Gregorian leap day: Difference between revisions

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-is  the number of years in the Gregorian calendar's leap cycle.
+Gregorian leap day is a rank-2 temperament which is produced by temperament-merging 97edo, which has the cardinality of leap years in Gregorian calendar's cycle, and 400edo, the whole duration of the cycle.
+== Theory ==
+is the number of years in the Gregorian calendar's leap cycle. They are not spread evenly, but if they were, this would produce a scale with a 33\400 generator which is associated to [[18/17]] and [[55/52]], three of which make [[19/16]]. Because the generator is mapped to 18/17, the temperament can be seen as an octavated version of [[18/17 equal-step tuning]]. Gregorian leap day has mos of size 12, 13, 25, 37, 49, 61, 73, and 97. [[1L 11s]] mos of this temperament is a barely noticeable circulating temperament for [[12edo]].
-edo contains GregorianLeapDay[97] scale, which is a [[maximal evenness]] version of the leap rule currently in use in the world today. The scale has a 33\400 generator which is associated to [[18/17]] and [[55/52]], three of which make [[19/16]]. The corresponding temperament is 97 & 400, with comma list 2432/2431, 2601/2600, 2926/2925, 6175/6174, 17689/17680, and 22477/22440.
+In the 7-limit, temperament reaches [[15/8]] in 11 generators, entirely contained within the 12-tone well temperament, and also [[7/5]] in 18 generators.
+[[Category: Rank 2]]
+== Temperament data ==
+Subgroup: 2.3.5.7
+Comma list: 67108864/66976875, 6281023877654589/6250000000000000
+{{mapping|legend=1| 1 10 -7 8 | 0 -102 113 131 }}
+: mapping generators: ~2 = 1\1, 160000/151263 = 98.998
+[[Support]]ing [[ET]]s: {{EDOs|97, 400}}, ...
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-[[1L 11s]] mos of this temperament is an octavated variant of [[18/17 equal-step tuning|18/17s equal temperament]], and a barely noticeable circulating temperament for [[12edo]].
+Comma list: 166698/166375, 422576/421875, 67108864/66976875
-[[Category: Rank 2]]
+{{mapping|legend=1| 1 10 -7 8 16 | 0 -102 113 131 -152 }}
+: mapping generators: ~2 = 1\1, 69120/65219 = 98.998
+[[Support]]ing [[ET]]s: {{EDOs|97, 303, 400}}, ...
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 676/675, 4096/4095, 166698/166375, 105644/105625
+{{mapping|legend=1| 1 10 -7 8 16 7 | 0 -102 113 131 -152 -40 }}
+: mapping generators: ~2 = 1\1, 55/52 = 98.998
+[[Support]]ing [[ET]]s: {{EDOs|97, 303, 400}}, ...
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 676/675, 4096/4095, 11016/11011, 14400/14399, 93639/93500
+{{mapping|legend=1| 1 10 -7 8 16 7 -12 | 0 -102 113 131 -152 -40 195 }}
+: mapping generators: ~2 = 1\1, 55/52 = 98.998
+[[Support]]ing [[ET]]s: {{EDOs|97, 303, 400}}, ...
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 676/675, 2926/2925, 4096/4095, 6175/6174, 11016/11011, 14400/14399
+{{mapping|legend=1| 1 10 -7 8 16 7 -12 4 | 0 -102 113 131 -152 -40 195 3}}
+: mapping generators: ~2 = 1\1, 55/52 = 98.998
+[[Support]]ing [[ET]]s: {{EDOs|97, 303, 400}}, ...