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 365.2420 to 365.2425 days. This range more restricted than Victor's 365.2420 to 365.2427 which is used in kp_NdaySolarCyc.html.

From these one can make all the other cycles whose mean year lies in between and hence in the range 365.2420 to 365.2425 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 show an example of all cycles for N=30 less than 1000 years.

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  33237    91      68  365.24176
 3  34698    95      71  365.24211
 3   1461     4       3  365.25
----------------------------------
 4  10592    29       9  365.24138
 4  48212   132      41  365.24242
 4  37620   103      32  365.24272
----------------------------------
 5  22645    62       3  365.24194
 5  60265   165       8  365.24242
 5  37620   103       5  365.24272
----------------------------------
 6  31776    87      76  365.24138
 6  34698    95      83  365.24211
 6   2922     8       7  365.25  
----------------------------------
 7  22645    62      11  365.24194
 7  84371   231      41  365.24242
 7  61726   169      30  365.24260
----------------------------------
 8  10592    29      19  365.24138
 8  96424   264     173  365.24242
 8  85832   235     154  365.24255
----------------------------------
 9  33237    91      53  365.24176
 9  70857   194     113  365.24227
 9  37620   103      60  365.24272
----------------------------------
10  45290   124      65  365.24194
10  82910   227     119  365.24229
10  37620   103      54  365.24272
----------------------------------
11  19723    54      11  365.24074
11  57343   157      32  365.24204
11  37620   103      21  365.24271
----------------------------------
12  31776    87      38  365.24138
12  69396   190      83  365.24211
12  37620   103      45  365.24272 
----------------------------------
13   7670    21       2  365.23810
13  57343   157      15  365.24204
13  49673   136      13  365.24265
----------------------------------
14  45290   124      11  365.24194
14 107016   293      24  365.24232
14  61726   169      15  365.24260
----------------------------------
15  67935   186      65  365.24194
15 105555   289     101  365.24221
15  37620   103      36  365.24272
----------------------------------
16  10592    29      24  365.24138
16 182256   499     418  365.24248
16 171664   470     394  365.24255
----------------------------------
17  11322    31      15  365.22581
17  12053    33      16  365.24242
17    731     2       1  365.5
----------------------------------
18  66474   182      53  365.24176
18 104094   285      83  365.24211
18  37620   103      30  365.24272
----------------------------------
19  78527   215      48  365.24186
19 116147   318      71  365.24214
19  37620   103      23  365.24272
----------------------------------
20  90580   248      65  365.24194
20 128200   351      92  365.24217
20  37620   103      27  365.24272
----------------------------------
21  67935   186      73  365.24194
21 107016   293     115  365.24232
21  39081   107      42  365.24299
----------------------------------
22  77066   211     127  365.24171
22 114686   314     189  365.24204
22  37620   103      62  365.24271
----------------------------------
23   9131    25      22  365.24
23 143175   392     345  365.24235
23 134044   367     323  365.24251
----------------------------------
24  31776    87      19  365.24138
24 107016   293      64  365.24232
24  75240   206      45  365.24272
----------------------------------
25 113225   310     189  365.24194
25 128200   351     214  365.24217
25  14975    41      25  365.24390
----------------------------------
26   7670    21       1  365.23810
26 107016   293      14  365.24232
26  99346   272      13  365.24265
----------------------------------
27  33237    91      48  365.24176
27 146097   400     211  365.2425
27 112860   309     163  365.24272
----------------------------------
28  90580   248      11  365.24194
28 107016   293      13  365.24232
28  16436    45       2  365.24444
----------------------------------
29 227911   624     371  365.24199
29 241425   661     393  365.24206
29  13514    37      22  365.24343
----------------------------------
30 135870   372      65  365.24194
30 173490   475      83  365.24211
30  37620   103      18  365.24272
----------------------------------

For example one can add together the examples for the 30-day cycle to get all cycles that use the 30-day cycle and are less than 1000 years. The sum shows how many of the first and third to add together.

 N  Days  Years LongYrs  YrLength    Sum
-----------------------------------------
30 135870   372      65  365.24194  (1,0)
30 173490   475      83  365.24211  (1,1)
30  37620   103      18  365.24272  (0,1)
-----------------------------------------
30 309360   847     148  365.24203  (2,1)
30 173490   475      83  365.24211  (1,1)
30 211110   578     101  365.24221  (1,2)
30 248730   681     119  365.24229  (1,3)
30 286350   784     137  365.24235  (1,4)
30 323970   887     155  365.24239  (1,5)
30 361590   990     173  365.24242  (1,6)
-----------------------------------------

Karl Palmen June 2003 (revised Apr 2006)