39edo: Difference between revisions
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== 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 | |||
|- | |||
| [[173zpi]] | |||
| 39.1237487937926 | |||
| 30.6719073963176 | |||
| 5.593908 | |||
| 0.926356 | |||
| 14.714802 | |||
| 39edo | |||
| 1196.20438845639 | |||
| 7 | |||
| 7 | |||
|} | |} | ||
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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 | ||
|- | |- | ||
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|+ 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* | ||
! Temperament | ! Temperament | ||
! MOS | ! MOS scales | ||
|- | |- | ||
| 1 | | 1 | ||
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|- | |- | ||
| 3 | | 3 | ||
| 8\39<br | | 8\39<br>(5\39) | ||
| 246.2<br | | 246.2<br>(153.8) | ||
| [[Triforce]] (39) | | [[Triforce]] (39) | ||
| [[3L 3s]], [[6L 3s]], [[9L 6s]], [[15L 9s]] | | [[3L 3s]], [[6L 3s]], [[9L 6s]], [[15L 9s]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 16\39<br | | 16\39<br>(3\39) | ||
| 492.3<br | | 492.3<br>(92.3) | ||
| [[Augene]] (39d) | | [[Augene]] (39d) | ||
| [[3L 3s]], [[3L 6s]], [[3L 9s]], [[12L 3s]], [[12L 15s]] | | [[3L 3s]], [[3L 6s]], [[3L 9s]], [[12L 3s]], [[12L 15s]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 17\39<br | | 17\39<br>(4\39) | ||
| 523.1<br | | 523.1<br>(123.0) | ||
| [[Deflated]] (39bd) | | [[Deflated]] (39bd) | ||
| [[3L 3s]], [[3L 6s]], [[9L 3s]], [[9L 12s]], [[9L 21s]] | | [[3L 3s]], [[3L 6s]], [[9L 3s]], [[9L 12s]], [[9L 21s]] | ||
|- | |- | ||
| 13 | | 13 | ||
| 16\39<br | | 16\39<br>(1\39) | ||
| 492.3<br | | 492.3<br>(30.8) | ||
| [[Tridecatonic]] | | [[Tridecatonic]] | ||
| [[13L 13s]] | | [[13L 13s]] | ||
|} | |} | ||
<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 | ||
== 39edo and world music == | == 39edo and world music == |