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
From these one can make all the other cycles whose mean year lies in between and hence in the range 365.2420 to 365.2427 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 61726 169 30 365.24260 7 39081 107 19 365.24299 ---------------------------------- 8 10592 29 19 365.24138 8 85832 235 154 365.24255 8 75240 206 135 365.24272 ---------------------------------- 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 49673 136 13 365.24265 13 42003 115 11 365.24348 ---------------------------------- 14 45290 124 11 365.24194 14 61726 169 15 365.24260 14 16436 45 4 365.24444 ---------------------------------- 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 161072 441 370 365.24263 16 150480 412 341 365.24272 ---------------------------------- 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 71 336.24214 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 124913 342 301 365.24269 23 115782 317 279 365.24290 ---------------------------------- 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 99346 272 13 365.24265 26 91676 251 12 365.24303 ---------------------------------- 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)