Gregorian leap day: Difference between revisions

VisualWikitext

@@ Line 1: / Line 1: @@
-is  the number of years in the Gregorian calendar's leap cycle.
+{{Novelty}}
+{{Distinguish|Leapday}}
+'''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.
-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.
+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]]. The optimal tuning is very close to 18/17, which makes it very similar to [[Galilei's 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]].
-[[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]].
+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, {{monzo| -13 3 -17 17 }}
+{{Mapping|legend=1| 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|legend=1| 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: {{mapping| 1 10 -7 8 16 | 0 -102 113 131 -152 }}
+Optimal tuning (CTE): ~2 = 1\1, 69120/65219 = 98.9994
+Optimal ET sequence: {{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: {{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: {{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: {{mapping| 1 10 -7 8 16 7 -12 | 0 -102 113 131 -152 -40 195 }}
+Optimal tuning (CTE): ~2 = 1\1, 18/17 = 98.9993
+Optimal ET sequence: {{Optimal ET sequence| 97g, 303g, 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: {{mapping| 1 10 -7 8 16 7 -12 4 | 0 -102 113 131 -152 -40 195 3 }}
+Optimal tuning (CTE): ~2 = 1\1, 18/17 = 98.9993
+Optimal ET sequence: {{Optimal ET sequence| 97g, 303g, 400 }}
+Badness: 0.0541
+[[Category:Gregorian leap day| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]