183edo: Difference between revisions
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 183 factors into 3 × 61, 183edo contains [[3edo]] and [[61edo]] as its subsets. | Since 183 factors into 3 × 61, 183edo contains [[3edo]] and [[61edo]] as its subsets. | ||
== 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 | |||
|- | |||
| [[1210zpi]] | |||
| 182.999728466810 | |||
| 6.55738677895164 | |||
| 11.020824 | |||
| 1.643410 | |||
| 19.731996 | |||
| 183edo | |||
| 1200.00178054815 | |||
| 18 | |||
| 18 | |||
|} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 21: | Line 53: | ||
! 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 75: | Line 107: | ||
|+ 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 | ||
|- | |- | ||
| Line 142: | Line 174: | ||
|- | |- | ||
| 3 | | 3 | ||
| 38\183<br | | 38\183<br>(23\183) | ||
| 249.18<br | | 249.18<br>(150.82) | ||
| 15/13<br | | 15/13<br>(12/11) | ||
| [[Hemiterm]] | | [[Hemiterm]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 76\183<br | | 76\183<br>(15\183) | ||
| 498.36<br | | 498.36<br>(98.36) | ||
| 4/3<br | | 4/3<br>(200/189) | ||
| [[Term]] / terminator | | [[Term]] / terminator | ||
|- | |- | ||
| 61 | | 61 | ||
| 38\183<br | | 38\183<br>(2\183) | ||
| 249.18<br | | 249.18<br>(13.11) | ||
| 13750/11907<br | | 13750/11907<br>(?) | ||
| [[Promethium]] | | [[Promethium]] | ||
|} | |} | ||
<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 == | ||