400edo: Difference between revisions
Clarified what LeapWeek[71] and LeapDay[97] are, and also discovered that LeapDay97's generator is 33\400 and also edited accordingly. |
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400edo is [[consistent]] in the [[21-odd-limit]]. It tempers out the unidecma, {{monzo| -7 22 -12 }}, and the qintosec comma, {{monzo| 47 -15 -10 }}, in the 5-limit; [[2401/2400]], 1959552/1953125, and 14348907/14336000 in the 7-limit; 5632/5625, [[9801/9800]], 117649/117612, and [[131072/130977]] in the 11-limit; [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]] and 39366/39325 in the 13-limit, [[support|supporting]] the [[decoid]] temperament and the [[quinmite]] temperament. It tempers out [[936/935]], [[1156/1155]], 2058/2057, [[2601/2600]], 4914/4913 and [[24576/24565]] in the 17-limit, and 969/968, [[1216/1215]], [[1521/1520]], and [[1729/1728]] in the 19-limit. | 400edo is [[consistent]] in the [[21-odd-limit]]. It tempers out the unidecma, {{monzo| -7 22 -12 }}, and the qintosec comma, {{monzo| 47 -15 -10 }}, in the 5-limit; [[2401/2400]], 1959552/1953125, and 14348907/14336000 in the 7-limit; 5632/5625, [[9801/9800]], 117649/117612, and [[131072/130977]] in the 11-limit; [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]] and 39366/39325 in the 13-limit, [[support|supporting]] the [[decoid]] temperament and the [[quinmite]] temperament. It tempers out [[936/935]], [[1156/1155]], 2058/2057, [[2601/2600]], 4914/4913 and [[24576/24565]] in the 17-limit, and 969/968, [[1216/1215]], [[1521/1520]], and [[1729/1728]] in the 19-limit. | ||
400 factors into 2<sup>4</sup> × 5<sup>2</sup>, with subset edos {{EDOs| 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, and 200 }}. Notably, 200edo holds a record for the best 3/2 fifth approximation. | |||
400 is also the number of years in the Gregorian calendar's leap cycle. 400edo supports the LeapWeek[71] scale with 231\400 as the generator, which is close to 5/12 syntonic comma meantone. Likewise, 400edo contains LeapDay[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]], making it an approximation of [[18/17 equal-step tuning]]. Since it tempers out the 93347/93312, a stack of three 18/17's is equated with 19/16. | 400 is also the number of years in the Gregorian calendar's leap cycle. 400edo supports the LeapWeek[71] scale with 231\400 as the generator, which is close to 5/12 syntonic comma meantone. Likewise, 400edo contains LeapDay[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]], making it an approximation of [[18/17 equal-step tuning]]. Since it tempers out the 93347/93312, a stack of three 18/17's is equated with 19/16. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{ | {{Harmonics in equal|400|columns=13}} | ||
== Selected intervals == | == Selected intervals == | ||