Kite Guitar

The Kite Guitar

The Kite guitar (or bass, mandolin, banjo, etc.) uses 41 divisions of the octave instead of 12. 41-tET approximates 7-limit just intonation to within 3-6¢, and chords sound gorgeous! But a guitar with 41 frets per octave is impractical. The Kite guitar cleverly omits every other fret. Thus while the frets are closer together than a standard guitar, they're not so close as to be unplayable. The interval between open strings is 13 steps of 41. 13 is an odd number, thus all 41 pitches are present on the guitar. Each string has only half of the pitches, but any adjacent pair of strings has all 41.

Omitting half the frets in effect moves certain pitches to remote areas of the fretboard, and makes certain intervals difficult to play. Miraculously, it works out that the remote intervals are the ones that don't work well in chords, and the ones that aren't remote are the ones that do work well. For example, the sweet 5-limit major 3rd, a 5/4 ratio, is easily accessible, but the dissonant 3-limit major 3rd 81/64 isn't. (3-limit & 5-limit refer to the largest prime number in the frequency ratio.)

In addition, important 7-limit intervals like 7/6, 7/5 and 7/4 are easy to play. This means the Kite guitar can do much more than just play sweet Renaissance music. It can put a whole new spin on jazz, blues and experimental music. The dom7 and dom9 chords are especially calm and relaxed, revealing just how poorly 12-tET tunes these chords. But dissonance is still possible, in fact 41-tET can be far more dissonant than 12-tET. And 41 notes means that the melodic and harmonic vocabulary is greatly expanded, allowing truly unique music that simply isn't possible with 12 notes.

For more info: http://tallkite.com/misc_files/The%20Kite%20Tuning.pdf

Chords

There are many chords to explore, but the obvious place to start is with those of 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.

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. 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.

Triads

Other voicings are possible; these are just the most convenient ones. The alternate names for the voicings are explained in the next section. The upmajor chord is a particularly dissonant triad.

	sus4	up or upmajor	down or downmajor	upminor	downminor	sus2	updim	downdim
	C4 = F2	C^	Cv	C^m	Cvm	C2 = G4	C^dim	Cvdim
close voicing (R 3 5 8)
frets	4 6 3 5	4 5 3 5	4 4 3 5	4 3 3 5	4 2 3 5	4 1 3 5	4 3 1 5	4 2 1 5
fingering	2 4 1 3	2 3 1 4	2 3 1 4	2 1 1 3	3 1 2 4	3 1 2 4	3 2 1 4	3 2 1 4
open or high-3 voicing (R 5 8 10)
frets	4 . 3 5 7	4 . 3 5 6	4 . 3 5 5	4 . 3 5 4	4 . 3 5 3	4 . 3 5 2	4 . 1 5 4	4 . 1 5 3
fingering	2 . 1 3 4	2 . 1 3 4	2 . 1 3 4	2 . 1 4 3	3 . 1 4 2	3 . 2 4 1	2 . 1 4 3	3 . 1 4 2
1st inversion or high-1 voicing (3 5 8)
frets	5 2 4	4 2 4	3 2 4	2 2 4	1 2 4	0 2 4	2 0 4	1 0 4
fingering	4 1 3	2 1 3	2 1 3	1 1 3	1 2 4	1 2 4	2 1 4	2 1 4
2nd inversion or low-5 voicing (5 R 3 5)
frets	2 4 6 3	2 4 5 3	2 4 4 3	2 4 3 3	2 4 2 3	2 4 1 3	(difficult)	(difficult)
fingering	1 3 4 2	1 3 4 2	1 3 4 2	1 4 2 3	1 3 1 2	2 4 1 3

Tetrads - 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).

Adding a major 9th to any of the first 4 tetrads sounds good. The up-7 chord is arguably improved by adding a 9th. 9ths are shown in parentheses.

