Kite Guitar originals: Difference between revisions

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A crash course for non-guitarists.
A crash course for non-guitarists.


===Notes and intervals ===
===Note names ===
The octave is divided into 41 equal steps, a tuning called 41-equal or 41edo or 41-ET or 41-TET. Whereas 12-equal has 100¢ steps, 41-equal has steps of 29.27¢. We can round this off to 30¢ for convenience, since a cent or two doesn't matter much in practice. This 30¢ interval is called an '''arrow''', because the little arrows by the noteheads raise or lower the pitch by 30¢. Notes are called '''up'''-E, '''down'''-F-sharp, etc., written ^E and vF#. A note that has no ups or downs is called '''plain'''. The 7 plain natural notes are close to 12-equal, but they do deviate slightly. The pattern is easy to see when the notes are arranged in chain-of-5ths order:
The octave is divided into 41 equal steps, a tuning called 41-equal or 41edo or 41-ET or 41-TET. Whereas 12-equal has 100¢ steps, 41-equal has steps of 29.27¢. We can round this off to 30¢ for convenience, since a cent or two doesn't matter much in practice. This 30¢ interval is called an '''arrow''', because the little arrows by the noteheads raise or lower the pitch by 30¢. Notes are called '''up'''-E, '''down'''-F-sharp, etc., written ^E and vF#. A note that has no ups or downs is called '''plain'''. The 7 plain natural notes are close to 12-equal, but they do deviate slightly. The pattern is easy to see when the notes are arranged in chain-of-5ths order:
{| class="wikitable center-all"
{| class="wikitable center-all"
Line 54: Line 54:
| style="width:40px;" |F#
| style="width:40px;" |F#
| style="width:40px;" |C#
| style="width:40px;" |C#
| style="width:40px;" | G#
| style="width:40px;" |G#
|-
|-
| -15¢
| -15¢
Line 66: Line 66:
| +5¢
| +5¢
| +7.5¢
| +7.5¢
| +10¢
| +10¢
| +12.5¢
| +12.5¢
| +15¢
| +15¢
|}
|}
Line 77: Line 77:
* C is -5¢, so vC is -35¢
* C is -5¢, so vC is -35¢


Intervals also use arrows. D is 0¢ and E is +5¢. This tells us that a major 2nd is 205¢, so an upmajor 2nd is 235¢. 
In the table above, D is the '''anchor note''' that agrees with standard tuning exactly. D is an ideal anchor because it makes the table symmetrical. But C, G, A and E have also been used.
 
These charts show the notes and intervals of 12-equal as a circle of 5ths.
[[File:12-edo circle with notes.png|left|thumb|400x400px]]
[[File:12-edo circle of 5ths.png|center|thumb|400x400px]]
 
 
 
 
But in 41-equal, G# ≠ Ab, the circle of fifths opens up into a spiral. Because this spiral is really a circle of 41 fifths, the innermost and outermost few notes are duplicates. In the 2nd chart, "-ish" means ±1 arrow.
[[File:41-edo spiral with notes and cents.png|left|thumb|400x400px]]
[[File:41-edo spiral.png|center|thumb|400x400px]]
 
 
 
 
In the tables and charts above, D is the '''anchor note''' that agrees with standard tuning exactly. D is an ideal anchor because it makes the table symmetrical. But C, G, A and E have also been used.  


Sometimes double arrows are needed. ^^C is called '''dup'''-C and vvC# is called '''dud'''-C-sharp (rhymes with cup and cud). Note that ^^C = vvC#. One more equivalence: ^^C = vDb. Thus 3 arrows = a minor 2nd. These equivalences are useful, because if you've already found vDb on your instrument, and you see ^^C or vvC# on the score, you know what to play.
Sometimes double arrows are needed. ^^C is called '''dup'''-C and vvC# is called '''dud'''-C-sharp (rhymes with cup and cud). Note that ^^C = vvC#. One more equivalence: ^^C = vDb. Thus 3 arrows = a minor 2nd. These equivalences are useful, because if you've already found vDb on your instrument, and you see ^^C or vvC# on the score, you know what to play.
 
