How to make a Kite Guitar: Difference between revisions
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== General Design Considerations == | == General Design Considerations == | ||
There are two types of Kite guitar fretboards, even-frets and odd-frets. In the former, all or almost all of the frets are an even number of 41-equal steps from the nut. In the latter, it's an odd number. The even-frets layout is for isomorphic ("same-shape") tunings and the odd-frets layout is for open tunings. Most of the research and development to date has focused on the even-frets layout. | |||
An odd-frets guitar can be converted to an even-frets one simply by capoing. An even-frets one can be converted to odd-frets similarly if there is an additional fret (or fret slot that accepts a temporary fret) near the nut. There are also advantages musically to this extra fret even if not using open tunings. The extra fret is named the "a-fret" if it's between the nut and the 1st fret, "b-fret" if it's between the 1st and 2nd frets, etc. A b-fret or b-fret-slot might be better for acoustics, which tend to have higher nuts. There is absolutely no downside to having either an a-slot or a b-slot, and it's highly recommended. | |||
Assuming one is using one of the isomorphic all-3rds tunings, a [[The Kite Guitar|Kite Guitar]] with 6 strings is a little limiting. 7 strings or even 8 is better. Arguably a slightly longer scale, say 27", is nice because it makes the frets less cramped. Fortunately 12-equal 7- and 8-string guitars often have longer scales anyway. But on the other hand, the Kite guitar's frets are not much tighter than a normal mandolin's, and some feel a longer scale isn't necessary. | |||
When converting a guitar, it's best to replace the entire fretboard, rather than removing the frets and putting new frets in the old fretboard. The 41-equal 5th is 702.5¢, so two frets will be only 2.5¢ away from the old ones, two will be 5¢ away, etc. So the old and new fret slots overlap, making conversion difficult. The following table shows the distance from the old fret to the new fret for close pairs. One could just use the old slots (or even the old frets) and accept a few cents error. But in certain keys a 5¢ error will make the major 3rd that's already 6¢ flat a full 11¢ flat. | |||
{| class="wikitable" | {| class="wikitable" | ||
|+distance between fret slots (center to center, scale = 25.5") | |+distance between fret slots (center to center, scale = 25.5") | ||
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|0.032" | |0.032" | ||
|} | |} | ||
Removing the entire fretboard also has the advantage that you can get a pre-slotted computer-cut fretboard fairly cheaply | Removing the entire fretboard also has the advantage that you can get a pre-slotted computer-cut fretboard fairly cheaply that has extremely accurate slot placement. | ||
One way to get an 8-string acoustic is to convert a 12-string guitar. The neck will be sufficiently strong and there will be enough tuners. There's fewer strings but more courses, so the new fretboard may need to be wider than the old one. The fretboard overhang can be filled with bondo to create a nice-feeling neck. Another possibility is to convert a 6-string classical nylon-string to 7 or 8 strings. The fingerboard is wide enough that it may suffice as is. The tension is low enough that an extra string or two won't break the guitar. The 3 holes on each side of the headstock that the tuner pegs go through can be filled and 4 new holes drilled. | One way to get an 8-string acoustic is to convert a 12-string guitar. The neck will be sufficiently strong and there will be enough tuners. There's fewer strings but more courses, so the new fretboard may need to be wider than the old one. The fretboard overhang can be filled with bondo to create a nice-feeling neck. Another possibility is to convert a 6-string classical nylon-string to 7 or 8 strings. The fingerboard is wide enough that it may suffice as is. The tension is low enough that an extra string or two won't break the guitar. The 3 holes on each side of the headstock that the tuner pegs go through can be filled and 4 new holes drilled. | ||
In any given key, the Kite guitar has multiple "rainbow zones" on the neck. Assuming the tonic falls in the "sweet spot" between the 4th and 11th fret, it takes about 28 frets to provide 2 zones in every key, but it takes the full 41 frets to provide 3 zones. This 3rd zone increases the range the lead guitarist has to solo in by a 5th or so. The highest frets are very tight, but still playable melodically. Chording is very difficult. Having a 41st fret makes intonating the guitar easier, see below. | In any given key, the Kite guitar has multiple "rainbow zones" on the neck. Assuming the tonic falls in the "sweet spot" between the 4th and 11th fret, it takes about 28 frets to provide 2 zones in every key, but it takes the full 41 frets to provide 3 zones. This 3rd zone increases the range the lead guitarist has to solo in by a 5th or so. The highest frets are very tight, but still playable melodically. Chording is very difficult. Having a 41st fret makes intonating the guitar easier, see below. In general, if you can fit in 41 frets, do so. | ||
