Re: Attic months

On 1/4/06, R A Brown <ray@...> wrote:
> > Perhaps, but the new-style calendar has a 400-year cycle, so I'd
> > expect 76 to be manageable.
>
> Yes, but in the new-style calendar it's only a matter of intercalating a
> single day every so often, and the rule is pretty simple: "A year is a
> leap year if it is evenly divisible by 4 and is not evenly divisible by
> 100, or is evenly divisible by 400."
True.  The Gregorian rule is designed to be easy to remember
(relatively!) rather than mathematically optimal.  To distribute the
leap years as evenly as possible, since there are 97 leap years in 400
years, a leap year would happen every time the year number hit the
first integer >= an even multiple of 400/97 =~ 4.1237.  So the leap
years would normally be 4 years apart but every once in a while they'd
be 5 years apart instead.  In the current system, thanks to the
non-leap centennial years, there are occasional 8-year gaps between
leap years.


> But with the Metonic & Callipic cycles it's a question of intercalating
> a whole month, and knowing whether the intercalated month is of 29 or 30
> days. One has to know where one is in the cycle. Even in the Metonic
> cycle, one has to know whether it is the 3rd, 5th, 8th, 11th, 16th or
> 19th year as those will contain 13 months, while the rest have only 12.
True.  Figuring out where you are in a 400-year cycle is pretty easy -
dividing the century by 4 is a lot simpler than dividing the whole
year number by 19 (or 76 or...).

Because of which, a version of the Gregorian calendar with
evenly-distributed leap years wouldn't be  that bad, even for human
brains.  In any given 400 year cycle, the first leap year would be the
5th, then every 4 years from that through the 33rd; then there's a
5-year gap, so the 37th year is not leap but the 38th is, and then the
42nd, 46th, etc, through the 66th, then another gap to the 71st, and
so on.  So every 33 years there's a 5-year gap; in between,  every 4th
year is leap; and at the very end of the 400-year cycle there's no
gap, so instead of skipping 5 years from 396, you have a typical
4-year gap and year 400 is leap.  Then you go back to the start of the
cycle.
So 2004, as the 4th year of the current cycle, would have been a
common year, but last year would have been leap.

Well, you do have to sort of divide a number between 1 and 400 by 33.
But that's still easier than the Metonic cycle. :)


> Although I haven't been able to discover details, presumably the
> Callipic cycle was not just four consecutive Metonic cycles; there must
> have been differences in each of the four 19-year periods, otherwise
> there'd be no point in having the longer cycle.
Based on some quick Internet research: if all you're using the cycle
for is to figure out when to intercalate a month, the Callipic cycle
is no improvement over the Metonic; it's just four Metonic cycles back
to back.  If, however, you're using the cycle to figure out whether
each month is full or hollow (instead of using direct observation of
the moon), then the Callipic cycle is more accurate, as it includes
one less day than four back-to-back Metonic cycles. (27,759 days vs
4x6,940 = 27,760 days).

> >>For a reasonable description of ancient Greek pronunciation, I suggest
> >>Sidney Allen's "Vox Graeca"
> >
> > That sounds like a winner; I own his _Vox_Latina_.  But shouldn't the
> > title of the Greek one be in Greek instead of Latin? :)
>
> Ἡ ἑλληνικὴ φωνή   ?
If you say so.  It looks Greek to me. :)

--
Mark J. Reed <markjreed@...>

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