87edo: Difference between revisions
m Cleanup |
→Scales: mode 16 -> mode 12 (its mode 16 isn't that great) |
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| Line 505: | Line 505: | ||
== Scales == | == Scales == | ||
=== Harmonic scale === | === Harmonic scale === | ||
87edo accurately approximates the mode 8 of [[harmonic series]], and the only | 87edo accurately approximates the mode 8 of [[harmonic series]], and the only interval pair not distinct is 14/13 and 15/14. It can also do mode 12 decently. | ||
==== Mode 8 ==== | ==== Mode 8 ==== | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
! Overtones | |||
| 8 | | 8 | ||
| 9 | | 9 | ||
| Line 520: | Line 520: | ||
| 16 | | 16 | ||
|- | |- | ||
! JI Ratios | |||
| 1/1 | | 1/1 | ||
| 9/8 | | 9/8 | ||
| Line 531: | Line 531: | ||
| 2/1 | | 2/1 | ||
|- | |- | ||
! … in cents | |||
| 0.0 | | 0.0 | ||
| 203.9 | | 203.9 | ||
| Line 542: | Line 542: | ||
| 1200.0 | | 1200.0 | ||
|- | |- | ||
! Degrees in 87edo | |||
| 0 | | 0 | ||
| 15 | | 15 | ||
| Line 553: | Line 553: | ||
| 87 | | 87 | ||
|- | |- | ||
! … in cents | |||
| 0.0 | | 0.0 | ||
| 206.9 | | 206.9 | ||
| Line 567: | Line 567: | ||
* The scale in adjacent steps is 15, 13, 12, 11, 10, 9, 9, 8. | * The scale in adjacent steps is 15, 13, 12, 11, 10, 9, 9, 8. | ||
==== Mode | ==== Mode 12 ==== | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
| | ! Overtones | ||
| 12 | |||
| 13 | |||
| 14 | |||
| 15 | |||
| 16 | |||
| 17 | | 17 | ||
| 18 | |||
| 19 | | 19 | ||
| 20 | |||
| 21 | | 21 | ||
| 22 | |||
| 23 | | 23 | ||
| | | 24 | ||
|- | |- | ||
! JI Ratios | |||
| 17/ | | 1/1 | ||
| | | 13/12 | ||
| | | 7/6 | ||
| | | 5/4 | ||
| | | 4/3 | ||
| | | 17/12 | ||
| | | 3/2 | ||
| | | 19/12 | ||
| 5/3 | |||
| 7/4 | |||
| 11/6 | |||
| 23/12 | |||
| 2/1 | |||
|- | |- | ||
! … in cents | |||
| | | 0.0 | ||
| | | 138.6 | ||
| | | 266.9 | ||
| | | 386.3 | ||
| | | 498.0 | ||
| | | 603.0 | ||
| | | 702.0 | ||
| | | 795.6 | ||
| 884.4 | |||
| 968.8 | |||
| 1049.4 | |||
| 1126.3 | |||
| 1200.0 | |||
|- | |- | ||
! Degrees in 87edo | |||
| | | 0 | ||
| | | 10 | ||
| | | 19 | ||
| | | 28 | ||
| | | 36 | ||
| | | 44 | ||
| | | 51 | ||
| | | 58 | ||
| 64 | |||
| 70 | |||
| 76 | |||
| 82 | |||
| 87 | |||
|- | |- | ||
! … in cents | |||
| | | 0.0 | ||
| | | 137.9 | ||
| | | 262.1 | ||
| | | 386.2 | ||
| | | 496.6 | ||
| | | 606.9 | ||
| | | 703.4 | ||
| | | 800.0 | ||
| 882.8 | |||
| 965.5 | |||
| 1048.3 | |||
| 1131.0 | |||
| 1200.0 | |||
|} | |} | ||
* The scale in adjacent steps is 8, 7, 7, 6, 6, 6, 6, 5, | * The scale in adjacent steps is 10, 9, 9, 8, 7, 7, 6, 6, 6, 6, 5. | ||
* 13, 15, 16, 18, 20, and 22 are close matches. | |||
* 21 | * 14 and 21 are flat; 17, 19, and 23 are sharp. Still decent all things considered. | ||
== Music == | == Music == | ||