138edo
| ← 137edo | 138edo | 139edo → |
138edo is the equal division of the octave into 138 parts of 8.6957 cents each.
It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 13-limit: <138 219 320 387 477 511| (patent val), <138 218 320 387 477 510| (138bf), and <138 219 321 388 478 511| (138cde).
Using the patent val, it tempers out the shibboleth comma, 1953125/1889568 and the misty comma, 67108864/66430125 in the 5-limit; 875/864, 1029/1024, and 1647086/1594323 in the 7-limit; 896/891, 1331/1323, 1375/1372, and 2401/2376 in the 11-limit; 196/195, 275/273, and 1575/1573 in the 13-limit.
Using the 138bf val, it tempers out the syntonic comma, 81/80 and 2288818359375/2199023255552 in the 5-limit; 2401/2400, 2430/2401, and 9765625/9633792 in the 7-limit; 385/384, 1375/1372, 1944/1925, and 9375/9317 in the 11-limit, supporting the cuboctahedra temperament; 625/624, 975/968, 1001/1000, and 1188/1183 in the 13-limit.
Using the 138cde val, it tempers out the diaschisma, 2048/2025 and the sensipent comma, 78732/78125 in the 5-limit; 1728/1715, 10976/10935, and 250047/250000 in the 7-limit; 176/175, 540/539, 896/891, and 85184/84375 in the 11-limit; 351/350, 352/351, 364/363, 640/637, and 2197/2187 in the 13-limit, supporting the echidna temperament.
138edo can be treated as the 2.7/5.11/5.13/3 subgroup temperament, which tempers out 24192/24167, 1449459/1449175, and 75000000/74942413.
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +2.39 | -3.71 | -3.61 | -3.91 | -3.49 | +2.95 | -1.31 | -0.61 | -1.86 | -1.22 | -2.19 |
| relative (%) | +28 | -43 | -41 | -45 | -40 | +34 | -15 | -7 | -21 | -14 | -25 | |
| Steps (reduced) |
219 (81) |
320 (44) |
387 (111) |
437 (23) |
477 (63) |
511 (97) |
539 (125) |
564 (12) |
586 (34) |
606 (54) |
624 (72) | |