Kite Guitar: Difference between revisions

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'''<big>The Beauty of 7-limit Just Intonation</big>'''

'''<big>The Freedom of an Equal Temperament</big>'''

== The Kite Guitar ==

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

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'''Saddle and Nut Compensation'''

To find the saddle compensation on a standard guitar, one compares the harmonic at the 12th fret with the fretted note at the 12th fret. For the Kite guitar, by a weird coincidence, one does the same! But the 12th fret now makes the 3rd harmonic, not the 2nd. Thus the two notes should be an octave apart, not a unison. If using a tuner, this is not a problem. But if using your ear, a unison is easier to hear than an octave. To get a unison, when you fret the string, play the 2nd harmonic with your other hand. With your forefinger or middle finger, touch the string midway between the 32nd and 33rd frets. Then stretch your hand and pluck with your thumb as close as you can get to the midpoint between your finger and the bridge. If this isn't feasible (e.g. with a bass guitar), you can capo the string at the 12th fret and use both hands to play the harmonic. And to be extremely precise, the fretted note should be 0.48¢ sharper than the harmonic. The 3rd harmonic is 701.96¢ and the 41-edo interval is 702.44¢.

'''Method #1:''' To find the saddle compensation on a standard guitar, one compares the harmonic at the 12th fret with the fretted note at the 12th fret. For the Kite guitar, by a weird coincidence, one does the same! But the 12th fret now makes the 3rd harmonic, not the 2nd. Thus the two notes should be an octave apart, not a unison. If using a tuner, this is not a problem. But if using your ear, a unison is easier to hear than an octave. To get a unison, when you fret the string, play the 2nd harmonic with your other hand. With your forefinger or middle finger, touch the string midway between the 32nd and 33rd frets. Then stretch your hand and pluck with your thumb as close as you can get to the midpoint between your finger and the bridge. If this isn't feasible (e.g. with a bass guitar), you can capo the string at the 12th fret and use both hands to play the harmonic. And to be extremely precise, the fretted note should be 0.48¢ sharper than the harmonic. The 3rd harmonic is 701.96¢ and the 41-edo interval is 702.44¢.

On a standard guitar, there's a formula for saddle compensation. Move the saddle point back by about 0.015" for every cent that the 12th fret note is sharp of the open string's 2nd harmonic. The 0.015" figure is more precisely the scale length times ln(2)/1200, which is scaleLength/1731. Saddle compensation flattens the 12th fret note twice as much as the open string note. So if the 12th fret note is 3¢ sharp, flattening the open string note by 3¢ (about 0.045") flattens the 12th fret note by 6¢, and the interval between them is flattened by 3¢ to an exact octave.

On a Kite guitar, the scaleLength/1731 formula still holds. But saddle compensation affects the 12th fret note only one and a half times as much as the open string note. Hence for each cent of sharpness, one must flatten by two cents. For example, suppose the 12th fret note is 2¢ sharp of the 3rd harmonic. It's supposed to be 0.48¢ sharp, so the actual sharpness is only 1.5¢. (In practice, if one's tuner isn't this accurate, one might simply round down a bit.) Move the saddle point back by twice this, 3¢ or 0.045". This ~~flattens~~ the 12th fret note by 4.5¢, narrowing the interval by 1.5¢ to an exact 41-edo 5th.

On a Kite guitar, the scaleLength/1731 formula still holds. But saddle compensation affects the 12th fret note only one and a half times as much as the open string note. Hence for each cent of sharpness, one must flatten by two cents. For example, suppose the 12th fret note is 2¢ sharp of the 3rd harmonic. It's supposed to be 0.48¢ sharp, so the actual sharpness is only 1.5¢. (In practice, if one's tuner isn't this accurate, one might simply round down a bit.) Move the saddle point back by twice this, 3¢ or 0.045". This will flatten the open string by 3¢ and the 12th fret note by 4.5¢, narrowing the interval by 1.5¢ to an exact 41-edo 5th. On the saddle, mark a point 0.045" behind the exit point, and file up to the mark.

