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

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autopatrolled, Sysops
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added the v,^7 and 7sus4 chords, other minor changes
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== Triads ==
== Triads ==
The alternate names for the voicings are explained in the next section. Other voicings are possible; these are just the most convenient ones. The upmajor chord is a particularly dissonant triad. See "Innate-comma chords" below for augmented triads. '''Added ninths are shown in parentheses.''' Adding a major 9th (ratio 9/4, example note D) to the up or down triad increases the intervallic odd-limit only slightly if at all. The up chord is arguably improved by adding a 9th.  
The alternate names for the voicings are explained in the next section. Other voicings are possible; these are just the most convenient ones. The upmajor chord is a particularly dissonant triad. See "Innate-comma chords" below for augmented triads. '''Added ninths are shown in parentheses.''' Adding a major 9th (ratio 9/4, example note D) to the up or down triad increases the intervallic odd-limit only slightly if at all. The up chord is arguably improved by adding a 9th. The sus4 chords have another homonym, the dom7sus4 chord, which is discussed below.  
{| class="wikitable"
{| class="wikitable"
!chord type ---->
!chord type ---->
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It's generally impossible to voice 7th chords in 1st, 2nd or 3rd inversion close voicings, because the 7th occurs on the same string as the 8ve. Instead voicings are named as close (root position, R 3 5 7), high-3 (3rd raised an 8ve) and low-5 (5th lowered an 8ve). A high-3 low-5 voicing (5 R 7 3) uses all 6 strings, thus is only sometimes possible. A high-3-7 voicing (R 5 3 7) requires 7 strings. Half-dim chords can alternatively be named as dim add-7 chords, e.g. the uphalfdim chord is C^dim^7 or C^o^7, spoken as updim-upseven.
It's generally impossible to voice 7th chords in 1st, 2nd or 3rd inversion close voicings, because the 7th occurs on the same string as the 8ve. Instead voicings are named as close (root position, R 3 5 7), high-3 (3rd raised an 8ve) and low-5 (5th lowered an 8ve). A high-3 low-5 voicing (5 R 7 3) uses all 6 strings, thus is only sometimes possible. A high-3-7 voicing (R 5 3 7) requires 7 strings. Half-dim chords can alternatively be named as dim add-7 chords, e.g. the uphalfdim chord is C^dim^7 or C^o^7, spoken as updim-upseven.


See "Innate-comma chords" below for dim7 chords. The upmajor7 chord C^M7 = C ^E G ^B is a possibility, but it's quite dissonant, with ^M7 = 27/14.
See "Innate-comma chords" below for dim7 chords and 5-limit dom7 chords.  
 
The upmajor7 chord C^M7 = C ^E G ^B is a possibility, but it's quite dissonant, with ^M7 = 27/14.


'''9ths are shown in parentheses'''. Adding a major 9th (ratio 9/4, example note D) to any of the first 4 tetrads increases the intervallic odd-limit only slightly if at all. The up-7 chord is arguably improved by adding a 9th. The no3, no5 and no7 (i.e. add9) versions of the ^9 and v9 chords are all 9-odd-limit chords.
'''9ths are shown in parentheses'''. Adding a major 9th (ratio 9/4, example note D) to any of the first 4 tetrads increases the intervallic odd-limit only slightly if at all. The up-7 chord is arguably improved by adding a 9th. The no3, no5 and no7 (i.e. add9) versions of the ^9 and v9 chords are all 9-odd-limit chords.
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|4 . 1 1 3
|4 . 1 1 3
|-
|-
| colspan="8" |'''<u>low-5 voicing</u> 5 R 3 7 (9)'''
| colspan="8" |'''<u>low-5 voicing</u> 5 R 3 (5) 7 (9)'''
|-
|-
|frets
|frets
|2 4 4 . 3 (2)
|2 4 4 (3) 3 (2)
|2 4 5 . 2 (2)
|2 4 5 (3) 2 (2)
|2 4 4 . 1 (2)
|2 4 4 (3) 1 (2)
|2 4 3 . 2 (2)
|2 4 3 (3) 2 (2)
|2 4 2 . 1
|2 4 2 (3) 1
| rowspan="2" |(difficult)
| rowspan="2" |(difficult)
| rowspan="2" |(difficult)
| rowspan="2" |(difficult)
|-
|-
|suggested fingerings
|suggested fingerings
|1 3 4 . 2 (1)
|1 3 4 (2) 2 (1)
|1 3 4 . 2 (2)
|1 3 4 (2) 1 (1)
1 3 4 . 1 (1)
|2 3 4 . 1
|2 3 4 . 1
1 3 4 (2) 1
2 3 4 . 2 (1)
1 3 4 . 1 (2)
|1 4 3 . 2 (2)
|1 4 3 . 2 (2)
1 3 2 . 1 (1)
1 3 2 (2) 1 (1)
|2 4 2 . 1
 
