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. It has 41 notes per the octave instead of 12. [[41edo|41-tET or 41-edo]] approximates 7-limit just intonation to within 3-6 [[cents]], and chords sound gorgeous! But a guitar with 41 frets per octave is difficult to play. 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 <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.

== About 41-EDO ==

[[41-edo]] approximates just intonation very closely. Prime 3 is extremely accurate, and primes 5 and 7 are both flat, which means their errors partially cancel out in ratios such as 7/5. Unfortunately prime 11 is sharp, so the errors add up, and 11/10 is nearly 11¢ sharp.   

|+ 41-edo notes from C to D

|+ 41-edo intervals from P1 to M2

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. [[File:41-edo_spiral.png|left|thumb|400x400px]] [[File:41-edo_spiral_with_notes.png|center|thumb|400x400px]]

These charts show the 7-limit and 11-limit lattices with 41-edo names and edosteps in place of ratios. Each color represents a separate plane of the lattice. In the 2nd lattice, the ~3 note in the center next to the P1 is simultaneously 7-limit (49/40 and 60/49), 11-limit (11/9 and 27/22) and 13-limit (16/13 and 39/32).

This chart shows the actual notes of an 8-string Kite guitar. The notes circled in red are the open strings of a 12-edo 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: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-edo as possible. The D note agrees exactly, the A note is 2.5¢ sharp of 12-edo, E is 5¢ sharp, and so forth along the spiral of 5ths.

In 12-edo, all 12 keys are needed so that a vocalist can get within 50¢ of their optimal range. In 41-edo, using only these 24 keys, one can get within 30¢ of the optimal range. 30¢ from optimal is sufficient, 15¢ from optimal is overkill, so the other 17 keys aren't really needed. Unless a song modulates by a single edostep, then one might be forced to play up the neck in an awkward key. Here's all the notes of the mid-6 tuning:

A fairly exhaustive survey of 41-edo chords is at '''[[Kite Guitar Chord Shapes (downmajor tuning)]].'''  

* [[Kite Giedraitis's Categorizations of 41edo Scales|'''Categorizations of 41edo Scales''']] (theoretical background, the 5 categories of scales)

Unlike relative tab, absolute tab doesn't require isomorphism, and can be applied to any guitar, as long as the dot locations are agreed on. Instead of counting kites, one simply numbers the dots directly, so KDF becomes DF. For 12-edo, dots are at frets 3, 5, 7, 9, 12, etc., thus the 10th fret is fourth-and-one. DF numbering can be applied to a Kite guitar with an odd-frets layout that puts dots on the harmonic series.  

The Kite guitar can be tuned to a specific pitch using a compatible tuner. The following options fully support 41-edo 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 41edo, 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".

== Translating 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. Generally the translated version is an improvement, because it's so well tuned. There follows some general advice on translating:

A translation can be either extremely faithful (note-for-note), somewhat faithful (chord voicings are changed), or not faithful (reharmonization occurs). In all but the last case, if someone who doesn't know the original were to translate the song back to 12-edo, they should arrive at the original. Back-translation means simply removing all ups and downs. Back-translation requires proper spelling: vDvm must be spelled vD vvF vA not vD ^E vA.

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 [[32805/32768|Layo]], [[225/224|Ruyoyo]], [[1029/1024|Latrizo]] and [[5120/5103|Saruyo]] minicommas. Then translate the JI to 41-edo. Another way is to use the spiral charts in the "About 41-edo" section.

12-edo's augmented triads and dim7 tetrads can be translated many ways. Ia can become I^a, Iva, Iv(vv#5) or even I^(^^5). Furthermore the root can be changed, so that Ca becomes ^E^(^^5)/C. Likewise Cd7 can become not only C^d7 or Cvd7, but also ^Avd7/C or vA^d7/C. The latter two are equivalent to C^d6 and Cvd6.  

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 <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.)   

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

The Bohlen-Pierce 13-EDT scale is a subset of 41edo, 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).  

A theoretical exploration of 41edo scales. The 5 categories are pentatonic, diatonic, semitonal, chromatic and microtonal.

=== [[Kite's Thoughts on 41edo Note Names and Key Signatures]] ===

=== [[41edo Chord Names]] ===

Avoid large numbers and tedious mental calculations.