147edo
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Prime factorization
3 × 72
Step size
8.16327¢
Fifth
86\147 (702.041¢)
(semiconvergent)
Semitones (A1:m2)
14:11 (114.3¢ : 89.8¢)
Consistency limit
5
Distinct consistency limit
5
| ← 146edo | 147edo | 148edo → |
(semiconvergent)
147 equal divisions of the octave (abbreviated 147edo or 147ed2), also called 147-tone equal temperament (147tet) or 147 equal temperament (147et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 147 equal parts of about 8.16 ¢ each. Each step represents a frequency ratio of 21/147, or the 147th root of 2.
Theory
147edo tempers out 32805/32768 in the 5-limit; 225/224 and 3125/3087 in the 7-limit; 243/242 in the 11-limit; 364/363 in the 13-limit; 442/441 and 595/594 in the 17-limit. It is the optimal patent val for 11-limit karadeniz, the 41 & 106 temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.00 | +0.09 | -2.64 | +2.60 | +3.78 | +0.29 | +1.17 | -3.64 | +0.30 | -1.01 | -2.18 |
| relative (%) | +0 | +1 | -32 | +32 | +46 | +4 | +14 | -45 | +4 | -12 | -27 | |
| Steps (reduced) |
147 (0) |
233 (86) |
341 (47) |
413 (119) |
509 (68) |
544 (103) |
601 (13) |
624 (36) |
665 (77) |
714 (126) |
728 (140) | |
Miscellaneous properties
Since 147 = 3 × 72, 147edo has subset edos 3, 7, 21 and 49.