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

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=== Augmented Chords ===

The Ruyoyo comma implies an augmented chord because it lets 5/4, 5/4 and 9/7 add up to 2/1. 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 augmented chords: upaug, downaug and down-halfaug. ~~Logically,~~ the last chord ~~should be called down-doubledownsharp5 or down-double-up5~~, ~~but those names are rather long. Instead it's named after its half-augmented 5th. This~~ 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.

The Ruyoyo comma implies an augmented chord because it lets 5/4, 5/4 and 9/7 add up to 2/1. 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 is down-dudsharp5 (dud is short for double-down).

There is another trio of aug chords: up-halfaug, upminor-halfaug and up-sesquiaug, all homonyms. 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-sesquiaug chord has ^^#5, a sesqui-augmented 5th ("sesqui-" means one-and-a-half). 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]].

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Note that the mid-5th is spelled as a ~~double-up dim~~ 5th from the chord root (^^Gb) if the 3rd is upped, but as a ~~double-down~~ 5th (vvG) if the 3rd is downed. This avoids the interval from the 3rd to the 5th being spelled with a triple up or down.

Note that the mid-5th is spelled as a dupdim 5th from the chord root (^^Gb) if the 3rd is upped, but as a dud 5th (vvG) if the 3rd is downed. This avoids the interval from the 3rd to the 5th being spelled with a triple up or down.

The most important chord with a mid 5th is the downup7 chord. When translating pre-20th-century music to the Kite Guitar, the 7-limit up7 and down7 chords often sound inappropriate. The two best 5-limit translations of the dom7 chord are the downadd7 chord and the downup7 chord. The latter is used in Kite's [[Kite Guitar Translations by Kite Giedraitis|Greensleeves translation]]. The mid-5th appears as the interval from the 3rd up to the 7th. In a 5-limit context it is 36/25. It's equated to 16/11 by the [[100/99|Luyoyo]] comma, and to 13/9 by the [[325/324|Thoyoyo]] comma.

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 === Augmented Chords ===
-The Ruyoyo comma implies an augmented chord because it lets 5/4, 5/4 and 9/7 add up to 2/1. 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 augmented chords: upaug, downaug and down-halfaug. Logically, the last chord should be called down-doubledownsharp5 or down-double-up5, but those names are rather long. Instead it's named after its half-augmented 5th. This 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.
+The Ruyoyo comma implies an augmented chord because it lets 5/4, 5/4 and 9/7 add up to 2/1. 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 is down-dudsharp5 (dud is short for double-down).
 There is another trio of aug chords: up-halfaug, upminor-halfaug and up-sesquiaug, all homonyms. 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-sesquiaug chord has ^^#5, a sesqui-augmented 5th ("sesqui-" means one-and-a-half). 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]].
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-Note that the mid-5th is spelled as a double-up dim 5th from the chord root (^^Gb) if the 3rd is upped, but as a double-down 5th (vvG) if the 3rd is downed. This avoids the interval from the 3rd to the 5th being spelled with a triple up or down.
+Note that the mid-5th is spelled as a dupdim 5th from the chord root (^^Gb) if the 3rd is upped, but as a dud 5th (vvG) if the 3rd is downed. This avoids the interval from the 3rd to the 5th being spelled with a triple up or down.
 The most important chord with a mid 5th is the downup7 chord. When translating pre-20th-century music to the Kite Guitar, the 7-limit up7 and down7 chords often sound inappropriate. The two best 5-limit translations of the dom7 chord are the downadd7 chord and the downup7 chord. The latter is used in Kite's [[Kite Guitar Translations by Kite Giedraitis|Greensleeves translation]]. The mid-5th appears as the interval from the 3rd up to the 7th. In a 5-limit context it is 36/25. It's equated to 16/11 by the [[100/99|Luyoyo]] comma, and to 13/9 by the [[325/324|Thoyoyo]] comma.