24edo: Difference between revisions
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The tunings supplied by 72 cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N_subgroups|3*24 subgroup]] 2.3.125.35.11.325.17 [[just_intonation_subgroup|just intonation subgroup]], making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11 and 17. Another approach would be to treat 24-EDO as a 2.3.11.17.19 subgroup temperament, on which it is quite accurate. | The tunings supplied by 72 cannot be used for all low-limit just intervals, but they can be used on the 17-limit [[k*N_subgroups|3*24 subgroup]] 2.3.125.35.11.325.17 [[just_intonation_subgroup|just intonation subgroup]], making some of the excellent approximations of 72 available in 24edo. Chords based on this subgroup afford considerable scope for harmony, including in particular intervals and chords using only 2, 3, 11 and 17. Another approach would be to treat 24-EDO as a 2.3.11.17.19 subgroup temperament, on which it is quite accurate. | ||
===Differences between distributionally-even scales and smaller edos=== | |||
{| class="wikitable" | |||
|+ | |||
!N | |||
!L-Nedo | |||
!s-Nedo | |||
|- | |||
|5 | |||
| 10¢ | |||
| -40¢ | |||
|- | |||
|7 | |||
|28.571¢ | |||
| -21.429¢ | |||
|- | |||
|9 | |||
|16.667¢ | |||
| -33.333¢ | |||
|- | |||
|10 | |||
|30¢ | |||
| -20¢ | |||
|- | |||
|11 | |||
|40.909¢ | |||
| -9.091¢ | |||
|- | |||
|13 | |||
| 7.692¢ | |||
| -42.308¢ | |||
|- | |||
|14 | |||
|14.286¢ | |||
| -35.714¢ | |||
|- | |||
|15 | |||
|20¢ | |||
| -30¢ | |||
|- | |||
|16 | |||
| 25¢ | |||
| -25¢ | |||
|- | |||
|17 | |||
|29.412¢ | |||
| -20.588¢ | |||
|- | |||
|18 | |||
|33.333¢ | |||
| -16.667¢ | |||
|- | |||
| 19 | |||
|36.842¢ | |||
| -13.158¢ | |||
|- | |||
|20 | |||
|10¢ | |||
| -40¢ | |||
|- | |||
|21 | |||
|42.857¢ | |||
| -7.143¢ | |||
|- | |||
|22 | |||
|45.4545¢ | |||
| -4.5455¢ | |||
|- | |||
|23 | |||
|47.826¢ | |||
| -2.174¢ | |||
|} | |||
= Notation = | = Notation = | ||
Line 898: | Line 968: | ||
* semaphore 5L4s 414144141 (generator: 5\24) | * semaphore 5L4s 414144141 (generator: 5\24) | ||
* mohajira 3L4s 3434343 (generator: 7\24) | * mohajira 3L4s 3434343 (generator: 7\24) | ||
* mohajira 7L3s 3313313313 (generator: 7\24) | * mohajira 7L3s [[Tel:3313313313|3313313313]] (generator: 7\24) | ||
{| class="wikitable right-2" | {| class="wikitable right-2" |