{| class="wikitable left-3 center-all"
*1 arrow = half a fret = a quarter-sharp or quarter-flat
|+
*2 arrows = 1 fret = half a sharp/flat
!arrows
*3 arrows = 1.5 frets = a minor 2nd
!frets
* 4 arrows = 2 frets = 1 sharp/flat = an augmented unison
!interval
!equivalence
|-
|1
|half a fret
|a quarter-sharp/flat or a desc. dim 2nd
|^C = B#
|-
|2
| 1 fret
|half a sharp/flat
|^^C = vvC#
|-
|3
| 1.5 frets
|a minor 2nd
|^^^C = Db
|-
| 4
|2 frets
| 1 sharp/flat = an augmented unison
|^^^^C = C#
|}
Since a minor 2nd and an augmented unison add up to a major 2nd, there are 7 arrows from C to D. In this table, the plain notes are bolded.
Since a minor 2nd and an augmented unison add up to a major 2nd, there are 7 arrows from C to D. In this table, the plain notes are bolded.
{| class="wikitable center-all"
{| class="wikitable center-all"
Line 108: Line 114:
!2
!2
!3
!3
!4
! 4
!5
!5
!6
!6
Line 115: Line 121:
| style="width:75px;" |'''C'''
| style="width:75px;" |'''C'''
| style="width:75px;" |^C
| style="width:75px;" |^C
| style="width:75px;" | ^^C = vvC#
| style="width:75px;" |^^C = vvC#
| style="width:75px;" |vC#
| style="width:75px;" |vC#
| style="width:75px;" |'''C#'''
| style="width:75px;" |'''C#'''
Line 126: Line 132:
|vDb
|vDb
|'''Db'''
|'''Db'''
|^Db
| ^Db
|^^Db = vvD
| ^^Db = vvD
| vD
|vD
|'''D'''
|'''D'''
|}
|}
Line 134: Line 140:
The interval from C# to Db is a diminished 2nd. Since this interval is 0¢ in 12-equal, musicians don't think about it much. But in 41-equal, a diminished 2nd is actually -30¢, and a <u>descending</u> dim 2nd = 1 arrow.
The interval from C# to Db is a diminished 2nd. Since this interval is 0¢ in 12-equal, musicians don't think about it much. But in 41-equal, a diminished 2nd is actually -30¢, and a <u>descending</u> dim 2nd = 1 arrow.


So how exactly would a vocalist or violinist or trombonist tune a precise number of cents sharp or flat? It helps to borrow a Kite guitar and familiarize oneself with the sound of the various intervals. It also helps to understand just intonation. See the [https://kiteguitar.com/what-it-is/ "What it is -- long explanation"] page for an overview.
In 12-equal, there are 3 "versions" of a note, for example Db, D and D# (not counting the occasional Dbb or D##). In 41-equal, there are 15 versions, running from vvDb to ^^D# (counting ^^Db and vvD separately even though they are the same note, likewise with ^^D and vvD#).
{| class="wikitable right-all"
|^^Db
|^^D
|^^D#
|-
|^Db
|^D
| ^D#
|-
|Db
|D
|D#
|-
|vDb
|vD
|vD#
|-
|vvDb
|vvD
|vvD#
|}
So how exactly would a vocalist or violinist or trombonist tune a precise number of cents sharp or flat? It helps to borrow a Kite guitar and familiarize oneself with the sound of the various intervals. It also helps to understand just intonation. See the [https://kiteguitar.com/what-it-is/ "What it is -- long explanation"] page for an overview.  


In practice, use the ups and downs as a rough guide, then listen to the other parts and try to blend. For example, the downmajor 3rd from D to vF# is 380¢, very close to the just intonation 5/4 of 386¢. So one simply flattens the 12-equal F# until the interference beats go away. But wait, should the 3rd be 380¢ or 386¢? In general, deviating slightly from 41-equal is fine, if it makes the chord smoother. The just harmonic 7th is only 3¢ sharp of the 41-equal downminor 7th, so such deviation is even less of an issue.
In practice, use the ups and downs as a rough guide, then listen to the other parts and try to blend. For example, the downmajor 3rd from D to vF# is 380¢, very close to the just intonation 5/4 of 386¢. So to play vF# over a D, one simply flattens the 12-equal F# until the interference beats go away. But wait, should the 3rd be 380¢ or 386¢? In general, deviating slightly from 41-equal is fine, if it makes the chord smoother. The just harmonic 7th is only 3¢ sharp of the 41-equal downminor 7th, so such deviation is even less of an issue.


Of course, not all composers use simple JI ratios in their harmonies!   
Beware, not all composers use simple just intonation ratios in their harmonies!   
 
