330edo: Difference between revisions
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{{EDO intro|330}} | |||
330edo has a flat tendency, with its 3rd, 5th, and 7th harmonics tuned progressively flatter. In the 11-limit, the 330e [[val]] scores significantly better in [[TE error]] than its [[patent val]] and allows an extension to the 13-limit. | 330edo has a flat tendency, with its 3rd, 5th, and 7th harmonics tuned progressively flatter. In the 11-limit, the 330e [[val]] {{val| 330 523 766 926 '''1141''' }} scores significantly better in [[TE error]] than its [[patent val]] {{val| 330 523 766 926 '''1142''' }} and allows an extension to the 13-limit. | ||
It tempers out 32805/32768 ([[schisma]]) in the [[5-limit]]; 250047/250000 (landscape comma), 703125/702464 ([[meter comma|meter]]) and 4802000/4782969 ([[canousma]]) in the [[7-limit]]. Using the 330e val, it tempers out 385/384 ([[keenanisma]]), 9801/9800 (kalisma), and 14641/14580 ([[semicanousma]]) in the [[11-limit]]; 847/845 (cuthbert) and 1001/1000 (sinbadma) in the [[13-limit]]. | It tempers out 32805/32768 ([[schisma]]) in the [[5-limit]]; 250047/250000 ([[landscape comma]]), 703125/702464 ([[meter comma|meter]]) and 4802000/4782969 ([[canousma]]) in the [[7-limit]]. Using the 330e val, it tempers out 385/384 ([[keenanisma]]), 9801/9800 ([[kalisma]]), and 14641/14580 ([[semicanousma]]) in the [[11-limit]]; 847/845 ([[847/845|cuthbert]]) and 1001/1000 ([[1001/1000|sinbadma]]) in the [[13-limit]]. | ||
It provides a nice tuning for [[keenanismic family|keenanismic]], the rank-4 temperament that tempers out 385/384 (even better than its [[optimal patent val]] [[284edo]]), and actually a | It provides a nice tuning for [[keenanismic family|keenanismic]], the rank-4 temperament that tempers out 385/384 (even better than its [[optimal patent val]] [[284edo]]), and actually a close-to-optimal tuning for 11-limit [[Canou family #semicanou|semicanou]], the rank-3 temperament that tempers out 9801/9800 and 14641/14580. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|330}} | |||
=== Subsets and supersets === | |||
Since 330 factors into 2 × 3 × 5 × 11, it has subset edos {{EDOs| 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, and 165 }}. | |||
[[Category:Canou]] | [[Category:Canou]] | ||
[[Category:Semicanousmic]] | [[Category:Semicanousmic]] | ||
[[Category:Keenanismic]] | [[Category:Keenanismic]] | ||
Revision as of 05:51, 9 June 2023
| ← 329edo | 330edo | 331edo → |
330edo has a flat tendency, with its 3rd, 5th, and 7th harmonics tuned progressively flatter. In the 11-limit, the 330e val ⟨330 523 766 926 1141] scores significantly better in TE error than its patent val ⟨330 523 766 926 1142] and allows an extension to the 13-limit.
It tempers out 32805/32768 (schisma) in the 5-limit; 250047/250000 (landscape comma), 703125/702464 (meter) and 4802000/4782969 (canousma) in the 7-limit. Using the 330e val, it tempers out 385/384 (keenanisma), 9801/9800 (kalisma), and 14641/14580 (semicanousma) in the 11-limit; 847/845 (cuthbert) and 1001/1000 (sinbadma) in the 13-limit.
It provides a nice tuning for keenanismic, the rank-4 temperament that tempers out 385/384 (even better than its optimal patent val 284edo), and actually a close-to-optimal tuning for 11-limit semicanou, the rank-3 temperament that tempers out 9801/9800 and 14641/14580.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.14 | -0.86 | -1.55 | +1.41 | -0.53 | +0.50 | +0.67 | +0.82 | -0.49 | +0.42 |
| Relative (%) | +0.0 | -3.8 | -23.6 | -42.7 | +38.8 | -14.5 | +13.7 | +18.4 | +22.5 | -13.4 | +11.5 | |
| Steps (reduced) |
330 (0) |
523 (193) |
766 (106) |
926 (266) |
1142 (152) |
1221 (231) |
1349 (29) |
1402 (82) |
1493 (173) |
1603 (283) |
1635 (315) | |
Subsets and supersets
Since 330 factors into 2 × 3 × 5 × 11, it has subset edos 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, and 165.