Kite Guitar: Difference between revisions

Line 51:

== About 41-EDO ==

[[41-edo]] approximates just intonation very closely. Prime 3 is extremely accurate, and primes 5 and 7 are both flat, which means their errors partially cancel out in ratios such as 7/5. Unfortunately prime 11 is sharp, so the errors add up, and 11/10 is nearly 11¢ sharp.

{| class="wikitable" style="text-align:center;"

|prime

|2/1

Line 106:

This chart is the same, but extends much further. Some ratios change in the higher octaves, e.g. 16/15 becomes not 32/15 but 15/7.

[[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.

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.

If the tonic is the ~~D at~~ the 14th fret~~, the open strings are in a rainbow zone~~.

[[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.

[[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.

[[File:The Kite Tuning 5.png|none|thumb|1131x1131px]]

== 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.

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.

Unlike relative tab, absolute tab doesn't require isomorphism, and can be applied to any guitar, as long as the dot locations are agreed on. For 12-edo, dots are at frets 3, 5, 7, 9, 12, etc., thus the 10th fret is four-and-one.

Relative and absolute tab are easy to tell apart. Relative tab always starts with plus, minus or zero, absolute tab never does. Note that in absolute tab, strings are numbered in descending order, but in relative tab, a positive move is an ascending move. Thus moving from the 3rd string to the 1st string is plus-two, not minus-two.

The Kite guitar can be tuned by ear using the octaves at (+1,+3+2). The open 6th string should be an octave bellow the 5th string's 14th fret. This can be written as (6,0) = (5,3+2). We can double-check the tuning using the unisons at (+2,-3-1). Thus the 6th string at the 13th fret should match the open 4th string, and (6,3+1) = (4,0). Finally, the 3rd harmonic of the 6th string should match the open 1st string (technically it should be half a cent sharp of it). Here are the full tuning instructions for a 6-string guitar:

{| class="wikitable"

|+

!octaves

!unisons

|-

|(6,0) = (5,3+2)

|(6,3+1) = (4,0)

|-

|(5,0) = (4,3+2)

|(5,3+1) = (3,0)

|-

|(4,0) = (3,3+2)

|(4,3+1) = (2,0)

|-

|(3,0) = (2,3+2)

|(3,3+1) = (1,0)

|-

|(2,0) = (1,3+2)

|(6,0) harmonic at 3rd dot = (1,0)

|}

== Chord shapes (downmajor tuning) ==

@@ Line 51: / Line 51: @@
 == About 41-EDO ==
 [[41-edo]] approximates just intonation very closely. Prime 3 is extremely accurate, and primes 5 and 7 are both flat, which means their errors partially cancel out in ratios such as 7/5. Unfortunately prime 11 is sharp, so the errors add up, and 11/10 is nearly 11¢ sharp.
-{| class="wikitable"  style="text-align:center;"
+{| class="wikitable" style="text-align:center;"
 |prime
 |2/1
@@ Line 106: / Line 106: @@
 This chart is the same, but extends much further. Some ratios change in the higher octaves, e.g. 16/15 becomes not 32/15 but 15/7.
 [[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.
+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.
-If the tonic is the D at the 14th fret, the open strings are in a rainbow zone.
-[[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.
 [[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.
 [[File:The Kite Tuning 5.png|none|thumb|1131x1131px]]
+== 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.
+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.
+Unlike relative tab, absolute tab doesn't require isomorphism, and can be applied to any guitar, as long as the dot locations are agreed on. For 12-edo, dots are at frets 3, 5, 7, 9, 12, etc., thus the 10th fret is four-and-one.
+Relative and absolute tab are easy to tell apart. Relative tab always starts with plus, minus or zero, absolute tab never does. Note that in absolute tab, strings are numbered in descending order, but in relative tab, a positive move is an ascending move. Thus moving from the 3rd string to the 1st string is plus-two, not minus-two.
+The Kite guitar can be tuned by ear using the octaves at (+1,+3+2). The open 6th string should be an octave bellow the 5th string's 14th fret. This can be written as (6,0) = (5,3+2). We can double-check the tuning using the unisons at (+2,-3-1). Thus the 6th string at the 13th fret should match the open 4th string, and (6,3+1) = (4,0). Finally, the 3rd harmonic of the 6th string should match the open 1st string (technically it should be half a cent sharp of it). Here are the full tuning instructions for a 6-string guitar:
+{| class="wikitable"
+|+
+!octaves
+!unisons
+|-
+|(6,0) = (5,3+2)
+|(6,3+1) = (4,0)
+|-
+|(5,0) = (4,3+2)
+|(5,3+1) = (3,0)
+|-
+|(4,0) = (3,3+2)
+|(4,3+1) = (2,0)
+|-
+|(3,0) = (2,3+2)
+|(3,3+1) = (1,0)
+|-
+|(2,0) = (1,3+2)
+|(6,0) harmonic at 3rd dot = (1,0)
+|}
 == Chord shapes (downmajor tuning) ==