147edo: Difference between revisions
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Note its accurate fifth and misc. cleanup |
441 mention |
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 147 = 3 × 7<sup>2</sup>, 147edo has subset edos {{EDOs| 3, 7, 21 and 49 }}. | Since 147 = 3 × 7<sup>2</sup>, 147edo has subset edos {{EDOs| 3, 7, 21 and 49 }}. | ||
[[441edo]], which triples it, provides strong corrections on the 5th and 7th harmonics and is a very notable 7-limit system. | |||
== Scales == | == Scales == | ||
Revision as of 14:25, 18 October 2024
| ← 146edo | 147edo | 148edo → |
(semiconvergent)
Theory
147edo has a very accurate fifth. Using the patent val, the equal temperament 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 (%) | +0.0 | +1.1 | -32.3 | +31.9 | +46.4 | +3.5 | +14.3 | -44.5 | +3.6 | -12.3 | -26.7 | |
| Steps (reduced) |
147 (0) |
233 (86) |
341 (47) |
413 (119) |
509 (68) |
544 (103) |
601 (13) |
624 (36) |
665 (77) |
714 (126) |
728 (140) | |
Subsets and supersets
Since 147 = 3 × 72, 147edo has subset edos 3, 7, 21 and 49.
441edo, which triples it, provides strong corrections on the 5th and 7th harmonics and is a very notable 7-limit system.