Kite Guitar: Difference between revisions

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== Chord shapes (downmajor tuning) ==

There are many chords to explore, but the obvious place to start is with those of [[odd-limit|intervallic odd-limit]] 9 or less. These chords are mostly subsets of the 4:5:6:7:9 pentad or the 9/(9:7:6:5:4) pentad. Thus most of these chords can be classified as either '''harmonic''' or '''subharmonic'''. The ~~only exceptions are the~~ ^m7 and vm7 chords (and their homonyms v6 and ^6)~~, which~~ are classified as '''stacked''' chords, because they are formed by stacking complimentary 3rds. (Some chords fall outside these 3 categories.)

There are many chords to explore, but the obvious place to start is with those of [[odd-limit|intervallic odd-limit]] 9 or less. These chords are mostly subsets of the 4:5:6:7:9 pentad or the 9/(9:7:6:5:4) pentad. Thus most of these chords can be classified as either '''harmonic''' or '''subharmonic'''. The ^m7 and vm7 chords (and their homonyms v6 and ^6) are classified as '''stacked''' chords, because they are formed by stacking complimentary 3rds. Some chords fall outside these 3 categories.)

These tables list all the 9-odd-limit chords, plus the vM7 tetrad, which is odd limit 15 and stacked. The chord shapes are written in tablature, using fret numbers. The root is placed arbitrarily on the 4th fret. In these tables, the interval between open strings is always a downmajor 3rd. This makes the Kite guitar isomorphic, thus a tab like 4 6 3 5 can start on the 6th, 5th or 4th string. A skipped string is indicated by a period. Alternate fingerings are possible, especially for 2-finger and 3-finger chords.

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!C^dim or C^o

!Cvdim or Cvo

|-

!example notes

!C F G

!C ^E G

!C vE G

!C ^Eb G

!C vEb G

!C D G

!C ^Eb Gb

!C vEb Gb

|-

!ratio of the 3rd

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|3 2 1 4

|-

|'''open or high-3 voicing R 5 8 10'''

|'''open or high-3 voicing R 5 8 3'''

|

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=== Seventh chords ===

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 ~~is possible~~ (5 R 7 3)~~. With 7~~ strings, a high-3-7 voicing ~~is possible~~ (R 5 3 7). Half-dim chords can alternatively be named as dim add-7 chords, e.g. the up-half-dim chord is C^dim,^7 or C^o,^7.

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 up-half-dim chord is C^dim,^7 or C^o,^7.

'''9ths are shown in parentheses'''. Adding a major 9th (ratio 9/4) to any of the first 4 tetrads ~~sounds good~~. 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) to any of the first 4 tetrads increases the 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.

{| class="wikitable"

!chord type

!~~downmajor-7~~

!downmajor7

(~~downmajor-9~~)

(downmajor9)

!~~up-7~~

!up7

(~~up-9~~)

(up9)

!~~down-7~~

!down7

(~~down-9~~)

(down9)

!~~upminor-7~~

!upminor7

(~~upminor-9~~)

(upminor9)

!~~downminor-7~~

!downminor7

!~~up-halfdim~~

!uphalfdim

!~~down-halfdim~~

!downhalfdim

|-

!example, with homonym

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(Cv9)

!C^m7 = ^Ebv6

(C^m9 ~~= ^EbvM7/C~~)

(C^m9)

!Cvm7 = vEb^6

!C^m7(b5) = ^Ebvm6

!Cvm7(b5) = vEb^m6

|-

!example notes

!C vE G vB

!C ^E G ^Bb

!C vE G vBb

!C ^Eb G ^Bb

!C vEb G vBb

!C ^Eb Gb ^Bb

!C vEb Gb vBb

|-

!ratio of the 3rd

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|4 2 1 1

|-

|'''high-3 voicing R 5 7 10'''

|'''high-3 voicing R 5 7 3'''

|

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|

|}

The downadd7no5 chord has 5/4 and 16/9. Surprisingly, this chord is also intervallic odd-limit 9. The interval from 5/4 up to 16/9 is 64/45. But because 41edo tempers out the [[225/224|Ruyoyo]] comma, it becomes 10/7. The high-3 voicing inverts this into an even smoother 7/5. Note that adding the 5th would increase the odd-limit to 27. In chord names, alterations are enclosed in parentheses, and additions are set off with a comma (the punctuation mark, not the interval!) In general, the comma is spoken as "add". Thus C-down add-seven is Cv,7 = C vE G Bb. Compare with C down-seven = Cv7 = C vE G vBb.