{| class="wikitable center-all"
This table lists all the notes and intervals. There are 7 versions of every scale degree. 3 major versions, 3 minor versions, and a '''mid''' version midway between major and minor (e.g. ~2). The 7 fourths overlap with the 7 fifths, making 4 tritones. There are only 3 versions of the octave. Just like the notes, most intervals have alternate names. A few are shown here, e.g. aug unisons and aug 5ths.
|+Reference table of 41-equal pitches
11 basic [[Ratio|frequency ratios]] are shown. There are 8 familiar ones that should "lock" right away, and 3 others (7/6, 7/5 and 7/4) that will lock with a little practice. There are many more ratios, enough to fill the whole column!
!
{| class="wikitable right-3 center-all"
!C anchor
!41-equal note
!G anchor
! colspan="2" |tuning
!D anchor
! colspan="4" |interval from D
!A anchor
!E anchor
!
|-
|'''C'''
|'''C +0¢'''
|'''C -2¢'''
|'''C -5¢'''
|'''C -7¢'''
|'''C -10¢'''
|'''C'''
|-
|^C
|C +29¢
|C +27¢
|C +24¢
|C +22¢
|C +20¢
|^C
|-
|^^C / vvC# / vDb
|C# -41¢
|C# -44¢
|C# -46¢
|C# -49¢
|C +49¢
|^^C / vvC# / vDb
|-
|vC# / Db
|C# -12¢
|C# -15¢
|C# -17¢
|C# -20¢
|C# -22¢
| vC# / Db
|-
|#C / ^Db
|C# +17¢
|C# +15¢
|C# +12¢
|C# +10¢
|C# +7¢
|#C / ^Db
|-
| ^C# / ^^Db / vvD
|C# +46¢
|C# +44¢
|C# +41¢
|C# +39¢
|C# +37¢
|^C# / ^^Db / vvD
|-
|vD
|D -24¢
|D -27¢
|D -29¢
|D -32¢
|D -34¢
|vD
|-
|-
|D
|'''D'''
|D
|'''D +5¢'''
| +0¢
|'''D +2¢'''
| rowspan="2" |1sns
|'''D +0¢'''
|P1
|'''D -2¢'''
|^d2
|'''D -5¢'''
|1/1
|'''D'''
|-
|-
|^D
|^D
|D
|D +34¢
| +29¢
|D +32¢
|^1
|D +29¢
|vvm2
|D +27¢
|
|D +24¢
|^D
|-
|-
| ^^D / vvD# / vEb
|Eb -37¢
|Eb -39¢
|Eb -41¢
|Eb -44¢
|Eb -46¢
|^^D / vvD# / vEb
|^^D / vvD# / vEb
|Eb
|  -41¢
| rowspan="7" |2nds
|vm2
|^^1 / vvA1
|
|-
|-
| vD# / Eb
|Eb -7¢
|Eb -10¢
|Eb -12¢
|Eb -15¢
|Eb -17¢
|vD# / Eb
|vD# / Eb
|Eb
|  -12¢
|m2
|vA1
|
|-
|-
| D# / ^Eb
|D# / ^Eb
|Eb
|Eb +22¢
| +17¢
|Eb +20¢
|^m2
|Eb +17¢
|A1
|Eb +15¢
|
|Eb +12¢
|D# / ^Eb
|-
|-
|^D# / ^^Eb / vvE
|^D# / ^^Eb / vvE
|Eb
|E -49¢
| +46¢
|Eb +49¢
|~2
|Eb +46¢
|^A1
|Eb +44¢
|
|Eb +41¢
|^D# / ^^Eb / vvE
|-
|-
|vE
|vE
|E
|E -20¢
| -24¢
|E -22¢
| vM2
|E -24¢
|
|E -27¢
|
|E -29¢
|vE
|-
|-
|E
|'''E'''
|E
|'''E +10¢'''
| +5¢
|'''E +7¢'''
| M2
|'''E +5¢'''
|
|'''E +2¢'''
|
|'''E +0¢'''
|'''E'''
|-
|-
|^E / vvF
|^E / vvF
|E
|E +39¢
| +34¢
|E +37¢
|^M2
|E +34¢
|
|E +32¢
|
|E +29¢
|^E / vvF
|-
|-
|^^E / vF
|^^E / vF
|F
|F -32¢
| -37¢
|F -34¢
| rowspan="7" |3rds
|F -37¢
|vm3
|F -39¢
|
|F -41¢
|7/6
|^^E / vF
|-
|-
|F
|'''F'''
| F
|'''F -2¢'''
| -7¢
|'''F -5¢'''
|m3
|'''F -7¢'''
|
|'''F -10¢'''
|
|'''F -12¢'''
|'''F'''
|-
|-
|^F
|^F
|F
|F +27¢
| +22¢
|F +24¢
|^m3
|F +22¢
|
|F +20¢
|6/5
|F +17¢
|^F
|-
|-
|^^F / vvF# / vGb
|^^F / vvF# / vGb
|F#
|F# -44¢
| -49¢
|F# -46¢
|~3
|F# -49¢
|
|F +49¢
|
|F +46¢
|^^F / vvF# / vGb
|-
|-
|vF# / Gb
|vF# / Gb
| F#
|F# -15¢
| -20¢
|F# -17¢
|vM3
|F# -20¢
|
|F# -22¢
|5/4
|F# -24¢
|vF# / Gb
|-
|-
|#F / ^Gb
|#F / ^Gb
|F#
|F# +15¢
| +10¢
|F# +12¢
|M3
|F# +10¢
|
|F# +7¢
|
|F# +5¢
|#F / ^Gb
|-
|-
|^F# / ^^Gb / vvG
|^F# / ^^Gb / vvG
|F#
|F# +44¢
| +39¢
|F# +41¢
|^M3
|F# +39¢
|
|F# +37¢
|
|F# +34¢
