How to make a Kite Guitar: Difference between revisions

Line 53:

== Fret Markers ==

Dots (fretboard markers) are placed every 4 frets in a cycle of single-double-triple. So, the 4th fret has a single dot, the 8th fret has double dots, the 12th fret has triple dots, and then the 16th fret is back to single, and so on. Thus, a 36-fret guitar has 18 dots, and a 41-fret guitar has 19 dots.

Dots (fretboard markers) are placed every 4 frets in a cycle of single-double-triple. So, the 4th fret has a single dot, the 8th fret has double dots, the 12th fret has triple dots, and then the 16th fret is back to single, and so on. Thus, a 36-fret guitar has 18 dots on 9 frets, and a 41-fret guitar has 19 dots on 10 frets.

== String Gauges ==

Line 69:

== Saddle and Nut Compensation ==

~~'''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¢~~.

Since the Kite guitar is so much more in tune than the 12-equal guitar, extra care should be taken with saddle compensation.

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 ~~roughly~~ 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.

'''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 approximately 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. (Because an octave has [[frequency ratio]] 2/1 = twice as much, and a fifth has 3/2 = one and a half as much.) Hence for each cent of sharpness, one must flatten by two cents.

Line 79:

Line 81:

'''Alternative method #1:''' If the guitar has a 41st fret, compensation can be done more easily and accurately by comparing the harmonic at the 41st fret (the 4th harmonic) with the fretted note at the 41st fret. They should be an exact unison, so no need to subtract a half cent, and no need to play the harmonic of the fretted note. The 4th harmonic is a double octave, with frequency ratio 4/1, so saddle compensation affects the 41st fret note four times as much as the open string note. Hence for each cent of sharpness, one must flatten by one-third cent.

In the previous example, the 12th fret harmonic was 2¢ sharper than the fretted note. This would make the 41st fret note 9¢ sharp of the 4th harmonic. Move the saddle point back by 1/3 this, 3¢ or 0.045". This will flatten the open string by 3¢ and the 41st fret note by 12¢, narrowing the interval by 9¢ to an exact double octave.

In the previous example, the 12th fret harmonic was 2¢ sharper than the fretted note. This would make the 41st fret note 9¢ sharp of the 4th harmonic. Move the saddle point back by 1/3 this, 3¢ or 0.045". This will flatten the open string by 3¢ and the 41st fret note by 12¢, narrowing the interval by 9¢ to an exact double octave. This method is more accurate because tuners aren't perfect, and an error affects the compensation distance only one-sixth as much. This method also works for 12-equal guitars on the 24th fret.

~~This method~~ is ~~more accurate because tuners aren~~'~~t perfect~~, and an ~~error affects the compensation distance only one~~-~~sixth as much~~.

'''Other alternatives:''' The 8th harmonic is at fret 4 and the 10th one is at fret 3. The 9th harmonic is midway between them. Play the 8th, 9th and 10th harmonics to get a do-re-mi melody. Now play those same harmonics just a few inches from the bridge. Practice until you can cleanly play the 9th harmonic with one hand. Next play that harmonic while fretting at the 24th fret (major 9th = 9/4 ratio). The fretted harmonic should be 1 cent sharper. For every cent of sharpness above that, flatten at the saddle by four-fifths of a cent. For example, if the fretted harmonic is 6¢ sharp, that's 5 extra cents of sharpness. Move the saddle point back by four-fifths of this, 4¢. This will flatten the open string by 4¢ and the 24th fret note by 9¢, narrowing the interval by 5¢ to an exact 41-edo major 9th.

The ~~following chart describes various fret comparisons~~.

The 7th harmonic is between the 4th and 5th frets. Find that same harmonic about 3-4" from the bridge. Play it one-handed both open and while fretting at the 37th fret (minor 7th plus an 8ve = 7/2 ratio). The fretted harmonic should be 3 cents flatter. For every cent of sharpness above that, flatten at the saddle by two-fifths of a cent. For example, if the fretted harmonic is 2¢ sharp, that's 5 extra cents of sharpness. Move the saddle point back by two-fifths of this, 2¢. This will flatten the open string by 2¢ and the 37th fret note by 7¢, narrowing the interval by 5¢ to an exact 41-edo downminor 7th.