The fret spacing is 1.7 times tighter than a 12- | The fret spacing is 1.7 times tighter than a 12-equal guitar. This chart compares it to the standard fret spacing. The spacing between the nut and the first fret is about the same as the space between the 12-equal 9th and 10th frets. Increasing the overall scale length will widen the spacing. | ||
[[File:Kite Guitar Fret chart.jpg|none|thumb]] | [[File:Kite Guitar Fret chart.jpg|none|thumb]] | ||
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== Fret Markers == | == Fret Markers == | ||
On an even-frets layout, 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. | |||
The small dots on the side of the neck follow the same single/double/triple pattern. The double and triple dots are oriented like the usual 12-equal double dots. Further up the neck, the triple dots are too wide to fit between the frets, but this is not a problem. | The small dots on the side of the neck follow the same single/double/triple pattern. The double and triple dots are oriented like the usual 12-equal double dots. Further up the neck, the triple dots are too wide to fit between the frets, but this is not a problem. | ||
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== String Gauges == | == String Gauges == | ||
A 6-string Kite guitar tuned in 3rds can be strung with a standard set of strings, but it's not ideal. The high strings will be somewhat slack, and the low strings will be somewhat tight. To find the appropriate gauges, use the D'Addario method: calculate each string's tension from its unit weight, length and pitch (frequency) by the formula T = (UW x (2 x L x F)<sup>2</sup>) / 386.4. For open strings, the length is the guitar's scale. The frequency in hertz of the Nth string of 8 strings tuned in the standard downmajor 3rds with a low string of vD is 440 * (2 ^ (-7/12 + (21 - 13*N) / 41)). For a 6-string guitar in mid-6 tuning, N ranges from 2 to 7. Or use the frequency table below. The unit weight is pounds per inch, and is a function of string gauge and string type (plain vs. wound, etc.). D'Addario has [https://www.daddario.com/globalassets/pdfs/accessories/tension_chart_13934.pdf published] their unit weights, thus the individual tensions can be calculated for a given set of strings. One can work backwards from this and select string gauges/types that give uniform tensions using this spreadsheet: [https://tallkite.com/misc_files/StringTensionCalculator.ods TallKite.com/misc_files/StringTensionCalculator.ods] The desired tension depends on the instrument, and of course personal taste. A steel-string acoustic guitar might have 25-30 lbs. tension for each string. A | A 6-string Kite guitar tuned in 3rds can be strung with a standard set of strings, but it's not ideal. The high strings will be somewhat slack, and the low strings will be somewhat tight. To find the appropriate gauges, use the D'Addario method: calculate each string's tension from its unit weight, length and pitch (frequency) by the formula T = (UW x (2 x L x F)<sup>2</sup>) / 386.4. For open strings, the length is the guitar's scale. The frequency in hertz of the Nth string of 8 strings tuned in the standard downmajor 3rds with a low string of vD is 440 * (2 ^ (-7/12 + (21 - 13*N) / 41)). For a 6-string guitar in mid-6 tuning, N ranges from 2 to 7. Or use the frequency table below. The unit weight is pounds per inch, and is a function of string gauge and string type (plain vs. wound, etc.). D'Addario has [https://www.daddario.com/globalassets/pdfs/accessories/tension_chart_13934.pdf published] their unit weights, thus the individual tensions can be calculated for a given set of strings. One can work backwards from this and select string gauges/types that give uniform tensions using this spreadsheet: [https://tallkite.com/misc_files/StringTensionCalculator.ods TallKite.com/misc_files/StringTensionCalculator.ods] The desired tension depends on the instrument, and of course personal taste. A steel-string acoustic guitar might have 25-30 lbs. tension for each string. A 12-equal 25.5" electric guitar strung with a standard 10-46 set has 15-20 lbs. With a 9-42 set it has 13-16 lbs. | ||
* A longer scale means a higher tension or a smaller gauge or a lower pitch (frequency) | * A longer scale means a higher tension or a smaller gauge or a lower pitch (frequency) | ||
* A higher tension means a longer scale or a bigger gauge or a higher pitch | * A higher tension means a longer scale or a bigger gauge or a higher pitch | ||
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* A higher pitch means a shorter scale or a higher tension or a smaller gauge | * A higher pitch means a shorter scale or a higher tension or a smaller gauge | ||
