Gregorian leap day: Difference between revisions
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{{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. | '''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]]. | 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]]. 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]]. | ||
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. | 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. | ||
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Mapping: {{mapping| 1 10 -7 8 16 7 -12 | 0 -102 113 131 -152 -40 195 }} | Mapping: {{mapping| 1 10 -7 8 16 7 -12 | 0 -102 113 131 -152 -40 195 }} | ||
Optimal tuning (CTE): ~2 = 1\1, | Optimal tuning (CTE): ~2 = 1\1, 18/17 = 98.9993 | ||
Optimal ET sequence: {{Optimal ET sequence| | Optimal ET sequence: {{Optimal ET sequence| 97g, 303g, 400 }} | ||
Badness: 0.0776 | Badness: 0.0776 | ||
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Mapping: {{mapping| 1 10 -7 8 16 7 -12 4 | 0 -102 113 131 -152 -40 195 3 }} | Mapping: {{mapping| 1 10 -7 8 16 7 -12 4 | 0 -102 113 131 -152 -40 195 3 }} | ||
Optimal tuning (CTE): ~2 = 1\1, | Optimal tuning (CTE): ~2 = 1\1, 18/17 = 98.9993 | ||
Optimal ET sequence: {{Optimal ET sequence| | Optimal ET sequence: {{Optimal ET sequence| 97g, 303g, 400 }} | ||
Badness: 0.0541 | Badness: 0.0541 | ||
[[Category: | [[Category:Gregorian leap day| ]] <!-- main article --> | ||
[[Category:Rank-2 temperaments]] | |||