1 4 3 (2) 1 (1)
 
1 4 2 (3) 1 (1)
|2 4 2 (3) 1
|}
|}
Flat-nine chords are possible. The plain minor 9th is 21/10, which is the sum of 7/5 and 3/2, thus a m9 works with either a perfect or diminished 5th. Examples:  
Flat-nine chords are possible. The plain minor 9th is 21/10, which is the sum of 7/5 and 3/2, thus a m9 works with either a perfect or diminished 5th. Examples:  
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|}
|}


=== 5-limit dominant7 chords ===
When translating pre-20th-century music to the Kite Guitar, the up7 and down7 chords often sound inappropriate. For a 5-limit tuning, the upmajor 3rd must be avoided, necessitating the downmajor 3rd. The 7-limit downminor 7th must also  be avoided, necessitating the upminor 7th or the plain minor 7th. The downadd7no5 chord was discussed in the previous section. Another possibility is the dom7sus4 chord (an up7 sus4 chord would have an offperfect interval).
In the downup7 chord, the interval from the 3rd up to the 7th is a mid 5th. 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. See also the section on mid-5th chords below.
The down add7 chord is difficult to finger, so the 5th is usually omitted.
{| class="wikitable"
!chord type ---->
!downup7
(down9up7)
!downadd7
!dom7sus4
!dom7sus4no5
|-
!example, with
homonyms
!Cv,^7
Cv9(^7)
!Cv,7
!C7sus4 = F4/9
= Bb6/9no3
!C7sus4no5
= F4 = Bb2
|-
!example notes
!C vE G ^Bb
!C vE G Bb
!C F G Bb
!C F Bb
|-
!ratio of the 3rd
!vM3 = 5/4
!vM3 = 5/4
!P4 = 4/3
!P4 = 4/3
|-
!ratio of the 5th
!P5 = 3/2
!P5 = 3/2
!P5 = 3/2
!------
|-
!ratio of the 7th
!^m7 = 9/5
!m7 = 16/9
!m7 = 16/9
!m7 = 16/9
|-
| colspan="5" |'''<u>close voicing</u> R 3 5 7 (9)'''
|-
|frets
|4 4 3 2 (2)
| rowspan="2" |(difficult)
| rowspan="2" |(difficult)
|4 6 8
|-
|suggested fingerings
|3 4 2 1 (1)
|1 3 4
1 2 4
|-
| colspan="5" |'''<u>high-3 voicing</u> R 5 7 (8) 3'''
|-
|frets
|4 . 3 2 5
| rowspan="2" |(difficult)
| rowspan="2" |(difficult)
| rowspan="2" |(difficult)
|-
|suggested fingerings
|3 . 2 1 4
|-
| colspan="5" |'''<u>low-5 voicing</u> 5 R 3 7 (9)'''
|-
|frets
|2 4 4 3 2 (2)
| rowspan="2" |(difficult)
|2 4 6 8
| rowspan="2" |(N/A)
|-
|suggested fingerings
|1 3 3 2 1 (1)
|1 2 3 4
|-
| colspan="5" |'''<u>low-7 voicing</u> 7 R 3 5 (7)'''
|-
|frets
|1 4 3 (2) (noR)
|7 4 4 3
|7 4 6 3
|7 4 6 8 (sus2-ish)
|-
|suggested fingerings
|1 4 3 2
|4 2 2 1
|4 2 3 1
|3 1 2 4
|}
=== Augmented Chords ===
=== 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 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.   


There is another group of aug chords: up-halfaug, upminor-halfaug and up-sesquiaug. 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. The upminor-halfaug chord's lowest 3rd is this small 3rd, and it's debatable if it can be called an augmented chord. "Sesqui-" means one-and-a-half, and the up-sesquiaug chord has ^^#5, a sesqui-augmented 5th. This is equivalent to a downmajor 6th, and again, it's debatable if this is really an augmented chord.
There is another group of aug chords: up-halfaug, upminor-halfaug and up-sesquiaug. 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. The upminor-halfaug chord's lowest 3rd is this small 3rd, and it's debatable if it can be called an augmented chord. "Sesqui-" means one-and-a-half, and the up-sesquiaug chord has ^^#5, a sesqui-augmented 5th. This is equivalent to a downmajor 6th, and again, it's debatable if this is really an augmented chord. The uphalfaug chord in close voicing uses every 3rd note of the [[Bohlen-Pierce|Bohlen-Pierce 13ED3 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 x56x0x.
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 x56x0x.
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