154edo
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Prime factorization
2 × 7 × 11
Step size
7.79221¢
Fifth
90\154 (701.299¢) (→45\77)
Semitones (A1:m2)
14:12 (109.1¢ : 93.51¢)
Consistency limit
3
Distinct consistency limit
3
| ← 153edo | 154edo | 155edo → |
154 equal divisions of the octave (abbreviated 154edo or 154ed2), also called 154-tone equal temperament (154tet) or 154 equal temperament (154et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 154 equal parts of about 7.79 ¢ each. Each step represents a frequency ratio of 21/154, or the 154th root of 2.
154edo is a contorted 77et in the 7-limit; in the 11-limit, it tempers out 126/125, 1029/1024 and 243/242, which define the 11-limit 31 & 123 temperament, for which 154 provides a good tuning, though 185edo gives the optimal patent val. In the 13-limit, it tempers out 196/195, 364/363 and 676/675.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.00 | -0.66 | +3.30 | -2.59 | +1.93 | +1.03 | -3.66 | -1.41 | +2.89 | -1.01 | +0.42 |
| relative (%) | +0 | -8 | +42 | -33 | +25 | +13 | -47 | -18 | +37 | -13 | +5 | |
| Steps (reduced) |
154 (0) |
244 (90) |
358 (50) |
432 (124) |
533 (71) |
570 (108) |
629 (13) |
654 (38) |
697 (81) |
748 (132) |
763 (147) | |
Subsets and supersets
154 = 2 × 7 × 11, 154edo has subset edos 2, 7, 11, 14, 22, and 77.