'''Method #2:''' The first method serves as a rough check of the saddle points. But it's much safer to check multiple frets. [http://tallkite.com/KiteGuitar/KiteGuitarNotes.pdf This table] has the pitch of every single note on the fretboard. The 2nd page omits some redundant information to make room to pencil in discrepancies in cents. But the open strings aren't reliable, because the nut is not yet compensated (nut compensation must be done after saddle compensation). Use a capo to remove the nut issue. Capo the string at the 1st fret (or 2nd or 3rd, if the capo doesn't fit your 8-string very well). Tune the capo'ed string to the table, then compare the other frets to the table. Important: do not remove the capo during this process, as that will change the tension, and thus the pitch. It's usually sufficient to check every 4th fret, i.e. every dot. Look for the general trend. If the saddle point is too far back, the higher frets will be increasingly flat. Too far forward, and they will trend sharp. If there's an outlier that breaks the pattern, check its neighboring frets. No guitar is perfect. If some frets are sharp and some equally flat, that's the best you can get. Once you find the trend, estimate how much cents error would be expected at the 5th dot, which is almost an octave. That's roughly how many cents to compensate by. (To be super-precise, you could increase the cents by about 3%, so that 6¢ becomes 6.2¢.) Compensate as in method #1 with the scaleLength/1731 formula.

Nut compensation can be done similarly to a standard guitar. But since the Kite guitar is so much more in tune, extra care might be taken here. One can shorten the fingerboard by around 0.030" (more if the nut action is high) to slightly overcompensate, then de-compensate empirically by filing the front of the nut to move the exit points back. One can determine the exact amount to file by finding the sharpness in cents with a tuner, then using the scaleLength/1731 formula. The front of the nut can be filed lengthwise to move all the exit points at once, or up and down to move individual exit points.

'''Nut compensation''' can be done similarly to a standard guitar, by comparing the open string to the fretted notes. But since the Kite guitar is so much more in tune, extra care might be taken here. One can shorten the fingerboard by around 0.030" (more if the nut action is high) to slightly overcompensate, then de-compensate empirically by filing the front of the nut to move the exit points back. One can determine the exact amount to file by finding the sharpness in cents with a tuner, then using the scaleLength/1731 formula. The front of the nut can be filed lengthwise to move all the exit points at once, or up and down to move individual exit points.

Final notes: String gauges can affect compensation, so try to choose the correct gauges first. One can avoid nut compensation by using a zero fret. Electric guitars have easily adjustable saddles. Here's an adjustable saddle for acoustic guitars: https://www.portlandguitar.com/collections/bridges

'''Final notes:''' 1) String gauges can affect compensation, so try to choose the correct gauges first. 2) One can avoid nut compensation by using a zero fret. 3) Electric guitars have easily adjustable saddles. Here's an adjustable saddle for acoustic guitars: https://www.portlandguitar.com/collections/bridges They also offer adjustable nuts.

For more on saddle and nut compensation, see

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A 6-string guitar is usually tuned to the middle 6 strings of the full 8 strings:

[[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)|~~chord~~ page]].

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]].

* 8-string guitar: full-8

* 7-string guitar: low-7 or high-7, or possibly mid-7 (low-7 plus a dot, E to Eb)

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

More scales are discussed on the [[The_Kite_Guitar_Scales|~~scale~~ page]].

More scales are discussed on the [[The_Kite_Guitar_Scales|scales page]] and at [[Kite Giedraitis's Categorizations of 41edo Scales|Scales on the Kite Guitar]].

