Kite Guitar: Difference between revisions

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== Fretboard Charts (downmajor tuning) ==

This chart is in relative not absolute notation, meaning it shows intervals not notes. Down at the bottom is P1, a perfect unison. This is the tonic of the scale, or the root of the chord. This chart shows all the intervals within easy reach of this note, up to an octave. There are four "rainbows": one of 2nds, one of 3rds, one of 6ths, and one of 7ths. These plus the 4th, 5th, 8ve, and a few other notes add up to 25 of the 41 notes. Every single ratio of [[odd-limit]] 9 or less appears here~~. See also the first chart in the "Scale Shapes" section~~.

This chart is in relative not absolute notation, meaning it shows intervals not notes. Down at the bottom is P1, a perfect unison. This is the tonic of the scale, or the root of the chord. This chart shows all the intervals within easy reach of this note, up to an octave. There are four "rainbows": one of 2nds, one of 3rds, one of 6ths, and one of 7ths. These plus the 4th, 5th, 8ve, and a few other notes add up to 25 of the 41 notes. Every single ratio of [[odd-limit]] 9 or less appears here.

[[File:The Kite Tuning.png|none|thumb|416x416px]]

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.

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=== Scale Shapes ===

Printer-friendly ~~chart~~ of scale degrees~~:[[File:Scale chart.png|thumb|none]]Here are~~ the three main scales. ~~Some~~ scale degrees appear more than once. In general, use the one that agrees with the current chord.

Printer-friendly charts, one of scale degrees, the other of the three main scales. In the latter, some scale degrees appear more than once. In general, use the one that agrees with the current chord.[[File:Scale chart.png|thumb|left]]

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

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These tables list all chords of odd-limit 9, plus a few with downmajor 7ths that are odd-limit 15. The chord shapes are written in tablature, using fret numbers. The root is placed arbitrarily on the 4th fret. In these tables, the interval between open strings is always a downmajor 3rd. This makes the Kite guitar isomorphic, thus a tab like 4 6 3 5 can start on the 6th, 5th or 4th string, and of course any fret of that string. A skipped string is indicated by a period. Alternate fingerings are possible, especially for 2-finger and 3-finger chords.

Chords are named using [[Ups and Downs Notation|ups and down notation]], see also the [http://tallkite.com/misc_files/notation%20guide%20for%20edos%205-72.pdf notation guide for edos 5-72]. Briefly, a "global" up or down immediately after the root affects the 3rd, 6th, 7th and/or the 11th, but not the 5th, 9th or 13th. Alterations are enclosed in parentheses, and additions are set off with a comma (the punctuation mark, not the interval!). In general, the comma is spoken as "add", e.g. Cv,9 = "C down add-9" = C vE G D. Chord progressions are written as Cv7 - vEb^m6 - Fv7 or Iv7 - vbIII^m6 - IVv7.

In general, an odd-limit 15 chord has only one 15-limit interval, and most of the others are much lower odd-limit. For example, the downmajor seven chord has intervals of odd-limit 3, 3, 5, 5, 5 and 15. The many low-limit intervals serve as "glue" to hold together the chord, despite the one 15-limit interval. This is the rationale for focusing on odd-limit 15 chords here and not those of odd-limit 11 or 13, for those chords have multiple intervals of high odd-limit. But see below, at the very end of this section.

These tables are fairly exhaustive. Don't get overwhelmed! The most essential chords are in the first two tables (triads and seventh chords). Here's a printer-friendly chart to get you started:

These tables are fairly exhaustive. Don't get overwhelmed! The most essential chords are in the first two tables (triads and seventh chords). Here's a printer-friendly chart to get you started, with and without fingerings:

[[File:Chord chart 2.png|left|thumb]]

[[File:Chord chart.png|thumb|none]]

=== Triads ===

The alternate names for the voicings are explained in the next section. Other voicings are possible; these are just the most convenient ones. The upmajor chord is a particularly dissonant triad. See "Innate-comma chords" below for augmented triads.

