Kite Guitar: Difference between revisions

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Sixth chords: added the high-3-5 voicing
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[[File:The Kite Tuning 2.png|none|thumb|1048x1048px]]
[[File:The Kite Tuning 2.png|none|thumb|1048x1048px]]
This chart extends even further, showing the "rainbow zones" and the "wolf zones". When two guitarists play together, it's very natural for one to play chords in the lower rainbow zone, and another to solo in the higher rainbow zone. The open strings tend to be in a wolf zone, unless the tonic is fairly close to the nut, or else up around the 14th fret. [[File:The Kite Tuning 3.png|none|thumb|1113x1113px]]
This chart extends even further, showing the "rainbow zones" and the "wolf zones". When two guitarists play together, it's very natural for one to play chords in the lower rainbow zone, and another to solo in the higher rainbow zone. The open strings tend to be in a wolf zone, unless the tonic is fairly close to the nut, or else up around the 14th fret. [[File:The Kite Tuning 3.png|none|thumb|1113x1113px]]
This chart shows the actual notes of an 8-string Kite guitar. A 6-string is usually tuned to the middle 6 strings of an 8-string. The ideal string gauges for this tuning are discussed in the "For Luthiers" section. Every 4th fret has a dot, and every 12th fret has a double dot. Three dots equals a 5th.
This chart shows the actual notes of an 8-string Kite guitar. A 6-string is usually tuned to the middle 6 strings of an 8-string. The ideal string gauges for this tuning are discussed in the "For Luthiers" section. Every 4th fret has a dot, and every 12th fret has a double dot. Three dots equals a 5th.  
[[File:The Kite Tuning 4.png|none|thumb|1150x1150px]]
[[File:The Kite Tuning 4.png|none|thumb|1150x1150px]]
This shows all the notes, not just the natural ones. But it's too much work to memorize all this. Just learn where the 7 natural notes are, and learn your intervals. Since the open strings don’t work as well, one tends to think more in terms of intervals than notes.  
This shows all the notes, not just the natural ones. But it's too much work to memorize all this. Just learn where the 7 natural notes are, and learn your intervals. Since the open strings don’t work as well, one tends to think more in terms of intervals than notes.  
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== Relative and Absolute Tab ==
== Relative and Absolute Tab ==
Since the fretboard is isomorphic, any interval can be expressed in '''relative tab''' as a vector. This is particularly useful for in-person oral instruction. For example, going up 2 strings and down 1 fret always takes you up a perfect 5th. In relative tab, that move is spoken as "plus-two minus-one", and written as (+2,-1). The perfect 5th also appears at oh-plus-twelve, (0,+12). The downmajor 3rd is at plus-one-oh, (+1,0). The octave is (+3,+1) and also (+1,+14). A jump of 14 frets can be referred to as a "3 and 2" jump, meaning 3 dots plus 2 frets. Mentally grouping four frets together into one dot facilitates large jumps up or down the fretboard. Thus the octave is at plus-one plus-three-and-two, or (+1,+3+2). The 5th is at oh-plus-three-and-none, or alternatively oh-plus-three-dots, (0,+3+0). The unison is plus-two minus-three-and-one, (+2,-3-1). An upward jump of 11 frets could be called either plus-two-and-three or plus-three-minus-one. Note that plus-three-oh means (+3,0), but plus-three-and-none means +3 dots.
Since the fretboard is isomorphic, any interval can be expressed in '''relative tab''' as a vector. This is particularly useful for in-person oral instruction. For example, going up 2 strings and down 1 fret always takes you up a perfect 5th. In relative tab, that move is spoken as "plus-two minus-one", and written as (+2,-1). The downmajor 2nd is at oh-plus-three, (0,+3). The downmajor 3rd is at plus-one-oh, (+1,0).
 
Every interval appears in several places on the fretboard. Typically one is within a few frets and another one is many frets away. Mentally grouping four frets together into one dot facilitates large jumps up and down the fretboard. The octave is (+3,+1) and also (+1,+14). A jump of 14 frets is a "3 and 2" jump, meaning 3 dots plus 2 frets. Thus the octave is at plus-one plus-three-and-two, or (+1,+3+2). The 5th is at oh-plus-three-and-none, or alternatively oh-plus-three-dots, (0,+3+0). The unison is plus-two minus-three-and-one, (+2,-3-1). An upward jump of 11 frets could be called either plus-two-and-three or plus-three-minus-one. Note that plus-three-oh means (+3,0), but plus-three-and-none means +3 dots.