== Relative and Absolute Tab ==

@@ Line 1: / Line 1: @@
+'''<big>The Beauty of 7-limit Just Intonation</big>'''
+'''<big>The Freedom of an Equal Temperament</big>'''
 == The Kite Guitar ==
-The Kite guitar (or bass, mandolin, banjo, etc.) uses 41 divisions of the octave instead of 12. [[41edo|41-tET or 41-edo]] 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.) has 41 notes per the octave instead of 12. [[41edo|41-tET or 41-edo]] 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.)
@@ Line 64: / Line 68: @@
 '''<u>Saddle and Nut Compensation</u>'''
-To find the saddle compensation on a standard guitar, one compares the harmonic at the 12th fret with the fretted note at the 12th fret. For the Kite guitar, by a weird coincidence, one does the same! But the 12th fret now makes the 3rd harmonic, not the 2nd. Thus the two notes should be an octave apart, not a unison. If using a tuner, this is not a problem. But if using your ear, a unison is easier to hear than an octave. To get a unison, when you fret the string, play the 2nd harmonic with your other hand. With your forefinger or middle finger, touch the string midway between the 32nd and 33rd frets. Then stretch your hand and pluck with your thumb as close as you can get to the midpoint between your finger and the bridge. If this isn't feasible (e.g. with a bass guitar), you can capo the string at the 12th fret and use both hands to play the harmonic. And to be extremely precise, the fretted note should be 0.48¢ sharper than the harmonic. The 3rd harmonic is 701.96¢ and the 41-edo interval is 702.44¢.
+'''Method #1:''' To find the saddle compensation on a standard guitar, one compares the harmonic at the 12th fret with the fretted note at the 12th fret. For the Kite guitar, by a weird coincidence, one does the same! But the 12th fret now makes the 3rd harmonic, not the 2nd. Thus the two notes should be an octave apart, not a unison. If using a tuner, this is not a problem. But if using your ear, a unison is easier to hear than an octave. To get a unison, when you fret the string, play the 2nd harmonic with your other hand. With your forefinger or middle finger, touch the string midway between the 32nd and 33rd frets. Then stretch your hand and pluck with your thumb as close as you can get to the midpoint between your finger and the bridge. If this isn't feasible (e.g. with a bass guitar), you can capo the string at the 12th fret and use both hands to play the harmonic. And to be extremely precise, the fretted note should be 0.48¢ sharper than the harmonic. The 3rd harmonic is 701.96¢ and the 41-edo interval is 702.44¢.
 On a standard guitar, there's a formula for saddle compensation. Move the saddle point back by about 0.015" for every cent that the 12th fret note is sharp of the open string's 2nd harmonic. The 0.015" figure is more precisely the scale length times ln(2)/1200, which is scaleLength/1731. Saddle compensation flattens the 12th fret note twice as much as the open string note. So if the 12th fret note is 3¢ sharp, flattening the open string note by 3¢ (about 0.045") flattens the 12th fret note by 6¢, and the <u>interval</u> between them is flattened by 3¢ to an exact octave.
-On a Kite guitar, the scaleLength/1731 formula still holds. But saddle compensation affects the 12th fret note only one and a half times as much as the open string note. Hence for each cent of sharpness, one must flatten by <u>two</u> cents. For example, suppose the 12th fret note is 2¢ sharp of the 3rd harmonic. It's supposed to be 0.48¢ sharp, so the actual sharpness is only 1.5¢. (In practice, if one's tuner isn't this accurate, one might simply round down a bit.) Move the saddle point back by twice this, 3¢ or 0.045". This flattens the 12th fret note by 4.5¢, narrowing the interval by 1.5¢ to an exact 41-edo 5th.
+On a Kite guitar, the scaleLength/1731 formula still holds. But saddle compensation affects the 12th fret note only one and a half times as much as the open string note. Hence for each cent of sharpness, one must flatten by <u>two</u> cents. For example, suppose the 12th fret note is 2¢ sharp of the 3rd harmonic. It's supposed to be 0.48¢ sharp, so the actual sharpness is only 1.5¢. (In practice, if one's tuner isn't this accurate, one might simply round down a bit.) Move the saddle point back by twice this, 3¢ or 0.045". This will flatten the open string by 3¢ and the 12th fret note by 4.5¢, narrowing the interval by 1.5¢ to an exact 41-edo 5th. On the saddle, mark a point 0.045" behind the exit point, and file up to the mark.
