400edo: Difference between revisions
m →Rank-2 temperaments: correction |
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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| Prime factorization = 2<sup>4</sup> × 5<sup>2</sup> | | Prime factorization = 2<sup>4</sup> × 5<sup>2</sup> | ||
| Step size = 3.00000¢ | | Step size = 3.00000¢ | ||
| Fifth = 234\400 (702.00¢) (→ [[200edo|117\ | | Fifth = 234\400 (702.00¢) (→ [[200edo|117\200]]) | ||
| Semitones = 38:30 (114.00¢ : 90.00¢) | | Semitones = 38:30 (114.00¢ : 90.00¢) | ||
| Consistency = 21 | | Consistency = 21 | ||
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400edo doubles [[200edo]], which holds a record for the best 3/2 fifth approximation. | 400edo doubles [[200edo]], which 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 | 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 === | ||
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* [[Huntington10]] | * [[Huntington10]] | ||
* [[Huntington17]] | * [[Huntington17]] | ||
* LeapWeek[71] | * LeapWeek[71] | ||
* LeapDay[97] | * LeapDay[97] | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||