Microtonalist and luthier Tom WInspear can provide custom string sets at his website [https://www.winspearinstrumental.com/ www.winspearinstrumental.com]. His approach is to extrapolate from familiar string sets. He says this about string gauges: "Gauges can be scaled at the same ratios as frequency. A 41- | Microtonalist and luthier Tom WInspear can provide custom string sets at his website [https://www.winspearinstrumental.com/ www.winspearinstrumental.com]. His approach is to extrapolate from familiar string sets. He says this about string gauges: "Gauges can be scaled at the same ratios as frequency. A 41-equal downmajor 3rd is 2^(13/41) = 1.2458, thus from string to string the gauge changes by 24.58%. But you can't do that across the plain to wound transition. To tune to different keys, increase the gauges by 5.95% for each 12-equal semitone of transposition, or 1.705% for each 41-equal step. All this assumes a 25.5" scale. For a scale of S inches, multiply each gauge by 25.5/S and round off. For scales longer than 25.5", err on the side of heavier and round up, as longer scales do feel more flexible loaded with the same tension. Likewise, for scales less than 25.5", err on the side of lighter and round down. However, the plain strings should always be rounded slightly down, and should utilize .0005" increment plain strings where available." | ||
[https://www.juststrings.com/ JustStrings.com] sells custom gauges singly or in bulk. Recommended (somewhat light) gauges for a 27" acoustic guitar: '''11.5 15 18 24 30 36 46 56''' (3 plain, 5 wound). For a 25.5" or 26.5" electric: '''10 13 16 22 26 32 42 52''', the wound 4th string could instead be a '''19''' plain. | [https://www.juststrings.com/ JustStrings.com] sells custom gauges singly or in bulk. Recommended (somewhat light) gauges for a 27" acoustic guitar: '''11.5 15 18 24 30 36 46 56''' (3 plain, 5 wound). For a 25.5" or 26.5" electric: '''10 13 16 22 26 32 42 52''', the wound 4th string could instead be a '''19''' plain. | ||
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Since the Kite guitar is so much more in tune than the 12-equal guitar, extra care should be taken with saddle compensation. | Since the Kite guitar is so much more in tune than the 12-equal guitar, extra care should be taken with saddle 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- | '''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-equal 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 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. | ||
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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. | 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. | ||
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- | 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-equal 5th. On the saddle, mark a point 0.045" behind the exit point, and file up to the mark. | ||
'''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. | '''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. | ||
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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. | 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. | ||
'''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- | '''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-equal major 9th. | ||
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- | 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-equal downminor 7th. | ||
{| class="wikitable" | {| class="wikitable" | ||
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|(N/A) | |(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. Furthermore each string's sideways movement increases as you get away from the nut. But the spacing widens further up the neck, making fretting cleanly easier, so this is not a problem. | ||
== Tables == | == Tables == | ||
=== Cents === | === Cents === | ||
Every note on the Kite Guitar fretboard. The outer columns show the dots on the fretboard. The low note is vD and the tuning is in downmajor 3rds. The note names in the table are 12- | Every note on the Kite Guitar fretboard. The outer columns show the dots on the fretboard. The low note is vD and the tuning is in downmajor 3rds. The note names in the table are 12-equal, not 41-equal. The low vD is written "D -29.3", meaning 12-equal D minus 29.3¢. The 7 natural notes in 41-equal are '''''<u>bolded and underlined italic</u>'''''. The full set of 41-equal names are here: [[:File:The Kite Tuning 5.png]] | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
| colspan="2" | | | colspan="2" | | ||
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===Frequencies=== | ===Frequencies=== | ||
41- | 41-equal frequencies in Hertz. D is tuned to standard A-440 pitch. vA is roughly 432hz, and vvB is roughly the ubiquitous 60hz mains hum. | ||
{| class="wikitable" | {| class="wikitable" | ||
| | | | ||