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

  1. The nearest shorter cycle to the cycle, which has a lesser mean year
  2. The cycle
  3. 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)