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Re: Accurate Lunisolar Calendar
by Brillig
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Dear Irv,
I didn't give the units leading to the fraction, which is dimensionless, so you can flip it either way. Just to illustrate:
year length : month length
would be the inverse of
year number : month number
As to whether the leap month is added or subtracted, it all depends on whether the driver is the year or the month. If it's the month as I described, yes, it is omitted. I still say it's an introduction of a leap month. Maybe I should say it's the introduction of an adjustment.
As far as target goes, I just wanted to see what one step more accurate than the Metonic cycle would yield. My goal was to use the numbers already inherent in the 19:235 ratio. Without extending the period ridiculously far, there were really only a small number of options, the most obvious ones being 18*19 and 19*19. I chose the former because it's more accurate. That it happens to come close to the mean tropical year is just an accident. I did not target it specifically.
I was expecting the delay remark, but I expected it from Karl and not Irv. I would like to see the mechanics of the delay, though. I formulated the scheme the way I did because the mechanics are simple. And as I said in my original post, you can tell exactly how far into the progression the device is by reading it like a clock. We don't worry about the large jump of an hour as we wait for the minute hand to go around. We can tell by how far around it is what the progress is.
Victor
I didn't give the units leading to the fraction, which is dimensionless, so you can flip it either way. Just to illustrate:
year length : month length
would be the inverse of
year number : month number
As to whether the leap month is added or subtracted, it all depends on whether the driver is the year or the month. If it's the month as I described, yes, it is omitted. I still say it's an introduction of a leap month. Maybe I should say it's the introduction of an adjustment.
As far as target goes, I just wanted to see what one step more accurate than the Metonic cycle would yield. My goal was to use the numbers already inherent in the 19:235 ratio. Without extending the period ridiculously far, there were really only a small number of options, the most obvious ones being 18*19 and 19*19. I chose the former because it's more accurate. That it happens to come close to the mean tropical year is just an accident. I did not target it specifically.
I was expecting the delay remark, but I expected it from Karl and not Irv. I would like to see the mechanics of the delay, though. I formulated the scheme the way I did because the mechanics are simple. And as I said in my original post, you can tell exactly how far into the progression the device is by reading it like a clock. We don't worry about the large jump of an hour as we wait for the minute hand to go around. We can tell by how far around it is what the progress is.
Victor
On Tue, May 19, 2009 at 9:05 PM, Irv Bromberg <irv.bromberg@...> wrote:
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*342-1Irv 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.
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