Notes can be referred to similarly in '''absolute tab''', which names each string/fret combination, i.e. each location on the fingerboard. For example, a low ^^G in the previous section's fretboard chart is at (7,3), meaning 7th string, 3rd fret. This is particularly useful when one wants to tell another guitarist what key they are in, without having to use note names. For example, one might be in the key of "fifth and two and three", meaning 5th string, 3 frets above the 2nd dot. "Sixth and two" means 6th string, 2nd fret, as opposed to "sixth and two dots". "Fourth and oh" means the open 4th string.
Notes can be referred to similarly in '''absolute tab''', which names each string/fret combination, i.e. each location on the fingerboard. For example, a low ^^G in the previous section's fretboard chart is at (7,3), meaning 7th string, 3rd fret. This is particularly useful when one wants to tell another guitarist what key they are in, without having to use note names. For example, one might be in the key of "fifth and two and three", meaning 5th string, 3 frets above the 2nd dot. "Sixth and two" means 6th string, 2nd fret, as opposed to "sixth and two dots". "Fourth and oh" means the open 4th string.
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=== Sixth chords ===
=== Sixth chords ===
Sixth chords are hard to voice. A close voicing in root position is generally impossible, because the 6th occurs on the same string as the 5th. One solution is to play a riff that alternates between the 5th and the 6th. Another is to omit the 5th, but then the chord can be mistaken for a triad in 1st inversion. Another voicing is the low-6 aka 3rd inversion (6 R 3 5). But this is the same as the close voicing of the corresponding 7th chord, and again the chord can be mistaken. A non-ambiguous voicing is low-5 (5 R 3 6), but it can be a difficult stretch. Also the 9th from the 5th to the 6th is usually not a plain 9th, and can be dissonant. A very good open voicing is high-3-5 (R 6 3 5). However, this voicing is only possible on a 6-string when the root can be played on the lowest string. Other possibilities are high-3-6 (R 5 3 6), high-5 (R 3 6 8 5) and high-6 (R 3 5 8 6).
Sixth chords are hard to voice. A close voicing in root position is generally impossible, because the 6th occurs on the same string as the 5th. One solution is to play a riff that alternates between the 5th and the 6th. Another is to omit the 5th, but then the chord can be mistaken for a triad in 1st inversion. Another voicing is the low-6 aka 3rd inversion (6 R 3 5). But this is the same as the close voicing of the corresponding 7th chord, and again the chord can be mistaken. A good non-ambiguous voicing is low-5 (5 R 3 6), but it can be a difficult stretch. Also the 9th from the 5th to the 6th is usually not a plain 9th, and can be dissonant. Other possibilities are high-3-5 (R 6 3 5), high-3-6 (R 5 3 6), high-5 (R 3 6 8 5) and high-6 (R 3 5 8 6).


The up-6 chord is particularly dissonant, unless voiced as its homonym, the vm7 chord.
The up-6 chord is particularly dissonant, unless voiced as its homonym, the vm7 chord.
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Adding a major 9th (ratio 9/4) to any of these chords will make a wolf 4th with the 6th. A 9th that is a P4 above the 6th (^M9 or vM9) will clash with the 5th, but can be added if the 5th is omitted. The chord becomes ambiguous. C^6,^9no5 is the same as ^Dv9no3. Cv6,v9no5 is vD^9no3. C^m6,^9no5 and Cvm6,v9no5 both have an awkward interval from the 3rd up to the 9th: a M7 = 40/21, odd-limit 21.
Adding a major 9th (ratio 9/4) to any of these chords will make a wolf 4th with the 6th. A 9th that is a P4 above the 6th (^M9 or vM9) will clash with the 5th, but can be added if the 5th is omitted. The chord becomes ambiguous. C^6,^9no5 is the same as ^Dv9no3. Cv6,v9no5 is vD^9no3. C^m6,^9no5 and Cvm6,v9no5 both have an awkward interval from the 3rd up to the 9th: a M7 = 40/21, odd-limit 21.


Adding an 11th (ratio 8/3) to either the ^m6 or the vm6 chord won't increase the odd limit above 9. But a Cvm6,11 chord is the same as an Fv9 chord, and every easy fingering puts the F in the bass, so it's hardly a distinct chord. Adding an 11th to a Cv6 chord makes Cv6,11, which is an FvM9 chord. Again, every easy fingering has F in the bass, and Cv6,11 isn't a distinct chord. Adding an 11th to a ^M6 chord raises the odd limit to 27. Thus adding an 11th only works well with the ^m6 chord.
Adding an 11th (ratio 8/3) to either the ^m6 or the vm6 chord won't increase the odd limit above 9. But a Cvm6,11 chord is the same as an Fv9 chord, and every easy fingering puts the F in the bass, so it's hardly a distinct chord. Adding an 11th to a Cv6 chord makes Cv6,11, which is an FvM9 chord. Again, every easy fingering has F in the bass, and Cv6,11 isn't a distinct chord.
{| class="wikitable"
{| class="wikitable"
!chord type
!chord type
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|1 3 2 4
|1 3 2 4
|1 3 1 4
|1 3 1 4
|-
|'''<u>high-3-5 voicing</u> R (4) 6 3 5'''
|
|
|
|
|-
|frets
|4 . 7 . 6 4
|4 . 6 . 5 4
|4 (6) 7 . 4 4
|4 . 6 . 3 4
|-
|suggested fingerings
|1 . 4 . 3 2
2 . 4 . 3 1
1 . 4 . 3 1
|1 . 4 . 3 2
1 . 3 . 2 1
1 1 3 . 2 1
|1 (3) 4 . 1 1
1 . 4 3 1 1
|2 . 4 . 1 3
3 . 4 . 1 2
|}
|}


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== Translating 12-edo Songs to 41-edo ==
== Translating 12-edo Songs to 41-edo ==
Obviously, the Kite Guitar can do much more than simply play conventional music. But a good starting place is to take what you know and find it on the Kite Guitar. Translating 12-edo music is sometimes problematic but never impossible.  
Obviously, the Kite Guitar can do much more than simply play conventional music. But a good starting place is to take what you know and find it on the Kite Guitar. Translating 12-edo music is sometimes problematic but never impossible. Quite often the translated version sounds better, because it's so well tuned.


One way to translate a conventional song is to first translate it to 7-limit JI, perhaps visualizing it on a lattice, keeping in mind that 41-edo tempers out the [[32805/32768|Layo]], [[225/224|Ruyoyo]] and [[5120/5103|Saruyo]] minicommas. Then translate the JI to 41edo. Another way is to use the spiral charts in the previous section.
One way to translate a conventional song is to first translate it to 7-limit JI, perhaps visualizing it on a lattice, keeping in mind that 41-edo tempers out the [[32805/32768|Layo]], [[225/224|Ruyoyo]] and [[5120/5103|Saruyo]] minicommas. Then translate the JI to 41edo. Another way is to use the spiral charts in the previous section.