The Kite Guitar
- 1 The Kite Guitar
- 2 Photographs
- 3 Recordings and Videos
- 4 For Luthiers
- 5 About 41-EDO
- 6 Tunings
- 7 Fretboard Charts (downmajor tuning)
- 8 Chord shapes (downmajor tuning)
- 9 Translating 12-edo Songs to 41-edo
The Kite Guitar
The Kite guitar (or bass, mandolin, banjo, etc.) uses 41 divisions of the octave instead of 12. 41-tET or 41-edo 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.
The Kite guitar has almost twice as many frets as a standard guitar. Even with these additional frets, the Kite guitar is still quite playable. The interval between open strings is usually a major 3rd, not a 4th. Thus new chord shapes must be learned. However, the Kite guitar is isomorphic, meaning that chord shapes can be moved not only from fret to fret but also from string to string. Thus there are far fewer shapes to learn. (Open tunings, which are non-isomorphic, are also possible.) Tuning in 3rds not 4ths reduces the overall range of the guitar. Thus a 7-string or even an 8-string guitar is desirable.
For more info: http://tallkite.com/misc_files/The%20Kite%20Tuning.pdf
Caleb Ramsey’s 8-string electric guitar, refretted by Vivian Cecylia Tylińska
Squire 6-string and Yamaha 6-string, both refretted by Matthew Autry
Five early prototypes with cable-tie frets, all refretted by Kite Giedraitis:
Recordings and Videos
A simple 12-bar blues by Aaron Wolf:
Open-tuning recordings by Sacred Skeleton aka Igliashon Jones:
- https://soundcloud.com/sacred-skeleton/modified-kite-guitar-take-1 (clean)
- https://soundcloud.com/sacred-skeleton/modified-kite-guitar-take-2 (fuzz)
Open tunings become more playable with the use of a "half-fret capo". From the liner notes:
"A couple of improvisations on a guitar loaned to me by Kite Giedratis. The guitar is fretted to 41 notes per double-octave, i.e. every other note of 41 notes per octave, using movable cable ties. On these tracks I modified the fretting slightly by moving the 2nd fret down one step of 41edo and then put a capo behind it, effectively moving all the frets above it UP by one step of 41edo, so that the frets all give odd-numbered pitches from 41edo instead of even-numbered ones. This gives frets for approximations to the ratios 21/20, 12/11, 9/8, 7/6, 6/5, 5/4, 9/7, 4/3, 11/8, and 10/7 relative to the open strings, which makes it possible to let the open strings ring out against pitches fretted low on the neck when the open strings are tuned to DADGAD or DGDGAD, my two favorite open tunings.
Without the offset I introduced, the normal fretting on Kite's guitar would have the lowest frets approximating 28/27, 16/15, 10/9, 8/7, 32/27, 11/9, 81/64, 15/11, 7/5, and 16/11, which doesn't work well for the open tunings I like but is rather designed to have the open strings tuned in parallel 3rds (5/4 or 6/5), for an isomorphic layout that facilitates chords built by stacking 3rds. I found that tuning somewhat challenging, being so unlike any open string tunings I've ever used before, and most of the intervals between non-adjacent open strings are rather discordant. Other players, whose styles don't lean as heavily on open strings and drones the way I do, may find Kite's original design preferable to my modification.
But anyway, the two designs can coexist on the same fretboard by simply inserting an extra fret between the 1st and 2nd instead of moving the 2nd fret lower as I have done, and by varying the tuning of the open strings as you please. It's a fantastic way to access the resources of 41edo on a guitar, without having an absurd number of very closely-spaced frets!"
Possible method for implementing the half-fret capo trick: An extra fret slot is cut to allow insertion of a temporary fret in between the 1st and 2nd (permanent) frets. The slot stops short of the treble side of the fretboard. So gravity holds it in place, plus of course the capo. The temporary fret has the barbs on the side of the tang filed off. The extra slot is a bit wider, so the fret can be pulled out easily. It goes in from the side, under the strings, so the strings don't need to be loosened. Should be able to insert it and remove it on stage between songs. The fret is a bit longer, sticks out about 1/2 inch, so that you can pull it out easily. There is a hole or something in the sticking-out part, to attach a wire or something, so that the fret can be attached to the capo. Keeps one from losing it.