The downmajor7sus4 chord (odd-limit 15) also has an innate ruyoyo comma. Its vM7 is a 5/4 above the 5th, making it 15/8. But it's also 7/5 above the 4th, making it 28/15. Its homonym is the sus2addb5 chord F2,b5 = F G Cb C. 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. Its b5 is a 7/5, but also 9/8 above the 3rd (ratio 5/4), making it a 45/32. Its homonym is the downadd7upflat5 chord Gbv,7(^b5) = Gb vBb ^Dbb Fb. The upflat five is enharmonically equivalent to an aug 4th = 10/7.

{| class="wikitable"

!chord type

!downadd7no5

!downmajor7sus4

!down7flat5

|-

!example, with homonym

!Cv,7no5

!CvM7(4) = F2,b5

!Cv7(b5) = Gbv,7(^b5)

|-

!example notes

!C vE Bb

!C F G vB

!C vE Gb vBb

|-

!ratio of the 3rd

!vM3 = 5/4

!P4 = 4/3

!vM3 = 5/4

|-

!ratio of the 5th

!none

!P5 = 3/2

!d5 = 7/5

|-

!ratio of the 7th

!m7 = 16/9

!vM7 = 15/8

!vm7 = 7/4

|-

|'''close voicing R 3 5 7 (8)'''

|

|-

|frets

|4 4 8 (5)

|4 6 3 3

|4 4 1 1

|-

|suggested fingerings

|1 1 4 (2)

|2 4 1 1

|3 4 1 1

|-

|'''high-3 voicing R 5 7 3'''

|

|-

|frets

|4 . 8 . 5

|4 . 3 3 7

|4 . 1 1 5

|-

|suggested fingerings

|1 . 4 . 2

|2 . 1 1 4

|3 . 1 1 4

|-

|'''low-5 voicing 5 R 3 7'''

|

|-

|frets

|(N/A)

|(difficult)

|0 4 4 . 1

|-

|suggested fingerings

|

|1 3 4 . 2

|}

11th chords include the vM9,v#11 (frets 4 4 3 3 2 2), vM11 (4 4 3 3 2 0), v11 (4 4 3 1 2 0), and ^m11 (4 3 3 2 2 1). All but the first of these contain a wolf 11th. Rather than 8/3, the vM11 and v11 chords have 21/8, and the ^m11 chord has 27/10. The first chord's v#11th is 45/16, which is equivalent to 14/5, because 41edo tempers out the [[225/224|Ruyoyo]] comma. Thus the chord's intervallic odd limit is only 15.

=== Sixth chords ===

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. Another is to omit the 5th, but then the chord can be mistaken for a triad in 1st inversion. Another voicing is the low-6 aka 3rd inversion (6 R 3 5). But this is the same as the close voicing of the corresponding 7th chord, and again the chord can be mistaken. A ~~good~~ 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. ~~Other possibilities are~~ high-3-5 (R 6 3 5), high-3-6 (R 5 3 6), high-5 (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. Another is to omit the 5th, but then the chord can be mistaken for a triad in 1st inversion. Another voicing is the low-6 aka 3rd inversion (6 R 3 5). But this is the same as the close voicing of the corresponding 7th chord, 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), but with only 6 strings, it often isn't possible. Other possibilities are high-3-6 (R 5 3 6), high-5 (R 3 6 8 5) and high-6 (R 3 5 8 6).

The up-6 chord is particularly dissonant, unless voiced as its homonym, the vm7 chord.

