Gregorian leap day
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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.
400 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.
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.
Temperament data
Subgroup: 2.3.5.7
Comma list: 67108864/66976875, [-13 3 -17 17⟩
Mapping: [⟨1 10 -7 8], ⟨0 -102 113 131]]
- mapping generators: ~2, 160000/151263
Optimal tuning (CTE): ~2 = 1\1, 160000/151263 = 98.9982
Optimal ET sequence: 97, 303, 400, 1297, 1697c
Badness: 1.10
11-limit
Subgroup: 2.3.5.7.11
Comma list: 166698/166375, 422576/421875, 67108864/66976875
Mapping: [⟨1 10 -7 8 16], ⟨0 -102 113 131 -152]]
Optimal tuning (CTE): ~2 = 1\1, 69120/65219 = 98.9994
Optimal ET sequence: 97, 303, 400
Badness: 0.251
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 4096/4095, 105644/105625, 166698/166375
Mapping: [⟨1 10 -7 8 16 7], ⟨0 -102 113 131 -152 -40]]
Optimal tuning (CTE): ~2 = 1\1, 55/52 = 98.9992
Optimal ET sequence: 97, 303, 400
Badness: 0.126
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 676/675, 4096/4095, 11016/11011, 14400/14399, 93639/93500
Mapping: [⟨1 10 -7 8 16 7 -12], ⟨0 -102 113 131 -152 -40 195]]
Optimal tuning (CTE): ~2 = 1\1, 55/52 = 98.9993
Optimal ET sequence: 97, 303, 400
Badness: 0.0776
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 676/675, 2926/2925, 4096/4095, 6175/6174, 11016/11011, 14400/14399
Mapping: [⟨1 10 -7 8 16 7 -12 4], ⟨0 -102 113 131 -152 -40 195 3]]
Optimal tuning (CTE): ~2 = 1\1, 55/52 = 98.9993
Optimal ET sequence: 97, 303, 400
Badness: 0.0541