Kite Guitar: Difference between revisions

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This is a brief explanation, see also the longer one at [[Kite Guitar explanation for non-microtonalists]].

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 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.

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 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 <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 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.)

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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:

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 ~~41edo~~. Another way is to use the spiral charts in the "About 41-edo" section.

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.

A somewhat faithful translation may have a slight reharmonization. Perhaps adding notes to a chord (e.g. adding 7ths to triads), or omitting notes (e.g. dropping the 3rd or 5th of a 6add9 chord to avoid a wolf interval).

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.

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.

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In general, chords shouldn't use offperfect intervals (^4, v4, ^5, v5, ^8 or v8). Downmajor is preferred over upmajor. Upminor is preferred for most folk, but downminor is preferred for most blues. In general, avoid using plain major and minor 3rds and 6ths in a chord.

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 [[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.

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.

Comma pumps, other than the aforementioned minicommas, cause pitch shifts, or occasionally, a tonic drift. The shift/drift is generally by a half-fret (a single edostep). Shifts of a full fret don't feel like shifts but more like reharmonizing/remelodizing, and full-fret drifts feel more like modulating.

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.

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.

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 This is a brief explanation, see also the longer one at [[Kite Guitar explanation for non-microtonalists]].
-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 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.
+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 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 <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 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.)
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 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:
-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 41edo. Another way is to use the spiral charts in the "About 41-edo" section.
+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.
+A somewhat faithful translation may have a slight reharmonization. Perhaps adding notes to a chord (e.g. adding 7ths to triads), or omitting notes (e.g. dropping the 3rd or 5th of a 6add9 chord to avoid a wolf interval).
+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.
 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.
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 In general, chords shouldn't use offperfect intervals (^4, v4, ^5, v5, ^8 or v8). Downmajor is preferred over upmajor. Upminor is preferred for most folk, but downminor is preferred for most blues. In general, avoid using plain major and minor 3rds and 6ths in a chord.
-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 [[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.
+-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.
+Comma pumps, other than the aforementioned minicommas, cause pitch shifts, or occasionally, a tonic drift. The shift/drift is generally by a half-fret (a single edostep). Shifts of a full fret don't feel like shifts but more like reharmonizing/remelodizing, and full-fret drifts feel more like modulating.
+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.
 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.