* fret = the Kite Guitar fret number

* harmonic = the ~~harmonic which shares~~ the fret~~'s pitch class~~

* octave difference = ~~how many octaves from the~~ fretted ~~pitch to the~~ harmonic

* cent ~~offset =~~ the ~~precise difference from the harmonic to~~ the fretted ~~pitch (ignoring octaves)~~

* location(s) = where to play the harmonic(s~~) separate from~~ the ~~fret in order to produce a same~~-~~octave comparison between the harmonic with~~ the open string ~~versus with~~ the fret ~~depressed~~

{| class="wikitable"

|+Best frets to check for Kite Guitar intonation setup

!fret

!interval

!ratio

!harmonic

!~~octave difference~~

!fretted note should be

!cent ~~offset~~

!for each cent of sharpness

!location~~(s)~~ to play shared harmonic

!location to play shared harmonic

|-

|12

|3

|5th

|1

|3/2

| +0.5¢

|3rd

|2/3 of string~~, in-~~between frets 32 and 33

| 0.5¢ sharp

|flatten by two cents

|2/3 of string: between frets 32 and 33

|-

|24

|9

|maj 9th

|2

|9/4

| +1¢

|9th

|~~7/9 or~~ 8/9 of string: ~~in the picking area~~ past the fretboard

| 1¢ sharp

|flatten by four-fifths of a cent

|8/9 of string: past the fretboard up by the bridge

|-

|37

|7

|vmin 7th

|1

|7/2

| -3¢

|7th

|6/7 of string: ~~in the picking area~~ past the fretboard

| 3¢ flat

|flatten by two-fifths of a cent

|6/7 of string: past the fretboard up by the bridge

|-

|41

|2

|dbl 8ve

|0

|4/1

|0

|4th

|1/2 of string: at the same fret 41

|the same

|flatten by one-third of a cent

|1/4 of string: at the same fret 41

|}

Line 127:

Line 133:

'''Method #2:''' The first method serves as a rough check of the saddle points. But it's much safer to check multiple frets. The cents table below (printable pdf [http://tallkite.com/KiteGuitar/KiteGuitarNotes.pdf here]) has the pitch of every single note on the fretboard. The 2nd page of the pdf 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, 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.

'''Nut compensation''' can be done similarly to a standard guitar, by comparing the open string to the fretted notes. But extra care might be taken here too. 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:'''

Line 141:

Line 147:

== String Spacing ==

~~(A work in progress)~~

The easiest way to get an 8-string acoustic guitar is to convert a 12-string guitar. This leads to a very tight string spacing. The spacing can be slightly improved as follows:

The easiest way to get an 8-string acoustic guitar is to convert a 12-string guitar. This leads to a ~~rather~~ tight string spacing. The spacing can be slightly improved as follows:

Conventional wisdom holds that there are two ways to space the strings: center-to-center and edge-to-edge. For the right hand, ~~the latter~~ is better than ~~the former~~, because otherwise it's harder to fit one's finger between the thicker strings. ~~Edge-to-edge~~ spacing ensures that the gap between strings is uniform, and each string is equally easy to pluck.

Conventional wisdom holds that there are two ways to space the strings: center-to-center (C2C) and edge-to-edge (E2E). For the right hand, E2E is better than C2C, because otherwise it's harder to fit one's finger between the thicker strings. E2E spacing ensures that the gap between strings is uniform, and each string is equally easy to pluck.

On the left hand, if the spacing is too tight, when one frets a string and plays the neighboring string either open or fretted further back, the finger can dampen the neighboring string. Thus the important gap is the gap between every other string. That is, when fretting the 2nd string, the important gap is between the inner edges of the 1st and 3rd string. When fretting the 3rd string, it's between the 2nd and 4th string. When fretting the 1st string, the gap is between the 1st and 2nd string, but if the 2nd string is more or less in the center of the 1st-to-3rd gap, the 1st-to-2nd gap will be sufficiently large.

