684edo: Difference between revisions
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 684 factors into {{factorization|684}}, 684edo has subset edos {{EDOs| 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, and 342 }}. | Since 684 factors into {{factorization|684}}, 684edo has subset edos {{EDOs| 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, and 342 }}. | ||
== Approximation to JI == | |||
=== Zeta peak index === | |||
{| class="wikitable center-all" | |||
|- | |||
! colspan="3" | Tuning | |||
! colspan="3" | Strength | |||
! colspan="2" | Closest edo | |||
! colspan="2" | Integer limit | |||
|- | |||
! ZPI | |||
! Steps per octave | |||
! Step size (cents) | |||
! Height | |||
! Integral | |||
! Gap | |||
! Edo | |||
! Octave (cents) | |||
! Consistent | |||
! Distinct | |||
|- | |||
| [[5818zpi]] | |||
| 683.938934890938 | |||
| 1.75454260429165 | |||
| 14.267321 | |||
| 1.773752 | |||
| 20.109967 | |||
| 684edo | |||
| 1200.10714133549 | |||
| 18 | |||
| 18 | |||
|} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning error | ! colspan="2" | Tuning error | ||
|- | |- | ||
| Line 45: | Line 77: | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| 18 | | 18 | ||
| 271\684<br | | 271\684<br>(5\684) | ||
| 475.44<br | | 475.44<br>(8.77) | ||
| 1053/800<br | | 1053/800<br>(1287/1280) | ||
| [[Semihemiennealimmal]] | | [[Semihemiennealimmal]] | ||
|- | |- | ||
| 38 | | 38 | ||
| 151\684<br | | 151\684<br>(7\684) | ||
| 264.91<br | | 264.91<br>(12.28) | ||
| 500/429<br | | 500/429<br>(144/143) | ||
| [[Semihemienneadecal]] | | [[Semihemienneadecal]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||