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

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Chords are named using [[Ups and Downs Notation|ups and down notation]], see also the [http://tallkite.com/misc_files/notation%20guide%20for%20edos%205-72.pdf notation guide for edos 5-72] and [[41edo Chord Names]]. Briefly, an up or down in the chord name immediately after the root affects the 3rd, 6th, 7th and/or the 11th, but not the 5th, 9th or 13th. Thus Gv9 is G vB D vF A. Alterations are enclosed in parentheses, as in Cvm7(b5). Additions are set off with a comma (the punctuation mark, not the interval!). In general, the comma is spoken as "add", e.g. Cv,9 = "C down add-9" = C vE G D. Chord progressions are written as Cv7 - vEb^m6 - Fv7 or Iv7 - vbIII^m6 - IVv7.  
Chords are named using [[Ups and Downs Notation|ups and down notation]], see also the [http://tallkite.com/misc_files/notation%20guide%20for%20edos%205-72.pdf notation guide for edos 5-72] and [[41edo Chord Names]]. Briefly, an up or down in the chord name immediately after the root affects the 3rd, 6th, 7th and/or the 11th, but not the 5th, 9th or 13th. Thus Gv9 is G vB D vF A. Alterations are enclosed in parentheses, as in Cvm7(b5). Additions are set off with a comma (the punctuation mark, not the interval!). In general, the comma is spoken as "add", e.g. Cv,9 = "C down add-9" = C vE G D. Chord progressions are written as Cv7 - vEb^m6 - Fv7 or Iv7 - vbIII^m6 - IVv7.  
Chord voicings are named using [[hi-lo notation]], as hi3, lo5, etc.


In general, an odd-limit 15 chord has only one 15-limit interval, and most of the others are much lower odd-limit. For example, the downmajor seven chord has intervals of odd-limit 3, 3, 5, 5, 5 and 15. The many low-limit intervals serve as "glue" to hold together the chord, despite the one 15-limit interval. This is the rationale for focusing on odd-limit 15 chords here and not those of odd-limit 11 or 13, for those chords have multiple intervals of high odd-limit. But see below, at the very end of this section.
In general, an odd-limit 15 chord has only one 15-limit interval, and most of the others are much lower odd-limit. For example, the downmajor seven chord has intervals of odd-limit 3, 3, 5, 5, 5 and 15. The many low-limit intervals serve as "glue" to hold together the chord, despite the one 15-limit interval. This is the rationale for focusing on odd-limit 15 chords here and not those of odd-limit 11 or 13, for those chords have multiple intervals of high odd-limit. But see below, at the very end of this section.
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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 two sus chords have another homonym, the dom7sus4 chord, which is discussed below. The cryptic superscripted-circle symbol for diminished can be replaced with the far more intuitive and obvious lower-case d.  
The 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 two sus chords have another homonym, the dom7sus4 chord, which is discussed below. The cryptic superscripted-circle symbol for diminished can be replaced with the far more intuitive and obvious lower-case d.  
{| class="wikitable"
{| class="wikitable"
!chord type ---->
!chord type ---->
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|3 2 1 4
|3 2 1 4
|-
|-
|'''<u>open or high-3 voicing</u> R 5 8 3'''
|'''<u>open or hi3 voicing</u> R 5 8 3'''
| colspan="8" |
| colspan="8" |
|-
|-
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|3 . 1 4 2
|3 . 1 4 2
|-
|-
|'''<u>high-R voicing</u> 3 5 8 (9) (1st inversion''')
|'''<u>hiR voicing</u> 3 5 8 (9) (1st inversion''')
| colspan="8" |
| colspan="8" |
|-
|-
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|2 1 4
|2 1 4
|-
|-
|'''<u>low-5 voicing</u> 5 R 3 5 (2nd inversion)'''
|'''<u>addlo5 voicing</u> 5 R 3 5 (2nd inversion)'''
| colspan="8" |
| colspan="8" |
|-
|-
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It's generally impossible to voice 7th chords in 1st, 2nd or 3rd inversion close voicings, because the 7th usually occurs on the same string as the 8ve. One exception is the dom7sus4 chord. Its 7th shares a string with the 5th, so the 5th is generally omitted.
It's generally impossible to voice 7th chords in 1st, 2nd or 3rd inversion close voicings, because the 7th usually occurs on the same string as the 8ve. One exception is the dom7sus4 chord. Its 7th shares a string with the 5th, so the 5th is generally omitted.