On the left hand, if the spacing is too tight, when one frets a string and plays the neighboring string either open or fretted further back, the finger can dampen the neighboring string. Thus the important gap is the gap between every other string. That is, when fretting the 2nd string, the important gap is between the inner edges of the 1st and 3rd string. When fretting the 3rd string, it's between the 2nd and 4th string. (When fretting the 1st string, the gap is between the 1st and 2nd string, but if the 2nd string is more or less in the center of the 1st-to-3rd gap, the 1st-to-2nd gap will be sufficiently large.)

~~Center~~-to-~~center~~ spacing results in the thicker strings being more crowded and harder to fret cleanly. ~~Edge-to-edge~~ spacing results in the thinner strings being harder to fret. The ideal string spacing for the left hand makes a uniform gap between alternate strings, with this gap measured edge-to-edge not center-to-center. This spacing is called edge-to-next-edge.

This spacing is called edge-to-next-edge (E2NE). It is different from the other two spacings. C2C spacing results in the thicker strings being more crowded and harder to fret cleanly. E2E spacing results in the thinner strings being more crowded.

But specifying that ~~this gap~~ be uniform doesn't completely specify ~~the~~ spacing, because one could shift every other string sideways without changing these gaps. Ideally each string should be midway between the nearest edges of the two neighboring strings, i.e. ~~the~~ center-to-edge spacing ~~should~~ be constant. But this is impossible. For example, the distance from the center of the 2nd string to the nearest edge of the 3rd string must be less than the distance from the center of the 3rd string to the nearest edge of the 2nd string, because the 2nd string is thinner.

But specifying that these gaps be uniform doesn't completely specify E2NE spacing, because one could shift every other string sideways without changing these gaps. So we need an additional requirement. Ideally each string should be midway between the nearest edges of the two neighboring strings, i.e. perfectly centered in its gap. The center-to-edge spacing would be constant for each string. But this is impossible. For example, the distance from the center of the 2nd string to the nearest edge of the 3rd string must be less than the distance from the center of the 3rd string to the nearest edge of the 2nd string, because the 2nd string is thinner.

~~So we need an additional requirement.~~ It is not yet ~~clear which one is best~~. ~~We might require that the distance from~~ the center of the 2nd string to the ~~nearest edge~~ of the 1st ~~string~~ be ~~half~~ the ~~size of this gap~~, ~~i.e~~. the ~~2nd string~~ is in the ~~middle~~ of the ~~1st-to~~-~~3rd gap~~. ~~In general~~, ~~none of~~ the ~~other inner strings will be centered like this~~.

It is not yet known how to maximize centeredness. Consider the center of the 2nd string, and the center of the gap between the 1st and 3rd strings' edges. Let x be the distance between the two, measured so that positive x corresponds to being closer to the 1st string. Each string except the 1st and last will have a similar distance from the center of the gap it is in, measured in the same direction, called its off-centeredness. For a given set of string gauges, how can one find the x that minimizes all the off-centerednesses? For gauges '''11.5 15 18 24 30 36 46 56''', the best x is zero.

In the next table, R1, R2, etc. is the radius of each string, and D is a constant roughly equal to 1/7th of the nut width. The value of D is not consistent from column to column.

In the next table, R1, R2, etc. is the radius of each string, and D is a constant roughly equal to 1/7th of the nut width. The value of D is not consistent from column to column. In E2E spacing, all off-centerednesses are zero. In C2C spacing, each string is off-center towards its thicker neighbor.

{| class="wikitable"

|+distance from center of 1st string to center of Nth string

!

