87edo: Difference between revisions
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== Intervals == | == Intervals == | ||
{| class="wikitable center-all right-2 left-3 left-4" | {| class="wikitable center-all right-2 left-3 left-4" | ||
|- | |||
! rowspan="2" | # | ! rowspan="2" | # | ||
! rowspan="2" | Cents | ! rowspan="2" | Cents | ||
| Line 348: | Line 349: | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br />8ve Stretch (¢) | ||
! colspan="2" | Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
| Line 407: | Line 409: | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br>per 8ve | ! Periods<br />per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br>Ratio* | ! Associated<br />Ratio* | ||
! Temperament | ! Temperament | ||
|- | |- | ||
| Line 474: | Line 476: | ||
|- | |- | ||
| 3 | | 3 | ||
| 18\87<br>(11\87) | | 18\87<br />(11\87) | ||
| 248.276<br>(151.724) | | 248.276<br />(151.724) | ||
| 15/13<br>(12/11) | | 15/13<br />(12/11) | ||
| [[Hemimist]] | | [[Hemimist]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 23\87<br>(6\87) | | 23\87<br />(6\87) | ||
| 317.241<br>(82.759) | | 317.241<br />(82.759) | ||
| 6/5<br>(21/20) | | 6/5<br />(21/20) | ||
| [[Tritikleismic]] | | [[Tritikleismic]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 28\87<br>(1\87) | | 28\87<br />(1\87) | ||
| 386.207<br>(13.793) | | 386.207<br />(13.793) | ||
| 5/4<br>(126/125) | | 5/4<br />(126/125) | ||
| [[Mutt]] | | [[Mutt]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 36\87<br>(7\87) | | 36\87<br />(7\87) | ||
| 496.552<br>(96.552) | | 496.552<br />(96.552) | ||
| 4/3<br>(18/17~19/18) | | 4/3<br />(18/17~19/18) | ||
| [[Misty]] | | [[Misty]] | ||
|- | |- | ||
| 29 | | 29 | ||
| 28\87<br>(1\87) | | 28\87<br />(1\87) | ||
| 386.207<br>(13.793) | | 386.207<br />(13.793) | ||
| 5/4<br>(121/120) | | 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 it is distinct | |||
87 can serve as a MOS in these: | 87 can serve as a MOS in these: | ||
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==== Mode 8 ==== | ==== Mode 8 ==== | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|- | |||
! Overtones | ! Overtones | ||
| 8 | | 8 | ||
| Line 579: | Line 582: | ||
==== Mode 12 ==== | ==== Mode 12 ==== | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|- | |||
! Overtones | ! Overtones | ||
| 12 | | 12 | ||