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(C^m6,11 = F^9)

!Cvm6 = vA^m7(b5)

|-

!example notes

!C ^E G ^A

!C vE G vA

!C ^Eb G ^A

!C vEb G vA

|-

!ratio of the 3rd

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|1 3 2 4

|1 3 1 4

|-

|'''high-3-5 voicing R 6 (8) 3 5'''

|

|-

|frets

|4 . 7 . 6 4

|4 . 6 (5) 5 4

|4 . 7 (5) 4 4

|4 . 6 (5) 3 4

|-

|suggested fingerings

|1 . 4 . 3 2

1 . 4 . 3 1

|1 . 4 . 3 2

1 . 4 (2) 3 1

|1 . 4 (2) 1 1

|?????

|}

11th chords include the vM9,v#11 (frets 4 4 3 3 2 2), vM11 (4 4 3 3 2 0), v11 (4 4 3 1 2 0), and ^m11 (4 3 3 2 2 1). All but the first of these contain a wolf 11th. Rather than 8/3, the vM11 and v11 chords have 21/8, and the ^m11 chord has 27/10. The first chord's v#11th is 45/16, which is equivalent to 14/5, because 41edo tempers out the [[225/224|Ruyoyo]] comma. Thus the chord's intervallic odd limit is only 15.

Another chord with an innate Ruyoyo comma is vM7sus4 (4 6 3 3), in which the vM7 is a 5/4 above the 5th, making it 15/8. But it's also 7/5 above the 4th, making it 28/15. Yet another is v7(b5) (4 4 1 1), in which the b5 is a 7/5, but also 9/8 above the 3rd (ratio 5/4), making it a 45/32.

