24ed7
Division of the 7th harmonic into 24 equal parts (24ed7) is related to the quanic temperament, which is a cluster temperament with nine clusters of notes in an octave. The step size is about 140.3677 cents, corresponding to 8.5490 edo.
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 140.3677 | 13/12, 25/23 | |
| 2 | 280.7355 | 20/17 | |
| 3 | 421.1032 | 14/11, 23/18, 32/25 | |
| 4 | 561.4710 | 18/13 | |
| 5 | 701.8387 | 3/2 | |
| 6 | 842.2065 | 13/8, 80/49 | |
| 7 | 982.5742 | 30/17 | |
| 8 | 1122.9420 | 21/11 | |
| 9 | 1263.3097 | 56/27, 27/13 | |
| 10 | 1403.6775 | 9/4 | |
| 11 | 1544.0452 | 56/23, 39/16, 22/9, 120/49 | |
| 12 | 1684.4130 | ||
| 13 | 1824.7807 | 63/22, 112/39, 23/8 | |
| 14 | 1965.1484 | 28/9 | |
| 15 | 2105.5162 | 27/8 | |
| 16 | 2245.8839 | 11/3 | |
| 17 | 2386.2517 | 119/30, 250/63 | |
| 18 | 2526.6194 | 30/7, 77/18, 56/13 | |
| 19 | 2666.9872 | 14/3 | |
| 20 | 2807.3549 | 91/18 | |
| 21 | 2947.7227 | 11/2 | |
| 22 | 3088.0904 | 119/20 | |
| 23 | 3228.4582 | 84/13 | |
| 24 | 3368.8259 | exact 7/1 | harmonic seventh plus two octaves |
24ed7 as a generator
24ed7 can also be thought of as a generator of the quanic temperament, which tempers out 352/351, 540/539, 729/728, and 1331/1323 in the 13-limit; 352/351, 442/441, 540/539, 561/560, and 715/714 in the 17-limit; 253/252, 345/343, 352/351, 391/390, 442/441, and 460/459 in the 2.3.5.7.11.13.17.23 subgroup.