Kite Guitar: Difference between revisions

* v8  P8  

The most dissonant intervals are the off-perfect ones ^1, v4, ^4, v5, ^5 and v8.  

!step

![[cents]]

!degree

![[41edo solfege|solfege]]

|-

|0

|0¢

| rowspan="2" |1sns

|Da

|-

|1

|29

|Du

|-

|2

|59

| rowspan="7" |2nds

|Fro

|-

|3

|88

|Fra

|-

|4

|117

|Fru

|-

|5

|146

|Ri

|-

|6

|176

|Ro

|-

|7

|205

|Ra

|-

|8

|234

|Ru

|-

|9

|263

| rowspan="7" |3rds

|No

|-

|10

|293

|Na

|-

|11

|322

|Nu

|-

|12

|351

|Mi

|-

|13

|380

|Mo

|-

|14

|410

|Ma

|-

|15

|439

|Mu

|-

|16

|468

| rowspan="3" |4ths

|Fo

|-

|17

|498

|Fa

|-

|18

|527

|Fu

|-

|19

|556

| rowspan="4" |tritones

|^^F, vGb

|-

|20

|585

|vF#, Gb

|-

|21

|615

|-

|22

|644

|^F#, vvG

|-

|23

|673

| rowspan="3" |5ths

|So

|-

|24

|702

|Sa

|-

|25

|732

|Su

|-

|26

|761

| rowspan="7" |6ths

|Flo

|-

|27

|790

|Fla

|-

|28

|820

|Flu

|-

|29

|849

|Li

|-

|30

|878

|Lo

|-

|31

|907

|La

|-

|32

|937

|Lu

|-

|33

|966

| rowspan="7" |7ths

|Tho

|-

|34

|995

|Tha

|-

|35

|1024

|Thu

|-

|36

|1054

|Ti

|-

|37

|1083

|To

|-

|38

|1112

|Ta

|-

|39

|1141

|Tu

|-

|40

|1171

| rowspan="2" |8ves

|Do

|-

|41

|1200

|Da

|}

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.

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.   

DADGAD lacks both the 4th and the four harmonic 6ths in the lower octave. A seven-string DGADGAD tuning remedies this.

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.  

[[File:The Kite Tuning.png|none|thumb|416x416px]]

[[File:Fretboard 4-6.png|none|thumb|900x900px]]

This is called the mid-6 tuning, as opposed to a low-6 tuning (vD to vA), or high-6 tuning (^A to ^E). Not to be confused with the low-6 or high-6 ''voicing'', see the [[The_Kite_Guitar_Chord_Shapes_(downmajor_tuning)|chords page]]. The various options:  

Another option is a baritone guitar tuned to the top 5 or 6 strings of the full-8, but lowered by an octave.

A bass guitar can of course be fretless and tuned EADG as usual. This avoids the need for extra strings and custom microtonal frets. If fretted, a bass would be tuned in major 3rds, similar to the lower strings of a Kite guitar but an octave lower. It would ideally have 6 strings. A conventional 5-string bass often has the 5th string tuned to B below low E. The analogous Kite bass has a Bb below the low vD. Tuning this way makes a deep-5 or deep-6 tuning.

This chart shows all the notes for the full-8 tuning, 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 anyway.  

[[File:The Kite Tuning 5.png|none|thumb|900x900px]]Some keys are somewhat awkward to play in. For example, a vG scale is either too close to the nut to have a plain major 2nd, or else way up at the 16th fret where the fret spacing is a little too cramped to play chords comfortably. There's a "sweet spot" for the tonic on the lowest 3 strings, from about the 4th fret to about the 11th fret. This defines a 3x8 rectangle containing 24 keys, roughly every other one of the 41 possible keys. The lowest string of an 8-string is tuned to vD not D so that the common keys of C, G, D, A and E fall in this sweet spot. D is tuned to A-440 standard pitch, to bring these 5 keys as close to 12-equal as possible. The D note agrees exactly, the A note is 2.5¢ sharp of 12-equal, E is 5¢ sharp, and so forth along the spiral of 5ths.

[[File:Fretboard chart w capo 2.png|none|thumb|900x900px]]

''Main article:'' '''[[Kite Guitar Chord Shapes (downmajor tuning)]].'''  

''Main article:'' [[Kite Guitar Scales|'''Kite Guitar Scales''']] (practical guide)

[[File:Scale chart.png|thumb|left]]

[[File:Scale chart 2.png|none|thumb]]

Since the fretboard is isomorphic, any interval can be expressed in '''relative tab''' as a vector. This is particularly useful for in-person oral instruction of chord shapes. For example, in the downmajor tuning, going up 2 strings and down 1 fret always takes you up a perfect 5th. In relative tab, that move is spoken as "plus-two, minus-one", and written as (+2,-1). The downmajor 2nd is at "oh, plus-three", (0,+3). The downmajor 3rd is at "plus-one, oh", (+1,0).  

