Re: Why not 13 months? (Was La Systeme Metrique)
Michael L. Siemon (mls@panix.com)
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 newmoon),
+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 (mls@panix.com)
"Stand, stand at the window, as the tears scald and start;
you shall love your crooked neighbor, with your crooked heart."
