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, key 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. These tables list them all, plus the vM7 tetrad, which is odd limit 15. In these tables, the root is always on the 4th fret. A skipped string is indicated by a period. Alternate fingerings are possible, especially for 2-finger and 3-finger chords. The alternate names for the voicings are explained in the next section. The upmajor chord is a particularly dissonant triad.

Triads

	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). Other tetrad voicings are possible; these are just the most convenient ones. With 7 strings, a high-3-5 voicing is possible (R 5 3 7).

The up-7 chord is often improved by adding a 9th.

	downmajor-7	up-7 (up-9)	down-7	upminor-7	downminor-7	up-halfdim	down-halfdim
	CvM7	C^7 (C^9)	Cv7	C^m7 = ^Ebv6	Cvm7 = vEb^6	C^m7(b5) = ^Ebvm6	Cvm7(b5) = vEb^m6
close voicing (R 3 5 7)
frets	4 4 3 3	4 5 3 2 (2)	4 4 3 1	4 3 3 2	4 2 3 1	4 3 1 2	4 2 1 1
fingering	3 4 2 2	3 4 2 1 (1)	3 4 2 1	4 2 3 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 4 5 . 2 (2)	2 4 4 . 1	2 4 3 . 2	2 4 2 . 1	(difficult)	(difficult)
fingering	1 3 4 . 2	1 3 4 . 2 (2) *	2 3 4 . 1	1 . 4 3 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 probably low-5 (5 R 3 6), but it can be a real stretch.

The up-6 chord is particularly dissonant.

	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. Often there is more than one obvious way to translate a song.

Stormy Monday

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

Gv7   D^m vE^m    Dvm     Gv9   |   Cv7   G^m vA^m   Gvm     Cv9
                                |
Gv7      /       ^Abv7     /    |   Gv7       /       /       / 
                                |
Cv7   G^m vA^m    Gvm     Cv9   |   Cv7       /       /       / 
                                |
Gv7      /        vA^m7     /   |  vB^m7      /     vBb^m7    / 
                                |
vA^m7    /          /       /   |   C^m7      /       /       /  
                                |
Gv7      /         Cv7      /   |   Gv7       /     Dvaug     /  

Chords for 6-string guitar (actual key is closer to A not G)

Gv7        6  x  5  3  7  x        (frets)
           3     2  1  4           (fingers, 1 = index, 2 = middle, 3 = ring, 4 = pinkie)

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:

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-half-dim 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 showcases resolving from upmajor to