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.

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.

[[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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The Kite guitar can be tuned to a specific pitch using the [http://tallkite.com/misc_files/EDOtuner.txt.zip EDOtuner], a free strobe tuner for microtonal guitars (requires [https://www.reaper.fm/ Reaper] or [https://www.reaper.fm/reaplugs/ ReaJS]).

== Chord ~~shapes~~ (downmajor tuning) ==

== Chord Shapes (downmajor tuning) ==

There are many chords to explore, but the obvious place to start is with those of [[odd-limit|intervallic odd-limit]] 9 or less. These chords are mostly subsets of the 4:5:6:7:9 pentad or the 9/(9:7:6:5:4) pentad. Thus most of these chords can be classified as either '''harmonic''' or '''subharmonic'''. The ^m7 and vm7 chords (and their homonyms v6 and ^6) are classified as '''stacked''' chords, because they are formed by stacking complimentary 3rds. Many chords fall outside these 3 categories.

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. A skipped string is indicated by a period. Alternate fingerings are possible, especially for 2-finger and 3-finger chords.

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.

~~Don't get overwhelmed! The first two tables contain all~~ the ~~essential chords~~. ~~Here are some charts~~ to ~~get you started:~~

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 will generally have multiple intervals of high odd-limit.

~~[[File:Chord chart~~.~~png|left|thumb]] [[File:Scale chart~~.~~png|center|thumb]]~~

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:

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

=== Triads ===

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!downhalfdim

|-

!example

!example, with

homonym

!CvM7

(CvM9)

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=== Innate-comma chords ===

The downadd7no5 chord has 5/4 and 16/~~9. Surprisingly, its intervallic odd-limit is only~~ 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.

The chords covered so far include every chords that map to a JI chord of intervallic odd-limit 9. However there are some 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.

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.

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.

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When the added b5 is voiced an 8ve higher, it becomes a v#11, and suggests the downmajor7downsharp11 and downmajor9downsharp11 chords (both odd-limit 15). No need to omit the 3rd, it makes a pleasant M9 = 9/4 with the 11th.

{| class="wikitable"

!

!chord type ---->

!downadd7no5

!downmaj7sus4

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Another possible aug chord is 7:9:11 = up-downsharp5 = C^(v#5) = C ^E vG#. Unfortunately it's very difficult to finger.

The updim7 and downdim7 chords are formed from stacked 6/5's and 7/6's, alternating to make 7/5's. The 7ths are rather dissonant. The updim7 chord has an innate Ruyoyo comma which equates its ^d7 = 42/25 to a M6 = 27/16. The downdim7 chord has an innate [[Mynucumic chords|Thuzozogu]] comma which equates vd7 = 49/30 with ~6 = 13/8.

The updim7 and downdim7 chords are formed from stacked 6/5's and 7/6's, alternating to make 7/5's. The 7ths are rather dissonant. The updim7 chord has an innate Ruyoyo comma which equates its ^d7 = 42/25 to a M6 = 27/16. The downdim7 chord has an innate [[Mynucumic chords|Thuzozogu]] comma which equates vd7 = 49/30 with ~6 = 13/8. Thus its odd-limit and prime-limit are both 13.

{| class="wikitable"

!

!chord -->

!upaug

!downaug

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|(difficult)

|}

== Scale Shapes (downmajor tuning) ==

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, use the one that agrees with the current chord.

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

== 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. Quite often the translated version sounds better, because it's so well tuned.

@@ Line 115: / Line 115: @@
 == 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.
+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.
 [[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 164: / Line 164: @@
 The Kite guitar can be tuned to a specific pitch using the [http://tallkite.com/misc_files/EDOtuner.txt.zip EDOtuner], a free strobe tuner for microtonal guitars (requires [https://www.reaper.fm/ Reaper] or [https://www.reaper.fm/reaplugs/ ReaJS]).
-== Chord shapes (downmajor tuning) ==
+== Chord Shapes (downmajor tuning) ==
 There are many chords to explore, but the obvious place to start is with those of [[odd-limit|intervallic odd-limit]] 9 or less. These chords are mostly subsets of the 4:5:6:7:9 pentad or the 9/(9:7:6:5:4) pentad. Thus most of these chords can be classified as either '''harmonic''' or '''subharmonic'''. The ^m7 and vm7 chords (and their homonyms v6 and ^6) are classified as '''stacked''' chords, because they are formed by stacking complimentary 3rds. Many chords fall outside these 3 categories.
-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. A skipped string is indicated by a period. Alternate fingerings are possible, especially for 2-finger and 3-finger chords.
+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.
-Don't get overwhelmed! The first two tables contain all the essential chords. Here are some charts to get you started:
+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 will generally have multiple intervals of high odd-limit.
-[[File:Chord chart.png|left|thumb]] [[File:Scale chart.png|center|thumb]]
+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:
+[[File:Chord chart.png|thumb|none]]
 === Triads ===
@@ Line 344: / Line 345: @@
 !downhalfdim
 |-
-!example
+!example, with
+homonym
 !CvM7
 (CvM9)
@@ Line 598: / Line 600: @@
 === Innate-comma chords ===
-The downadd7no5 chord has 5/4 and 16/9. Surprisingly, its intervallic odd-limit is only 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.
+The chords covered so far include every chords that map to a JI chord of intervallic odd-limit 9. However there are some 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.
+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.
 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 610: / Line 614: @@
 When the added b5 is voiced an 8ve higher, it becomes a v#11, and suggests the downmajor7downsharp11 and downmajor9downsharp11 chords (both odd-limit 15). No need to omit the 3rd, it makes a pleasant M9 = 9/4 with the 11th.
 {| class="wikitable"
-!
+!chord type ---->
 !downadd7no5
 !downmaj7sus4
@@ Line 738: / Line 742: @@
 Another possible aug chord is 7:9:11 = up-downsharp5 = C^(v#5) = C ^E vG#. Unfortunately it's very difficult to finger.
-The updim7 and downdim7 chords are formed from stacked 6/5's and 7/6's, alternating to make 7/5's. The 7ths are rather dissonant. The updim7 chord has an innate Ruyoyo comma which equates its ^d7 = 42/25 to a M6 = 27/16. The downdim7 chord has an innate [[Mynucumic chords|Thuzozogu]] comma which equates vd7 = 49/30 with ~6 = 13/8.
+The updim7 and downdim7 chords are formed from stacked 6/5's and 7/6's, alternating to make 7/5's. The 7ths are rather dissonant. The updim7 chord has an innate Ruyoyo comma which equates its ^d7 = 42/25 to a M6 = 27/16. The downdim7 chord has an innate [[Mynucumic chords|Thuzozogu]] comma which equates vd7 = 49/30 with ~6 = 13/8. Thus its odd-limit and prime-limit are both 13.
 {| class="wikitable"
-!
+!chord -->
 !upaug
 !downaug
@@ Line 861: / Line 865: @@
 |(difficult)
 |}
+== Scale Shapes (downmajor tuning) ==
+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, use the one that agrees with the current chord.
+[[File:Scale chart 2.png|none|thumb]]
 == 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. Quite often the translated version sounds better, because it's so well tuned.