|^F# / ^^Gb / vvG
|-
|-
|vG
|vG
|G
|G -27¢
| -32¢
|G -29¢
| rowspan="3" |4ths
|G -32¢
|v4
|G -34¢
|
|G -37¢
|
|vG
|-
|-
| G
|'''G'''
|G
|'''G +2¢'''
| -2¢
|'''G +0¢'''
|P4
|'''G -2¢'''
|
|'''G -5¢'''
|4/3
|'''G -7¢'''
|'''G'''
|-
|-
|^G
|^G
| G
|G +32¢
| +27¢
|G +29¢
|^4
|G +27¢
|
|G +24¢
|
|G +22¢
|^G
|-
|-
|^^G / vvG# / vAb
|^^G / vvG# / vAb
| G#
|G# -39¢
| -44¢
|G# -41¢
| rowspan="4" |tritones
|G# -44¢
|~4 / vd5
|G# -46¢
|
|G# -49¢
|
|^^G / vvG# / vAb
|-
|-
|vG# / Ab
|vG# / Ab
|G#
|G# -10¢
| -15¢
|G# -12¢
|vA4 / d5
|G# -15¢
|
|G# -17¢
|7/5
|G# -20¢
|vG# / Ab
|-
|-
|#G / ^Ab
|#G / ^Ab
|G#
|G# +20¢
| +15¢
|G# +17¢
|A4 / ^d5
|G# +15¢
|
|G# +12¢
|
|G# +10¢
|#G / ^Ab
|-
|-
|^G# / ^^Ab / vvA
|^G# / ^^Ab / vvA
|G#
|G# +49¢
| +44¢
|G# +46¢
|^A4 / ~5
|G# +44¢
|
|G# +41¢
|
|G# +39¢
|^G# / ^^Ab / vvA
|-
|-
|vA
|vA
|A
|A -22¢
| -27¢
|A -24¢
| rowspan="3" |5ths
|A -27¢
|v5
|A -29¢
|
|A -32¢
|
|vA
|-
|-
|A
|'''A'''
|A
|'''A +7¢'''
| +2¢
|'''A +5¢'''
|P5
|'''A +2¢'''
|
|'''A +0¢'''
|3/2
|'''A -2¢'''
|'''A'''
|-
|-
|^A
|^A
|A
|A +37¢
| +32¢
|A +34¢
|^5
|A +32¢
|
|A +29¢
|
|A +27¢
|^A
|-
|-
|^^A / vvA# / vBb
|^^A / vvA# / vBb
|Bb
|Bb -34¢
| -39¢
|Bb -37¢
| rowspan="7" |6ths
|Bb -39¢
|vm6
|Bb -41¢
|^^5 / vvA5
|Bb -44¢
|
|^^A / vvA# / vBb
|-
|-
| vA# / Bb
|Bb -5¢
|Bb -7¢
|Bb -10¢
|Bb -12¢
|Bb -15¢
|vA# / Bb
|vA# / Bb
|Bb
|  -10¢
|m6
|vA5
|
|-
|-
|A# / ^Bb
|A# / ^Bb
|Bb
|Bb +24¢
| +20¢
|Bb +22¢
|^m6
|Bb +20¢
|A5
|Bb +17¢
|8/5
|Bb +15¢
|A# / ^Bb
|-
|-
|^A# / ^^Bb / vvB
|^A# / ^^Bb / vvB
|Bb
|B -46¢
| +49¢
|B -49¢
|~6
|Bb +49¢
|^A5
|Bb +46¢
|
|Bb +44¢
| ^A# / ^^Bb / vvB
|-
|-
|vB
|vB
|B
|B -17¢
| -22¢
|B -20¢
|vM6
|B -22¢
|
|B -24¢
|5/3
|B -27¢
|vB
|-
|-
| B
|'''B'''
|B
|'''B +12¢'''
| +7¢
|'''B +10¢'''
|M6
|'''B +7¢'''
|
|'''B +5¢'''
|
|'''B +2¢'''
|'''B'''
|-
|-
|^B / vvC
|^B / vvC
|B
|B +41¢
| +37¢
|B +39¢
| ^M6
|B +37¢
|
|B +34¢
|
|B +32¢
|^B / vvC
|-
|-
|^^B / vC
|^^B / vC
|C
|C -29¢
| -34¢
|C -32¢
| rowspan="7" |7ths
|C -34¢
|vm7
|C -37¢
|
|C -39¢
|7/4
|^^B / vC
|-
|-
|C
|'''C'''
|C
|'''C +0¢'''
| -5¢
|'''C -2¢'''
|m7
|'''C -5¢'''
|
|'''C -7¢'''
|
|'''C -10¢'''
|'''C'''
|-
|-
|^C
!
|C
!C anchor
|  +24¢
!G anchor
|^m7
!D anchor
|
!A anchor
|
!E anchor
|-
!
|^^C / vvC# / vDb
|C#
|  -46¢
| ~7
|
|
|-
|vC# / Db
|C#
|  -17¢
|vM7
|
|
|-
|#C / ^Db
|C#
|  +12¢
|M7
|
|
|-
|^C# / ^^Db / vvD
|C#
|  +41¢
|^M7
|
|
|-
|vD
|D
|  -29¢
| rowspan="2" |8ves
|v8
|
|
|-
|D
|D
|  +0¢
|P8
|
| 2/1
|}
|}
See also: [[Ups and downs notation]]  
See also: [[Ups and downs notation]]  
Line 454: Line 525:
Any scale without arrows is just as one would expect. D minor is still D E F G A Bb C D. Adding up or down to the scale name alters the <u>3rd, 6th and 7th</u>. Thus D upminor is D E ^F G A ^Bb ^C D. If the tonic has an arrow, it's added to every note: vD upminor = vD vE F vG vA Bb C vD.  
Any scale without arrows is just as one would expect. D minor is still D E F G A Bb C D. Adding up or down to the scale name alters the <u>3rd, 6th and 7th</u>. Thus D upminor is D E ^F G A ^Bb ^C D. If the tonic has an arrow, it's added to every note: vD upminor = vD vE F vG vA Bb C vD.  


