Solar Calendar Cycles for N-day Cycles
Here is a list of calendar cycles for a solar calendar
where every year has a whole number N-day cycles.
For example, N=7 the year has a whole number of weeks most years have 52 weeks,
but some have 53 weeks.
Victor listed one cycle for each N at
VECyc.txt. Each such cycle is the shortest
whose mean year falls in the range of 365.2420 to 365.2427 days.
However I want to list more cycles, so I list three cycles
- The nearest shorter cycle to the cycle, which has a lesser mean year
- The cycle
- The nearest shorter cycle to the cycle, which has a greater mean year
where the cycle is the shortest cycle
with mean year in range 365.2416 to 365.2428 days,
which just includes the range of mean durations of
the various types of tropical year.
From these one can make all the other cycles
whose mean year lies in between and hence in
the range 365.2416 to 365.2428 days.
The cycle is
the sum of the other two,
where the sum is formed by the concatenation of the cycles.
The number of days, years and long years in a the sum of two cycles
are the sums of the respective quantities in the cycles being summed.
The mean year of a sum is between the mean years of the summed.
To make any cycle whose mean year lies in between those of
any two of the three cycles listed,
one adds together whole number of these two cycles.
I've listed for all N-day cycles up to 30 days.
N Days Years LongYrs YrLength
---------------------------------
1 10592 29 7 365.24138
1 12053 33 8 365.24242
1 1461 4 1 365.25
----------------------------------
2 10592 29 18 365.24138
2 24106 66 41 365.24242
2 13514 37 23 365.24324
----------------------------------
3 31776 87 65 365.24138
3 33237 91 68 365.24176
3 1461 4 3 365.25
----------------------------------
4 10592 29 9 365.24138
4 37620 103 32 365.24272
4 27028 74 23 365.24324
----------------------------------
5 7670 21 1 365.23810
5 22645 62 3 365.24194
5 14975 41 2 365.24390
----------------------------------
6 31776 87 76 365.24138
6 34698 95 83 365.24211
6 2922 8 7 365.25
----------------------------------
7 6209 17 3 365.23529
7 22645 62 11 365.24194
7 16436 45 8 364.24444
----------------------------------
8 10592 29 19 365.24138
8 75240 206 135 365.24272
8 64648 177 116 365.24294
----------------------------------
9 28854 79 46 365.24051
9 33237 91 53 365.24176
9 4383 12 7 365.25
----------------------------------
10 7670 21 11 365.23810
10 37620 103 54 365.24272
10 29950 82 45 365.24390
----------------------------------
11 19723 54 11 365.24074
11 37620 103 21 365.24271
11 17897 49 10 365.24490
----------------------------------
12 31776 87 38 365.24138
12 37620 103 45 365.24272
12 5844 16 7 365.25
----------------------------------
13 7670 21 2 365.23810
13 49673 136 13 365.24265
13 42003 115 11 365.24348
----------------------------------
14 28854 79 7 365.24051
14 45290 124 11 365.24194
14 16436 45 4 365.24444
----------------------------------
15 30315 83 29 365.24096
15 37620 103 36 365.24272
15 7305 20 7 365.25
----------------------------------
16 10592 29 24 365.24138
16 150480 412 341 365.24272
16 139888 383 317 365.24282
----------------------------------
17 11322 31 15 365.22581
17 12053 33 16 365.24242
17 731 2 1 365.5
----------------------------------
18 28854 79 23 365.24051
18 37620 103 30 365.24272
18 8766 24 7 365.25
----------------------------------
19 3287 9 2 365.22222
19 37620 103 23 365.24272
19 34333 94 21 365.24468
----------------------------------
20 15340 42 11 365.23810
20 37620 103 27 365.24272
20 22280 61 16 365.24590
----------------------------------
21 28854 79 31 365.24051
21 67935 186 73 365.24194
21 39081 107 42 365.24299
----------------------------------
22 1826 5 3 365.2
22 37620 103 62 365.24271
22 35794 98 59 365.24490
----------------------------------
23 9131 25 22 365.24
23 124913 342 301 365.24269
23 115782 317 279 365.24290
----------------------------------
24 31776 87 19 365.24138
24 75240 206 45 365.24272
24 43464 119 26 365.24370
----------------------------------
25 83275 228 139 365.24123
25 98250 269 164 365.24164
25 14975 41 25 365.24390
----------------------------------
26 7670 21 1 365.23810
26 99346 272 13 365.24265
26 91676 251 12 365.24303
----------------------------------
27 20088 55 29 365.23624
27 33237 91 48 365.24176
27 13149 36 19 365.25
----------------------------------
28 74144 203 9 365.24138
28 90580 248 11 365.24194
28 16436 45 2 365.24444
----------------------------------
29 173855 476 283 365.24160
29 187369 513 305 365.24172
29 13514 37 22 365.24343
----------------------------------
30 23010 63 11 365.23810
30 37620 103 18 365.24272
30 14610 40 9 365.25
----------------------------------
Karl Palmen July 2003 (revised Apr 2006)