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

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== Overview ==

There are many chords on the [[The_Kite_Guitar|Kite Guitar]] 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'''. Chords such as vM7, ^m7, vm7 and v6 are classified as '''stacked''' chords, because they are formed by stacking complimentary 3rds. Many chords fall outside these 3 categories.

There are many chords on the [[The_Kite_Guitar|Kite Guitar]] 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 9:7:6:5:4 pentad. Thus most of these chords can be classified as either '''harmonic''' or '''subharmonic'''. Chords such as vM7, ^m7, vm7 and v6 are classified as '''stacked''' chords, because they are formed by stacking complimentary 3rds. Many chords fall outside these 3 categories.

~~'''~~Homonyms~~'''~~ are to chords what modes are to scales. C6 and Am7 are homonyms (same notes, different root). In theory, every tetrad has 3 other homonyms, but in practice many are too implausible (e.g. Am7 = G6/9sus4no5). Most tetrads and pentads have at least one plausible homonym.

[[Chord homonym|Homonyms]] are to chords what modes are to scales. C6 and Am7 are homonyms (same notes, different root). In theory, every tetrad has 3 other homonyms, but in practice many are too implausible (e.g. Am7 = G6/9sus4no5). Most tetrads and pentads have at least one plausible homonym.

These tables list all chords of odd-limit 9, plus a few with downmajor 7ths that are odd-limit 15. The example chords are arbitrarily rooted on C. The chord shapes are written in tablature, using fret numbers. The root is placed arbitrarily on the 4th fret, even though C is not 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, and of course any fret of that 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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|}

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:

* the upminor-7 flat-9 chord = C^~~m7,b9~~ = C ^Eb G ^Bb Db = 4 3 3 2 0

* the upminor-7 flat-9 chord = C^m7b9 = C ^Eb G ^Bb Db = 4 3 3 2 0

* the upminor-7 flat-5 flat-9 chord = C^m7(b5)b9 = C ^Eb Gb ^Bb Db = 4 3 1 2 0

* the downminor-7 flat-9 chord = ~~Cvm7,b9~~ = C vEb G vBb Db = 4 2 3 1 0

* the downminor-7 flat-9 chord = Cvm7b9 = C vEb G vBb Db = 4 2 3 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.

== 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.

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 ~~(root on the 6th string)~~. Other possibilities are hi36 (R 5 3 6), hi5 (R 3 6 5 or R 3 6 8 5) and hi6add8 (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 it spans 6 strings, and isn't possible for all chords unless you have 8 strings. Other possibilities are hi36 (R 5 3 6), hi5 (R 3 6 5 or R 3 6 8 5) and hi6add8 (R 3 5 8 6).

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

Adding a major 9th (ratio 9/4) to any of these chords will make an offperfect 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 an offperfect 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. Cv6v9no5 is the same as vD^9no3 (or vD^m9no3). C^6^9no5 is ^Dv9no3. C^m6^9no5 and Cvm6v9no5 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 hi35lo11, so that the 11th is a 4th. This is equivalent to a lo5 voicing of its homonym the ^9 chord.

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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 C4vM7 = C F G vB is the sus2addb5 chord F2b5 = 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.

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!example w homonym

!Cv,7no5 = Bb2(b5)

!~~C4,vM7~~ = ~~F2,b5~~

!C4vM7 = F2b5

!CvM7(b5) = vE2^m6

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

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|C vEb vvG vBb

|4 2 2 1 <u>or</u> 4 . 2 1 3

|vEbv,^6

|vEbv^6

|-

|down up-6

|Cv,^6

|Cv^6

|C vE G ^A

|4 . 7 (5) 5 4

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|C ^Eb ^^Gb ^Bb

|4 3 2 2 <u>or</u> 4 . 2 2 4

|^Eb^~~m,v6~~

|^Eb^mv6

|-

|upminor down-6

|C^~~m,v6~~

|C^mv6

|C ^Eb G vA

|4 . 6 (5) 4 4

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|-

!example

!Cv,^7 or Cv9(^7)

