152edo: Difference between revisions
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 152 factors into 2<sup>3</sup> × 19, 152edo has subset edos {{EDOs| 2, 4, 8, 19, 38, 76 }}. | Since 152 factors into 2<sup>3</sup> × 19, 152edo has subset edos {{EDOs| 2, 4, 8, 19, 38, 76 }}. | ||
== 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 | |||
|- | |||
| [[965zpi]] | |||
| 152.052848107925 | |||
| 7.89199291517551 | |||
| 10.468420 | |||
| 1.593855 | |||
| 19.487224 | |||
| 152edo | |||
| 1199.58292310668 | |||
| 15 | |||
| 15 | |||
|} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 69: | Line 101: | ||
|+ 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 130: | Line 162: | ||
|- | |- | ||
| 2 | | 2 | ||
| 43\152<br | | 43\152<br>(33\152) | ||
| 339.47<br | | 339.47<br>(260.53) | ||
| 243/200<br | | 243/200<br>(64/55) | ||
| [[Hemiamity]] | | [[Hemiamity]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 55\152<br | | 55\152<br>(21\152) | ||
| 434.21<br | | 434.21<br>(165.79) | ||
| 9/7<br | | 9/7<br>(11/10) | ||
| [[Supers]] | | [[Supers]] | ||
|- | |- | ||
| 4 | | 4 | ||
| 63\152<br | | 63\152<br>(13\152) | ||
| 497.37<br | | 497.37<br>(102.63) | ||
| 4/3<br | | 4/3<br>(35/33) | ||
| [[Undim]] / [[unlit]] | | [[Undim]] / [[unlit]] | ||
|- | |- | ||
| 8 | | 8 | ||
| 63\152<br | | 63\152<br>(6\152) | ||
| 497.37<br | | 497.37<br>(47.37) | ||
| 4/3<br | | 4/3<br>(36/35) | ||
| [[Twilight]] | | [[Twilight]] | ||
|- | |- | ||
| 8 | | 8 | ||
| 74\152<br | | 74\152<br>(2\152) | ||
| 584.21<br | | 584.21<br>(15.79) | ||
| 7/5<br | | 7/5<br>(126/125) | ||
| [[Octoid]] (152f) / [[octopus]] (152) | | [[Octoid]] (152f) / [[octopus]] (152) | ||
|- | |- | ||
| 19 | | 19 | ||
| 63\152<br | | 63\152<br>(1\152) | ||
| 497.37<br | | 497.37<br>(7.89) | ||
| 4/3<br | | 4/3<br>(225/224) | ||
| [[Enneadecal]] | | [[Enneadecal]] | ||
|- | |- | ||
| 38 | | 38 | ||
| 63\152<br | | 63\152<br>(1\152) | ||
| 497.37<br | | 497.37<br>(7.89) | ||
| 4/3<br | | 4/3<br>(225/224) | ||
| [[Hemienneadecal]] | | [[Hemienneadecal]] | ||
|} | |} | ||
<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 == | ||