140edo: Difference between revisions
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 140 factors into {{factorisation|140}}, 140edo has subset edos {{EDOs| 2, 4, 5, 7, 10, 14, 20, 28, 35, and 70 }}. | Since 140 factors into {{factorisation|140}}, 140edo has subset edos {{EDOs| 2, 4, 5, 7, 10, 14, 20, 28, 35, and 70 }}. | ||
== 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 | |||
|- | |||
| [[872zpi]] | |||
| 139.990541024216 | |||
| 8.57200773152536 | |||
| 10.076688 | |||
| 1.548424 | |||
| 19.514765 | |||
| 140edo | |||
| 1200.08108241355 | |||
| 10 | |||
| 10 | |||
|} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 27: | Line 59: | ||
! 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 74: | Line 106: | ||
|+ 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 129: | Line 161: | ||
|- | |- | ||
| 2 | | 2 | ||
| 41\140<br | | 41\140<br>(29\140) | ||
| 351.43<br | | 351.43<br>(248.57) | ||
| 49/40<br | | 49/40<br>(15/13) | ||
| [[Semihemi]] | | [[Semihemi]] | ||
|- | |- | ||
| 4 | | 4 | ||
| 37\140<br | | 37\140<br>(2\140) | ||
| 317.14<br | | 317.14<br>(17.14) | ||
| 6/5<br | | 6/5<br>(126/125) | ||
| [[Quadritikleismic]] | | [[Quadritikleismic]] | ||
|- | |- | ||
| 4 | | 4 | ||
| 58\140<br | | 58\140<br>(12\140) | ||
| 497.14<br | | 497.14<br>(102.86) | ||
| 4/3<br | | 4/3<br>(35/33) | ||
| [[Undim]] | | [[Undim]] | ||
|- | |- | ||
| 5 | | 5 | ||
| 37\140<br >(9\140) | | 37\140<br>(9\140) | ||
| 317.14<br >(77.14) | | 317.14<br>(77.14) | ||
| 6/5<br | | 6/5<br>(24/23) | ||
| [[Thunderclysmic]] | | [[Thunderclysmic]] | ||
|- | |- | ||
| 5 | | 5 | ||
| 43\140<br | | 43\140<br>(13\140) | ||
| 368.57<br | | 368.57<br>(111.43) | ||
| 1024/891<br | | 1024/891<br>(16/15) | ||
| [[Quintosec]] | | [[Quintosec]] | ||
|- | |- | ||
| 10 | | 10 | ||
| 29\140<br | | 29\140<br>(1\140) | ||
| 248.57<br | | 248.57<br>(8.57) | ||
| 15/13<br | | 15/13<br>(176/175) | ||
| [[Decoid]] | | [[Decoid]] | ||
|- | |- | ||
| 20 | | 20 | ||
| 54\140<br | | 54\140<br>(2\140) | ||
| 497.14<br | | 497.14<br>(17.14) | ||
| 4/3<br | | 4/3<br>(126/125) | ||
| [[Degrees]] | | [[Degrees]] | ||
|- | |- | ||
| 28 | | 28 | ||
| 54\140<br | | 54\140<br>(2\140) | ||
| 497.14<br | | 497.14<br>(17.14) | ||
| 4/3<br | | 4/3<br>(126/125) | ||
| [[Oquatonic]] | | [[Oquatonic]] | ||
|} | |} | ||
<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 | ||
== Instruments == | == Instruments == | ||