To place the frets on a Kite guitar, simply replace the 12th root of 2 = 1.059463 with the 41st root of 4 = 1.034390. Or purchase a pre-slotted fingerboard from Precision Pearl in Austin, Texas. It comes radiused, tapered and inlaid, so all you need to do is glue it on and put in the frets. Replacing 24 old frets makes 41 new frets, but the last few are very tight. One might instead replace 21 old frets to make 36 new frets.
To find the saddle compensation on a standard guitar, one compares the harmonic at the 12th fret with the fretted note at the 12th fret. For the Kite guitar, by a weird coincidence, one does the same! But the 12th fret now makes the 3rd harmonic, not the 2nd. Thus the two notes should be an 8ve apart, not a unison. To get a unison, when you fret the string, play the 2nd harmonic with your other hand. With your forefinger or middlefinger, touch the string midway between the 32nd and 33rd frets. Then stretch your hand and pluck with your thumb as close as you can get to the midpoint between your finger and the bridge. If this isn't feasible (e.g. with a bass guitar), you can capo the string at the 12th fret and use both hands to play the harmonic. And to be extremely precise, the fretted note should be 0.48¢ sharper than the harmonic.
The 41 notes can be named with ups and downs:
vm2 m2 ^m2 ~2 vM2 M2 ^M2
vm3 m3 ^m3 ~3 vM3 M3 ^M3
v4 P4 ^4 ~4 vA4/d5 A4/^d5 ~5 v5 P5 ^5
vm6 m6 ^m6 ~6 vM6 M6 ^M6
vm7 m7 ^m7 ~7 vM7 M7 ^M7
This chart shows 41-edo in terms of 12-edo. "-ish" means ±1 edostep. The 12 categories circled in red correspond to the notes of 12-edo. The two innermost and two outermost intervals are duplicates.
The same spiral, with notes not intervals. Again, the two innermost and two outermost notes are duplicates.
The standard tuning is the downmajor tuning, in which adjacent open strings are tuned a downmajor 3rd apart. Alternate tunings use an upminor 3rd or an upmajor 3rd. All three tunings are isomorphic, thus there is only one shape to learn for any chord. A "semi-isomorphic" tuning alternates downmajor and upminor 3rds. There are two shapes for every chord. In addition, there are open tunings such as DADGAD. See the Recordings and Videos section for more on this.
Tuning the Kite guitar to EADGBE doesn't work, because the conventional chord shapes create wolves. For example, the usual E major chord shape 0 2 2 1 0 0 would translate to either 0 3 3 2 0 0 = E vB vE G# B E, or else 0 4 4 2 0 0 = E ^B ^E G# B E. Either way, the chord contains 3 wolf octaves and two wolf fifths. In addition, the major 3rd isn't 5/4 but 14/11.
Fretboard Charts (downmajor tuning)
This chart is in relative not absolute notation, meaning it shows intervals, not notes. Down at the bottom is P1, a perfect unison. This is the tonic of the scale, or the root of the chord. This chart shows all the intervals within easy reach of this note, up to an octave. There are four "rainbows": one of 2nds, one of 3rds, one of 6ths, and one of 7ths. These plus the 4th, 5th, 8ve, and a few other notes add up to 25 of the 41 notes. Every single ratio of odd-limit 9 or less appears here.
This chart is the same, but extends much further. Some ratios change in the higher octaves, e.g. 16/15 becomes not 32/15 but 15/7.
This chart extends even further, showing the "rainbow zones" and the "wolf zones". When two guitarists play together, it's very natural for one to play chords in the lower rainbow zone, and another to solo in the higher rainbow zone.
If the tonic is the D at the 14th fret, the open strings are in a rainbow zone.
This chart shows the actual notes of an 8-string Kite guitar. A 6-string is usually tuned to the middle 6 strings of an 8-string. Every 4th fret has a dot, and every 12th fret has a double dot.
This shows all the notes, not just the natural ones. But it's too much work to memorize all this. Just learn where the 7 natural notes are, and learn your intervals. Since the open strings don’t work as well, one tends to think more in terms of intervals than notes.
Chord shapes (downmajor tuning)
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. (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.
