following month-lengths (in days): 30–(29)– 30 – (30)– 30 – (29)– 30 – (29)– 30 –
(29)–30 (brackets indicate months that are not allocated to the overseers,
mostly of 29 days). The alternation of 29- and 30-day months is characteristic
of schematic lunar calendars, because calendars based on empirical observa-
tion do not yield regular, alternating sequences (see Huber 1982: 24–5).
The only anomaly in this sequence is the succession of three 30-day months
(months 3–5 in the sequence), which is possible in empirical calendars but
unusual in calendrical schemes. However, this anomaly has been plausibly
explained as the result of an arithmetical scheme that was tied to the civil
calendar. The beginning dates of the priestly periods (i.e. alternate lunar
months) are given in this document as II Shemu 26, IV Shemu 25, II Akhet
20, IV Akhet 19, II Peret 18, IV Peret 17. The arithmetical rule is thus simply
to recede every other month by one day in the civil calendar. This yields, for
example between II Shemu 26 and IIII Shemu 25, a total of 59 days, hence one
full and one hollow lunar month. From Shemu to Akhet, however, the date
recedes by 5 days (in this particular case, from IIII Shemu 25 to II Akhet 20) to
take account of the intervening epagomenal days.Why it does not recede by 6
days (i.e. 5 for the epagomenals + 1 as in all other alternate months) remains a
little unclear; but this is the arithmetical rule that appears to be followed, and
this is what leads to the anomalous run of three 30-day months.^61
The evidence of these two documents from the Illahun archive, the
first suggesting empirical observation and the second an arithmetical, calen-
drical scheme, is not necessarily contradictory. The context of the second
document—a schedule for the allocation of supplies of almonds and honey—
suggests that it was redacted in advance, at the beginning of the year, when the
dates of the forthcoming lunar months were possibly not yet known. If so, its
arithmetical scheme could have been used as a provisional working model, on
the understanding that the lunar dates would be adjusted later during the year
on the basis of empirical observation.^62 The evidence, however, remains too
limited and tenuous for any general orfirm conclusion to be reached.
Much later, in the Ptolemaic period (305– 30 BCE), evidence begins to emerge
of elaborate, schematic lunar calendars, whose significance—and whether they
indicate a general shift, in this later period, to the use of schematic calendars—
will be discussed below.
(^61) Depuydt (1997) 180–2. This rule, with three consecutive 30-day months, results in a lunar
year of 355 days, which is only slightly excessive (12 average lunar months are about 354⅓days).
This was also the year length of the Roman calendar in the Republican period, probably the
survival of an earlier lunar calendar (see Ch. 4 n. 133). 62
Ibid.
146 Calendars in Antiquity