== Translating 12-edo Songs to 41-edo ==

@@ Line 167: / Line 167: @@
 == Chord shapes (downmajor tuning) ==
-There are many chords to explore, but the obvious place to start is with those of [[odd-limit|intervallic odd-limit]] 9 or less. These chords are mostly subsets of the 4:5:6:7:9 pentad or the 9/(9:7:6:5:4) pentad. Thus most of these chords can be classified as either '''harmonic''' or '''subharmonic'''. The only exceptions are the ^m7 and vm7 chords (and their homonyms v6 and ^6), which are classified as '''stacked''' chords, because they are formed by stacking complimentary 3rds. (Some chords fall outside these 3 categories.)
+There are many chords to explore, but the obvious place to start is with those of [[odd-limit|intervallic odd-limit]] 9 or less. These chords are mostly subsets of the 4:5:6:7:9 pentad or the 9/(9:7:6:5:4) pentad. Thus most of these chords can be classified as either '''harmonic''' or '''subharmonic'''. The ^m7 and vm7 chords (and their homonyms v6 and ^6) are classified as '''stacked''' chords, because they are formed by stacking complimentary 3rds. Some chords fall outside these 3 categories.)
 These tables list all the 9-odd-limit chords, plus the vM7 tetrad, which is odd limit 15 and stacked. The chord shapes are written in tablature, using fret numbers. The root is placed arbitrarily on the 4th fret. In these tables, the interval between open strings is always a downmajor 3rd. This makes the Kite guitar isomorphic, thus a tab like 4 6 3 5 can start on the 6th, 5th or 4th string. A skipped string is indicated by a period. Alternate fingerings are possible, especially for 2-finger and 3-finger chords.
@@ Line 194: / Line 194: @@
 !C^dim or C^o
 !Cvdim or Cvo
+|-
+!example notes
+!C F G
+!C ^E G
+!C vE G
+!C ^Eb G
+!C vEb G
+!C D G
+!C ^Eb Gb
+!C vEb Gb
 |-
 !ratio of the 3rd
@@ Line 246: / Line 256: @@
 |3 2 1 4
 |-
-|'''<u>open or high-3 voicing</u> R 5 8 10'''
+|'''<u>open or high-3 voicing</u> R 5 8 3'''
 |
 |
@@ Line 340: / Line 350: @@
 === Seventh chords ===
-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 is possible (5 R 7 3). With 7 strings, a high-3-7 voicing is possible (R 5 3 7). Half-dim chords can alternatively be named as dim add-7 chords, e.g. the up-half-dim chord is C^dim,^7 or C^o,^7.
+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 up-half-dim chord is C^dim,^7 or C^o,^7.
-'''9ths are shown in parentheses'''. Adding a major 9th (ratio 9/4) to any of the first 4 tetrads sounds good. 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) to any of the first 4 tetrads increases the 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.
 {| class="wikitable"
 !chord type
-!downmajor-7
+!downmajor7
-(downmajor-9)
+(downmajor9)
-!up-7
+!up7
-(up-9)
+(up9)
-!down-7
+!down7
-(down-9)
+(down9)
-!upminor-7
+!upminor7
-(upminor-9)
+(upminor9)
-!downminor-7
+!downminor7
-!up-halfdim
+!uphalfdim
-!down-halfdim
+!downhalfdim
 |-
 !example, with homonym
@@ Line 365: / Line 375: @@
 (Cv9)
 !C^m7 = ^Ebv6
-(C^m9 = ^EbvM7/C)
+(C^m9)
 !Cvm7 = vEb^6
 !C^m7(b5) = ^Ebvm6
 !Cvm7(b5) = vEb^m6
+|-
+!example notes
+!C vE G vB
+!C ^E G ^Bb
+!C vE G vBb
+!C ^Eb G ^Bb
+!C vEb G vBb
+!C ^Eb Gb ^Bb
+!C vEb Gb vBb
 |-
 !ratio of the 3rd
@@ Line 431: / Line 450: @@
 |4 2 1 1
 |-
-|'''<u>high-3 voicing</u> R 5 7 10'''
+|'''<u>high-3 voicing</u> R 5 7 3'''
 |
 |
@@ Line 489: / Line 508: @@
 |
 |}
+The downadd7no5 chord has 5/4 and 16/9. Surprisingly, this chord is also intervallic odd-limit 9. The interval from 5/4 up to 16/9 is 64/45. But because 41edo tempers out the [[225/224|Ruyoyo]] comma, it becomes 10/7. The high-3 voicing inverts this into an even smoother 7/5. Note that adding the 5th would increase the odd-limit to 27. In chord names, alterations are enclosed in parentheses, and additions are set off with a comma (the punctuation mark, not the interval!) In general, the comma is spoken as "add". Thus C-down add-seven is Cv,7 = C vE G Bb. Compare with C down-seven = Cv7 = C vE G vBb.