The key signature is divided into two regions. The sharp/flat region is as usual, except it can also have double-sharps or double-flats (e.g. Db minor has Bbb). The arrow region consists of up to two stacks, a '''quadruple stack''' for the tonic, 2nd 4th and 5th, and a '''triple stack''' for the 3rd, 6th and 7th. Both stacks always have the exact same shape. The lowest arrow in the quadruple stack always indicates the tonic. The triple stack's lowest arrow indicates the 3rd, and its highest arrow indicates the 7th. Thus it's quite easy to deduce the tonic. Note that C downmajor and vA upminor have different key signatures.
The key signature is divided into two regions. The sharp/flat region is as usual, except it can also have double-sharps or double-flats (e.g. Db minor has Bbb). The arrow region consists of up to two stacks, a '''quadruple stack''' for the tonic, 2nd 4th and 5th, and/or a '''triple stack''' for the 3rd, 6th and 7th.  
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 462: Line 533:
!down-D
!down-D
|-
|-
!major
! major
|[[File:D major.png|frameless|137x137px]]
|[[File:D major.png|frameless|137x137px]]
D E F# G A B C# D
D E F# G A B C# D
Line 470: Line 541:
vD vE vF# vG vA vB vC# vD
vD vE vF# vG vA vB vC# vD
|-
|-
!downmajor
! downmajor
|[[File:D downmajor.png|frameless|137x137px]]
|[[File:D downmajor.png|frameless|137x137px]]
D E vF# G A vB vC# D
D E vF# G A vB vC# D
Line 495: Line 566:
|}
|}
Upmajor and downminor work similarly.
Upmajor and downminor work similarly.
Both stacks always have the exact same shape. The only differences are whether the arrows point up or down, and whether they are single or double. The lowest arrow in the quadruple stack always indicates the tonic. The triple stack's lowest arrow indicates the 3rd, and its highest arrow indicates the 7th. Thus it's quite easy to deduce the tonic. Note that C downmajor and vA upminor have slightly different key signatures. The former has plain D and the latter has down D.