	downmajor-7	up-7 (up-9)	down-7	upminor-7	downminor-7	up-halfdim	down-halfdim
	CvM7 (CvM9)	C^7 (C^9)	Cv7	C^m7 = ^Ebv6 (C^m9)	Cvm7 = vEb^6	C^m7(b5) = ^Ebvm6	Cvm7(b5) = vEb^m6
close voicing (R 3 5 7)
frets	4 4 3 3 (2)	4 5 3 2 (2)	4 4 3 1	4 3 3 2 (2)	4 2 3 1	4 3 1 2	4 2 1 1
fingering	3 4 2 2 (1)	3 4 2 1 (1)	3 4 2 1	4 2 3 1 (1)	4 2 3 1	4 3 1 2	4 2 1 1
high-3 voicing (R 5 7 10)
frets	4 . 3 3 5	4 . 3 2 6	4 . 3 1 5	4 . 3 2 4	4 . 3 1 3	4 . 1 2 4	4 . 1 1 3
fingering	2 . 1 1 3	3 . 2 1 4	3 . 2 1 4	3 . 2 1 4	4 . 2 1 3	3 . 1 2 4	4 . 1 1 3
low-5 voicing (5 R 3 7)
frets	2 4 4 . 3 (2)	2 4 5 . 2 (2)	2 4 4 . 1	2 4 3 . 2 (2)	2 4 2 . 1	(difficult)	(difficult)
fingering	1 3 4 . 2 (1)	1 3 4 . 2 (2) *	2 3 4 . 1	1 . 4 3 2 (2) *	2 4 2 . 1 (?)

These chords can also be fingered as barre chords.

Tetrads - 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. The least ambiguous non-riffing voicing is low-5 (5 R 3 6), but it can be a difficult stretch.

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

Adding a major 9th to any of these chords will make a wolf 4th with the 6th. Adding an 11th to either the ^m6 or the vm6 chord won't increase the odd limit above 9.

	up-6 or upmajor-6	down-6 or downmajor-6	upminor-6	downminor-6
	C^6 = ^Avm7	Cv6 = vA^m7	C^m6 = ^Avm7(b5)	Cvm6 = vA^m7(b5)
close voicing for riffing (R 3 5/6)
frets	4 5 3/7	4 4 3/6	4 3 3/7	4 2 3/6
fingering	2 3 1/4	2 3 1/4	2 1 1/4	3 1 2/4
close no-5th voicing (R 3 6)	C^6no5 = ^Avm	Cv6no5 = vA^m	C^m6no5 = ^Avdim	Cvm6no5 = vA^dim
frets	4 5 7	4 4 6	4 3 7	4 2 6
fingering	1 2 4	1 1 3	2 1 4	2 1 4
low-6 voicing (6 R 3 5)
frets	6 4 5 3	5 4 4 3	6 4 3 3	5 4 2 3
fingering	4 2 3 1	4 2 3 1	4 2 1 1	4 3 1 2
low-5 voicing (5 R 3 6)
frets	2 4 5 7	2 4 4 6	2 4 3 7	2 4 2 6
fingering	1 2 3 4	1 2 3 4	1 3 2 4	1 3 1 4

Songs

These conventional songs have been translated from 12edo to 41edo. One way to do this is to first translate it to 7-limit JI, perhaps visualizing it on a lattice, keeping in mind that 41-edo tempers out the Layo, Ruyoyo and Saruyo minicommas. Then translate the JI to 41edo. Another way is to use this chart which shows 41-edo in terms of 12-edo. The 12 categories circled in red correspond to the notes of 12-edo.

Often there is only one obvious way to translate a song. "La Bamba" is Iv - IVv - Vv7. Sometimes there are multiple obvious translations. For example, the first 3 chords of "When I Was Your Man" are II7 - IIm7 - I. That could become vII^7 - vII^m7 - Iv, or it could become ^IIv7 - ^IIvm7 - Iv.

In general, upperfect and downperfect intervals are to be avoided. Downmajor is preferred over upmajor. Upminor is preferred for most folk, but downminor is preferred for most blues. Avoid plain major and minor 3rds and 6ths. Comma pumps, other than the aforementioned minicommas, cause pitch shifts, or occasionally, a tonic drift. The choice of which two chords contain the shift can be tricky.

On a six string guitar, if one wants certain voicings of chords and root movements, the choices of key are limited. A seven-string or even an eight-string gives much more freedom.

Stormy Monday

This song showcases the 4:5:6:7 tetrad as the main chord for the blues.

