578edo: Difference between revisions
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{{EDO intro|578}} | |||
578edo is [[contorted]] in the [[5-limit]], tempering out [[32805/32768]] (schisma) with the same tuning as [[289edo]]. It tempers out 10976/10935 ([[hemimage comma]]) and 65625/65536 ([[horwell comma]]) in the [[7-limit]], supporting [[bisupermajor]], the 22 & 118 temperament, and 119098/117649 which together with the schisma gives 7-limit [[pogo]] temperament, the 94 & 130 temperament. In the [[11-limit]] it tempers out [[540/539]] and [[4000/3993]] and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[hades]], as well as other temperaments tempering out 540/539, the rank-4 temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], and provides the optimal patent val for 13-limit pogo. | |||
578 factors as 2 × 17<sup>2</sup>, with divisors 2, 17, 34, and 289. | 578 factors as 2 × 17<sup>2</sup>, with divisors 2, 17, 34, and 289. | ||
{{Harmonics in equal|578|columns=11}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 18:45, 17 August 2022
578edo is contorted in the 5-limit, tempering out 32805/32768 (schisma) with the same tuning as 289edo. It tempers out 10976/10935 (hemimage comma) and 65625/65536 (horwell comma) in the 7-limit, supporting bisupermajor, the 22 & 118 temperament, and 119098/117649 which together with the schisma gives 7-limit pogo temperament, the 94 & 130 temperament. In the 11-limit it tempers out 540/539 and 4000/3993 and provides the optimal patent val for 11-limit pogo and the planar temperament hades, as well as other temperaments tempering out 540/539, the rank-4 temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out 729/728, 1575/1573, 1716/1715 and 2080/2079, and provides the optimal patent val for 13-limit pogo.
578 factors as 2 × 172, with divisors 2, 17, 34, and 289.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.225 | -0.155 | +0.724 | +0.931 | +0.303 | +0.927 | -0.627 | +0.791 | +0.181 | +0.985 |
| Relative (%) | +0.0 | -10.8 | -7.4 | +34.9 | +44.9 | +14.6 | +44.6 | -30.2 | +38.1 | +8.7 | +47.5 | |
| Steps (reduced) |
578 (0) |
916 (338) |
1342 (186) |
1623 (467) |
2000 (266) |
2139 (405) |
2363 (51) |
2455 (143) |
2615 (303) |
2808 (496) |
2864 (552) | |