330edo: Difference between revisions

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~~'''330edo''' divides the octave into~~ 330 ~~equal parts of 3.6364 cents each.~~

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 ~~next~~-to-optimal tuning for 11-limit [[Canou family #semicanou|semicanou]], the rank-3 temperament that tempers out 9801/9800 and 14641/14580.

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 ===

=== 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:Equal divisions of the octave|###]] ~~

[[Category:Canou]]

[[Category:Semicanousmic]]

[[Category:Keenanismic]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''330edo''' divides the octave into 330 equal parts of 3.6364 cents each.
+{{EDO intro|330}}
-edo 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.
+edo 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 next-to-optimal tuning for 11-limit [[Canou family #semicanou|semicanou]], the rank-3 temperament that tempers out 9801/9800 and 14641/14580.
+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:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Canou]]
 [[Category:Semicanousmic]]
 [[Category:Keenanismic]]