Chords for 6-string guitar (actual key is closer to A than G)

Gv7 6 x 5 3 7 x (frets) 3 2 1 4 (fingers) D^m x x 5 4 4 x 3 2 2 vE^m x x 8 7 7 x (slide into this chord from the previous D^m) 3 2 2 Dvm x x 5 3 4 x (actually the top part of a Gv9 chord) 3 1 2 Gv9 6 x 5 3 4 x (actually Gv9no3) 4 3 1 2 Cv7 x 8 8 7 5 x 3 4 2 1 G^m x x x 7 6 6 3 2 2 vA^m x x x 10 9 9 (slide into this chord from the previous G^m) 3 2 2 Gvm x x x 7 5 6 3 1 2 Cv9 x 8 x 7 5 6 4 3 1 2 ^Abv7 8 x 7 5 9 x 3 2 1 4 vA^m7 9 x 8 7 9 x 3 2 1 4 vB^m7 x 6 x 5 4 6 3 2 1 4 vBb^m7 x 4 x 3 2 4 3 2 1 4 C^m7 x 8 7 7 6 x (some people play a different chord here) 4 2 3 1 Dvaug x x 5 5 6 6 (could be translated as Dv(^^5) which is x x 5 5 5 6) 1 1 2 3

I Will Survive

This song pumps the Saruyo comma, which equates 21/20 to 256/243. As a result, several pitches shift a comma flat during the progression, but then shift back to where they started. On the Kite guitar, the chord progression walks up the neck and then leaps down 12 frets, only to walk up back to where it started.

I^m7 IV^m7 bVIIv7 bIIIvM7 bVIvM7 IIvm7(b5) Vsus4 Vv7

Chords for a 6-string guitar in the key of vD upminor:

I^m7 . 8 . 7 6 8 (frets) 3 2 1 4 (fingers) IV^m7 . . 10 9 9 8 4 2 3 1 bVIIv7 11 . 10 8 12 . 3 2 1 4 bIIIvM7 . 13 13 12 12 . 3 4 2 2 (there may be a better fingering) bVIvM7 . 1 1 0 0 2 1 2 3 IIvm7(b5) . . 5 3 2 2 (a down-halfdim chord) 3 2 1 1 Vsus4 6 8 5 7 . . 2 4 1 3 Vv7 6 6 5 3 . . 3 4 2 1 Vv7 6 . 5 3 7 . (switch to this voicing halfway through the measure, 3 2 1 4 (for better voice leading into the I^m7 chord)

Manhattan Island Serenade

This particular translation adds 7ths to all the chords and features ^7 and ^9 chords resolving to ^m7 and v7 chords. The key is upminor, even though downminor is usually better than upminor for bluesy songs. But this song modulates to the relative major, and starting in downminor would lead to a dissonant upmajor key.

Chords for six-string guitar in the key of Bb:

I^m7 7 . . 5 7 7 (high-3-5 voicing, fingering is 2 1 3 4) IV^m7 . 9 . 8 7 9 V4 . . 6 8 5 7 V^7 . . 6 7 5 4 (awkward shift of fingering from V4, oh well) ^bVIv7 . . 8 8 7 5 (could instead use a low-5 voicing) ^bIII . 6 . 5 3 7 ^bVII 4 . 3 1 5 . IV^9 . 9 10 8 7 7

Girl From Ipanema

The famous melody is not written out, but for each chord, each note (i. e. pitch) of the melody is written once only. For example, the "Tall and tan and young and lovely" line has the melody 9 7 7 6 9 7 7 7, but only the notes 9 7 and 6 are shown. The melody notes are shown in 3 ways: a (string, fret) format that shows where it's played on guitar, the note's interval from the tonic, and the note's interval from the current chord's root.

The A part has an 81/80 comma issue. If the 3rd chord is rooted on II, its ^m7 (which is a prominent melody note) is an ^8, not an 8. This translation instead roots the chord on the vII, to avoid the melody straying from the tonic. If a bass line is added, the 2 - v2 melody might be awkward. Perhaps better to play the 4, changing the chord from vII^m7 to IVv6? Arguably a II^m7 chord would be better. Another possibility would be a IIm7 chord, but that's a little dissonant, also it's difficult to play on the Kite guitar.

In the B part, this translation has the song pumping the Layo comma, causing it to travel around the fingerboard quite a bit. The melody strays quite far from the original key, using e.g. ^5 and ^8. These notes seem far less offensive in the B part than in the A part, because there is no I chord in the entire B part.

The harmonies are translated as primarily 5-limit, except for dom7 chords which are of course 4:5:6:7. The key is B, which is far from the original key of F. That key was chosen so that the first #11 chord could take advantage of an open string. Unfortunately, the 2nd #11 chord can't do that, so a dom7addb5 chord is used instead.