See also: [[Kite's Thoughts on 41edo Note Names and Key Signatures]]
See also: [[Kite's Thoughts on 41edo Note Names and Key Signatures]]


=== Cancelling rules===
===Cancelling rules===
Arrows behave just like accidentals. If a middle-C on the score has an up, any middle-Cs following it in the same measure inherit that up. Any C in another octave does not. If an up-C is followed by a down-C, the down-arrow cancels the up-arrow.
Arrows behave just like accidentals. If a middle-C on the score has an up, any middle-Cs following it in the same measure inherit that up. Any C in another octave does not. If an up-C is followed by a down-C, the down-arrow cancels the up-arrow.


Line 531: Line 604:
|^^<big>♮</big>
|^^<big>♮</big>
|#
|#
| ^#
|^#
|^^#
|^^#
|-
|-
Line 538: Line 611:
|^<big>♮</big>
|^<big>♮</big>
|
|
|#
| #
|^#
|^#
|^^#
|^^#
Line 545: Line 618:
|<big>♮</big>
|<big>♮</big>
|^<big>♮</big>
|^<big>♮</big>
| ^^<big>♮</big>
|^^<big>♮</big>
|
|
|^#
|^#
Line 562: Line 635:
|^<big>♮</big>
|^<big>♮</big>
|^^<big>♮</big>
|^^<big>♮</big>
|#
| #
|^#
|^#
|
|
Line 581: Line 654:
!^^C#
!^^C#
|-
|-
!C
! C
|
|
|^
|^
|^^
|^^
|#
| #
|^#
| ^#
|^^#
|^^#
|-
|-
Line 599: Line 672:
!^^C
!^^C
|<big>♮</big>
|<big>♮</big>
|^
| ^
|
|
|#
|#
Line 607: Line 680:
!C#
!C#
|<big>♮</big>
|<big>♮</big>
|^<big>♮</big>
| ^<big>♮</big>
|^^<big>♮</big>
|^^<big>♮</big>
|
|
Line 613: Line 686:
|^^
|^^
|-
|-
!^C#
! ^C#
|<big>♮</big>
|<big>♮</big>
|^<big>♮</big>
|^<big>♮</big>
Line 629: Line 702:
|
|
|}
|}
A 3rd approach has arrows and accidentals behave independently of each other, and not cancel each other. This approach is always indicated at the top of the score. Consider these 15 versions of D:
A 3rd approach has arrows and accidentals behave independently of each other, and not cancel each other. This approach is always indicated at the top of the score. Remember the 15 versions of D?
{| class="wikitable"
{| class="wikitable right-all"
|+
|+
| ^^Db
|^^Db
|^^D
|^^D
| ^^D#
| ^^D#
|-
|-
| ^Db
|^Db
|^D
|^D
|^D#
|^D#
Line 648: Line 721:
|vD#
|vD#
|-
|-
|vvDb
| vvDb
|vvD
|vvD
|vvD#
| vvD#
|}
|}
Adding an accidental moves you sideways. Adding an arrow moves you up or down. Thus a sharpened D followed by a downed D is vD#. This approach requires the '''plain sign''' ◇ (mnemonic: it looks like an up and a down fused together), which is analogous to a natural sign.  
Adding an accidental moves you sideways. Adding an arrow moves you up or down. Thus a sharpened D followed by a downed D is vD#. This approach requires the '''plain sign''' ◇ (mnemonic: it looks like an up and a down fused together), which is analogous to a natural sign.  
Line 663: Line 736:
!^C
!^C
!^^C
!^^C
!C#
! C#
!^C#
!^C#
!^^C#
!^^C#
Line 675: Line 748:
|^^#
|^^#
|-
|-
!^C
! ^C
| ◇
| ◇
|
|
Line 688: Line 761:
|
|
|◇#
|◇#
| ^#
|^#
|#
|#
|-
|-
! C#
!C#
|<big>♮</big>
|<big>♮</big>
| ^<big>♮</big>
|^<big>♮</big>
|^^<big>♮</big>
|^^<big>♮</big>
|
|
|^
|^
| ^^
|^^
|-
|-
!^C#
!^C#
Line 703: Line 776:
|<big>♮</big>
|<big>♮</big>
|^^<big>♮</big>
|^^<big>♮</big>
| ◇
|◇
|
|
|^^
|^^
Line 718: Line 791:


See also: [[Kite's Thoughts on 41edo Note Names and Key Signatures]]
See also: [[Kite's Thoughts on 41edo Note Names and Key Signatures]]
===Interval names===
Intervals also use arrows. If D is 0¢ and E is +5¢, a major 2nd is 205¢, so an upmajor 2nd must be about 235¢.
This table lists all the intervals. There are 7 versions of every scale degree: 3 major versions, 3 minor versions, and a '''mid''' version midway between major and minor (e.g. ~2). The 7 fourths overlap with the 7 fifths, making 4 tritones. There are only 3 versions of the octave. Just like the notes, most intervals have alternate names. A few are shown here, e.g. aug unisons and aug 5ths.
11 basic [[Ratio|frequency ratios]] are shown. There are 8 familiar ones that should "lock" right away, and 3 others (7/6, 7/5 and 7/4) that will lock with a little practice. "7/6 -3¢" means that the downminor 3rd is 3¢ flat of 7/6, and one should <u>sharpen</u> it by 3¢ to tune it exactly. There are many more ratios, enough to fill the whole column!
{| class="wikitable center-all"
!
!cents
!ratio
!degree
! colspan="2" |name
! colspan="2" |alternate name
|-
|0
|0¢
|1/1
| rowspan="2" |1sns
|P1
|perfect 1sn
|^d2
|updim 2nd
|-
|1
|29
|
|^1
|aug 1sn
|vvm2
|dudminor 2nd
|-
|2
|59
|
| rowspan="7" |2nds
|vm2
|downminor 2nd
|^^1 / vvA1
|dup 1sn
|-
|3
|88
|
|m2
|minor 2nd
|vA1
|downaug 1sn
|-
|4
|117
|
|^m2
|upminor 2nd
|A1
|aug 1sn
|-
|5
|146
|
|~2
|mid 2nd
|^A1
|upaug 1sn
|-
|6
|176
|
|vM2
|downmajor 2nd
|
|
|-
|7
|205
|
|M2
|major 2nd
|
|
|-
|8
|234
|
|^M2
|upmajor 2nd
|
|
|-
|9
|263
|'''7/6 -3¢'''
| rowspan="7" |3rds
|vm3
|downminor 3rd
|
|
|-
|10
|293
|
|m3
|minor 3rd
|
|
|-
|11
|322
|6/5 +6¢
|^m3
|upminor 3rd
|
|
|-
|12
|351
|
|~3
|mid 3rd
|
|
|-
|13
|380
|5/4 -6¢
|vM3
|downmajor 3rd
|
|
|-
|14
|410
|
|M3
|major 3rd
|
|
|-
|15
|439
|
|^M3
|upmajor 3rd
|
|
|-
|16
|468
|
| rowspan="3" |4ths
|v4
|down 4th
|
|
|-
|17
|498
|4/3
|P4
|perfect 4th
|
|
|-
|18
|527
|
|^4
|up 4th
|
|
|-
|19
|556
|
| rowspan="4" |tritones
|~4
|mid 4th
|vd5
|downdim 5th
|-
|20
|585
|'''7/5 +3¢'''
|vA4
|downaug 4th
|d5
|dim 5th
|-
|21
|615
|
|A4
|aug 4th
|^d5
|updim 5th
|-
|22
|644
|
|^A4
|upaug 4th
|~5
|mid 5th
|-
|23
|673
|
| rowspan="3" |5ths
|v5
|down 5th
|
|
|-
|24
|702
|3/2
|P5
|perfect 5th
|
|
|-
|25
|732
|
|^5
|up 5th
|
|
|-
|26
|761
|
| rowspan="7" |6ths
|vm6
|downminor 6th
|^^5 / vvA5
|dup 5th
|-
|27
|790
|
|m6
|minor 6th
|vA5
|downaug 5th
|-
|28
|820
|8/5 +6¢
|^m6
|upminor 6th
|A5
|aug 5th
|-
|29
|849
|
|~6
|mid 6th
|^A5
|upaug 5th
|-
|30
|878
|5/3 -6¢
|vM6
|downmajor 6th
|
|
|-
|31
|907
|
|M6
|major 6th
|
|
|-
|32
|937
|
|^M6
|upmajor 6th
|
|
|-
|33
|966
|'''7/4 -3¢'''
| rowspan="7" |7ths
|vm7
|downminor 7th
|
|
|-
|34
|995
|
|m7
|minor 7th
|
|
|-
|35
|1024
|
|^m7
|upminor 7th
|
|
|-
|36
|1054
|
|~7
|mid 7th
|
|
|-
|37
|1083
|
|vM7
|downmajor 7th
|
|
|-
|38
|1112
|
|M7
|major 7th
|
|
|-
|39
|1141
|
|^M7
|upmajor 7th
|
|
|-
|40
|1171
|
| rowspan="2" |8ves
|v8
|down 8ve
|
|
|-
|41
|1200
|2/1
|P8
|8ve
|
|
|}
===Chord names===
===Chord names===
Any chord name without arrows is as expected. Cm7 is still C Eb G Bb. But in practice most chords have arrows in them. An arrow between the chord root and the chord type (e.g. C^m7) raises or lowers the 3rd, and also the 6th, 7th or 11th, if present. Thus C down-seven is the usual C7 chord with the 3rd and 7th downed: Cv7 = C vE G vBb. Mnemonic: every other note of a stacked-3rds chord with a 6th below the root is affected: '''6th''' - root - '''3rd''' - 5th - '''7th''' - 9th - '''11th''' - 13th. Note that the 6th is affected, but the 13th is not.  
Any chord name without arrows is as expected. Cm7 is still C Eb G Bb. But in practice most chords have arrows in them. An arrow between the chord root and the chord type (e.g. C^m7) raises or lowers the 3rd, and also the 6th, 7th or 11th, if present. Thus C down-seven is the usual C7 chord with the 3rd and 7th downed: Cv7 = C vE G vBb. Mnemonic: every other note of a stacked-3rds chord with a 6th below the root is affected: '''6th''' - root - '''3rd''' - 5th - '''7th''' - 9th - '''11th''' - 13th. Note that the 6th is affected, but the 13th is not.  
Line 733: Line 1,166:
*[[41edo Chord Names]]
*[[41edo Chord Names]]
*[[Kite Guitar Chord Shapes (downmajor tuning)]]
*[[Kite Guitar Chord Shapes (downmajor tuning)]]
===The circle of fifths===
These charts show the notes and intervals of 12-equal as a circle of 5ths.[[File:12-edo circle with notes.png|left|thumb|400x400px]]
[[File:12-edo circle of 5ths.png|center|thumb|400x400px]]
But in 41-equal, G# ≠ Ab, the circle of fifths opens up into a spiral. Because this spiral is really a circle of 41 fifths, the innermost and outermost few notes are duplicates. In the 2nd chart, "-ish" means ±1 arrow.
[[File:41-edo spiral with notes and cents.png|left|thumb|400x400px]]
[[File:41-edo spiral.png|center|thumb|400x400px]]