+The downmajor7sus4 chord (odd-limit 15) also has an innate ruyoyo comma. Its vM7 is a 5/4 above the 5th, making it 15/8. But it's also 7/5 above the 4th, making it 28/15. Its homonym is the sus2addb5 chord F2,b5 = F G Cb C. 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. Its b5 is a 7/5, but also 9/8 above the 3rd (ratio 5/4), making it a 45/32. Its homonym is the downadd7upflat5 chord Gbv,7(^b5) = Gb vBb ^Dbb Fb. The upflat five is enharmonically equivalent to an aug 4th = 10/7.
+{| class="wikitable"
+!chord type
+!downadd7no5
+!downmajor7sus4
+!down7flat5
+|-
+!example, with homonym
+!Cv,7no5
+!CvM7(4) = F2,b5
+!Cv7(b5) = Gbv,7(^b5)
+|-
+!example notes
+!C vE Bb
+!C F G vB
+!C vE Gb vBb
+|-
+!ratio of the 3rd
+!vM3 = 5/4
+!P4 = 4/3
+!vM3 = 5/4
+|-
+!ratio of the 5th
+!none
+!P5 = 3/2
+!d5 = 7/5
+|-
+!ratio of the 7th
+!m7 = 16/9
+!vM7 = 15/8
+!vm7 = 7/4
+|-
+|'''<u>close voicing</u> R 3 5 7 (8)'''
+|
+|
+|
+|-
+|frets
+|4 4 8 (5)
+|4 6 3 3
+|4 4 1 1
+|-
+|suggested fingerings
+|1 1 4 (2)
+|2 4 1 1
+|3 4 1 1
+|-
+|'''<u>high-3 voicing</u> R 5 7 3'''
+|
+|
+|
+|-
+|frets
+|4 . 8 . 5
+|4 . 3 3 7
+|4 . 1 1 5
+|-
+|suggested fingerings
+|1 . 4 . 2
+|2 . 1 1 4
+|3 . 1 1 4
+|-
+|'''<u>low-5 voicing</u> 5 R 3 7'''
+|
+|
+|
+|-
+|frets
+|(N/A)
+|(difficult)
+|0 4 4 . 1
+|-
+|suggested fingerings
+|
+|
+|1 3 4 . 2
+|}
+th chords include the vM9,v#11 (frets 4 4 3 3 2 2), vM11 (4 4 3 3 2 0), v11 (4 4 3 1 2 0), and ^m11 (4 3 3 2 2 1). All but the first of these contain a wolf 11th. Rather than 8/3, the vM11 and v11 chords have 21/8, and the ^m11 chord has 27/10. The first chord's v#11th is 45/16, which is equivalent to 14/5, because 41edo tempers out the [[225/224|Ruyoyo]] comma. Thus the chord's intervallic odd limit is only 15.
 === Sixth chords ===
-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. Another is to omit the 5th, but then the chord can be mistaken for a triad in 1st inversion. Another voicing is the low-6 aka 3rd inversion (6 R 3 5). But this is the same as the close voicing of the corresponding 7th chord, and again the chord can be mistaken. A good 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. Other possibilities are high-3-5 (R 6 3 5), high-3-6 (R 5 3 6), high-5 (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. Another is to omit the 5th, but then the chord can be mistaken for a triad in 1st inversion. Another voicing is the low-6 aka 3rd inversion (6 R 3 5). But this is the same as the close voicing of the corresponding 7th chord, 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), but with only 6 strings, it often isn't possible. Other possibilities are high-3-6 (R 5 3 6), high-5 (R 3 6 8 5) and high-6 (R 3 5 8 6).
 The up-6 chord is particularly dissonant, unless voiced as its homonym, the vm7 chord.
@@ Line 513: / Line 615: @@
 (C^m6,11 = F^9)
 !Cvm6 = vA^m7(b5)
+|-
+!example notes
+!C ^E G ^A
+!C vE G vA
+!C ^Eb G ^A
+!C vEb G vA
 |-
 !ratio of the 3rd
@@ Line 604: / Line 712: @@
 |1 3 2 4
 |1 3 1 4
+|-
+|'''<u>high-3-5 voicing</u> R 6 (8) 3 5'''
+|
+|
+|
+|
+|-
+|frets
+|4 . 7 . 6 4
+|4 . 6 (5) 5 4
+|4 . 7 (5) 4 4
+|4 . 6 (5) 3 4
+|-
+|suggested fingerings
+|1 . 4 . 3 2
+. 4 . 3 1
+|1 . 4 . 3 2
+. 4 (2) 3 1
+|1 . 4 (2) 1 1
+|?????
 |}
-th chords include the vM9,v#11 (frets 4 4 3 3 2 2), vM11 (4 4 3 3 2 0), v11 (4 4 3 1 2 0), and ^m11 (4 3 3 2 2 1). All but the first of these contain a wolf 11th. Rather than 8/3, the vM11 and v11 chords have 21/8, and the ^m11 chord has 27/10. The first chord's v#11th is 45/16, which is equivalent to 14/5, because 41edo tempers out the [[225/224|Ruyoyo]] comma. Thus the chord's intervallic odd limit is only 15.
-Another chord with an innate Ruyoyo comma is vM7sus4 (4 6 3 3), in which the vM7 is a 5/4 above the 5th, making it 15/8. But it's also 7/5 above the 4th, making it 28/15. Yet another is v7(b5) (4 4 1 1), in which the b5 is a 7/5, but also 9/8 above the 3rd (ratio 5/4), making it a 45/32.
 == Translating 12-edo Songs to 41-edo ==