In the two #11 chords near the end, the #11 could have been translated as 11/4, a ~11. But arguably the reason the 9th is flat is to justify/reinforce the #11. The b9 along with the b7 and #11 create a harmonious 1st inversion major triad. Since the b7 is 7/4, the b9 must be 21/10 and the #11 must be 14/5. To make this upper structure clearer, in the chord name the 11th is called a b12, not a v#11.

Chords for 6-string guitar:

----------CHORDS------------- -----MELODY NOTES-------------- --------REMARKS---------------------------- IvM9 9 9 8 8 7 . (2,7) (3,8) (3,5) (on guitar) If the melody is played/sung by another, 3 4 2 2 1 9 v7 6 (from tonic) the 9th is supplied by the melody, 9 v7 6 (from root) and this chord could be a vM7 chord instead. IIv6 . 6 6 8 7 . (2,7) (3,8) (3,5) 1 1 3 2 9 v7 6 8 v6 5 vII^m7 12 11 11 10 . . (3,10) (4,11) (4,8) Could have been an ^m9 chord. 4 2 3 1 8 v6 5 Could also have been a II^m7 chord, see above. ^b7 5 ^4 #Iv7(b5) 11 11 8 8 . . (3,8) (4,8) (5,11) Could be called an ^bII chord. 3 4 1 1 v7 5 4 vb7 b5 v3 IvM7 9 9 8 8 . . (4,8) The fingering is chosen to easily slide into 3 4 1 1 5 the next chord. 5 #Iv7(b5) 11 11 8 8 . . 3 4 1 1 #IvM7 11 11 10 10 . . (3,10) (3,12) (4,13) Could have been an ^m9 chord. 3 4 1 1 8 ^b9 b7 Could be called an ^bII chord. v7 8 v6 #IVv7 . 13 13 12 10 . (4,10) (4,13) Should be a v9 chord, but I only have 4 fingers! 3 4 2 1 ^b6 b7 Could have a low-5 voicing. 9 v10 #I^m9 11 10 10 9 9 . (2,9) (2,1) (3,12) If the melody supplies the 9th, could be a ^m7 chord. 4 3 2 2 1 ^b10 ^10 #8 The ^b10 from the tonic can be thought of as a #9. 9 ^b10 8 ^VIv7 . 10 12 12 . 9 (3,9) (3,12) 2 3 4 1 ^7 #8 9 v10 ^II^m9 13 12 12 11 11 . (2,11) (2,13) (3,14) If the melody supplies the 9th, could be a ^m7 chord. 4 2 3 1 1 ^10 ~11 ^9 9 ^b10 8 ~VIIv7 . 12 14 14 . 11 (3,11) (3,14) (2,11) (2,13) Again, should really be a v9 chord. 2 3 4 1 ^^8 ^9 ^10 ~11 9 v10 b12 12 III^m7 . . 3 2 2 1 (2,16)(3,2)(3,5)(2,2)(2,4)(1,1) 4 2 3 1 ^12 ^5 6 7 ^8 ^9 ^b10 ^b3 4 5 v6 ^b7 VIv7b9b12 4 . 3 1 0 2 (1,2) (1,4) If the melody supplies the b12th, could be a v7b9 chord, 4 3 1 2 b10 10 played as 4 4 3 1 0 . b12 12 II^m7 . 6 5 5 4 . (1,6)(4,5)(4,8)(3,5)(3,8)(2,4) (3,8) could be (2,2) = 7 = 6, or even (3,9) = ^7 = ^6 4 2 3 1 ^11 ^4 5 6 v7 ^8 ^b10 ^b3 4 5 v6 ^b7 Vv7b5 . 6 8 8 5 5 (2,5) Should be a v7b9b12 chord, not enough strings or fingers! 2 3 4 1 1 b9 (Vv7b5 means add a flat 5, and Vv7(b5) means flatten the 5.) b5 vII^m9 (2,10) (3,10) (4,11) Ending melody: "When she passes I" v10 8 v6 If the melody supplies the 9th, could be a ^m7 chord. 9 ^b7 5 #Iv7(b5) (1,9) (3,8) (4,11) "smile, but she doesn't" 12 v7 v6 b12 vb7 vb6 IvM7 (3,8) "see" v7 v7 #Iv7(b5) (3,8) (4,1) "She just doesn't" v7 v6 vb7 vb6