!~~center-to-center~~

!C2C

!~~edge-to-edge~~

!E2E

!~~edge-to-next~~-~~edge~~

!E2NE

!E2NE off-centeredness

|-

!2nd string

|D

|D + R1 + R2

|D + R1

|D - x + R1

|x

|-

!3rd string

Line 172:

Line 178:

|2D + R1 + 2R2 + R3

|2D + R1 + R3

| -x - (R3-R2)

|-

!4th string

|3D

|3D + R1 + 2R2 + 2R3 + R4

|3D + R1 + R2 + R4

|3D - x + R1 + R2 + R4

|x + (R3-R2) - (R4-R3)

|-

!5th string

Line 182:

Line 190:

|4D + R1 + 2R2 + 2R3 + 2R4 + R5

|4D + R1 + 2R3 + R5

| -x - (R3-R2) + (R4-R3) - (R5-R4)

|-

!6th string

|5D

|5D + R1 + 2R2 + 2R3 + 2R4 + 2R5 + R6

|5D + R1 + R2 + 2R4 + R6

|5D - x + R1 + R2 + 2R4 + R6

|x + (R3-R2) - (R4-R3) + (R5-R4) - (R6-R5)

|-

!7th string

Line 192:

Line 202:

|6D + R1 + 2R2 + 2R3 + 2R4 + 2R5 + 2R6 + R7

|6D + R1 + 2R3 + 2R5 + R7

| -x - (R3-R2) + (R4-R3) - (R5-R4) + (R6-R5) - (R7-R6)

|-

!8th string

|7D

|7D + R1 + 2R2 + 2R3 + 2R4 + 2R5 + 2R6 + 2R7 + R8

|7D + R1 + R2 + 2R4 + 2R6 + R8

|7D - x + R1 + R2 + 2R4 + 2R6 + R8

|(N/A)

|}

Note that the nut is slotted edge-to-next-edge but the bridge is edge-to-edge, so as one plays further up the neck, the spacing deviates from the ideal. But the spacing widens further up the neck, making fretting cleanly easier, so this is not a problem.

Note that the nut is slotted edge-to-next-edge but the bridge is edge-to-edge, so as one plays further up the neck, the spacing deviates from the ideal. But the spacing widens further up the neck, making fretting cleanly easier, so this is not a problem. Also each string's sideways movement increases as you get away from the nut, but again the widening neck counteracts that.