Since the usual inversions aren't possible in close voicings, the terminology changes. Voicings are named as close (root position, R 3 5 7), high-3 (3rd raised an 8ve) and low-5 (5th lowered an 8ve). The high-3 low-5 voicing (5 R 7 3) and the high-3-5 voicing R 7 3 5) both use all 6 strings, thus they are only sometimes possible. A high-3-7 voicing (R 5 3 7) requires 7 strings.  
Since the usual inversions aren't possible in close voicings, the terminology changes. Voicings are named using [[hi-lo notation]] as close (root position, R 3 5 7), hi3 (3rd raised an 8ve), lo5 (5th lowered an 8ve), etc. The hi3lo5 voicing (5 R 7 3) and the hi35 voicing (R 7 3 5) both use all 6 strings, thus they are only sometimes possible. A hi37 voicing (R 5 3 7) requires 7 strings.  


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 yet more dom7 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 yet more dom7 chords.
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1 2 4
1 2 4
|-
|-
| colspan="9" |'''<u>high-3 voicing</u> R 5 7 3'''
| colspan="9" |'''<u>hi3 voicing</u> R 5 7 3'''
|-
|-
|frets
|frets
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|4 . 1 1 3
|4 . 1 1 3
|-
|-
| colspan="8" |'''<u>low-5 voicing</u> 5 R 3 (5) 7 (9)'''
| colspan="9" |'''<u>lo5 voicing</u> 5 R 3 (5) 7 (9)'''
|'''<u>low-7 voicing</u>'''
|-
|-
|frets
|frets
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| rowspan="2" |(difficult)
| rowspan="2" |(difficult)
| rowspan="2" |(difficult)
| rowspan="2" |(difficult)
|7 4 6 8
| rowspan="2" |(difficult)
|-
|-
|suggested
|suggested
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1 4 2 (3) 1 (1)
1 4 2 (3) 1 (1)
|2 4 2 (3) 1
|2 4 2 (3) 1
|-
| colspan="9" |'''<u>lo7 voicing</u> 7 R 4 5'''
|-
|frets
| rowspan="2" |(N/A)
| rowspan="2" |(N/A)
| rowspan="2" |(N/A)
| rowspan="2" |(N/A)
| rowspan="2" |(N/A)
| rowspan="2" |(N/A)
| rowspan="2" |(N/A)
|7 4 6 8
|-
|suggested
fingerings
|3 1 2 4
|3 1 2 4
|}
|}
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* the downminor-7 flat-5 flat-9 chord = Cvm7(b5)b9 = C vEb Gb vBb Db = 4 2 1 1 0
* the downminor-7 flat-5 flat-9 chord = Cvm7(b5)b9 = C vEb Gb vBb Db = 4 2 1 1 0
The upminor 9th (15/7) is also possible, but hard to play, Example: the downmajor-7 upflat-9 chord = CvM7,^b9 = C vE G vB ^Db. Note that ^Db is enharmonically equivalent to C#, the augmented 8ve. Thus this chord's homonym is vE^m6/C.
The upminor 9th (15/7) is also possible, but hard to play, Example: the downmajor-7 upflat-9 chord = CvM7,^b9 = C vE G vB ^Db. Note that ^Db is enharmonically equivalent to C#, the augmented 8ve. Thus this chord's homonym is vE^m6/C.
The voicing terminology can be expanded to cover all cases: 5 7 8 10 is low-5-7 or high-root-3. 5 7 10 15 is high-3-8. R 2 3 5 7 is low-9, and 2 5 R 3 7 is low-2-5.


