22edo: Difference between revisions

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22et can also be treated as adding harmonics 3 and 5 to 11edo's 2.9.15.7.11.17 subgroup, making it a rather accurate 2.3.5.7.11.17 [[subgroup]] temperament. Let us also mind its approximation of the 31st harmonic is within half a cent, which is fairly accurate. It also approximates some intervals involving the 29th harmonic well, especially 29/24, which is also matched within half a cent. This leaves us with 2.3.5.7.11.17.29.31.

22et is ~~very close to an extended "quarter~~-~~comma archy", a tuning analogous to~~ quarter~~-comma meantone except that it tempers out~~ the septimal comma [[64/63]] ~~instead of~~ the ~~syntonic comma [[81/80]]. Because of this it has nearly pure~~ septimal ~~major thirds~~ ([[9/7]]).

Since 22et's fifth is sharp of just by approximately one-quarter of the septimal comma ([[64/63]]), and since it tunes the septimal supermajor third ([[9/7]]) almost exactly just, it is equivalent for all practical purposes to an extended "quarter-comma archy", in the same way that 31edo is practically idential to quarter-comma meantone.

~~=== Prime harmonics ===~~

~~{{Harmonics in equal|22|columns=11}}~~

~~=== Subsets and supersets ===~~

~~As 22~~ is ~~divisible by 11, a 22edo instrument can play any music in 11edo~~, in the same way that 12edo can play 6edo (the whole tone scale). 11edo is interesting for sounding melodically very similar to 12edo (whole steps, half steps and minor thirds in the familiar 1:2:3 ratio), but harmonically very different, in particular because it lacks perfect fifths/fourths and 5-limit major thirds/minor sixths. Similarly, 22edo is ~~melodically similar~~ to ~~24edo as both contain~~ quarter-~~tones and minor, neutral, and major seconds; but 22edo offers much better all-around harmonies than 24. In [[Sagittal notation]], 11 can be notated as every other note of 22~~.

== Intervals ==

@@ Line 18: / Line 18: @@
 et can also be treated as adding harmonics 3 and 5 to 11edo's 2.9.15.7.11.17 subgroup, making it a rather accurate 2.3.5.7.11.17 [[subgroup]] temperament. Let us also mind its approximation of the 31st harmonic is within half a cent, which is fairly accurate. It also approximates some intervals involving the 29th harmonic well, especially 29/24, which is also matched within half a cent. This leaves us with 2.3.5.7.11.17.29.31.
-et is very close to an extended "quarter-comma archy", a tuning analogous to quarter-comma meantone except that it tempers out the septimal comma [[64/63]] instead of the syntonic comma [[81/80]]. Because of this it has nearly pure septimal major thirds ([[9/7]]).
+Since 22et's fifth is sharp of just by approximately one-quarter of the septimal comma ([[64/63]]), and since it tunes the septimal supermajor third ([[9/7]]) almost exactly just, it is equivalent for all practical purposes to an extended "quarter-comma archy", in the same way that 31edo is practically idential to quarter-comma meantone.
-=== Prime harmonics ===
-{{Harmonics in equal|22|columns=11}}
-=== Subsets and supersets ===
-As 22 is divisible by 11, a 22edo instrument can play any music in 11edo, in the same way that 12edo can play 6edo (the whole tone scale). 11edo is interesting for sounding melodically very similar to 12edo (whole steps, half steps and minor thirds in the familiar 1:2:3 ratio), but harmonically very different, in particular because it lacks perfect fifths/fourths and 5-limit major thirds/minor sixths. Similarly, 22edo is melodically similar to 24edo as both contain quarter-tones and minor, neutral, and major seconds; but 22edo offers much better all-around harmonies than 24. In [[Sagittal notation]], 11 can be notated as every other note of 22.
 == Intervals ==