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

Michael L. Siemon (
Tue, 11 Jul 1995 00:24:11 -0400

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-
ation. 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.

[*] 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!
Michael L. Siemon (

"Stand, stand at the window, as the tears scald and start;
you shall love your crooked neighbor, with your crooked heart."