22edo: Difference between revisions

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=== 7-limit commas ===

In the 7-limit 22edo tempers out certain commas also tempered out by 12et; this relates 12et to 22 in a way different from the way in which meantone systems are akin to it. [[50/49]] (the jubilisma), and 64/63 (the septimal comma) are tempered out in both systems, so they both equate the two septimal tritones of 7/5 and 10/7, and because of 64/63 the dominant seventh chord and an otonal tetrad are represented by the same chord. Hence both also temper out {{nowrap|(50/49)/(64/63) {{=}} 225/224}}, the [[septimal kleisma]], so that the septimal kleisma augmented triad is a chord of 22et, as it also is of any meantone tuning. A septimal comma not tempered out by 12et which 22et does temper out is 1728/1715, the [[1728/1715|orwell comma]]; and the [[orwell tetrad]] is also a chord of 22et.

~~=== 11-limit commas===~~

In the 11-limit, 22edo tempers out the [[quartisma]], leading to a stack of five 33/32 quartertones being equated with one 7/6 subminor third. This is a trait which, while shared with [[24edo]], is surprisingly ''not'' shared with a number of other relatively small edos such as [[17edo]], [[26edo]] and [[34edo]]. In fact, not even the famous [[53edo]] has this property—although it should be noted that the related [[159edo]] ''does''.

=== Other features ===

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== Instruments ==

=== Keyboards ===

[[File:22-tone halberstadt layout~~.png|link=https://en.xen.wiki/w/File:22-tone%20halberstadt%20layout~~.png|alt=|frameless]]

[[File:22-tone halberstadt layout.png|alt=|frameless]]

A potential layout for a 22edo keyboard with both split black and white keys.

@@ Line 42: / Line 42: @@
 === 7-limit commas ===
 In the 7-limit 22edo tempers out certain commas also tempered out by 12et; this relates 12et to 22 in a way different from the way in which meantone systems are akin to it. [[50/49]] (the jubilisma), and 64/63 (the septimal comma) are tempered out in both systems, so they both equate the two septimal tritones of 7/5 and 10/7, and because of 64/63 the dominant seventh chord and an otonal tetrad are represented by the same chord. Hence both also temper out {{nowrap|(50/49)/(64/63) {{=}} 225/224}}, the [[septimal kleisma]], so that the septimal kleisma augmented triad is a chord of 22et, as it also is of any meantone tuning. A septimal comma not tempered out by 12et which 22et does temper out is 1728/1715, the [[1728/1715|orwell comma]]; and the [[orwell tetrad]] is also a chord of 22et.
-=== 11-limit commas===
-In the 11-limit, 22edo tempers out the [[quartisma]], leading to a stack of five 33/32 quartertones being equated with one 7/6 subminor third. This is a trait which, while shared with [[24edo]], is surprisingly ''not'' shared with a number of other relatively small edos such as [[17edo]], [[26edo]] and [[34edo]]. In fact, not even the famous [[53edo]] has this property—although it should be noted that the related [[159edo]] ''does''.
 === Other features ===
@@ Line 1,493: / Line 1,490: @@
 == Instruments ==
 === Keyboards ===
-[[File:22-tone halberstadt layout.png|link=https://en.xen.wiki/w/File:22-tone%20halberstadt%20layout.png|alt=|frameless]]
+[[File:22-tone halberstadt layout.png|alt=|frameless]]
 A potential layout for a 22edo keyboard with both split black and white keys.