however, was never exploited by Greek historians. Astronomical calendars
were invented by astronomers for their own use, and had only a limited impact
on Greek society, culture, and Greek views of history.
Geminus’history of Greek calendarsAnother function of astronomical calendars may have been to rationalize, for
purely speculative, intellectual purposes, the chaos that in real life pervaded
the Greek civil calendars. This may be apparent in Geminus’ history of
calendars, where the Greek calendar is conceived as evolving from one astro-
nomical scheme to the next with ever-increasing accuracy. According to
Geminus, the ancient Greek calendar originally consisted of 30-day months
only, with the intercalation of a thirteenth month every other year. This
scheme was superseded by the eight-year cycle (octaeteris), with three inter-
calations in eight years and a regular alternation of 29- and 30-day months.
This was superseded in turn by a 16-year cycle, then by a 160-year cycle
(both elaborations of the octaeteris), thereafter by the 19-year cycle (here
attributed only to contemporaries of Meton), and finally by the 76-year
cycle of Callippus.^109
The historicity of this account is clearly dubious. A calendar consisting of
30-day months only—the earliest stage in Geminus’history—could never have
sustained itself as lunar, as after only one year the month would have begun at
thefirst quarter (instead of the new moon), and after two years at the full
moon. Moreover, intercalations in alternate years would have been blatantly
excessive (after 24 years, the new year would have shifted by one whole
season). It is implausible, therefore, that this scheme was ever used in practice
in the archaic period.^110 Geminus’later schemes, although much more accu-
rate, were similarly never adopted or used at Athens or in any other Greek city
(as discussed above). Geminus’account should best be read, therefore, as a
(^109) Geminus,Elem. Astr.8. 26–60; see also Censorinus,DeDieNatali, 18. 2–5. Both are cited
and discussed in Samuel (1972) 33 110 – 49, Hannah (2005) 32–3.
As apparently assumed by Bickerman (1968) 28, 38, although he concedes elsewhere
(pp. 29–30), somewhat inconsistently, that this account of Geminus’would have been irrelevant
to actual calendrical practice. Hannah (2005) 29, 32–4 gives too much credence to Geminus’
account, but still concludes that intercalation in alternate years (or the‘dieteris’) must have been
‘impractical and unpracticed’in ancient Greece. The notion of the dieteris existed—if only as a
notion—quite early on, as it is assumed by Herodotus (1. 32; see also 2. 4) in a speech attributed
to Solon; but significantly, Solon is only using this scheme for the purpose of an approximate
calculation. This passage does not serve as evidence, therefore, that in early sixth-centuryBCE
Athens the dieteris was followed in practice. On the theory that this scheme was used in early
Ptolemaic Egypt, during the reign of Ptolemy II Philadelphus, see Ch. 3. 2.
56 Calendars in Antiquity