāh by Ibn Iṣḥāq (Ibn Hishām's edition), translated as "the Life of Muhammad" by A. Guillaume (p. 439 of the published Arabic, p. 296 of the translation):
 << ... God sent a rain which turned the soft sand of the wadi into a compact surface which did not hinder the apostle's movements but which gravely restricted the movements of the Quraysh. ... >>

Another objection to Perceval's reconstruction is that it places Muhammad's retreat in a cave and his dzing off in midday, when he recieved his "revelation" in Ramadan to winter. OTOH I think that temprature variation in the Hijaz is not that great.
Hashim Amir Ali also (rightly in my opinion) casts doubt that there was a purely lunar calendar before the introduction of the Nasi. rather, he regards this as a reform of a very poorly regulated intercalation, as a purely lunar calendar would serve no purpose, and would be against the practices of all the neighbors of the Arabs. and since a purely lunar calendar serves no purpose, I would conclude that the Islamic calendar arose only because of Muhammad's express interdiction.
 F.A. Shamsi in "Perceval's Reconstruction of the Pre-Islamic Calendar" in  Islamic Studies, Vol. 37, No. 3 (Autumn 1998), pp. 353-369 http://www.jstor.org/stable/20837003 voices the same objections and offers a similar solution. he mentions the problem of the Battle of Badr. he also says that "`Abd Allāh ibn Mas`ūd (apud Ibn Sa`d) reports that it was a hot day, and, it seems, the corpses of those who had been killed in the battle putrefied the same day.39". This sort of contradicts the report of rain. Shamsi contends that the Hijri calendar (without intercalation) and the Arabian calendar (with accurate intercalation) were different in Muhammad's lifetime, that some dates reported in the chronicles are that of the Hijri calendar and some in the Arabian calendar. He also contends that the `umra in Rajab was made the main pilgrimage and hence the ḥajj and that Dhū al-Ḥijja of the Last Pilgrimage was Rajab of the pagans and that Muhammad called Dhū al-Ḥijja. I find this is too fantastic. in his view:
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... the Muslim calendar was established in circa December 629 CE but the (Pagan) Arabs were allowed to retain their calendar till ca. March 631 CE although Makkah had in the meantime been conquered on 08.06.630 CE. However, it seems that despite its abolition by the Muslim government, the Arabian calendar remained in use at least among historians for very many years till `Umar saw to it that it went out of use.
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I think that the etymology of the month names support an intercalation in pre-Islamic times. I also support Perceval's view that it was a three year intercalation and that caused an eventual wandering through the seasons. But F. de Blois is right about the etymology of nasī' as "postponement". one of the meanings was simply changing the sacredness of a month by arbitrary decision, though it was also used for intercalation.