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The Jalālī Calendar: the enigma of its radix date

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Abstract

The Jalālī (or Malikī) Calendar is well known to Iranian and Western researchers. It was established by the order of Sulṭān Jalāl al-Dīn Malikshāh-i Saljūqī in the 5th c. A.H. (The dates which are designated with A.H. indicate the Hijrī Calendar.)/11th c. A.D. in Isfahan. After the death of Yazdigird III (the last king of the Sassanid dynasty), the Yazdigirdī Calendar, as a solar one, gradually lost its position, and the Hijrī Calendar replaced it. After the rise of Islam, nonetheless, Iranians preferred various solar calendars to the Hijrī one. The Jalālī Calendar must be considered the culmination of such efforts. The present article deals with the riddle of the radix date (epoch) of the Jalālī Calendar. The author examines the problem through a historical approach and provides a novel solution to the question.

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Notes

  1. For instance, Riāhī (1956) wrote on the problem of the Jalālī Calendar’s systems of intercalation without considering the historical sources. For the astronomers and orientalists who presented their intercalary systems for the Jalālī Calendar without considering the historical facts, see Taqi Zadeh (1939: 113–117).

  2. For a list of different calendars that were used in important Islamic zījes, see van Dalen (2000).

  3. Al-Bīrūnī (1983: 238). For different lists of the Sassanid Kings, see al-Bīrūnī (1878: 120–131). See also al-Khāzinī, al-Zīj al-Mu‘tabar al-Sanjarī, Vatican MS Arabo 761, fol. 119r.

  4. Al-Farghānī (1669: 30) and Abdollahi (1996: 249).

  5. For more descriptions, see Kūshyār b. Labbān (2009: 10) and al-Khāzinī, Wajīz al-Zīj al-Sanjarī, Sepahsālar MS 682, fol. 1v-2r.; the manuscript is an abridgment of al-Khāzinī’s Muctabar al-Sanjarī Zīj. Al-Khāzinī compiled Wajīz al-Zīj al-Sanjarī, in 524 A.H./1130 A.D. For important zījes that discuss the Yazdigirdī Calendar, see van Dalen (2000: 265).

  6. Al-Mascūdī (1861–1877, II: 345), al-Bīrūnī (1878: 11), and Kūshyār b. Labbān (2009).

  7. Al-Bīrūnī (1954–1956, I: 142).

  8. The Yazdīgirdī Calendar appears in many important zījes, including al-Battānī (1899–1907), al-Ṭūsī’s Zīj-i Īlkhānī, British Library India Office MS Or. 7464, and Zīj-i Ulugh Beg (1847–1853).

  9. Al-Ṭabarī (1897, V: 2480) and al-Yacqūbī (1960 II: 145).

  10. Walker (1941: 3, 25 and 162).

  11. For a list of important zījes, including three mentioned calendars and more additional ones, see van Dalen (2000).

  12. van Dalen (2000).

  13. For instance see Ibn Yūnus (1804: 197–217) and al-Bīrūnī (1962: 86 and 91).

  14. See al-Battānī (1899–1907, II: 9–18) and al-Khāzinī, Wajīz al-Zīj al-Sanjarī, Sepahsālar MS 682, fol. 1v.

  15. Al-Bīrūnī (1878: 31–34), Ibn al-Athīr (1965–1966, VII: 469) and Taqizadeh (1939: 109–110).

  16. Al-Bīrūnī (1878).

  17. Al-Bīrūnī (1878: 30–31,142) and al-Qumī (1982: 242). For further explanation of the Majūsī Calendar, see Abdollahi (1996: 271–27, English dissertation:130).

  18. See Sanjar-i Kamālī, Zīj-i Ashrafī, Bibliothèque Nationale de France, MS persan, 1488, fol. 3r-3v.

  19. It is clear that after the extinction of the Sassanid Dynasty, the Persian territory went under the supervision of the Umayyad and cAbbāsid Caliphs. However, some aspects of pre-Islamic culture, like employing a solar calendar, remained among ordinary people and elites in the ancient territory of Iran.

  20. Al-Bīrūnī (1878: 215–218).

  21. For instance, see al-Ḥillī (1994, I:194–195) and Majlisī (1957, LVI: 91). For research on Shiite Imams and the importance of hadīths, see Waines (20032: 155–173). For research concerning the chapter of Nowrūz in al-Majlisī’s Biḥār Al-Anwār, see Walbridge (1997: 83–92).

  22. For these appellations, see al-Khāzinī, Wajīz al-Zīj al-Sanjarī Sepahsālār MS 682 fols. 2v-3r and Naṣīr al-Dīn al-Ṭūsī, Zīj-i Īlkhānī, British Library (India Office) MS OR 7464, fol. 20 v.

