22edo/Unque's compositional approach: Difference between revisions

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=== The thirds of 22edo ===

22edo has two pairs of thirds: ~~a major/minor~~ pair, and ~~a supermajor/subminor pair~~; despite most often being viewed as an 11-limit system, it lacks clear representation for the neutral thirds that are characteristic of 11-limit harmony.

22edo has two pairs of thirds: one pair characteristic of the Superpyth diatonic scale, and one characteristic of Zarlino diatonic; despite most often being viewed as an 11-limit system, it lacks clear representation for the neutral thirds that are characteristic of 11-limit harmony.

The ~~subminor~~ third at 5\22 represents 7/6 with moderate accuracy, though it is often noted to be significantly less concordant than the JI representation. Its fifth complement is the ~~supermajor~~ third at 8\22, which is an excellent representation of 9/7. This interval is perhaps better paired with 14\22 than with 13\22, as the former can be interpreted as 11/7 and thus provides the more consonant otonal 7:9:11 triad.

The superpyth minor third at 5\22 represents 7/6 with moderate accuracy, though it is often noted to be significantly less concordant than the JI representation. Its fifth complement is the superpyth major third at 8\22, which is an excellent representation of 9/7. This interval is perhaps better paired with 14\22 than with 13\22, as the former can be interpreted as 11/7 and thus provides the more consonant otonal 7:9:11 triad.

The minor third at 6\22 is contentious in its interpretation; it is quite sharp for a minor third, though not nearly sharp enough to constitute a neutral third; by patent val, it represents 6/5 and 11/9, though in practice it does not accurately represent either of the two. Its fifth complement, the major third at 7\22, is a much clearer 5/4, having a relative error of less than 10%.

The zarlino minor third at 6\22 is contentious in its interpretation; it is quite sharp for a minor third, though not nearly sharp enough to constitute a neutral third; by patent val, it represents 6/5 and 11/9, though in practice it does not accurately represent either of the two. Its fifth complement, the zarlino major third at 7\22, is a much clearer 5/4, having a relative error of less than 10%.

== Scales ==

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!Scales of Common Occurance

|-

|Major

|Major (Zarlino)

|C maj

|C - vE - G

Line 866:

|2L 8s; 3L 2M 2s

|-

|Minor

|Minor (Zarlino)

|c min

|C - ^E♭ - G

Line 875:

|2L 8s; 3L 2M 2s

|-

|~~Supermajor~~

|Major (Superpyth)

|C saj

|C - E - G

Line 884:

|5L 2s; 2L 8s

|-

|~~Subminor~~

|Minor (Superpyth)

|c sin

|C - E♭ - G

@@ Line 183: / Line 183: @@
 === The thirds of 22edo ===
-edo has two pairs of thirds: a major/minor pair, and a supermajor/subminor pair; despite most often being viewed as an 11-limit system, it lacks clear representation for the neutral thirds that are characteristic of 11-limit harmony.
+edo has two pairs of thirds: one pair characteristic of the Superpyth diatonic scale, and one characteristic of Zarlino diatonic; despite most often being viewed as an 11-limit system, it lacks clear representation for the neutral thirds that are characteristic of 11-limit harmony.
-The subminor third at 5\22 represents 7/6 with moderate accuracy, though it is often noted to be significantly less concordant than the JI representation. Its fifth complement is the supermajor third at 8\22, which is an excellent representation of 9/7. This interval is perhaps better paired with 14\22 than with 13\22, as the former can be interpreted as 11/7 and thus provides the more consonant otonal 7:9:11 triad.
+The superpyth minor third at 5\22 represents 7/6 with moderate accuracy, though it is often noted to be significantly less concordant than the JI representation. Its fifth complement is the superpyth major third at 8\22, which is an excellent representation of 9/7. This interval is perhaps better paired with 14\22 than with 13\22, as the former can be interpreted as 11/7 and thus provides the more consonant otonal 7:9:11 triad.
-The minor third at 6\22 is contentious in its interpretation; it is quite sharp for a minor third, though not nearly sharp enough to constitute a neutral third; by patent val, it represents 6/5 and 11/9, though in practice it does not accurately represent either of the two. Its fifth complement, the major third at 7\22, is a much clearer 5/4, having a relative error of less than 10%.
+The zarlino minor third at 6\22 is contentious in its interpretation; it is quite sharp for a minor third, though not nearly sharp enough to constitute a neutral third; by patent val, it represents 6/5 and 11/9, though in practice it does not accurately represent either of the two. Its fifth complement, the zarlino major third at 7\22, is a much clearer 5/4, having a relative error of less than 10%.
 == Scales ==
@@ Line 857: / Line 857: @@
 !Scales of Common Occurance
 |-
-|Major
+|Major (Zarlino)
 |C maj
 |C - vE - G
@@ Line 866: / Line 866: @@
 |2L 8s; 3L 2M 2s
 |-
-|Minor
+|Minor (Zarlino)
 |c min
 |C - ^E♭ - G
@@ Line 875: / Line 875: @@
 |2L 8s; 3L 2M 2s
 |-
-|Supermajor
+|Major (Superpyth)
 |C saj
 |C - E - G
@@ Line 884: / Line 884: @@
 |5L 2s; 2L 8s
 |-
-|Subminor
+|Minor (Superpyth)
 |c sin
 |C - E♭ - G