Lunisolar Cycles a multiple of the 293-year solar cycle

[Karl Palmen]

Dear Calendar People

In my lunisolar spreadsheets at http://www.the-light.com/cal/kp_Lunisolar_xls.html I have just three lunisolar cycles that are a multiple of the 293-year cycle of 294 years of 364 days. They are listed in

http://www.the-light.com/cal/Lunisolar4.html

and are

Ten 293-year cycles with nine truncations of the 19-year cycle (by one Octaeteris) with mean month of 29.5306162 days.

247 293-year cycles with 209 truncations of the 19-year cycle with mean month of 29.5305931 days.

353 293-year cycles with 293 truncations of the 19-year cycle with mean month of 29.5305862 days.

The third example has one truncation every 353 years exactly so is a multiple of the 353-year cycle, which Irv has stated is very accurate for the 293-year cycle.

Let’s look at half the difference between the two long cycles:

53 293-year cycles with 42 truncations of the 19-year cycle with mean month of 29.5305701 days.

Now we can use the ten-293-year cycle to adjust this:

Adding three cycles of ten-293-year cycles gives a cycle of

83 293-year cycles with 69 truncations of the 19-year cycle with mean month of 29.5305867 days.

When I tried this cycle of 83 on my lunisolar spreadsheet, I found that the equivalent lunar cycle has 18,400 yerms in it; a nice round number!

If instead, you add one or four cycles of ten 293-year cycles, the resulting cycle divides by three giving

21 293-year cycles with 17 truncations of the 19-year cycle with mean month of 29.5305774 days and

31 293-year cycles with 26 truncations of the 19-year cycle with mean month of 29.5305899 days respectively.

Another interesting cycle is the mean of the two long examples:

300 293-year cycles with  251 truncations of the 19-year cycle with mean month of 29.5305890 days. It has 19 truncations less than 30  ten-293-year cycles and hence one month more than 30 ten-293-year cycles.  It’s lunar cycle has an average of exactly  227 yerms each 293-year cycle.

I’ve also found

114 293-year cycles with 95 truncations of the 19-year cycle with mean month of 29.5305876 days. It is 5 months short of 293*6=1758 Metonic cycles.

A final interesting (but not very accurate) example is

19 293-year cycles with 19 truncations of the 19-year cycle with a mean month of 29.5306591 days. It has once truncation every 293 years on average and is one month short of 293 Metonic cycles.

In each case, the number of 293-year cycles plus the number of truncations is a multiple of 19. This arises because 293 has a remainder of 8 (the number of years truncated) when divided by 19.

Karl

10(14(17

--
Scanned by iCritical.