Note that in absolute tab, strings are numbered in descending order, but in relative tab, a positive move is an ascending move. Thus moving from the 3rd string to the 1st string is plus-two, not minus-two.

The Kite guitar in downmajor tuning can be tuned by ear using the octaves at (+1,+3+2) (see the explanation of relative tab above). The open 6th string should be an octave bellow the 5th string's 14th fret. This can be written as (6th, 0) = (5th, 3rd & 2). We can double-check the tuning using the unisons at (+2,-3-1). Thus the 6th string at the 13th fret should match the open 4th string, and (6th, 3rd & 1) = (4th, 0). Finally, the 3rd harmonic of the 6th string should match the open 1st string (technically it should be half a cent sharp of it). Here are the full tuning instructions for a 6-string guitar:

{| class="wikitable"

!unisons

|-

|-

|-

|-

|-

|(6th, 0) harmonic at 3rd dot = (1st, 0)

|}

In the '''upmajor''' tuning, the octave is at (+1,+3+1), and (6th, 0) = (5th, 3rd & 1). The unison is at (+2,-3-3), and (6th, 3rd & 3) = (4th, 0).  

The Kite guitar can be tuned to a specific pitch using a compatible tuner. The following options fully support 41-equal with appropriate names and tuning calibration:

[http://lingot.nongnu.org/ '''LINGOT'''] is a free tuner for GNU/Linux which supports any tuning system and imports scala files. To set it to 41-equal, download and import this [https://gitlab.com/41edo/kite-guitar-method/-/raw/master/Tools/41-edo.scl 41-edo.scl] file. Then, set the frequency of pitch "1" to D by replacing the "mid-C" text with the frequency number "587.33".

''Main article:'' [[Kite Guitar translations|'''Kite Guitar translations''']]

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

Obviously 7-limit JI material translates easily. Material in either 19-equal or 22-equal usually translates fairy easily. 19-equal tempers out 81/80 but inflates 64/63 to a full edostep. Vice versa for 22-equal. (In fact, 41-equal is somewhat like a cross between the two edos. 41-equal's edomapping is the sum of those of 19 and 22 for most primes except 13 and 23.) Just as translating 12-equal or 19-equal material with an 81/80 comma pump requires a half-fret pitch shift, translating 22-equal material with a [[250/243|Triyo aka Porcupine]] comma pump does too. As does translating 19-equal material with a [[49/48|Zozo]] comma pump. The same rules apply.   

The Bohlen-Pierce 13-EDT scale is a subset of 41-equal, so a direct translation is possible, but usually awkward to play. Another possibility is translating to one of the [[Kite Guitar Scales#Octotonic (3L 3m 2s)|Octotonic (3L 3m 2s)]] scales, which have unequal steps, but avoid the 3 wolves of B-P (^5, v8 and M10).  

''Main article:'' [[Kite Guitar originals|'''Kite Guitar originals''']]

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

Ratios and cents, just intonation and EDOs, and the how and why of the Kite Guitar

General Design Considerations

Cents Table and Hertz Table

Various exercises and techniques by various teachers. The circle of 5ths, half-fret bends, etc.

The Kite guitar can be tuned to edos 19, 22, 41, 60, 63, 85 and 104, as well as rank-2 Laquinyo/Magic.

A theoretical exploration of 41-equal scales. The 5 categories are pentatonic, diatonic, semitonal, trientonal (fretwise) and microtonal.

How to name any note in any chord on any root in any key, using ups and downs. Suggested formats for key signatures.

How to name various triads and tetrads, even those not easily playable on the Kite guitar such as C~7.

Avoid large numbers and tedious mental calculations by counting kites, dots and frets.

Explores lattices and commas, aimed at composers.

The Kite guitar was invented in April 2019 by Kite Giedraitis. He was directly inspired by Matthew Autry's experiments with [[Skip-fretting|skip-frettings]]. Matthew explored large edos like 72 and 130, but had never explored 41. Others had previously come close to the Kite guitar, but either didn't use 41-edo, or had unequally spaced frets. See Graham Breed's [[Magic Guitar]] (2013) and Mason Green's [[Devadoot]] guitar (2016).

Kite's May 2019 paper announcing the invention (16 page pdf): [http://tallkite.com/misc_files/The%20Kite%20Tuning.pdf The Kite Tuning (original announcement)]

The term "Kite" as in Kite guitar, Kite keyboard, Kite trumpet, etc., refers to [[Skip fretting|skipping]] every other step of 41-edo, so that adjacent notes are 2\41 apart, and notes 1\41 away are less accessible. Thus Kite guitar is short for Kite-fretted guitar, Kite keyboard is short for Kite-keyed keyboard, etc.