The alternate names for the voicings are explained in the next section. Other voicings are possible; these are just the most convenient ones. The upmajor chord is a particularly dissonant triad. See "Innate-comma chords" below for augmented triads. '''Added ninths are shown in parentheses.''' Adding a major 9th (ratio 9/4, example note D) to the up or down triad increases the intervallic odd-limit only slightly if at all. The up chord is arguably improved by adding a 9th.

{| class="wikitable"

!chord type ---->

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!up or

upmajor

(up add 9)

!down or

downmajor

(down add 9)

!upminor

!downminor

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!example, with homonym

!C4 = F2

!C^

!C^ (C^,9)

!Cv

!Cv (Cv,9)

!C^m

!Cvm

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!d5 = 7/5

|-

|'''close voicing R 3 5 8'''

|'''close voicing R 3 5 8 (9)'''

| colspan="8" |

|-

|frets

|4 6 3 5

|4 5 3 5

|4 5 3 5 (2)

|4 4 3 5

|4 4 3 5 (2)

|4 3 3 5

|4 2 3 5

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|3 . 1 4 2

|-

|'''high-R voicing 3 5 8~~'''~~ (~~'''~~1st inversion''')

|'''high-R voicing 3 5 8 (9) (1st inversion''')

| colspan="8" |

|-

|frets

|5 2 4

|4 2 4

|4 2 4 (1)

|3 2 4

|3 2 4 (1)

|2 2 4

|1 2 4

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=== Innate-comma chords ===

We've covered every chord that maps to a JI chord of intervallic odd-limit 9. However there are many Kite guitar chords that don't, although their individual intervals do. These chords are called [[Dyadic chord|innate-comma chords aka essentially tempered chords]]. Almost every easily reachable interval on the fretboard is odd-limit 9. The only exceptions are ~4, ~5, vM7, ^M7, vm9 and ^m9. Thus the majority of Kite guitar chord shapes are intervallic odd-limit 9.

We've covered every chord that maps to a JI chord of intervallic odd-limit 9. However there are many Kite guitar chords that don't, although their individual intervals do. These chords are called [[Dyadic chord|innate-comma chords aka essentially tempered chords]]. Such chords often have a mysterious sound. Almost every easily reachable interval on the fretboard is odd-limit 9. The only exceptions are ~4, ~5, vM7, ^M7, vm9 and ^m9. Thus the majority of Kite guitar chord shapes are intervallic odd-limit 9.

For example, the downadd7no5 chord has 5/4 and 16/9. The interval from 5/4 up to 16/9 is 64/45. But because 41edo tempers out the [[225/224|Ruyoyo]] comma of only 8¢, 64/45 is equivalent to 10/7. The high-3 voicing inverts this into an even smoother 7/5. This dom7 chord is often appropriate for translating 12-edos V7 -- I cadence: relaxed but not too relaxed. Note that adding the 5th would increase the odd-limit to 27. In chord names, alterations are enclosed in parentheses, and additions are set off with a comma (the punctuation mark, not the interval!) In general, the comma is spoken as "add". Thus C-down add-seven is Cv,7 = C vE G Bb. Compare with C down-seven = Cv7 = C vE G vBb.

For example, the downadd7no5 chord has 5/4 and 16/9. The interval from 5/4 up to 16/9 is 64/45. But because 41edo tempers out the [[225/224|Ruyoyo]] comma of only 8¢, 64/45 is equivalent to 10/7. The high-3 voicing inverts this into an even smoother 7/5. This dom7 chord is often appropriate for translating 12-edos V7 -- I cadence: relaxed but not too relaxed. Note that adding the 5th would increase the odd-limit to 27.

The downmajor7sus4 chord (odd-limit 15) also has an innate Ruyoyo comma. The chord is quite striking in close voicing. The interval from 4/3 up to 15/8 is 45/32, equivalent to 7/5. The homonym of CvM7(4) is the sus2addb5 chord F2,b5 = F G Cb C. In 41-edo, Cb is enharmonically equivalent to vB. In chord names, "(b5)" means alter the 5th by flattening it, but ",b5" means add a flat 5th alongside the perfect 5th.