  23. Neugebauer (1975, I:10).

  24. See Sacdī (2006: 9).

  25. Taqi Zadeh (1991) and Ginzel (1906: 300–304), reprinted by F. Sezgin et al. (1998, XXIV: 176–180).

  26. Al-Khāzinī, Al-Zīj al-Mu‘tabar al-Sanjarī, Vatican MS Arabo 761, fol. 122v and Ibn al-Athīr (1965–1966, X: 98).

  27. It seems that al-Wābkanwī pointed to the observational records, not astronomical tables, since the tables must have been prepared after the period of observation.

  28. Al-Wābkanwī, Zīj-i Muḥaqqaq-i Sulṭānī, Aya Sofya Library MS 2694, fol. 24v.

  29. Ibn al-Athīr (1965–1966, X: 98) and Sayılı (1960: 162).

  30. Ibn al-Athīr (1965–1966, X: 98) named al-Khayyām, Muẓaffar-i Isfazārī, and Maymūn b. Najīb al-Wāsiṭī. Quṭb al-Dīn al-Shīrāzī, in his al-Tuḥfa al-Shāhīyya, Majlis Library MS. 6130, fol. 130v-131r., asserted that the group consisted of eight astronomers. However, he named only al-Khayyām and Abū l-cAbbās al-Lawkarī. Ulugh Beg named al-Khāzinī in his zīj. See: Ulugh Beg (1998, LII: 309–310 and LIII: 27).

    Sayılı (1960:165) named more persons: Abbās-i Wāsim, Bahrām, and al-Macmūrī from other sources.

  31. Taqi Zadeh (1939: 113–117).

  32. Al-Khāzinī, Al-Zīj al-Mu‘tabar al-Sanjarī, Vatican MS Arabo 761, fols. 16v-17r.

  33. Al-Khāzinī, Al-Zīj al-Mu‘tabar al-Sanjarī, Vatican MS Arabo 761, fol. 191v.

  34. Ulugh Beg (1998, LII: 309–310); Nīshābūrī, Sharḥ-i Sī Faṣl, Majlis Library MS 3328, fol. 50r;

    Sayılı (1960: 165).

  35. cAlī Shāh-i Bukhārī, cUmday-i Īlkhānyya, Malik Library MS 3367, fols. 11r-11v.

  36. See Naṣīr al-Dīn al-Ṭūsī, Zīj-i Īlkhānī, British Library India Office MS Or. 7464, fol. 21v., who dated the radix as 19 Farvardīn 448 Yazdgirdī (Friday). See also Sanjar-i Kamālī, Zīj-i Ashrafī, Bibliothèque nationale de France (BNF), MS persan, 1488, fol. 3r., dated the radix as 18 Farvardīn (Thursday).

  37. Khāzinī, al-Zīj al-Mu‘tabar al-Sanjarī, Vatican MS Arabo 761 fol.122v. See also Ibn al-Athīr (1965–1966, X: 98).

  38. Based on CALH Software, 5 Shacbān 468 A.H. and 10t Ramaḍān 471A.H. were Sunday and Friday, respectively. The software, specialized for conversions between the Hijrī, Yazdīgirdī and Jalālī calendars among others, was prepared by Dr. Benno van Dalen.

  39. Ulugh Beg (1998 LII: 309–310).

  40. Naṣīr al-Dīn al-Ṭūsī, Zīj-i Īlkhānī, British Library India Office MS Or. 7464, fol. 21v. It should be noted that the radix date of the star table in the Zīj-i Malīkshāhī is 448 Yazdigirdī (see Plat 1). Interestingly, the solar table in the Zīj-i Īlkhānī, begins with the year of 448 Yazdigirdī as well (see Fig. 3).

  41. It seems that Zīj-i Īlkhānī and Zīj-i Ulugh Beg were the most important zījes of the next generation of Persian zījes.

  42. Al-Khāzinī, Wajīz al-Zīj al-Mu‘tabar al-Sanjarī, Sepahsālār MS 682, fol. 3v.

  43. Al-Khāzinī, Wajīz al-Zīj al-Muctabar al-Sanjarī, Süleimaniye Library Hamidiye MS 859, fol. 4v. The manuscript is another copy of the abridgment of al-Khāzinī’s Muctabar al-Zīj al-Sanjarī.

  44. This translation depends on the definition of ‘day’ in Zīj-i Ulugh Beg. He stated that “astronomers in our provinces and in western (?) territories take the beginning of a new day when the sun crosses midday (the local meridian)”. See Ulugh Beg (1998 LII: 292).

  45. Sédillot’s French translation differs from the other two translations proposed above: “Le commencement de 1’année Djélaléenne coïncide avec le jour de l’entrée du soleil dans le Bélier à midi” See Ulugh Beg (1998 LIII: 27).

  46. We have translated sāl as the chronological period.

  47. The simultaneous occurrence of the two events would be a rare phenomenon. Thus, I think that a situation very near to the above-mentioned perfect assumption could have been acceptable at the time. The solar ecliptic longitude on 14 March 1076 A.D. was equal to 359.9704° and very near to the local meridian of Isfahan (See Table 2).

  48. See Ulugh Beg.

  49. See Ideler (1818: 139). I have used the “Alcyon Ephemeris” computer program (by Prof. N. Swerdlow, and R. Lange) for my re-computations. (See Table 2).

