Kite Guitar chord shapes (downmajor tuning): Difference between revisions

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The Ruyoyo comma implies an augmented chord because it equates the octave with 5/4 plus 5/4 plus 9/7. In 12-edo, the aug chord is symmetrical, and it is its own homonym. But in 41edo, it's asymmetrical. Its homonyms are also augmented chords, but of a different type. Thus there are three basic augmented chords: upaug, downaug and down-halfaug. In the last chord, the 5th is spelled as vv#5 rather than ^^5 so that the interval from the 3rd to the 5th is spelled as vM3 not ^<sup>3</sup>m3. An alternative name for down-halfaug is down-dudsharp5 (dud is short for double-down).

There is another trio of aug chords: up-halfaug, upminor-halfaug and up-dupaug, all homonyms. Dup is short for double-up. Their innate comma is the [[Sensamagic chords|Zozoyo comma]], which equates the octave with 9/7 plus 9/7 plus 6/5. Thus one 3rd is quite smaller than the other two. Only the uphalfaug is clearly an augmented chord. Since the 3rd is upped, the chord's 5th is spelled as ^^5 not vv#5. The upminor-halfaug chord's lowest 3rd is this small 3rd, and it really can't be called an augmented chord. The up-dupaug chord has ^^#5, a dupaugmented 5th. This is equivalent to a downmajor 6th, and again, it's debatable if this is really an augmented chord. In close voicing it uses every 3rd note of the [[~~Bohlen-Pierce|Bohlen-Pierce 13ED3~~ scale]].

There is another trio of aug chords: up-halfaug, upminor-halfaug and up-dupaug, all homonyms. Dup is short for double-up. Their innate comma is the [[Sensamagic chords|Zozoyo comma]], which equates the octave with 9/7 plus 9/7 plus 6/5. Thus one 3rd is quite smaller than the other two. Only the uphalfaug is clearly an augmented chord. Since the 3rd is upped, the chord's 5th is spelled as ^^5 not vv#5. The upminor-halfaug chord's lowest 3rd is this small 3rd, and it really can't be called an augmented chord. The up-dupaug chord has ^^#5, a dupaugmented 5th. This is equivalent to a downmajor 6th, and again, it's debatable if this is really an augmented chord. In close voicing it uses every 3rd note of the [[Bohlen–Pierce scale]].

All six chords are odd-limit 9. Another possible aug chord is odd-limit 11. Unlike the others, it has no innate comma. 7:9:11 = up-downsharp5 = C^(v#5) = C ^E vG#. Unfortunately it's very difficult to finger. Using an open string, it's 5 6 x 0. But see [[Kite Guitar Exercises and Techniques by Kite Giedraitis#Primes 11 and 13]] for an alternative way to play this chord, as well as 8:10:13 = down-upsharp5 = Cv(^#5) = C vE ^G#.

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 The Ruyoyo comma implies an augmented chord because it equates the octave with 5/4 plus 5/4 plus 9/7. In 12-edo, the aug chord is symmetrical, and it is its own homonym. But in 41edo, it's asymmetrical. Its homonyms are also augmented chords, but of a different type. Thus there are three basic augmented chords: upaug, downaug and down-halfaug. In the last chord, the 5th is spelled as vv#5 rather than ^^5 so that the interval from the 3rd to the 5th is spelled as vM3 not ^<sup>3</sup>m3. An alternative name for down-halfaug is down-dudsharp5 (dud is short for double-down).
-There is another trio of aug chords: up-halfaug, upminor-halfaug and up-dupaug, all homonyms. Dup is short for double-up. Their innate comma is the [[Sensamagic chords|Zozoyo comma]], which equates the octave with 9/7 plus 9/7 plus 6/5. Thus one 3rd is quite smaller than the other two. Only the uphalfaug is clearly an augmented chord. Since the 3rd is upped, the chord's 5th is spelled as ^^5 not vv#5. The upminor-halfaug chord's lowest 3rd is this small 3rd, and it really can't be called an augmented chord. The up-dupaug chord has ^^#5, a dupaugmented 5th. This is equivalent to a downmajor 6th, and again, it's debatable if this is really an augmented chord. In close voicing it uses every 3rd note of the [[Bohlen-Pierce|Bohlen-Pierce 13ED3 scale]].
+There is another trio of aug chords: up-halfaug, upminor-halfaug and up-dupaug, all homonyms. Dup is short for double-up. Their innate comma is the [[Sensamagic chords|Zozoyo comma]], which equates the octave with 9/7 plus 9/7 plus 6/5. Thus one 3rd is quite smaller than the other two. Only the uphalfaug is clearly an augmented chord. Since the 3rd is upped, the chord's 5th is spelled as ^^5 not vv#5. The upminor-halfaug chord's lowest 3rd is this small 3rd, and it really can't be called an augmented chord. The up-dupaug chord has ^^#5, a dupaugmented 5th. This is equivalent to a downmajor 6th, and again, it's debatable if this is really an augmented chord. In close voicing it uses every 3rd note of the [[Bohlen–Pierce scale]].
 All six chords are odd-limit 9. Another possible aug chord is odd-limit 11. Unlike the others, it has no innate comma. 7:9:11 = up-downsharp5 = C^(v#5) = C ^E vG#. Unfortunately it's very difficult to finger. Using an open string, it's 5 6 x 0. But see [[Kite Guitar Exercises and Techniques by Kite Giedraitis#Primes 11 and 13]] for an alternative way to play this chord, as well as 8:10:13 = down-upsharp5 = Cv(^#5) = C vE ^G#.