== Tables ==

@@ Line 53: / Line 53: @@
 == Fret Markers ==
-Dots (fretboard markers) are placed every 4 frets in a cycle of single-double-triple. So, the 4th fret has a single dot, the 8th fret has double dots, the 12th fret has triple dots, and then the 16th fret is back to single, and so on.  Thus, a 36-fret guitar has 18 dots, and a 41-fret guitar has 19 dots.
+Dots (fretboard markers) are placed every 4 frets in a cycle of single-double-triple. So, the 4th fret has a single dot, the 8th fret has double dots, the 12th fret has triple dots, and then the 16th fret is back to single, and so on.  Thus, a 36-fret guitar has 18 dots on 9 frets, and a 41-fret guitar has 19 dots on 10 frets.
 == String Gauges ==
@@ Line 69: / Line 69: @@
 == Saddle and Nut Compensation ==
-'''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¢.
+Since the Kite guitar is so much more in tune than the 12-equal guitar, extra care should be taken with saddle compensation.
-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 roughly 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.
+'''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 approximately 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. (Because an octave has [[frequency ratio]] 2/1 = twice as much, and a fifth has 3/2 = one and a half as much.)  Hence for each cent of sharpness, one must flatten by <u>two</u> cents.
@@ Line 79: / Line 81: @@
 '''Alternative method #1:''' If the guitar has a 41st fret, compensation can be done more easily and accurately by comparing the harmonic at the 41st fret (the 4th harmonic) with the fretted note at the 41st fret. They should be an exact unison, so no need to subtract a half cent, and no need to play the harmonic of the fretted note. The 4th harmonic is a double octave, with frequency ratio 4/1, so saddle compensation affects the 41st fret note four times as much as the open string note. Hence for each cent of sharpness, one must flatten by <u>one-third</u> cent.
-In the previous example, the 12th fret harmonic was 2¢ sharper than the fretted note. This would make the 41st fret note 9¢ sharp of the 4th harmonic. Move the saddle point back by 1/3 this, 3¢ or 0.045". This will flatten the open string by 3¢ and the 41st fret note by 12¢, narrowing the interval by 9¢ to an exact double octave.
+In the previous example, the 12th fret harmonic was 2¢ sharper than the fretted note. This would make the 41st fret note 9¢ sharp of the 4th harmonic. Move the saddle point back by 1/3 this, 3¢ or 0.045". This will flatten the open string by 3¢ and the 41st fret note by 12¢, narrowing the interval by 9¢ to an exact double octave. This method is more accurate because tuners aren't perfect, and an error affects the compensation distance only one-sixth as much. This method also works for 12-equal guitars on the 24th fret.
-This method is more accurate because tuners aren't perfect, and an error affects the compensation distance only one-sixth as much.
+'''Other alternatives:''' The 8th harmonic is at fret 4 and the 10th one is at fret 3. The 9th harmonic is midway between them. Play the 8th, 9th and 10th harmonics to get a do-re-mi melody. Now play those same harmonics just a few inches from the bridge. Practice until you can cleanly play the 9th harmonic with one hand. Next play that harmonic while fretting at the 24th fret (major 9th = 9/4 ratio). The fretted harmonic should be 1 cent sharper. For every cent of sharpness above that, flatten at the saddle by <u>four-fifths</u> of a cent. For example, if the fretted harmonic is 6¢ sharp, that's 5 extra cents of sharpness. Move the saddle point back by four-fifths of this, 4¢. This will flatten the open string by 4¢ and the 24th fret note by 9¢, narrowing the interval by 5¢ to an exact 41-edo major 9th.
-The following chart describes various fret comparisons.
+The 7th harmonic is between the 4th and 5th frets. Find that same harmonic about 3-4" from the bridge. Play it one-handed both open and while fretting at the 37th fret (minor 7th plus an 8ve = 7/2 ratio). The fretted harmonic should be 3 cents <u>flatter</u>. For every cent of sharpness above that, flatten at the saddle by <u>two-fifths</u> of a cent. For example, if the fretted harmonic is 2¢ sharp, that's 5 extra cents of sharpness. Move the saddle point back by two-fifths of this, 2¢. This will flatten the open string by 2¢ and the 37th fret note by 7¢, narrowing the interval by 5¢ to an exact 41-edo downminor 7th.
-* fret = the Kite Guitar fret number
-* harmonic = the harmonic which shares the fret's pitch class
-* octave difference = how many octaves from the fretted pitch to the harmonic
