87edo: Difference between revisions
ArrowHead294 (talk | contribs) m Formatting |
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=== Interval mappings === | === Interval mappings === | ||
{{Q-odd-limit intervals|87}} | {{Q-odd-limit intervals|87}} | ||
=== 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 | |||
|- | |||
| [[483zpi]] | |||
| 87.0139255957575 | |||
| 13.7908960178956 | |||
| 8.869041 | |||
| 1.439474 | |||
| 18.061741 | |||
| 87edo | |||
| 1199.80795355692 | |||
| 16 | |||
| 14 | |||
|} | |||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 354: | Line 385: | ||
! 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 410: | Line 441: | ||
|+ 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 | ||
|- | |- | ||
| Line 477: | Line 508: | ||
|- | |- | ||
| 3 | | 3 | ||
| 18\87<br | | 18\87<br>(11\87) | ||
| 248.276<br | | 248.276<br>(151.724) | ||
| 15/13<br | | 15/13<br>(12/11) | ||
| [[Hemimist]] | | [[Hemimist]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 23\87<br | | 23\87<br>(6\87) | ||
| 317.241<br | | 317.241<br>(82.759) | ||
| 6/5<br | | 6/5<br>(21/20) | ||
| [[Tritikleismic]] | | [[Tritikleismic]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 28\87<br | | 28\87<br>(1\87) | ||
| 386.207<br | | 386.207<br>(13.793) | ||
| 5/4<br | | 5/4<br>(126/125) | ||
| [[Mutt]] | | [[Mutt]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 36\87<br | | 36\87<br>(7\87) | ||
| 496.552<br | | 496.552<br>(96.552) | ||
| 4/3<br | | 4/3<br>(18/17~19/18) | ||
| [[Misty]] | | [[Misty]] | ||
|- | |- | ||
| 29 | | 29 | ||
| 28\87<br | | 28\87<br>(1\87) | ||
| 386.207<br | | 386.207<br>(13.793) | ||
| 5/4<br | | 5/4<br>(121/120) | ||
| [[Mystery]] | | [[Mystery]] | ||
|} | |} | ||
<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 | ||
87 can serve as a mos in these: | |||
* [[Avicenna (temperament)|Avicenna]] ([[Breed|87 & 270]]) {{multival| 24 -9 -66 12 27 … }} | |||
* [[Breed|87 & 494]] {{multival| 51 -1 -133 11 32 … }} | |||
|- | |||
| 1 | |||
== Scales == | == Scales == | ||
=== | === Mos scales === | ||
{{main|List of MOS scales in 87edo}} | {{main|List of MOS scales in 87edo}} | ||