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.
|chord type||sus4||up or
|example, with homonym||C4 = F2||C^||Cv||C^m||Cvm||C2 = G4||C^dim or C^o||Cvdim or Cvo|
|ratio of the 3rd||P4 = 4/3||^M3 = 9/7||vM3 = 5/4||^m3 = 6/5||vm3 = 7/6||M2 = 9/8||^m3 = 6/5||vm3 = 7/6|
|ratio of the 5th||P5 = 3/2||P5 = 3/2||P5 = 3/2||P5 = 3/2||P5 = 3/2||P5 = 3/2||d5 = 7/5||d5 = 7/5|
|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|
|suggested fingerings||2 4 1 3||2 3 1 4||2 3 1 4
2 2 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|
|suggested fingerings||2 . 1 3 4||2 . 1 3 4||2 . 1 3 4
2 . 1 4 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|
|suggested fingerings||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)|
|suggested fingerings||1 3 4 2||1 3 4 2||1 3 4 2||1 4 2 3
1 3 2 2
|1 3 1 2||2 4 1 3|
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.
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.
|example, with homonym||CvM7
|C^m7 = ^Ebv6
(C^m9 = ^EbvM7/C)
|Cvm7 = vEb^6||C^m7(b5) = ^Ebvm6||Cvm7(b5) = vEb^m6|
|ratio of the 3rd||vM3 = 5/4||^M3 = 9/7||vM3 = 5/4||^m3 = 6/5||vm3 = 7/6||^m3 = 6/5||vm3 = 7/6|
|ratio of the 5th||P5 = 3/2||P5 = 3/2||P5 = 3/2||P5 = 3/2||P5 = 3/2||d5 = 7/5||d5 = 7/5|
|ratio of the 7th||vM7 =15/8||^m7 = 9/5||vm7 = 7/4||^m7 = 9/5||vm7 = 7/4||^m7 = 9/5||vm7 = 7/4|
|close voicing R 3 5 7 (9)|
|frets||4 4 3 3 (2)||4 5 3 2 (2)||4 4 3 1 (2)||4 3 3 2 (2)||4 2 3 1||4 3 1 2||4 2 1 1|
|suggested fingerings||3 4 2 2 (1)
3 3 2 2 (1)
1 1 1 1 (1)
|3 4 2 1 (1)||3 4 2 1
4 4 3 1 (2)
|4 2 3 1 (1)
4 3 2 1 (1)
3 2 2 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|
|suggested fingerings||2 . 1 1 3||3 . 2 1 4||3 . 2 1 4||3 . 2 1 4
2 . 1 1 4
|4 . 2 1 3||3 . 1 2 4||4 . 1 1 3|
|low-5 voicing 5 R 3 7 (9)|
|frets||2 4 4 . 3 (2)||2 4 5 . 2 (2)||2 4 4 . 1 (2)||2 4 3 . 2 (2)||2 4 2 . 1||(difficult)||(difficult)|
|suggested fingerings||1 3 4 . 2 (1)||1 3 4 . 2 (2)
1 3 4 . 1 (1)
|2 3 4 . 1
2 3 4 . 2 (1)
|1 4 3 . 2 (2)
1 3 2 . 1 (1)
|2 4 2 . 1|
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).
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 a wolf 4th with the 6th. A 9th that is a P4 above the 6th (^M9 or vM9) will clash with the 5th, but can be added if the 5th is omitted. The chord becomes ambiguous. C^6,^9no5 is the same as ^Dv9no3. Cv6,v9no5 is vD^9no3. C^m6,^9no5 and Cvm6,v9no5 both have an awkward interval from the 3rd up to the 9th: a M7 = 40/21, odd-limit 21.
Adding an 11th (ratio 8/3) to either the ^m6 or the vm6 chord won't increase the 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.
|chord type||up-6 or
|example, with homonym||C^6 = ^Avm7||Cv6 = vA^m7||C^m6 = ^Avm7(b5)
(C^m6,11 = F^9)
|Cvm6 = vA^m7(b5)|
|ratio of the 3rd||^M3 = 9/7||vM3 = 5/4||^m3 = 6/5||vm3 = 7/6|
|ratio of the 5th||P5 = 3/2||P5 = 3/2||P5 = 3/2||P5 = 3/2|
|ratio of the 6th||^M6 = 12/7||vM6 = 5/3||^M6 = 12/7||vM6 = 5/3|
|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|
|suggested fingerings||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|
|suggested fingerings||1 2 4||1 1 3||2 1 4||2 1 4|
|low-6 voicing 6 R 3 5 (11)|
|frets||6 4 5 3||5 4 4 3||6 4 3 3 . (7)||5 4 2 3|
|suggested fingerings||4 2 3 1||4 2 3 1||4 2 1 1
3 2 1 1 . (4)
|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|
|suggested fingerings||1 2 3 4||1 2 3 4||1 3 2 4||1 3 1 4|
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 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
Obviously, the Kite Guitar can do much more than simply play conventional music. But a good starting place is to take what you know and find it on the Kite Guitar. Translating 12-edo music is sometimes problematic but never impossible. Quite often the translated version sounds better, because it's so well tuned.