-* cent offset = the precise difference from the harmonic to the fretted pitch (ignoring octaves)
-* location(s) = where to play the harmonic(s) separate from the fret in order to produce a same-octave comparison between the harmonic with the open string versus with the fret depressed
 {| class="wikitable"
 |+Best frets to check for Kite Guitar intonation setup
 !fret
+!interval
+!ratio
 !harmonic
-!octave difference
+!fretted note should be
-!cent offset
+!for each cent of sharpness
-!location(s) to play shared harmonic
+!location to play shared harmonic
 |-
 |12
-|3
+|5th
-|1
+|3/2
-| +0.5¢
+|3rd
-|2/3 of string, in-between frets 32 and 33
+| 0.5¢ sharp
+|flatten by two cents
+|2/3 of string: between frets 32 and 33
 |-
 |24
-|9
+|maj 9th
-|2
+|9/4
-| +1¢
+|9th
-|7/9 or 8/9 of string: in the picking area past the fretboard
+| 1¢ sharp
+|flatten by four-fifths of a cent
+|8/9 of string: past the fretboard up by the bridge
 |-
 |37
-|7
+|vmin 7th
-|1
+|7/2
-| -3¢
+|7th
-|6/7 of string: in the picking area past the fretboard
+| 3¢ flat
+|flatten by two-fifths of a cent
+|6/7 of string: past the fretboard up by the bridge
 |-
 |41
-|2
+|dbl 8ve
-|0
+|4/1
-|0
+|4th
-|1/2 of string: at the same fret 41
+|the same
+|flatten by one-third of a cent
+|1/4 of string: at the same fret 41
 |}
@@ Line 127: / Line 133: @@
 '''Method #2:''' The first method serves as a rough check of the saddle points. But it's much safer to check multiple frets. The cents table below (printable pdf [http://tallkite.com/KiteGuitar/KiteGuitarNotes.pdf here]) has the pitch of every single note on the fretboard. The 2nd page of the pdf 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, 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.
+'''Nut compensation''' can be done similarly to a standard guitar, by comparing the open string to the fretted notes. But extra care might be taken here too. 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:'''
@@ Line 141: / Line 147: @@
 == String Spacing ==
-(A work in progress)
+The easiest way to get an 8-string acoustic guitar is to convert a 12-string guitar. This leads to a very tight string spacing. The spacing can be slightly improved as follows:
-The easiest way to get an 8-string acoustic guitar is to convert a 12-string guitar. This leads to a rather tight string spacing. The spacing can be slightly improved as follows:
-Conventional wisdom holds that there are two ways to space the strings: center-to-center and edge-to-edge. For the right hand, the latter is better than the former, because otherwise it's harder to fit one's finger between the thicker strings. Edge-to-edge spacing ensures that the gap between strings is uniform, and each string is equally easy to pluck.
+Conventional wisdom holds that there are two ways to space the strings: center-to-center (C2C) and edge-to-edge (E2E). For the right hand, E2E is better than C2C, because otherwise it's harder to fit one's finger between the thicker strings. E2E spacing ensures that the gap between strings is uniform, and each string is equally easy to pluck.
-On the left hand, if the spacing is too tight, when one frets a string and plays the neighboring string either open or fretted further back, the finger can dampen the neighboring string. Thus the important gap is the gap between every other string. That is, when fretting the 2nd string, the important gap is between the inner edges of the 1st and 3rd string. When fretting the 3rd string, it's between the 2nd and 4th string. When fretting the 1st string, the gap is between the 1st and 2nd string, but if the 2nd string is more or less in the center of the 1st-to-3rd gap, the 1st-to-2nd gap will be sufficiently large.
+On the left hand, if the spacing is too tight, when one frets a string and plays the neighboring string either open or fretted further back, the finger can dampen the neighboring string. Thus the important gap is the gap between every <u>other</u> string. That is, when fretting the 2nd string, the important gap is between the inner edges of the 1st and 3rd string. When fretting the 3rd string, it's between the 2nd and 4th string. (When fretting the 1st string, the gap is between the 1st and 2nd string, but if the 2nd string is more or less in the center of the 1st-to-3rd gap, the 1st-to-2nd gap will be sufficiently large.)
-Center-to-center spacing results in the thicker strings being more crowded and harder to fret cleanly. Edge-to-edge spacing results in the thinner strings being harder to fret. The ideal string spacing for the left hand makes a uniform gap between alternate strings, with this gap measured edge-to-edge not center-to-center. This spacing is called edge-to-next-edge.
