udazallû (day-correction / UD.DA.ZAL.LÁ-e)

Definition

Udazallû (Akkadian; from Sumerogram UD.DA.ZAL.LÁ-e, "remainder/leftover of the day") is the MUL.APIN technical term for a sexagesimal-fractional "correction" added to a calendrical or astronomical observation to align lunar months with the solar year. The procedure at MUL.APIN II ii 13-17 instructs the reader to obtain the udazallû for day, month, and year: the day-correction is 0;1,40; multiplied by 30 days it gives the monthly correction 0;50; multiplied by 12 months it gives the yearly correction 10 — the 10 "days in excess" (UDmeš atrūti / DIRI).

In Tradition

Hunger and Steele, with Hunger and Pingree concurring, treat udazallû as the foundational arithmetical parameter of MUL.APIN's intercalation-mathematics: the day → month → year correction chain that reconciles the 360-day schematic calendar with luni-solar reality. The procedure is computed backwards from the three-year intercalation rule (3 × 10 = 30 days = one intercalary month); the same 1,40 / 50 / 10 figures appear in i.NAM.giš.ḫur.an.ki.a and BM 37175.

In Practice

For the reader of MUL.APIN II ii 13-17, the udazallû procedure is the arithmetic recipe that turns the schematic 360-day year into a working lunisolar calendar. The procedure-text rule reads, in Hunger-Steele's rendering: "If you are to see the correction for day, month, and year" — followed by the chain that multiplies 0;1,40 by 30 to obtain 0;50, then by 12 to obtain 10. Hunger and Pingree extend the reach: the same arithmetical-correction technique underlies later Babylonian astronomical-mathematical texts (ACT ephemerides, Goal-Year periods), where sexagesimal-fractional corrections to base values are the standard computational instrument. Late-Babylonian BM 37175 (Steele) gives a fuller version that adds the final step 10 days × 3 years = 30 days = one intercalary month — making the three-year rule arithmetically explicit. The udazallû thus operates at three levels: as the day-correction parameter, as the cumulative monthly and yearly correction values, and as the underlying logic of every Babylonian intercalation calendar from MUL.APIN through the Seleucid period.

Historical Origin

Attested across MUL.APIN II ii 13-17 (~1000 BCE composition; Neo-Assyrian transmission), the Late-Babylonian MUL.APIN-based text BM 37175 (Steele, in press), and i.NAM.giš.ḫur.an.ki.a (Livingstone 1986; earliest exemplar c. -683). Modern critical treatments: Hermann Hunger & John Steele, *The Babylonian Astronomical Compendium MUL.APIN* (Routledge 2019), pp. 144-146, pp. 336-337, Index p. 386; primary edition: Alasdair Livingstone, *Mystical and Mythological Explanatory Works of Assyrian and Babylonian Scholars* (Oxford 1986), pp. 17-49.

Further Reading

• Hermann Hunger & John Steele, The Babylonian Astronomical Compendium MUL.APIN
• Hermann Hunger & David Pingree, Astral Sciences in Mesopotamia