@@ Line 117: / Line 117: @@
 == Fretboard Charts (downmajor tuning) ==
-This chart is in relative not absolute notation, meaning it shows intervals not notes. Down at the bottom is P1, a perfect unison. This is the tonic of the scale, or the root of the chord. This chart shows all the intervals within easy reach of this note, up to an octave. There are four "rainbows": one of 2nds, one of 3rds, one of 6ths, and one of 7ths. These plus the 4th, 5th, 8ve, and a few other notes add up to 25 of the 41 notes. Every single ratio of [[odd-limit]] 9 or less appears here. See also the first chart in the "Scale Shapes" section.
+This chart is in relative not absolute notation, meaning it shows intervals not notes. Down at the bottom is P1, a perfect unison. This is the tonic of the scale, or the root of the chord. This chart shows all the intervals within easy reach of this note, up to an octave. There are four "rainbows": one of 2nds, one of 3rds, one of 6ths, and one of 7ths. These plus the 4th, 5th, 8ve, and a few other notes add up to 25 of the 41 notes. Every single ratio of [[odd-limit]] 9 or less appears here.
 [[File:The Kite Tuning.png|none|thumb|416x416px]]
 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.
@@ Line 128: / Line 128: @@
 === Scale Shapes ===
-Printer-friendly chart of scale degrees:[[File:Scale chart.png|thumb|none]]Here are the three main scales. Some scale degrees appear more than once. In general, use the one that agrees with the current chord.
+Printer-friendly charts, one of scale degrees, the other of the three main scales. In the latter, some scale degrees appear more than once. In general, use the one that agrees with the current chord.[[File:Scale chart.png|thumb|left]]
 [[File:Scale chart 2.png|none|thumb]]
@@ Line 174: / Line 174: @@
 These tables list all chords of odd-limit 9, plus a few with downmajor 7ths that are odd-limit 15. The chord shapes are written in tablature, using fret numbers. The root is placed arbitrarily on the 4th fret. In these tables, the interval between open strings is always a downmajor 3rd. This makes the Kite guitar isomorphic, thus a tab like 4 6 3 5 can start on the 6th, 5th or 4th string, and of course any fret of that string. A skipped string is indicated by a period. Alternate fingerings are possible, especially for 2-finger and 3-finger chords.
+Chords are named using [[Ups and Downs Notation|ups and down notation]], see also the [http://tallkite.com/misc_files/notation%20guide%20for%20edos%205-72.pdf notation guide for edos 5-72]. Briefly, a "global" up or down immediately after the root affects the 3rd, 6th, 7th and/or the 11th, but not the 5th, 9th or 13th. Alterations are enclosed in parentheses, and additions are set off with a comma (the punctuation mark, not the interval!). In general, the comma is spoken as "add", e.g. Cv,9 = "C down add-9" = C vE G D. Chord progressions are written as Cv7 - vEb^m6 - Fv7 or Iv7 - vbIII^m6 - IVv7.
 In general, an odd-limit 15 chord has only one 15-limit interval, and most of the others are much lower odd-limit. For example, the downmajor seven chord has intervals of odd-limit 3, 3, 5, 5, 5 and 15. The many low-limit intervals serve as "glue" to hold together the chord, despite the one 15-limit interval. This is the rationale for focusing on odd-limit 15 chords here and not those of odd-limit 11 or 13, for those chords have multiple intervals of high odd-limit. But see below, at the very end of this section.
-These tables are fairly exhaustive. Don't get overwhelmed! The most essential chords are in the first two tables (triads and seventh chords). Here's a printer-friendly chart to get you started:
+These tables are fairly exhaustive. Don't get overwhelmed! The most essential chords are in the first two tables (triads and seventh chords). Here's a printer-friendly chart to get you started, with and without fingerings:
+[[File:Chord chart 2.png|left|thumb]]
 [[File:Chord chart.png|thumb|none]]
 === Triads ===
