Kite Guitar: Difference between revisions

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== The Kite Guitar ==

The Kite guitar (or bass, mandolin, banjo, etc.) uses 41 divisions of the octave instead of 12. 41-tET 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.

The Kite guitar (or bass, mandolin, banjo, etc.) uses 41 divisions of the octave instead of 12. [[41edo|41-tET]] 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, ~~key~~ 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.

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.

For more info: http://tallkite.com/misc_files/The%20Kite%20Tuning.pdf

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== Songs ==

These conventional songs have been translated from 12edo to 41edo. ~~The process~~ is to first translate it to 7-limit JI, perhaps visualizing it on a lattice, keeping in mind the Layo, Ruyoyo and Saruyo minicommas. Then translate the JI to 41edo.

These conventional songs have been translated from 12edo to 41edo. One way to do this 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]] and [[5120/5103|Saruyo]] minicommas. Then translate the JI to 41edo.

Often there is more than one obvious way to translate a song. In general, downmajor is preferred over upmajor, but ~~either upminor or~~ downminor ~~are OK~~. Comma pumps, other than the aforementioned minicommas, cause pitch shifts, or occasionally, a tonic drift. The choice of which two chords contain the shift can be tricky.

Often there is more than one obvious way to translate a song. This chart shows 41-edo in terms of 12-edo. The 12 categories circled in red correspond to the notes of 12-edo.

[[File:41-edo spiral.png|673x673px]]

In general, downmajor is preferred over upmajor. Upminor is preferred for folk, but downminor is preferred for 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 choice of which two chords contain the shift can be tricky.

=== Stormy Monday ===

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=== I Will Survive ===

This song pumps the Saruyo comma, which equates 21/20 to 256/243. As a result, several pitches shift a comma flat during the progression, but then shift back to where they started. On the Kite guitar, the chord progression walks up the neck and then leaps down 12 frets, only to walk up back to where it started.

This song pumps the [[5120/5103|Saruyo]] comma, which equates 21/20 to 256/243. As a result, several pitches shift a comma flat during the progression, but then shift back to where they started. On the Kite guitar, the chord progression walks up the neck and then leaps down 12 frets, only to walk up back to where it started.

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 == The Kite Guitar ==
-The Kite guitar (or bass, mandolin, banjo, etc.) uses 41 divisions of the octave instead of 12. 41-tET 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.
+The Kite guitar (or bass, mandolin, banjo, etc.) uses 41 divisions of the octave instead of 12. [[41edo|41-tET]] 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, key 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.
+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.
 For more info: http://tallkite.com/misc_files/The%20Kite%20Tuning.pdf
@@ Line 359: / Line 359: @@
 == Songs ==
-These conventional songs have been translated from 12edo to 41edo. The process is to first translate it to 7-limit JI, perhaps visualizing it on a lattice, keeping in mind the Layo, Ruyoyo and Saruyo minicommas. Then translate the JI to 41edo.
+These conventional songs have been translated from 12edo to 41edo. One way to do this 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]] and [[5120/5103|Saruyo]] minicommas. Then translate the JI to 41edo.
-Often there is more than one obvious way to translate a song. In general, downmajor is preferred over upmajor, but either upminor or downminor are OK. Comma pumps, other than the aforementioned minicommas, cause pitch shifts, or occasionally, a tonic drift. The choice of which two chords contain the shift can be tricky.
+Often there is more than one obvious way to translate a song. This chart shows 41-edo in terms of 12-edo. The 12 categories circled in red correspond to the notes of 12-edo.
+[[File:41-edo spiral.png|673x673px]]
+In general, downmajor is preferred over upmajor. Upminor is preferred for folk, but downminor is preferred for 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 choice of which two chords contain the shift can be tricky.
 === Stormy Monday ===
@@ Line 430: / Line 435: @@
 === I Will Survive ===
-This song pumps the Saruyo comma, which equates 21/20 to 256/243. As a result, several pitches shift a comma flat during the progression, but then shift back to where they started. On the Kite guitar, the chord progression walks up the neck and then leaps down 12 frets, only to walk up back to where it started.
+This song pumps the [[5120/5103|Saruyo]] comma, which equates 21/20 to 256/243. As a result, several pitches shift a comma flat during the progression, but then shift back to where they started. On the Kite guitar, the chord progression walks up the neck and then leaps down 12 frets, only to walk up back to where it started.
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