+This spacing is called edge-to-next-edge (E2NE). It is different from the other two spacings. C2C spacing results in the thicker strings being more crowded and harder to fret cleanly. E2E spacing results in the thinner strings being more crowded.
-But specifying that this gap be uniform doesn't completely specify the spacing, because one could shift every other string sideways without changing these gaps. Ideally each string should be midway between the nearest edges of the two neighboring strings, i.e. the center-to-edge spacing should be constant. But this is impossible. For example, the distance from the center of the 2nd string to the nearest edge of the 3rd string must be less than the distance from the center of the 3rd string to the nearest edge of the 2nd string, because the 2nd string is thinner.
+But specifying that these gaps be uniform doesn't completely specify E2NE spacing, because one could shift every other string sideways without changing these gaps. So we need an additional requirement. Ideally each string should be midway between the nearest edges of the two neighboring strings, i.e. perfectly centered in its gap. The center-to-edge spacing would be constant for each string. But this is impossible. For example, the distance from the center of the 2nd string to the nearest edge of the 3rd string must be less than the distance from the center of the 3rd string to the nearest edge of the 2nd string, because the 2nd string is thinner.
-So we need an additional requirement. It is not yet clear which one is best. We might require that the distance from the center of the 2nd string to the nearest edge of the 1st string be half the size of this gap, i.e. the 2nd string is in the middle of the 1st-to-3rd gap. In general, none of the other inner strings will be centered like this.
+It is not yet known how to maximize centeredness. Consider the center of the 2nd string, and the center of the gap between the 1st and 3rd strings' edges. Let x be the distance between the two, measured so that positive x corresponds to being closer to the 1st string. Each string except the 1st and last will have a similar distance from the center of the gap it is in, measured in the same direction, called its off-centeredness. For a given set of string gauges, how can one find the x that minimizes all the off-centerednesses? For gauges '''11.5 15 18 24 30 36 46 56''', the best x is zero.
-In the next table, R1, R2, etc. is the radius of each string, and D is a constant roughly equal to 1/7th of the nut width. The value of D is not consistent from column to column.
+In the next table, R1, R2, etc. is the radius of each string, and D is a constant roughly equal to 1/7th of the nut width. The value of D is not consistent from column to column. In E2E spacing, all off-centerednesses are zero. In C2C spacing, each string is off-center towards its thicker neighbor.
 {| class="wikitable"
 |+distance from center of 1st string to center of Nth string
 !
-!center-to-center
+!C2C
-!edge-to-edge
+!E2E
-!edge-to-next-edge
+!E2NE
+!E2NE off-centeredness
 |-
 !2nd string
 |D
 |D + R1 + R2
-|D + R1
+|D - x + R1
+|x
 |-
 !3rd string
@@ Line 172: / Line 178: @@
 |2D + R1 + 2R2 + R3
 |2D + R1 + R3
+| -x - (R3-R2)
 |-
 !4th string
 |3D
 |3D + R1 + 2R2 + 2R3 + R4
-|3D + R1 + R2 + R4
+|3D - x + R1 + R2 + R4
+|x + (R3-R2) - (R4-R3)
 |-
 !5th string
@@ Line 182: / Line 190: @@
 |4D + R1 + 2R2 + 2R3 + 2R4 + R5
 |4D + R1 + 2R3 + R5
+| -x - (R3-R2) + (R4-R3) - (R5-R4)
 |-
 !6th string
 |5D
 |5D + R1 + 2R2 + 2R3 + 2R4 + 2R5 + R6
-|5D + R1 + R2 + 2R4 + R6
+|5D - x + R1 + R2 + 2R4 + R6
+|x + (R3-R2) - (R4-R3) + (R5-R4) - (R6-R5)
 |-
 !7th string
@@ Line 192: / Line 202: @@
 |6D + R1 + 2R2 + 2R3 + 2R4 + 2R5 + 2R6 + R7
 |6D + R1 + 2R3 + 2R5 + R7
+| -x - (R3-R2) + (R4-R3) - (R5-R4) + (R6-R5) - (R7-R6)
 |-
 !8th string
 |7D
 |7D + R1 + 2R2 + 2R3 + 2R4 + 2R5 + 2R6 + 2R7 + R8
-|7D + R1 + R2 + 2R4 + 2R6 + R8
+|7D - x + R1 + R2 + 2R4 + 2R6 + R8
+|(N/A)
 |}
-Note that the nut is slotted edge-to-next-edge but the bridge is edge-to-edge, so as one plays further up the neck, the spacing deviates from the ideal. But the spacing widens further up the neck, making fretting cleanly easier, so this is not a problem.
+Note that the nut is slotted edge-to-next-edge but the bridge is edge-to-edge, so as one plays further up the neck, the spacing deviates from the ideal. But the spacing widens further up the neck, making fretting cleanly easier, so this is not a problem. Also each string's sideways movement increases as you get away from the nut, but again the widening neck counteracts that.
 == Tables ==