-The alternate names for the voicings are explained in the next section. Other voicings are possible; these are just the most convenient ones. The upmajor chord is a particularly dissonant triad. See "Innate-comma chords" below for augmented triads.
+The alternate names for the voicings are explained in the next section. Other voicings are possible; these are just the most convenient ones. The upmajor chord is a particularly dissonant triad. See "Innate-comma chords" below for augmented triads. '''Added ninths are shown in parentheses.''' Adding a major 9th (ratio 9/4, example note D) to the up or down triad increases the intervallic odd-limit only slightly if at all. The up chord is arguably improved by adding a 9th.
 {| class="wikitable"
 !chord type ---->
@@ Line 187: / Line 190: @@
 !up or
 upmajor
+(up add 9)
 !down or
 downmajor
+(down add 9)
 !upminor
 !downminor
@@ Line 197: / Line 204: @@
 !example, with homonym
 !C4 = F2
-!C^
+!C^ (C^,9)
-!Cv
+!Cv (Cv,9)
 !C^m
 !Cvm
@@ Line 235: / Line 242: @@
 !d5 = 7/5
 |-
-|'''<u>close voicing</u> R 3 5 8'''
+|'''<u>close voicing</u> R 3 5 8 (9)'''
 | colspan="8" |
 |-
 |frets
 |4 6 3 5
-|4 5 3 5
+|4 5 3 5 (2)
-|4 4 3 5
+|4 4 3 5 (2)
 |4 3 3 5
 |4 2 3 5
@@ Line 283: / Line 290: @@
 |3 . 1 4 2
 |-
-|'''<u>high-R voicing</u> 3 5 8''' ('''1st inversion''')
+|'''<u>high-R voicing</u> 3 5 8 (9) (1st inversion''')
 | colspan="8" |
 |-
 |frets
 |5 2 4
-|4 2 4
+|4 2 4 (1)
-|3 2 4
+|3 2 4 (1)
 |2 2 4
 |1 2 4
@@ Line 612: / Line 619: @@
 === Innate-comma chords ===
-We've covered every chord that maps to a JI chord of intervallic odd-limit 9. However there are many Kite guitar chords that don't, although their individual intervals do. These chords are called [[Dyadic chord|innate-comma chords aka essentially tempered chords]]. Almost every easily reachable interval on the fretboard is odd-limit 9. The only exceptions are ~4, ~5, vM7, ^M7, vm9 and ^m9. Thus the majority of Kite guitar chord shapes are intervallic odd-limit 9.
+We've covered every chord that maps to a JI chord of intervallic odd-limit 9. However there are many Kite guitar chords that don't, although their individual intervals do. These chords are called [[Dyadic chord|innate-comma chords aka essentially tempered chords]]. Such chords often have a mysterious sound. Almost every easily reachable interval on the fretboard is odd-limit 9. The only exceptions are ~4, ~5, vM7, ^M7, vm9 and ^m9. Thus the majority of Kite guitar chord shapes are intervallic odd-limit 9.
-For example, the downadd7no5 chord has 5/4 and 16/9. The interval from 5/4 up to 16/9 is 64/45. But because 41edo tempers out the [[225/224|Ruyoyo]] comma of only 8¢, 64/45 is equivalent to 10/7. The high-3 voicing inverts this into an even smoother 7/5. This dom7 chord is often appropriate for translating 12-edos V7 -- I cadence: relaxed but not too relaxed. Note that adding the 5th would increase the odd-limit to 27. In chord names, alterations are enclosed in parentheses, and additions are set off with a comma (the punctuation mark, not the interval!) In general, the comma is spoken as "add". Thus C-down add-seven is Cv,7 = C vE G Bb. Compare with C down-seven = Cv7 = C vE G vBb.
+For example, the downadd7no5 chord has 5/4 and 16/9. The interval from 5/4 up to 16/9 is 64/45. But because 41edo tempers out the [[225/224|Ruyoyo]] comma of only 8¢, 64/45 is equivalent to 10/7. The high-3 voicing inverts this into an even smoother 7/5. This dom7 chord is often appropriate for translating 12-edos V7 -- I cadence: relaxed but not too relaxed. Note that adding the 5th would increase the odd-limit to 27.
 The downmajor7sus4 chord (odd-limit 15) also has an innate Ruyoyo comma. The chord is quite striking in close voicing. The interval from 4/3 up to 15/8 is 45/32, equivalent to 7/5. The homonym of CvM7(4) is the sus2addb5 chord F2,b5 = F G Cb C. In 41-edo, Cb is enharmonically equivalent to vB. In chord names, "(b5)" means alter the 5th by flattening it, but ",b5" means add a flat 5th alongside the perfect 5th.