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The new moon interval NA and the beginning of the Babylonian month

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Abstract

This study examines Babylonian records of the new moon interval NA (sunset to moonset on the day of first lunar visibility) and the connection of this interval to the length of the moon. I show that the NA intervals in the Normal Star Almanacs were computed using the goal-year method and were then used in turn to predict the lengths of each month of the year. I further argue that these predicted month lengths, adjusted occasionally on the basis of observation in cases where the moon’s visibility was considered marginal, formed the basis of the Late Babylonian calendar.

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Data availability

The datasets generated during and/or analysed during the current study are available in the Brown Digital Repository, https://repository.library.brown.edu/studio/item/bdr:h8g2gwjv/.

Notes

  1. It is possible that if two or more consecutive missed sightings of the new moon crescent which should trigger 29-day months but according to this rule would yield 30-day months occurred, the new moon crescent would be visible on the evening that begins the 29th day if the next month should also be a 29-day month, resulting instead in a month of only 28 days. Such cases would be quite rare, however.

  2. Beaulieu (1993).

  3. The Astronomical Diaries preserve 72 reports of 29-day months where the moon was recorded as being seen on the 30th evening and 40 reports where the moon was not seen. Similarly, the Goal-Year Texts contain 52 reports where the moon was seen and 27 where the moon was not seen. The earliest clearly preserved such case dates to the 25th year of Nebuchadnezzar II (580–579 BC), where we have the statement that the first day of Month IX followed a 29-day month but that the moon was not seen [ADART V 49 Rev. I 11′; on the date and layout of this text, see Huber and Britton (2007)].

  4. Steele (2007, 2012). For TU 11 and related texts, see Brack-Bernsen and Hunger (2002, 2008).

  5. Huber and Steele (2007), Hunger (2014: XI), Ossendrijver (2012: 537–538).

  6. For the present purposes I ignore the distinction between Diaries, Short Diaries, and Preliminary Observation Reports—the latter two being preliminary stages in the production of the Diaries (see Mitsuma 2015)—since they contain exactly the same type of astronomical data.

  7. All known Astronomical Diaries are published by Sachs and Hunger (1988, 1989, 1996, 2022) [hereafter ADART I–IV]; relevant Compilation Texts are published by Hunger (2001) [hereafter ADART V] supplemented by Huber and Steele (2007) and Steele (2018); the Goal-Year Texts are published by Hunger (2006) [hereafter ADART VI]; and the Almanacs and Normal Star Almanacs are published by Hunger (2014) [hereafter ADART VII].

  8. Unfortunately, we have few sources of month length data outside of astronomical texts. Where we do, this data is in agreement with that in the astronomical texts.

  9. Hunger translates ‘30’ as ‘(the 1st of which was identical with) the 30th (of the preceding month)’ and ‘1’ as ‘the 1st (of which followed the 30th of the preceding month)’.

  10. Knapp and Steele (2023).

  11. Sachs and Hunger (1988: 22).

  12. See the detailed discussion of this text in Steele (2007).

  13. The fact that the NA interval was not observed does not guarantee that the moon was not seen. It is possible, for example, that the moon was seen briefly but that bad weather prevented its setting from being observed. A very small number of reports describe such a situation. For example, ADART I -373B Rev. 6′ reads ‘[Month XII …] the moon was visible in a cloud; 15,40 NA, not [observed]’. I have included such cases among the ‘observed’ category. In the absence of a statement such as this, however, I have assumed that the fact the NA interval was not observed indicates that the moon was not seen.

  14. In ADART I–III, Hunger restores a considerable number of month lengths on this basis. With only a few exceptions, I have accepted Hunger’s restorations.

  15. One caveat should be made here. It is possible that some of the undated reports duplicate either one another or a dated report. The number of such possible duplicates is very small, however, and so will not significantly bias any of the analysis.

  16. Huber (2017).

  17. ADART VII 26 Obv. II 1 contains the only example of a third designation: x TIM. The NA interval is 11 UŠ, which is comparable to those entries which have ina KAL, so perhaps TIM carries the same meaning.

  18. See Kugler (1909–1924: 536) and Hunger (2014: XIII).

  19. Contra Kugler (1909–1924: 536). As noted by Hunger (2014: XIII), a single instance of the term ina KAL appears in the Astronomical Diary ADART III –77. In this case, the NA value is stated to have been computed, not observed. It seems very likely that the scribe copied the NA interval from a Normal Star Almanac and in doing so (accidently) also copied the phrase ina KAL.

  20. See in particular Brack-Bernsen (1997, 1999a, 2002, 2011) and Brack-Bernsen and Hunger (2002, 2008).

  21. BM 42282 + 42,294 Obv. 6–13; translation adapted from Brack-Bernsen and Hunger (2008: 6).

  22. We know of a small number of cases where overlapping observational texts contain slightly different values – see Gray and Steele (2008: 573). Such discrepancies may simply reflect copying errors.

  23. Preliminary results from a much more exhaustive study of the calculation of all six of the lunar six intervals using the goal-year procedure currently being undertaken by myself and Taylor Knapp show that this is true for all of the lunar six data in the Normal Star Almanacs and the calculated lunar six data found in observational texts.

  24. For Brack-Bernsen’s reconstruction of this rule, see Brack-Bernsen (2002) and Brack-Bernsen and Hunger (2002). For BM 57980, see Brack-Bernsen and Walker (2007).

  25. The tablet clearly has 12;40 written here, however, so this would have to be an ancient scribal error not a modern reading error.

  26. At least during the Seleucid Era when Normal Star Almanacs were being regularly produced, but almost certainly by the same calculational methods in earlier periods as well.

  27. Although I am talking about agreement with Babylonian calculation here, the same argument extends to comparison with modern computation. Jones (2004: 527–528) found that the rate of discrepancy between month lengths in the Diaries and those computed by Parker and Dubberstein (1956) was typically less than 9%, which is too good if the calendar was based purely on sighting the lunar crescent.

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  1. Department of Egyptology and Assyriology, Brown University, 2 Prospect Street, Box 1899, Providence, RI, 02912, USA

    John Steele

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Steele, J. The new moon interval NA and the beginning of the Babylonian month. Arch. Hist. Exact Sci. (2024). https://doi.org/10.1007/s00407-023-00325-x

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