Re: Why not 13 months? (Was La Systeme Metrique)

Whittet (
11 Jul 1995 19:19:01 GMT

In article <>, says...
>In article <3tsqpn$4u4@lace.Colorado.EDU>, hgibbons@hoshi.Colorado.EDU
>(Hugh Gibbons) wrote:
>+If you assume that the original definition of the month was based on
>+the lunar period (full moon to full moon or new moon to new-moon),
>+twelve would be a closer approximation than 13. (There are
>+12.37 cycles of the moon per year.)
>Yes. This is the basis of "cycles" of intercalation of months in luni-
>solar calendars. To be pedantic, the mean tropical year of 365.24189...
>days and mean synodic month of 29.05309... days have a ratio of
>12.36826..., with a minor (over the historical period) secular vari-

Actually , the actual period of rotation of the moon around the earth
is closer to 28 days. (27 days, 7 hours, 43 minutes and 11.43 seconds.)
It is the apparent motion due to the fact that both are moving relative
to each other which is 29 days 12 hours 44 minutes and 2.78 seconds
aproximately 29.05309... days . The natural cycles of flora and fauna
appear to be tuned to the actual rotation however, and not the apparent
motion. Thus twelve lunar cycles of 28 days work well with a 364 day year.

The classic "oktaeteris" of 8 years with 3 intercalary months
>has a characteristic 3/8 fraction (0.375) roughly approximating this
>0.36826... excess. You can work out your own intercalation cycles on
>the basis of this: N intercalary months implies N/0.36826 years as
>the length of the cycle (rounded of course :-)) Thus, one gets the 3/8
>approximation of the oktaeteris, or the (excellent!) 7/19 = 0.36842...
>approximation of the Metonic cycle. No other possibility[*] is even
>remotely as close to fact as the Metonic 235 months in 19 years.

It is interesting, none the less that the Assyrians and both muslims and
jews use a lunar calender of 354 days with 355 on leap years.

The Western Semitic peoples whose linquistics are most closely tied to
those of Crete also usded a calender of 364 days, divided into 13 months
of 28 days.

With this calender everything was very neatly divided into periods of
7 day weeks with an intercalcatory day and a fraction to give a year
and a day as equal to the period in which the earth revolves around
the sun.

>[*] in small integer values; obviously, one can find better approxi-
>mations in larger spans of years -- but it may surprise you just HOW
>much larger than 19 years you have to allow to get a better value of
>the solar/lunar ratio!

The best aproximation that was possible in antiquity was a nineteen year
period with seven of these nineteen years having 13 months
>Michael L. Siemon