== Sixth chords ==
== Sixth chords ==
Every 6th chord has a 7th chord homonym, and vice versa. But a 7th chord with some sort of major 7th doesn't "flip" to a 6th chord as easily, because the 6th would be some sort of minor 6th, which is rare.
Every 6th chord has a 7th chord homonym, and vice versa. But a 7th chord with some sort of major 7th doesn't "flip" to a 6th chord as easily, because the 6th would be some sort of minor 6th, which is rare.


Sixth chords are hard to voice. A close voicing in root position is generally impossible, because the 6th occurs on the same string as the 5th. One solution is to play a riff that alternates between the 5th and the 6th (3/6 in the tab indicates alternating between the 3rd and 6th fret). Another is to omit the 5th, but then the chord can be mistaken for a triad in 1st inversion. It helps to double the root at the octave, i.e. play R 3 6 8 not R 3 6. Another voicing is the low-6 (6 R 3 5) i.e. the 3rd inversion. But this is the same as the close voicing of its 7th chord homonym, and again the chord can be mistaken. A non-ambiguous voicing is low-5 (5 R 3 6), but it can be a difficult stretch. Also the 9th from the 5th to the 6th is usually not a plain 9th, and can be dissonant. The best voicing is high-3-5 (R 6 3 5 or R 6 8 3 5), but with only 6 strings, it's only possible for root-4 chords. Other possibilities are high-3-6 (R 5 3 6), high-5 (R 3 6 5 or R 3 6 8 5) and high-6 (R 3 5 8 6).
Sixth chords are hard to voice. A close voicing in root position is generally impossible, because the 6th occurs on the same string as the 5th. One solution is to play a riff that alternates between the 5th and the 6th (3/6 in the tab indicates alternating between the 3rd and 6th fret). Another is to omit the 5th, but then the chord can be mistaken for a triad in 1st inversion. It helps to double the root at the octave, i.e. play R 3 6 8 not R 3 6. Another voicing is the lo6 (6 R 3 5) i.e. the 3rd inversion. But this is the same as the close voicing of its 7th chord homonym, and again the chord can be mistaken. A non-ambiguous voicing is lo5 (5 R 3 6), but it can be a difficult stretch. Also the 9th from the 5th to the 6th is usually not a plain 9th, and can be dissonant. The best voicing is hi35 (R 6 3 5 or R 6 8 3 5), but with only 6 strings, it's only possible for root-6 chords. Other possibilities are hi36 (R 5 3 6), hi5 (R 3 6 5 or R 3 6 8 5) and hi6 (R 3 5 8 6).


The up-6 chord is particularly dissonant, unless voiced as its homonym, the vm7 chord.
The up-6 chord is particularly dissonant, unless voiced as its homonym, the vm7 chord.
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Adding a major 9th (ratio 9/4) to any of these chords will make a wolf 4th with the 6th. A 9th that is a P4 above the 6th (^M9 or vM9) will clash with the 5th. It can be safely added if the 5th is omitted, but then the chord becomes ambiguous. Cv6,v9no5 is the same as vD^9no3 (or vD^m9no3). C^6,^9no5 is ^Dv9no3. C^m6,^9no5 and Cvm6,v9no5 both have an awkward interval from the 3rd up to the 9th: a M7 = 40/21.
Adding a major 9th (ratio 9/4) to any of these chords will make a wolf 4th with the 6th. A 9th that is a P4 above the 6th (^M9 or vM9) will clash with the 5th. It can be safely added if the 5th is omitted, but then the chord becomes ambiguous. Cv6,v9no5 is the same as vD^9no3 (or vD^m9no3). C^6,^9no5 is ^Dv9no3. C^m6,^9no5 and Cvm6,v9no5 both have an awkward interval from the 3rd up to the 9th: a M7 = 40/21.


