53edo: Difference between revisions
→Intervals: added my solfege. Fixed an obvious mistake in the other solfege (Andrew Heathwaite's?) where both vm6 and ^M6 were named Lo. Changed Lo to Li to match his 41edo solfege. |
→Intervals: fixed my solfege, other minor changes |
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| Line 59: | Line 59: | ||
| double-up unison, <br>double-down minor 2nd | | double-up unison, <br>double-down minor 2nd | ||
| ^^D, <br>vvEb | | ^^D, <br>vvEb | ||
| | |Di / Fre | ||
| Daw | | Daw | ||
|- | |- | ||
| Line 104: | Line 104: | ||
| upmid 2nd | | upmid 2nd | ||
| vvE | | vvE | ||
| | |Re | ||
| Ruh | | Ruh | ||
|- | |- | ||
| Line 140: | Line 140: | ||
| double-up major 2nd, <br>double-down minor 3rd | | double-up major 2nd, <br>double-down minor 3rd | ||
| ^^E, <br>vvF | | ^^E, <br>vvF | ||
| | |Ri / Ne | ||
| Raw | | Raw | ||
|- | |- | ||
| Line 185: | Line 185: | ||
| upmid 3rd | | upmid 3rd | ||
| vvF# | | vvF# | ||
| | |Me | ||
| Muh | | Muh | ||
|- | |- | ||
| Line 221: | Line 221: | ||
| double-up major 3rd, <br>double-down 4th | | double-up major 3rd, <br>double-down 4th | ||
| ^^F#, <br>vvG | | ^^F#, <br>vvG | ||
| | |Mi / Fe | ||
| Maw | | Maw | ||
|- | |- | ||
| Line 266: | Line 266: | ||
| upmid 4th, <br>downdim 5th | | upmid 4th, <br>downdim 5th | ||
| vvG#, <br>vAb | | vvG#, <br>vAb | ||
| | |Pe / Sho | ||
| Fuh | | Fuh | ||
|- | |- | ||
| Line 302: | Line 302: | ||
| upmid 5th | | upmid 5th | ||
| vvA | | vvA | ||
| | |Pi / Se | ||
| Su | | Su | ||
|- | |- | ||
| Line 338: | Line 338: | ||
| double-up 5th, <br>double-down minor 6th | | double-up 5th, <br>double-down minor 6th | ||
| ^^A, <br>vvBb | | ^^A, <br>vvBb | ||
| | |Si / Fle | ||
| Saw | | Saw | ||
|- | |- | ||
| Line 383: | Line 383: | ||
| upmid 6th | | upmid 6th | ||
| vvB | | vvB | ||
| | |Le | ||
| Luh | | Luh | ||
|- | |- | ||
| Line 419: | Line 419: | ||
| double-up major 6th, <br>double-down minor 7th | | double-up major 6th, <br>double-down minor 7th | ||
| ^^B, <br>vvC | | ^^B, <br>vvC | ||
| | |Li / The | ||
| Law | | Law | ||
|- | |- | ||
| Line 464: | Line 464: | ||
| upmid 7th | | upmid 7th | ||
| vvC# | | vvC# | ||
| | |Te | ||
| Tuh | | Tuh | ||
|- | |- | ||
| Line 500: | Line 500: | ||
| double-up major 7th, <br>double-down 8ve | | double-up major 7th, <br>double-down 8ve | ||
| ^^C#, <br>vvD | | ^^C#, <br>vvD | ||
| | |Ti / De | ||
| Taw | | Taw | ||
|- | |- | ||
| Line 653: | Line 653: | ||
Whereas 12edo has a circle of twelve 5ths, 53edo has a spiral of twelve 5ths (since 31\53 is on the 7\12 kite in the scale tree). This shows 53edo in a 12edo-friendly format. Excellent for introducing 53edo to musicians unfamiliar with microtonal music. The two innermost and two outermost intervals on the spiral are duplicates. | Whereas 12edo has a circle of twelve 5ths, 53edo has a spiral of twelve 5ths (since 31\53 is on the 7\12 kite in the scale tree). This shows 53edo in a 12edo-friendly format. Excellent for introducing 53edo to musicians unfamiliar with microtonal music. The two innermost and two outermost intervals on the spiral are duplicates. | ||
[[File:53-edo spiral.png| | [[File:53-edo spiral.png|588x588px]] | ||
== JI approximation == | == JI approximation == | ||
| Line 680: | Line 680: | ||
| +1.34 cents | | +1.34 cents | ||
|- | |- | ||
| Major | | rowspan="2" | Major second | ||
| 9/8 | | 9/8 | ||
| 9 | | 9 | ||
| −0.14 cents | | −0.14 cents | ||
|- | |- | ||
| 10/9 | | 10/9 | ||
| 8 | | 8 | ||
| −1.27 cents | | −1.27 cents | ||
|- | |- | ||
| | | Minor second | ||
| 16/15 | | 16/15 | ||
| 5 | | 5 | ||
| Line 696: | Line 695: | ||
|} | |} | ||
Because the 5th is so very accurate, 53edo also offers good approximations for Pythagorean thirds. In addition, the 43\53 interval is only 4.8 cents wider than the just ratio 7/4, so 53edo can also be used for 7-limit harmony, tempering out the [[septimal kleisma]], 225/224. | |||
=== 15-odd-limit interval mappings === | === 15-odd-limit interval mappings === | ||