Re: Attic months

staving Mark J Reed:
>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.
I've been doing some experimentation, and I've come up with a 128 year
cycle that I might use for a conculture.

The 128-year cycle is divided into three 33-year blocks and one 29-year block.
Each 33-year block contains seven 4-year blocks and one 5-year block, while
the 29-year block contains six 4-year blocks and one 5-year block. Each of
the 4 or 5-year blocks contains 1 leap year, thus making 31 leap years in
128 years. Should be accurate to about 1 day in 80000 years. I'm also
working on a 5000 year calendar, with a mean year length of 365.2422 days.

Pete