156edo
| ← 155edo | 156edo | 157edo → |
156 equal divisions of the octave (abbreviated 156edo or 156ed2), also called 156-tone equal temperament (156tet) or 156 equal temperament (156et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 156 equal parts of about 7.692 ¢ each. Each step represents a frequency ratio of 21/156, or the 156th root of 2.
It supports compton temperament. It is the smallest EDO to contain both 12edo and 13edo as subsets.
It tempers out 531441/524288 (pythagorean comma) and 1220703125/1207959552 (ditonmic comma) in the 5-limit, as well as 1224440064/1220703125 (parakleisma); 225/224, 250047/250000, and 589824/588245 in the 7-limit. Using the patent val, it tempers out 441/440, 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; 351/350, 364/363, 625/624, 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out 385/384, 540/539, 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, 847/845, and 1001/1000 in the 13-limit.
Harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -1.96 | -1.70 | +0.40 | +3.78 | +2.53 | -2.07 | -3.65 | +2.74 | +2.49 | -1.55 | +2.49 |
| relative (%) | -25 | -22 | +5 | +49 | +33 | -27 | -47 | +36 | +32 | -20 | +32 | |
| Steps (reduced) |
247 (91) |
362 (50) |
438 (126) |
495 (27) |
540 (72) |
577 (109) |
609 (141) |
638 (14) |
663 (39) |
685 (61) |
706 (82) | |
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