Adding an 11th (ratio 8/3) to either the ^m6 or the vm6 chord won't increase the intervallic odd-limit above 9. But a Cvm6,11 chord is the same as an Fv9 chord, and every easy fingering puts the F in the bass, so it's hardly a distinct chord. Adding an 11th to a Cv6 chord makes Cv6,11, which is an FvM9 chord. Again, every easy fingering has F in the bass, and Cv6,11 isn't a distinct chord. The ^m6,11 chord can be voiced high-3-5 low-11, so that the 11th is a 4th. This is equivalent to a low-5 voicing of its homonym the ^9 chord.
Adding an 11th (ratio 8/3) to either the ^m6 or the vm6 chord won't increase the intervallic odd-limit above 9. But a Cvm6,11 chord is the same as an Fv9 chord, and every easy fingering puts the F in the bass, so it's hardly a distinct chord. Adding an 11th to a Cv6 chord makes Cv6,11, which is an FvM9 chord. Again, every easy fingering has F in the bass, and Cv6,11 isn't a distinct chord. The ^m6,11 chord can be voiced hi35lo11, so that the 11th is a 4th. This is equivalent to a lo5 voicing of its homonym the ^9 chord.
{| class="wikitable"
{| class="wikitable"
!chord type ---->
!chord type ---->
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|3 1 2/4
|3 1 2/4
|-
|-
|'''<u>close no-5th voicing</u> R 3 6 8'''
|'''<u>close no5add8 voicing</u> R 3 6 8'''
| colspan="4" |
| colspan="4" |
|-
|-
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|2 1 4 3
|2 1 4 3
|-
|-
|'''<u>low-6 voicing</u> 6 R 3 5 (11)'''
|'''<u>lo6 voicing</u> 6 R 3 5 (11)'''
| colspan="4" |
| colspan="4" |
|-
|-
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|4 3 1 2
|4 3 1 2
|-
|-
|'''<u>low-5 voicing</u> 5 R 3 6'''
|'''<u>lo5 voicing</u> 5 R 3 6'''
| colspan="4" |
| colspan="4" |
|-
|-
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|1 3 1 4
|1 3 1 4
|-
|-
|'''<u>high-3-5 voicing</u> R (4) 6 (8) 3 5'''
|'''<u>hi35 voicing</u> R (4) 6 (8) 3 5'''
| colspan="4" |
| colspan="4" |
|-
|-
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(T = thumb)
(T = thumb)
|}
|}
If you play a 7th chord in close root position on the upper 4 strings, you can drop the 3rd of the chord down an octave to get a high-3-5 voicing of the corresponding 6th chord.  
If you play a 7th chord in close root position on the upper 4 strings, you can drop the 3rd of the chord down an octave to get a hi35 voicing of the corresponding 6th chord.  
* x x A x E ^G '''^C''' (clearly A^m7)
* x x A x E ^G '''^C''' (clearly A^m7)
* x x A '''^C''' E ^G x  (ambiguous but slightly more A^m7)
* x x A '''^C''' E ^G x  (ambiguous but slightly more A^m7)
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We've covered every chord that maps to a JI chord of intervallic odd-limit 9. However there are many Kite guitar chords that don't, although their individual intervals do. These chords are called [[Dyadic chord|innate-comma chords aka essentially tempered chords]]. Such chords often have a mysterious sound. Almost every easily reachable interval on the fretboard is odd-limit 9. The only exceptions are ~4, ~5, vM7, ^M7, vm9 and ^m9. Thus the majority of random Kite guitar chord shapes are intervallic odd-limit 9.  
We've covered every chord that maps to a JI chord of intervallic odd-limit 9. However there are many Kite guitar chords that don't, although their individual intervals do. These chords are called [[Dyadic chord|innate-comma chords aka essentially tempered chords]]. Such chords often have a mysterious sound. Almost every easily reachable interval on the fretboard is odd-limit 9. The only exceptions are ~4, ~5, vM7, ^M7, vm9 and ^m9. Thus the majority of random Kite guitar chord shapes are intervallic odd-limit 9.  