!Cv^7 or Cv9(^7)

|-

!example notes

@@ Line 2: / Line 2: @@
 == Overview ==
-There are many chords on the [[The_Kite_Guitar|Kite Guitar]] 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'''. Chords such as vM7, ^m7, vm7 and v6 are classified as '''stacked''' chords, because they are formed by stacking complimentary 3rds. Many chords fall outside these 3 categories.
+There are many chords on the [[The_Kite_Guitar|Kite Guitar]] 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 9:7:6:5:4 pentad. Thus most of these chords can be classified as either '''harmonic''' or '''subharmonic'''. Chords such as vM7, ^m7, vm7 and v6 are classified as '''stacked''' chords, because they are formed by stacking complimentary 3rds. Many chords fall outside these 3 categories.
-'''Homonyms''' are to chords what modes are to scales. C6 and Am7 are homonyms (same notes, different root). In theory, every tetrad has 3 other homonyms, but in practice many are too implausible (e.g. Am7 = G6/9sus4no5). Most tetrads and pentads have at least one plausible homonym.
+[[Chord homonym|Homonyms]] are to chords what modes are to scales. C6 and Am7 are homonyms (same notes, different root). In theory, every tetrad has 3 other homonyms, but in practice many are too implausible (e.g. Am7 = G6/9sus4no5). Most tetrads and pentads have at least one plausible homonym.
 These tables list all chords of odd-limit 9, plus a few with downmajor 7ths that are odd-limit 15. The example chords are arbitrarily rooted on C. The chord shapes are written in tablature, using fret numbers. The root is placed arbitrarily on the 4th fret, even though C is not 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, and of course any fret of that string. A skipped string is indicated by a period. Alternate fingerings are possible, especially for 2-finger and 3-finger chords.
@@ Line 358: / Line 358: @@
 |}
 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:
-* the upminor-7 flat-9 chord = C^m7,b9 = C ^Eb G ^Bb Db = 4 3 3 2 0
+* the upminor-7 flat-9 chord = C^m7b9 = C ^Eb G ^Bb Db = 4 3 3 2 0
 * the upminor-7 flat-5 flat-9 chord = C^m7(b5)b9 = C ^Eb Gb ^Bb Db = 4 3 1 2 0
-* the downminor-7 flat-9 chord = Cvm7,b9 = C vEb G vBb Db = 4 2 3 1 0
+* the downminor-7 flat-9 chord = Cvm7b9 = C vEb G vBb Db = 4 2 3 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.
 == 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.
-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 (root on the 6th string). Other possibilities are hi36 (R 5 3 6), hi5 (R 3 6 5 or R 3 6 8 5) and hi6add8 (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 it spans 6 strings, and isn't possible for all chords unless you have 8 strings. Other possibilities are hi36 (R 5 3 6), hi5 (R 3 6 5 or R 3 6 8 5) and hi6add8 (R 3 5 8 6).
 The up-6 chord is particularly dissonant, unless voiced as its homonym, the vm7 chord.
-Adding a major 9th (ratio 9/4) to any of these chords will make an offperfect 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 an offperfect 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. Cv6v9no5 is the same as vD^9no3 (or vD^m9no3). C^6^9no5 is ^Dv9no3. C^m6^9no5 and Cvm6v9no5 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 hi35lo11, so that the 11th is a 4th. This is equivalent to a lo5 voicing of its homonym the ^9 chord.
@@ Line 512: / Line 512: @@
 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 C4vM7 = C F G vB is the sus2addb5 chord F2b5 = 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.
@@ Line 533: / Line 533: @@
 !example w homonym
 !Cv,7no5 = Bb2(b5)
-!C4,vM7 = F2,b5
+!C4vM7 = F2b5
 !CvM7(b5) = vE2^m6
 !Cv7(b5) = Gbv,7(^b5)
@@ Line 871: / Line 871: @@
 |C vEb vvG vBb
 |4 2 2 1 <u>or</u> 4 . 2 1 3
-|vEbv,^6
+|vEbv^6
 |-
 |down up-6
-|Cv,^6
+|Cv^6
 |C vE G ^A
 |4 . 7 (5) 5 4
@@ Line 889: / Line 889: @@
 |C ^Eb ^^Gb ^Bb
 |4 3 2 2 <u>or</u> 4 . 2 2 4
-|^Eb^m,v6
+|^Eb^mv6
 |-
 |upminor down-6
-|C^m,v6
+|C^mv6
 |C ^Eb G vA
 |4 . 6 (5) 4 4
@@ Line 918: / Line 918: @@
 |-
 !example
-!Cv,^7 or Cv9(^7)
+!Cv^7 or Cv9(^7)
 |-
 !example notes