9edo: Difference between revisions

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Here the characterizations are taken from [[Scala]], which also describes the scale itself as "Pelog Nawanada: Sunda". Chords such as 1/1 - 7/6 - 49/36 - 12/7 are therefore natural ones for 9edo. The above scale generates the [[just intonation subgroup]] 2.27/25.7/3, which is closely related to 9edo.

Apart from the above fractional subgroup, which 9edo approximates very accurately, 9edo has very little to offer in terms of ~~accurate temperaments, even uncommon ones~~. Most other systems that lack good perfect fifths such as [[6edo]] and [[~~11edo~~]] at least contain a reasonable approximation of 9/8 (or (3/2)^2), so they can ~~support low-error~~ temperaments in subgroups like 2.9.5 and 2.9.7. 9edo, on the other hand, completely misses both 3/2 and 9/8. You could then try to treat 9edo as an entirely no-threes system with no perfect fifth or any power of it, in a subgroup like 2.5.7.11, but even here 9edo performs somewhat poorly, because its best [[7/4]] is much closer to 12/7 and is off by 36 cents, while its best [[11/8]] is off by 18 cents.

Apart from the above fractional subgroup, which 9edo approximates very accurately, 9edo has very little to offer in terms of accuracy for simple harmonics. Most other systems that lack good perfect fifths such as [[6edo]], [[11edo]], [[13edo]] and [[18edo]] at least contain a reasonable approximation of 9/8 (or (3/2)^2), so they can be viewed as temperaments in subgroups like 2.9.5 and 2.9.7. 9edo, on the other hand, completely misses both 3/2 and 9/8. You could then try to treat 9edo as an entirely no-threes system with no perfect fifth or any power of it, in a subgroup like 2.5.7.11, but even here 9edo performs somewhat poorly, because its best [[7/4]] is much closer to 12/7 and is off by 36 cents, while its best [[11/8]] is off by 18 cents.

9edo's fifth of 5\9 is near the boundary of "perfect fifth" and "subfifth" so it sounds quite dirty but still recognizable.

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 Here the characterizations are taken from [[Scala]], which also describes the scale itself as "Pelog Nawanada: Sunda". Chords such as 1/1 - 7/6 - 49/36 - 12/7 are therefore natural ones for 9edo. The above scale generates the [[just intonation subgroup]] 2.27/25.7/3, which is closely related to 9edo.
-Apart from the above fractional subgroup, which 9edo approximates very accurately, 9edo has very little to offer in terms of accurate temperaments, even uncommon ones. Most other systems that lack good perfect fifths such as [[6edo]] and [[11edo]] at least contain a reasonable approximation of 9/8 (or (3/2)^2), so they can support low-error temperaments in subgroups like 2.9.5 and 2.9.7. 9edo, on the other hand, completely misses both 3/2 and 9/8. You could then try to treat 9edo as an entirely no-threes system with no perfect fifth or any power of it, in a subgroup like 2.5.7.11, but even here 9edo performs somewhat poorly, because its best [[7/4]] is much closer to 12/7 and is off by 36 cents, while its best [[11/8]] is off by 18 cents.
+Apart from the above fractional subgroup, which 9edo approximates very accurately, 9edo has very little to offer in terms of accuracy for simple harmonics. Most other systems that lack good perfect fifths such as [[6edo]], [[11edo]], [[13edo]] and [[18edo]] at least contain a reasonable approximation of 9/8 (or (3/2)^2), so they can be viewed as temperaments in subgroups like 2.9.5 and 2.9.7. 9edo, on the other hand, completely misses both 3/2 and 9/8. You could then try to treat 9edo as an entirely no-threes system with no perfect fifth or any power of it, in a subgroup like 2.5.7.11, but even here 9edo performs somewhat poorly, because its best [[7/4]] is much closer to 12/7 and is off by 36 cents, while its best [[11/8]] is off by 18 cents.
 edo's fifth of 5\9 is near the boundary of "perfect fifth" and "subfifth" so it sounds quite dirty but still recognizable.