One way to translate a conventional song 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 the spiral charts in the previous section.
Often there is only one obvious way to translate a song. I - V - VIm - IV becomes Iv - Vv - vVI^m - IVv. 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 within chords 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 two most common commas that cause issues are the Gu and Ru commas. The choice of which two chords in the pump contain the pitch shift can be tricky. Generally, a root movement by an ^4, v4, ^5 or v5 is avoided. This usually necessitates a root movement by a plain major or minor interval.
For example, I - VIm - IIm - V7 - I is a Gu pump. Without the pump, I - VIm would be translated as Iv - vVI^m, to avoid shifts. The roots would move by a vM6. With the pump, this might translate to Iv - VI^m - II^m - Vv7 - Iv. The first root movement is by a M6. The tonic and the major 3rd both shift between the I chord and the VI chord. Sometimes an up- or down-perfect root movement is better, see the "I Will" translation.
Likewise, I7 - IV7 - V7 - I7 is a Ru pump. The usual translation is Iv7 - IVv7 - Vv7 - Iv7, with the 4th shifting between the IV and V chords. Another example is Im7 - bIIIm6 - bVII7 - IV7 - I7. The root movements are m3, P5, P5, P5. Without the pump, the m3 movement would be translated to vm3. With the pump, to avoid an ^5 movement, the translation is Iv7 - bIII^m6 - bVIIv7 - IVv7 - I.
One way to hide pitch shifts is to voice the two occurrences of the pitch in different octaves. Another way is to omit the 5th in one of the chords. Thus in the Gu example, the 2nd chord might be VI^mno5.
In much music, especially pre-20th-century music, the dissonance of the dom7 chord is what drives the V7 - I cadence and gives the music momentum. But 41-edo's smooth v7 chord is like a guard dog that smiles and wags its tail at strangers instead of barking. It's too relaxed! And the 7-limit intervals can sound out of place in a pre-20th-century context. One might instead use Vv,7 (down add-7, with a plain minor 7th) or Vv,^7 (down up-7, with an upminor 7th). For example, Am - G - F - E7 can be translated as A^m - ^Gv - ^Fv - Ev,^7. (This also avoids a pitch shift.)
For 20th-century music, a Vv7 chord is often appropriate. But when a stronger V7 - I cadence is desired, a V^7 chord often works. For example, IIm7 - V7 - IM7 could be translated as either II^m7 - Vv7 - IvM7 or IIvm7 - Vv7 - IvM7. But the v7 chord is actually smoother than the vM7 chord, so the latter progression feels unfinished. Better is II^m7 - V^7 - IvM7. The II^m7 chord has two notes in common with V^7. It feels somewhat like a V11no1no3 chord. If a 9th is added to the ^7 chord, there are three common notes, and the progression feels even more connected.
However, if the I chord has no 7th, or a minor 7th, either II^m7 - Vv7 - Iv(7) or IIvm7 - Vv7 - Iv(7) works. The IIvm7 chord is more connected to the V chord than II^m7.
Actual song translations are on separate xenwiki pages, grouped by translator. if you have any translations, feel free to create your own page and link to it here!
Stormy Monday (T-Bone Walker, Bobby Bland, Allman Brothers)
I Will Survive (Gloria Gaynor)
Manhattan Island Serenade (Leon Russell)
Girl From Ipanema (Antônio Carlos Jobim)
I Will (The Beatles)
And I Love Her (The Beatles)
Fast Car (Tracy Chapman)
Every Breath You Take (The Police)
Kusuva Musha (mbira)
My old Kentucky Home (barbershop tag)
I Hear Numbers (Tall Kite)
Hotel California (The Eagles)
Stairway To Heaven intro (Led Zeppelin)