400edo: Difference between revisions
updated the terms to clarify, also Sintel's temp finder says 55/52 is the gen for Gregorian leap day, not 18/17 but 33\400 assigns both to this step |
→Scales: added another scale |
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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 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 GregorianLeapWeek[71] scale with 231\400 as the generator, which is close to 5/12 syntonic comma meantone. Likewise, 400edo 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]], and the corresponding temperament is 97 & 400, with comma list 2432/2431, 2601/2600, 2926/2925, 6175/6174, 17689/17680, and 22477/22440. | 400 is also the number of years in the Gregorian calendar's leap cycle. 400edo supports the GregorianLeapWeek[71] scale with 231\400 as the generator, which is close to 5/12 syntonic comma meantone. An interesting variation upon the scale would be the ISOWeek[71], which contains all the years which [[Wikipedia:ISO week date|have 53 weeks]] in the current calendar system. Likewise, 400edo 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]], and the corresponding temperament is 97 & 400, with comma list 2432/2431, 2601/2600, 2926/2925, 6175/6174, 17689/17680, and 22477/22440. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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* [[Huntington17]] | * [[Huntington17]] | ||
* GregorianLeapWeek[71] | * GregorianLeapWeek[71] | ||
* ISOWeek[71] | |||
* GregorianLeapDay[97] | * GregorianLeapDay[97] | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||