The 360-year Cycle of the Meyer- Palmen Soli-lunar Calendar
by Karl Palmen

If a 360-year cycle is used instead of the 60-year cycle, the formula for the 1st remainder becomes (360*c + y)*L mod Y < L where L=2519=7*360-1 and Y=6840=19*360.

(360*c + y)*L mod Y can be expressed as

( 3960*c + y*L ) mod Y

Noting that 3960 = 11*360, L is 7*360 - 1 and Y is 19*360 we have

( 360*( 11*c + 7*y mod 19) - y ) mod Y

From this we can obtain this remainder modulo 360 (which I call b). It is

b = (-y) mod Y

Because y is between 1 and 360 inclusive it is

b = 360-y

If this is subtracted from the full remainder one gets

(360*(11*c+7*y mod 19) - 360 ) mod Y

which is

360*( 11*c+7*y - 1 mod 19 )

which gives the 360s part of the remainder a as

a = 11*c + 7*y - 1 mod 19

The long years are those years for which a<7, except year 00-001 for which the remainder is L, giving a=6 and b=359.

Last modified: 1999-05-05 CE / 102-25-02-21 MP

Some Properties of the Meyer-Palmen Soli-lunar Calendar
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