77edo: Difference between revisions
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{{Sharpness-sharp7}} | {{Sharpness-sharp7}} | ||
== 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 | |||
|- | |||
| [[414zpi]] | |||
| 76.9918536925042 | |||
| 15.5860645308353 | |||
| 8.194847 | |||
| 1.311364 | |||
| 17.029289 | |||
| 77edo | |||
| 1200.12696887432 | |||
| 10 | |||
| 10 | |||
|} | |||
== 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 | ||
|- | |- | ||
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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* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperament | ! Temperament | ||
|- | |- | ||
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| 529.87 | | 529.87 | ||
| 512/375 | | 512/375 | ||
| [[Tuskaloosa]]<br | | [[Tuskaloosa]]<br>[[Muscogee]] | ||
|- | |- | ||
| 7 | | 7 | ||
| 32\77<br | | 32\77<br>(1\77) | ||
| 498.70<br | | 498.70<br>(15.58) | ||
| 4/3<br | | 4/3<br>(81/80) | ||
| [[Absurdity]] | | [[Absurdity]] | ||
|- | |- | ||
| 11 | | 11 | ||
| 32\77<br | | 32\77<br>(3\77) | ||
| 498.70<br | | 498.70<br>(46.75) | ||
| 4/3<br | | 4/3<br>(36/35) | ||
| [[Hendecatonic]] | | [[Hendecatonic]] | ||
|} | |} | ||
<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 | ||
== Music == | == Music == | ||