On 2009 May 19, at 18:06 , Victor Engel wrote:
This operation effectively introduces a leap month every 342 Metonic cycles. This gives a month:year ratio of:
19*342 : 235*342-1
Irv replies: I assume that Victor meant year:month ratio, or else to invert the given fraction.
The last thing that the Metonic cycle needs is an extra leap month! Surely he meant that a leap month is omitted every 343 Metonic cycles? It looks like that, because of the minus one at the end of the given ratio. Indeed, the numeric value of his ratio, when inverted to actually show months:years, is slightly less than my 4366:353 cycle, so it seems that he targeted the mean tropical year or 365+31/128 days (exact value depends on the assumed lunation period) whereas I target the mean northward equinoctial year.
The very long cycle = 6498 years has exaggerated equinox wobble and medium-term drift because it takes a full cycle before it makes the one month correction. A smoother correction can be obtained by periodically delaying the leap month for a year (as done in the 353-year cycle with 4366 months), rather than omitting it entirely.
-- Irv Bromberg, Toronto, Canada
