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 ==

Line 857:

!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 1,056:

The C Ionian scale in Superpyth is a perfect showcase of how common-practice harmony differs from that of 22edo; specifically, quartal harmony tends to provide a more resolved sound than tertian harmony does, due to the sharp fifth exaggerating the size of the chroma. Thus, our progression can resolve quite nicely to the tonic chord, Csus4 or G4/C.

A supermajor triad can be found over the fifth degree of the Ionian mode, which is much tenser than the major triad found in Meantone tunings due to the ~~major~~ seventh (the third of the V chord) being significantly sharper; this increases the strength of the pull towards the tonic, as well as destabilizes the V chord, making it clear that this is not a place of rest and thus negating the need for a dominant seventh over that chord. This allows us to restrict our progression to three-part harmony rather than switching between three- and four-part harmony as is often done in common-practice progressions.

A supermajor triad can be found over the fifth degree of the Ionian mode, which is much tenser than the major triad found in Meantone tunings due to the seventh degree (the third of the V chord) being significantly sharper; this increases the strength of the pull towards the tonic, as well as destabilizes the V chord, making it clear that this is not a place of rest and thus negating the need for a dominant seventh over that chord. This allows us to restrict our progression to three-part harmony rather than switching between three- and four-part harmony, or doubling voices as is often done in common-practice progressions.

Note also that a ~~leading tone~~ occurs between the notes E and F; this allows us to achieve a false resolution onto the Fsus4 chord, or C4/F, in our progression by way of voice leading from a chord on E. For this example, I have chosen to use the Orwell Diminished triad over E, which provides a tense sound without sounding nasty. The Fsus4 and Eow chords also introduce B♭, which contrasts with the B♮ found in the Gsaj chord, displaying how notes pulled from outside of the ~~original~~ scale can be quite useful in writing harmonies.

Note also that a diatonic semitone occurs between the notes E and F; this allows us to achieve a false resolution onto the Fsus4 chord, or C4/F, in our progression by way of voice leading from a chord on E. For this example, I have chosen to use the Orwell Diminished triad over E, which provides a tense sound without sounding nasty. The Fsus4 and Eow chords also introduce B♭, which contrasts with the B♮ found in the Gsaj chord, displaying how notes pulled from outside of the base scale can be quite useful in writing harmonies.

[[File:Isus4 - iiiow - IVsus4 - Vsaj.mp3|thumb|The Csus4 - Eow - Fsus4 - Gsaj chord progression]]

Thus, our four-chord progression is Csus4 - Eow - Fsus4 - Gsaj. This series of chords uses a combination of voice leading, tension-and-release paradigms, and circle of fifths movement to provide a dynamic and functional harmonic progression.

@@ 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
@@ Line 1,056: / Line 1,056: @@
 The C Ionian scale in Superpyth is a perfect showcase of how common-practice harmony differs from that of 22edo; specifically, quartal harmony tends to provide a more resolved sound than tertian harmony does, due to the sharp fifth exaggerating the size of the chroma.  Thus, our progression can resolve quite nicely to the tonic chord, Csus4 or G<sup>4</sup>/C.
-A supermajor triad can be found over the fifth degree of the Ionian mode, which is much tenser than the major triad found in Meantone tunings due to the major seventh (the third of the V chord) being significantly sharper; this increases the strength of the pull towards the tonic, as well as destabilizes the V chord, making it clear that this is not a place of rest and thus negating the need for a dominant seventh over that chord.  This allows us to restrict our progression to three-part harmony rather than switching between three- and four-part harmony as is often done in common-practice progressions.
+A supermajor triad can be found over the fifth degree of the Ionian mode, which is much tenser than the major triad found in Meantone tunings due to the seventh degree (the third of the V chord) being significantly sharper; this increases the strength of the pull towards the tonic, as well as destabilizes the V chord, making it clear that this is not a place of rest and thus negating the need for a dominant seventh over that chord.  This allows us to restrict our progression to three-part harmony rather than switching between three- and four-part harmony, or doubling voices as is often done in common-practice progressions.
-Note also that a leading tone occurs between the notes E and F; this allows us to achieve a false resolution onto the Fsus4 chord, or C<sup>4</sup>/F, in our progression by way of voice leading from a chord on E.  For this example, I have chosen to use the Orwell Diminished triad over E, which provides a tense sound without sounding nasty.  The Fsus4 and E<sup>ow</sup> chords also introduce B♭, which contrasts with the B♮ found in the Gsaj chord, displaying how notes pulled from outside of the original scale can be quite useful in writing harmonies.
+Note also that a diatonic semitone occurs between the notes E and F; this allows us to achieve a false resolution onto the Fsus4 chord, or C<sup>4</sup>/F, in our progression by way of voice leading from a chord on E.  For this example, I have chosen to use the Orwell Diminished triad over E, which provides a tense sound without sounding nasty.  The Fsus4 and E<sup>ow</sup> chords also introduce B♭, which contrasts with the B♮ found in the Gsaj chord, displaying how notes pulled from outside of the base scale can be quite useful in writing harmonies.
 [[File:Isus4 - iiiow - IVsus4 - Vsaj.mp3|thumb|The Csus4 - E<sup>ow</sup> - Fsus4 - Gsaj chord progression]]
 Thus, our four-chord progression is Csus4 - E<sup>ow</sup> - Fsus4 - Gsaj.  This series of chords uses a combination of voice leading, tension-and-release paradigms, and circle of fifths movement to provide a dynamic and functional harmonic progression.