If a 360-year cycle is used instead of the 60-year cycle, the formula for the 1st remainder becomes

The 360-year Cycle of the Meyer-

Palmen Soli-lunar Calendarby Karl Palmen

(360*c + y)*L mod Y < LwhereL=2519=7*360-1 andY=6840=19*360.

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

( 3960*c + y*L ) mod YNoting that 3960 = 11*360,

Lis 7*360 - 1 andYis 19*360 we have

( 360*( 11*c + 7*y mod 19) - y ) mod YFrom this we can obtain this remainder modulo 360 (which I call

b). It is

b = (-y) mod YBecause

yis between 1 and 360 inclusive it is

b = 360-yIf this is subtracted from the full remainder one gets

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

360*( 11*c+7*y - 1 mod 19 )which gives the 360s part of the remainder

aas

a = 11*c + 7*y - 1 mod 19The long years are those years for which

a<7, except year 00-001 for which the remainder isL, givinga=6 andb=359.Last modified: 1999-05-05 CE / 102-25-02-21 MP

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