For example, the downadd7no5 chord has 5/4 and 16/9. The interval from 5/4 up to 16/9 is 64/45. But because 41edo tempers out the [[225/224|Ruyoyo comma]] of only 8¢, 64/45 is equivalent to 10/7. The high-3 voicing inverts this into an even smoother 7/5. This dom7 chord is often appropriate for translating 12-edo's V7 -- I cadence: relaxed but not too relaxed. Adding the 5th creates a plain minor 3rd interval with the 7th. If the m3 is interpreted as 32/27, this increases the odd limit to 27. But if interpreted as 13/11, the odd limit is only 13.
For example, the downadd7no5 chord has 5/4 and 16/9. The interval from 5/4 up to 16/9 is 64/45. But because 41edo tempers out the [[225/224|Ruyoyo comma]] of only 8¢, 64/45 is equivalent to 10/7. The hi3 voicing inverts this into an even smoother 7/5. This dom7 chord is often appropriate for translating 12-edo's V7 -- I cadence: relaxed but not too relaxed. Adding the 5th creates a plain minor 3rd interval with the 7th. If the m3 is interpreted as 32/27, this increases the odd limit to 27. But if interpreted as 13/11, the odd limit is only 13.


The sus4downmajor7 chord (odd-limit 15) also has an innate Ruyoyo comma. The chord is quite striking in close voicing. The interval from 4/3 up to 15/8 is 45/32, equivalent to 7/5. The homonym of C4,vM7 = C F G vB is the sus2addb5 chord F2,b5 = F G Cb C. In 41-edo, Cb is enharmonically equivalent to vB. In chord names, "(b5)" means alter the 5th by flattening it, but ",b5" means add a flat 5th alongside the perfect 5th.
The sus4downmajor7 chord (odd-limit 15) also has an innate Ruyoyo comma. The chord is quite striking in close voicing. The interval from 4/3 up to 15/8 is 45/32, equivalent to 7/5. The homonym of C4,vM7 = C F G vB is the sus2addb5 chord F2,b5 = F G Cb C. In 41-edo, Cb is enharmonically equivalent to vB. In chord names, "(b5)" means alter the 5th by flattening it, but "b5" means add a flat 5th alongside the perfect 5th.


The down7flat5 chord (odd-limit 9) is also innate-ruyoyo. The interval from 5/4 up to 7/5 is 28/25, equivalent to 9/8. The homonym of Cv7(b5) is the Gb downadd7upflat5 chord Gbv,7(^b5) = Gb vBb ^Dbb Fb. Enharmonic equivalences: ^Dbb = C, Fb = vE, and upflat 5th = aug 4th = 10/7.
The down7flat5 chord (odd-limit 9) is also innate-ruyoyo. The interval from 5/4 up to 7/5 is 28/25, equivalent to 9/8. The homonym of Cv7(b5) is the Gb downadd7upflat5 chord Gbv,7(^b5) = Gb vBb ^Dbb Fb. Enharmonic equivalences: ^Dbb = C, Fb = vE, and upflat 5th = aug 4th = 10/7.


All three of these chords contain the chord shape 4 1 1. This 3-note "nugget" implies the Ruyoyo comma: 9/8 plus 5/4 equals 7/5. By itself, it's the v,7no5 chord in low-7 voicing. The v7(b5) chord in close voicing (4 4 1 1) also contains the octave inverse of this nugget, 4 4 1. By itself, this inverse nugget makes Cv(b5) = C vE Gb (odd-limit 9). Beware, "C-down flat-5" = Cv(b5) sounds much like "C downflat-5" = C(vb5) = C E vGb = C E ^^F = 8:10:11. To avoid ambiguity, one could say "C-downmajor flat-5".  
All three of these chords contain the chord shape 4 1 1. This 3-note "nugget" implies the Ruyoyo comma: 9/8 plus 5/4 equals 7/5. By itself, it's the v,7no5 chord in lo7 voicing. The v7(b5) chord in close voicing (4 4 1 1) also contains the octave inverse of this nugget, 4 4 1. By itself, this inverse nugget makes Cv(b5) = C vE Gb (odd-limit 9). Beware, "C-down flat-5" = Cv(b5) sounds much like "C downflat-5" = C(vb5) = C E vGb = C E ^^F = 8:10:11. To avoid ambiguity, one could say "C-downmajor flat-5".  