+'''Method #2:''' The first method serves as a rough check of the saddle points. But it's much safer to check multiple frets. [http://tallkite.com/KiteGuitar/KiteGuitarNotes.pdf This table] has the pitch of every single note on the fretboard. The 2nd page omits some redundant information to make room to pencil in discrepancies in cents. But the open strings aren't reliable, because the nut is not yet compensated (nut compensation must be done after saddle compensation). Use a capo to remove the nut issue. Capo the string at the 1st fret (or 2nd or 3rd, if the capo doesn't fit your 8-string very well). Tune the capo'ed string to the table, then compare the other frets to the table. <u>Important</u>: do not remove the capo during this process, as that will change the tension, and thus the pitch. It's usually sufficient to check every 4th fret, i.e. every dot. Look for the general trend. If the saddle point is too far back, the higher frets will be increasingly flat. Too far forward, and they will trend sharp. If there's an outlier that breaks the pattern, check its neighboring frets. No guitar is perfect. If some frets are sharp and some equally flat, that's the best you can get. Once you find the trend, estimate how much cents error would be expected at the 5th dot, which is almost an octave. That's roughly how many cents to compensate by. (To be super-precise, you could increase the cents by about 3%, so that 6¢ becomes 6.2¢.) Compensate as in method #1 with the scaleLength/1731 formula.
-Nut compensation can be done similarly to a standard guitar. But since the Kite guitar is so much more in tune, extra care might be taken here. One can shorten the fingerboard by around 0.030" (more if the nut action is high) to slightly <u>over</u>compensate, then <u>de</u>-compensate empirically by filing the front of the nut to move the exit points back. One can determine the exact amount to file by finding the sharpness in cents with a tuner, then using the scaleLength/1731 formula. The front of the nut can be filed lengthwise to move all the exit points at once, or up and down to move individual exit points.
+'''Nut compensation''' can be done similarly to a standard guitar, by comparing the open string to the fretted notes. But since the Kite guitar is so much more in tune, extra care might be taken here. One can shorten the fingerboard by around 0.030" (more if the nut action is high) to slightly <u>over</u>compensate, then <u>de</u>-compensate empirically by filing the front of the nut to move the exit points back. One can determine the exact amount to file by finding the sharpness in cents with a tuner, then using the scaleLength/1731 formula. The front of the nut can be filed lengthwise to move all the exit points at once, or up and down to move individual exit points.
-Final notes: String gauges can affect compensation, so try to choose the correct gauges first. One can avoid nut compensation by using a zero fret. Electric guitars have easily adjustable saddles. Here's an adjustable saddle for acoustic guitars: https://www.portlandguitar.com/collections/bridges
+'''Final notes:''' 1) String gauges can affect compensation, so try to choose the correct gauges first. 2) One can avoid nut compensation by using a zero fret. 3) Electric guitars have easily adjustable saddles. Here's an adjustable saddle for acoustic guitars: https://www.portlandguitar.com/collections/bridges They also offer adjustable nuts.
 For more on saddle and nut compensation, see
@@ Line 191: / Line 197: @@
 A 6-string guitar is usually tuned to the middle 6 strings of the full 8 strings:
 [[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)|chord page]].
+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]].
 * 8-string guitar: full-8
 * 7-string guitar: low-7 or high-7, or possibly mid-7 (low-7 plus a dot, E to Eb)
@@ Line 219: / Line 225: @@
 [[File:Scale chart 2.png|none|thumb]]
-More scales are discussed on the [[The_Kite_Guitar_Scales|scale page]].
+More scales are discussed on the [[The_Kite_Guitar_Scales|scales page]] and at [[Kite Giedraitis's Categorizations of 41edo Scales|Scales on the Kite Guitar]].
 == Relative and Absolute Tab ==