  50. Bīrjandī, Sharḥ-i Zīj-i Sulṭānī (i.e., Zīj-i Ulugh Beg), Majlis Library, MS 4716, fol. 10v.

  51. Ulugh Beg (1998, LII: 296).

  52. Al-Bīrūnī (1983: 229).

  53. I have used the CALH Computer Program, and Moon C52, prepared by Munzur Ahmed, which computes TCV (based on an un-aided and an aided eye).

  54. Sarton (1975, I: 760) and Sayılı (1960: 163–164).

  55. According to Ḥāsib-i Ṭabarī, Malikshāh’s astronomers observed in Isfahan, whereas he simultaneously observed in Ᾱmul (a city north of Iran). See Ḥāsib-i Ṭabarī, Zīj-i Mufrad, Cambridge University Library MS Browne O.1.(10), fol. 15r.; Indeed, Zīj-i Mufrad is the first zīj compiled in Persian.

  56. It should be noted that if the computations were to be based on true crescent visibility, not the conventional lunar calendar, 6 Shacbān could be changed to 5 Shacbān. The day of the week, however, would change to Monday not Sunday (see Fig. 2).

  57. I have used the “Alcyon Ephemeris” computer program for this computation (See Table 2).

  58. Al-Bīrūnī, al-Āthār al-bāqiya (1878: 45), The English translation is from Sachau (1879: 55).

  59. Naṣīr al-Dīn al-Ṭūsī defined qubbat al-arḍ as a point at the terrestrial equator, whose longitude was taken to be 90º from the Khālidāt Islands (today’s Canary Islands) toward the east (about the region of the Maldives today). See Zīj-i Īlkhānī, British Library India Office MS Or. 7464, fols. 21v-22r.; See also al-Bīrunī (1983: 193).

  60. Rukn al-Dīn al-Āmulī in his Zīj-i Jāmic-i Sacīdī, Majlis Library MS183, fol. 1v. Stated that after al-Ṭūsī’s death, some astronomers at the Marāgha Observatory proposed some corrections based on the latest observations. For instance, they finally subtracted about 3 min of arc of the solar ecliptic longitudes. This correction brought their results nearer to the modern re-computations (see Table 3).

  61. Sayılı (1960: 166).

  62. For a list of such zījes, see van Dalen (2000). See also Table 1.

  63. According to de Blois (1996:42), the Jalālī Calendar never played a role in official timekeeping, but found fairly broad acceptance as an agricultural calendar. De Blois gave no reference for his claim.

  64. Neugebauer (1975, I:10).

  65. Bīrjandī, Sharḥ-i Zīj-i Sulṭānī (i.e., Zīj-i Ulugh Beg), Majlis Library MS 4716, fol. 8r.

  66. Indeed, in the Ilāhī calendar, Farvardīn-māh-i Yazdigirdī has changed to Farvardīn-māh-i Ilāhī, and this pattern continues to Isfand-māh-e Ilāhī, as the twelfth month of this calendar. See cAllāmī (1893 I: 194).

  67. cAllamī (1893 III: 216,219).

  68. Maḥmūd-i Qumī (1861:1–13).

  69. Hājjī Khalīfa (1982 II: col. 972).

  70. Ḥāsib-i Ṭabarī, Zīj-i Mufrad, Cambridge University Library Browne MS O.1.(10), fol.15r.; It is unclear why Ṭabarī did not record his observation using Jalālī years, but it is clear that he conducted his observation in the year of 5 Jalālī.

  71. Some traces and tables of the Zīj-i Malikshāhī (including a stars table) appeared in the Dustūr al-Munajjimīn. For an analysis of the stars table there, see Rozenfeld, and Yushkevich (1961: 225–235). For a whole report on Dustūr al-Munajjimīn, see van Dalen (2017: 117–135).

  72. See Abdollahi (1996: 287, English dissertation: 135).

  73. cAlī Shāh-i Bukhārī, cUmday-i Īlkhāniyya, Malik Library MS 3367, fols. 11r-11v.

  74. Al- Baghdādī, al-Zīj al-Baghdādī, Bibliothèque nationale de France MS Arabe 5968, fol. 6v.

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Acknowledgements

My research was financed by the University of Tehran (through the Calendar Council at the Institute of Geophysics, Project No. 6220952/1/03). The author gratefully acknowledges this support. I would like to express my gratitude to Prof. Saliba, Prof. Morrison, and Dr. Benno van Dalen for their comments on this article. I also thank Mr. Ghassemlou with whom I had useful discussions on this article.

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  1. History of Science Department, Encyclopaedia Islamica Foundation, P.O. Box 14155-6195, Tehran, Iran

    Hamid-Reza Giahi Yazdi

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Giahi Yazdi, HR. The Jalālī Calendar: the enigma of its radix date. Arch. Hist. Exact Sci. 74, 165–182 (2020). https://doi.org/10.1007/s00407-019-00240-0

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