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12 months Edit

Systematic month lengths in 12-month calendars
Year Half Third Quarter Sixth Month Irregular 61-day double-month 91-day quarter 30-day month
Greg/Jul common 31:30 30:31 31:30* 30:31* common 31:30:30 30:31:30 30:30:31 5:4:4 4:5:4 4:4:5
Y H1 T1 Q1 S1 M01 365⁺ 181⁺ 120⁺ 90⁺ 59⁺ 31 366⁻ 183 122 61 92 31 91 30 92 31 91 30 364⁺ 182 91 122 61 31 121 61 30 121 60 30 126 63 35 119 63 28 119 56 28 360⁺ 180 120 90 60 30
M02 28⁺ 30 31 30 31 30 31 30 28 35 28 30
S2 M03 61 31 61 31 30 31 30 61 30 60 30 61 31 63 28 56 28 63 35 60 30
Q2 M04 91 30 91 30 92 31 91 30 92 31 91 31 30 30 35 28 28 90 30
T2 S3 M05 123 61 31 122 61 31 30 31 30 121 60 30 122 61 31 121 61 30 119 56 28 126 63 35 119 63 28 120 60 30
M06 30 30 31 30 31 30 30 31 28 28 35 30
H2 Q3 S4 M07 184 92 62 31 183 61 92 31 91 30 91 30 92 31 182 91 61 31 61 30 60 30 63 35 63 28 56 28 180 90 60 30
M08 31 30 31 31 30 30 31 30 28 35 28 30
T3 S5 M09 122 61 30 122 61 31 30 30 31 121 61 30 121 60 30 122 61 31 119 63 28 119 56 28 126 63 35 120 60 30
Q4 M10 92 31 91 30 92 31 92 31 91 30 91 31 30 30 35 28 28 90 30
S6 M11 61 30 61 31 30 30 31 60 30 61 31 61 30 56 28 63 35 63 28 60 30
M12 31 30 31 31 30 30 30 31 28 28 35 30
Ordinal start dates in 12-month calendars
Year Half Third Quarter Sixth Month Irregular 61-day double-month 91-day quarter Constant
Greg/Jul 31:30 30:31 31:30* 30:31* 31:30:30 30:31:30 30:30:31 5:4:4 4:5:4 4:4:5 30
Y H1 T1 Q1 S1 M01 001 001 001 001 001 001 001 001 001 001 001 001
M02 032 032 031 032 031 032 031 031 036 029 029 031
S2 M03 060+ 062 062 062 062 062 062 061 064 064 057 061
Q2 M04 091+ 093 092 093 092 092 092 092 092 092 092 091
T2 S3 M05 121+ 123 123 123 123 123 122 122 127 120 120 121
M06 152+ 154 153 154 153 153 153 152 155 155 148 151
H2 Q3 S4 M07 182+ 184 184 184 184 183 183 183 183 183 183 181
M08 213+ 215 214 214 215 214 213 213 218 211 211 211
T3 S5 M09 244+ 245 245 245 245 244 244 243 246 246 239 241
Q4 M10 274+ 276 275 275 276 274 274 274 274 274 274 271
S6 M11 305+ 306 306 306 306 305 304 304 309 302 302 301
M12 335+ 337 336 336 337 335 335 334 337 337 330 331
Comparison to legacy months in common years of 12-month calendars
Difference 61-day double-month 91-day quarter Constant
31:30 30:31 31:30* 30:31* 31:30:30 30:31:30 30:30:31 5:4:4 4:5:4 4:4:5 30
length +3…+7 1 1 1 4 4 4
+2 1 1 1 1 1
+1 2 2 4 1 1 2
±0 6 5 10 1 6 5 4 1 0 1 4
−1 3 4 1 6 4 5 5 7
−2…−3 7 8 7
offsets +3…+6 6 2
+2 8 3 5 6 2 1 2 2
+1 2 7 5 4 4 4 4 2 2 2 1
±0 2 1 2 1 6 5 4 2 2 2 3
−1 1 1 2 4 1 1 3
−2…−5 3 7 5

13 months Edit

Systematic month lengths in 13-month calendars
Year Month 4-week
Y M01 364⁺ 28
M02 28
M03 28
M04 28
M05 28
M06 28
M07 28
M08 28
M09 28
M10 28
M11 28
M12 28
M13 28

14 months Edit

Systematic lengths in 14-month calendars
Year Half Seventh Month common (regular) 4-week
26 3–4 3–4* 4–3 4–3*
Y H1 S1 M01 364⁺ 182 52 26 56 28 56 28 56 28 56 28
M02 26 28 28 28 28
S2 M03 52 26 49 21 49 28 49 28 49 21
M04 26 28 21 21 28
S3 M05 52 26 56 28 56 28 56 28 56 28
M06 26 28 28 28 28
S4 M07 52 26 49 21 49 21 49 21 49 21
H2 M08 182 26 28 28 28 28
S5 M09 52 26 49 28 49 28 56 28 56 28
M10 26 21 28 28 28
S6 M11 52 26 56 28 56 28 49 21 49 21
M12 26 28 28 28 28
S7 M13 52 26 49 28 49 28 49 28 49 28
M14 26 21 21 21 21

10 months Edit

Systematic lengths in 10-month calendars
Year Half Fifth Month (alternating) (constant) 5-week
common 36:37 37:36 36⁺ common 1st 2nd 3rd 4th 5th
Y H1 F1 M01 365⁺ 73 182 36 183 37 360⁺ 180 72 36 364⁺ 182 77 42 77 35 70 35 70 35 70 35
M02 37 36 36 35 42 35 35 35
F2 M03 73 36 37 72 36 70 35 70 35 77 42 77 35 70 35
M04 37 36 36 35 35 35 42 35
F3 M05 73 36 37 72 36 77 35 70 35 70 35 70 35 77 42
H2 M06 183 37 182 36 180 36 182 42 35 35 35 35
F4 M07 73 36 37 72 36 70 35 77 42 77 35 70 35 70 35
M08 37 36 36 35 35 42 35 35
F5 M09 73 36 37 72 36 70 35 70 35 70 35 77 42 77 35
M10 37 36 36 35 35 35 35 42

11 months Edit

Systematic month lengths in 11-month calendars
Year Month equal 2 longer
33 leap month 3–4–4 4–3–4 4–4–3
Y M01 363⁺ 33 350 (385) 35 365⁺ 33 33 33
M02 33 35 33 33 33
M03 33 35 33 33 33
M04 33 35 33 34 34
M05 33 35 33 33 33
M06 33 35 33 33 33
M07 33 35 34 33 33
M08 33 35 33 33 34
M09 33 35 33 33 33
M10 33 35 33 33 33
M11 33 (35) 34 34 33

10+1 months Edit

A calendar with ten regular and one leap month, where each month has exactly five weeks of seven days, has years either 350 or 385 days long. This can only be compatible with leap cycles that have a number of days divisible by five, i.e. not the popular 293 and 400-year cycles (146097 and 107016 days respectively).

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