The downaddflat5 chord Cv,b5 (odd-limit 15) has both a perfect and a diminished 5th. This chord is best voiced low-5. In other voicings, the two 5ths are on the same string, and one must play a riff that alternates between the two (indicated as 1/3 in the tab, 1st and 3rd fret).  
The downaddflat5 chord Cv,b5 (odd-limit 15) has both a perfect and a diminished 5th. This chord is best voiced lo5. In other voicings, the two 5ths are on the same string, and one must play a riff that alternates between the two (indicated as 1/3 in the tab, 1st and 3rd fret).  


When the added b5 is voiced an 8ve higher, it becomes a v#11, and suggests the downmajor7downsharp11 and downmajor9downsharp11 chords (both odd-limit 15). No need to omit the 3rd, it makes a pleasant M9 = 9/4 with the 11th.
When the added b5 is voiced an 8ve higher, it becomes a v#11, and suggests the downmajor7downsharp11 and downmajor9downsharp11 chords (both odd-limit 15). No need to omit the 3rd, it makes a pleasant M9 = 9/4 with the 11th.
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|3 4 2 2 1 1
|3 4 2 2 1 1
|-
|-
| colspan="8" |'''<u>high-3 voicing</u> R 5 7 (8) 3'''
| colspan="8" |'''<u>hi3 voicing</u> R 5 7 (8) 3'''
|-
|-
|frets
|frets
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|2 . 3 3 4 1
|2 . 3 3 4 1
|-
|-
| colspan="8" |'''<u>low-5 voicing</u> 5 R 3 7'''
| colspan="8" |'''<u>lo5 voicing</u> 5 R 3 7'''
|-
|-
|frets
|frets
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|1 3 4 . 2 1 1
|1 3 4 . 2 1 1
|-
|-
| colspan="8" |'''<u>low-7 voicing</u> 7 R 3 (7)'''
| colspan="8" |'''<u>lo7 voicing</u> 7 R 3 (7)'''
|-
|-
|frets
|frets
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|1 2 4 (3)
|1 2 4 (3)
|-
|-
| colspan="7" |'''<u>high-3 voicing</u> R 5 (8) 3'''
| colspan="7" |'''<u>hi3 voicing</u> R 5 (8) 3'''
|-
|-
|frets
|frets
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|1 . 3 (2) 4
|1 . 3 (2) 4
|-
|-
| colspan="7" |'''<u>high-R voicing</u> 3 5 8 (3) (1st inversion)'''
| colspan="7" |'''<u>hiR voicing</u> 3 5 8 (3) (1st inversion)'''
|-
|-
|
|
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|see ^(^^5)
|see ^(^^5)
|-
|-
| colspan="7" |'''<u>low-5 voicing</u> 5 R 3 (5) (2nd inversion)'''
| colspan="7" |'''<u>lo5 voicing</u> 5 R 3 (5) (2nd inversion)'''
|-
|-
|
|
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|3 2 1/4
|3 2 1/4
|-
|-
| colspan="5" |'''<u>high-3 voicing</u> R 5 7 3'''
| colspan="5" |'''<u>hi3 voicing</u> R 5 7 3'''
|-
|-
|frets
|frets
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|3 . 2 1 4
|3 . 2 1 4
|-
|-
| colspan="5" |'''<u>high-3-5 voicing</u> R 6 (8) 3 5'''
| colspan="5" |'''<u>hi35 voicing</u> R 6 (8) 3 5'''
|-
|-
|frets
|frets
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|3 4 2 1 (1)
|3 4 2 1 (1)
|-
|-
|'''<u>high-3 voicing</u> R 5 7 3'''
|'''<u>hi3 voicing</u> R 5 7 3'''
|
|
|-
|-
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|3 . 2 1 4
|3 . 2 1 4
|-
|-
|'''<u>low-5 voicing</u> 5 R 3 5 7 (9)'''
|'''<u>addlo5 voicing</u> 5 R 3 5 7 (9)'''
|
|
|-
|-
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|1 3 3 2 1 (1)
|1 3 3 2 1 (1)
|-
|-
|'''<u>low-7 voicing</u> 7 3 5 7''' (noR)
|'''<u>noRaddlo7 voicing</u> 7 3 5 7'''
|
|
|-
|-
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