Kite Guitar: Difference between revisions

The Kite guitar (or bass, mandolin, banjo, etc.) combines the beauty of just intonation with the freedom of an equal temperament. Kite guitar is short for Kite-''fretted'' guitar. It has 41 notes per the octave instead of 12. [[41edo|41-tET aka 41-equal aka 41edo]] approximates 7-limit just intonation to within 3-6 [[cents]], and chords sound gorgeous! But a guitar with 41 frets per octave is physically challenging to play. Kite-fretting cleverly omits every other fret. Thus while the frets are closer together than a standard guitar, the Kite guitar is still quite playable. There are 20'''½''' frets per octave, thus it's about as playable as [[19edo|19-equal]] or [[22edo|22-equal]]. The interval between open strings is 13 steps of 41. Because 13 is an odd number, <u>all 41 pitches are present on the guitar</u>. Each string has only half of the pitches, but any adjacent pair of strings has all 41.

Omitting half the frets (known as [[skip-fretting]]) in effect moves certain pitches to remote areas of the fretboard, and makes certain intervals difficult to play. Magically, 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.

[[41-edo|41-equal (aka 41edo)]] has steps of 29.27¢. It approximates 7-limit [[just intonation]] very closely. Prime 3 is extremely accurate, and primes 5 and 7 are both tuned flat, which means their errors partially cancel out in ratios such as 7/5. Prime 11 is also quite accurate. But unfortunately it's tuned sharp, so the errors can add up, and 11/10 is nearly 11¢ sharp. Primes 13 and 17 are further off, and accurate intonation requires microbending.   

Unfortunately, tuning the Kite guitar to EADGBE causes the conventional chord shapes to have 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 three wolf octaves and two wolf fifths. (In addition, the major 3rd isn't 5/4 but 81/64.) The usual Em, A, Am, D, Dm, G and C chord shapes also have wolves. The tuning can be slightly adjusted so that one of these chord shapes is in tune. For example, E ^A ^D ^G B E puts E downmajor = 0 3 3 1 0 0 in tune, as well as E upminor = 0 3 3 0 0 0.  While this is an improvement, the other chord shapes still have wolves. No adjustment to EADGBE will get more than a few of the conventional chord shapes in tune. Thus learning new chord shapes is inevitable.

There are two types of Kite guitar fretboards, even-frets and odd-frets. In the former, all or almost all of the frets are an even number of edosteps from the nut. In the latter, it's an odd number. In general, the even-fret layout is for isomorphic tunings and the odd-frets layout is for open tunings.

Isomorphic means "same shape", and there is only one shape to learn for any chord. The standard isomorphic tuning is the '''downmajor tuning''', in which adjacent open strings are tuned a downmajor 3rd apart. Alternative isomorphic tunings use an upminor 3rd or an upmajor 3rd. A '''dimorphic''' ("two shapes") tuning alternates downmajor 3rds with upminor 3rds, or 4ths with major 2nds. The drawback to dimorphism is that every chord has two shapes. The advantage is that the open strings make a diatonic scale.   

Open tunings become more playable with the use of a "half-fret capo". From Jason Yerger's liner notes (see the "Recordings" section):

Jason has since explored other tunings besides DADGAD and DGDGAD, such as E A vC# vG B ^^D (a 3:4:5:7:9:11 chord) and D A D vF# vC E (a 2:3:4:5:7:9 chord). He prefers placing the first fret 3 edosteps above the nut. This creates a half-fret offset without a capo. A capo on the 1st fret could remove the half-fret offset, if desired.

This chart is in relative not absolute notation, meaning it shows intervals not notes. 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 shows the actual notes of an 8-string Kite guitar. The notes circled in red are the open strings of a 12-equal guitar. The ideal string gauges for this tuning are discussed in the [[Kite Guitar Information For Luthiers|Information For Luthiers]] page. Every 4th fret has one, two or three dots. The dots run single-double-triple-single-double-triple etc. Three dots equals a 5th.  

[[File:Fretboard 4.png|none|thumb|900x900px]]

The two most common commas that cause issues are the [[81/80|Gu]] and [[64/63|Ru]] commas. The choice of which two chords in the pump contain the pitch shift can be tricky. Generally, root movement by an offperfect interval is avoided. This usually necessitates a root movement by a plain major or minor interval.   

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-equal's smooth v7 chord is like a guard dog that smiles and wags its tail at strangers instead of barking. It's <u>too</u> 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 cadence to the I chord is desired, a V^7 chord often works better. 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 both progressions feel unfinished. Often II^m7 - V^7 - IvM7 is better. 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 V^7 chord, there are three common notes, and the progression feels even more connected.  

Remember, these are all just guidelines, not hard and fast rules! There is often more than one good way to translate a song.  

Like translations, these are grouped by the creator. If you have originals, feel free to create your own page and link to it!