[[Category:Kite Guitar]]
[[Category:Kite Guitar]]
[[Category:Guitar]]
[[Category:Guitar]]
[[Category:41edo]]
[[Category:41edo]]

Revision as of 11:40, 18 May 2023

The following songs have been composed for the Kite Guitar. To search for a certain song, artist or translator, use control-F in your browser. All tabs are for a guitar tuned in downmajor 3rds, unless otherwise noted. See Kite Guitar Chord Shapes (downmajor tuning) for reference on fingerings, inversions, etc.

Actual compositions are on separate xenwiki pages, grouped by composer. if you have any compositions, feel free to create your own page and link to it here! To keep this page current, please copy the table of contents from your page and paste it here (see this page for help).


By Kite Giedraitis

Main article: Kite Guitar Originals by Kite Giedraitis

By Praveen Venkataramana

Main article: Kite Guitar Originals by Praveen Venkataramana

How to read the scores

A crash course for non-guitarists.

Note names

The octave is divided into 41 equal steps, a tuning called 41-equal or 41edo or 41-ET or 41-TET. Whereas 12-equal has 100¢ steps, 41-equal has steps of 29.27¢. We can round this off to 30¢ for convenience, since a cent or two doesn't matter much in practice. This 30¢ interval is called an arrow, because the little arrows by the noteheads raise or lower the pitch by 30¢. Notes are called up-E, down-F-sharp, etc., written ^E and vF#. A note that has no ups or downs is called plain. The 7 plain natural notes are close to 12-equal, but they do deviate slightly. The pattern is easy to see when the notes are arranged in chain-of-5ths order:

Ab Eb Bb F C G D A E B F# C# G#
-15¢ -12.5¢ -10¢ -7.5¢ -5¢ -2.5¢ 0¢ +2.5¢ +5¢ +7.5¢ +10¢ +12.5¢ +15¢

All the notes with sharps are extra-sharp. All the notes with flats are extra-flat. Note that G# is sharper than Ab by one arrow. Thus G# is also ^Ab, and Ab is also vG#. (Likewise C# = ^Db, vD# = Eb, etc.)

Let's use that 30¢ figure to find some pitches.

  • D is 0¢, so ^D is 30¢ sharp and vD is 30¢ flat
  • Bb is -10¢, so ^Bb is +20¢
  • C is -5¢, so vC is -35¢

In the table above, D is the anchor note that agrees with standard tuning exactly. D is an ideal anchor because it makes the table symmetrical. But C, G, A and E have also been used.

Sometimes double arrows are needed. ^^C is called dup-C and vvC# is called dud-C-sharp (rhymes with cup and cud). Note that ^^C = vvC#. One more equivalence: ^^C = vDb. Thus 3 arrows = a minor 2nd. These equivalences are useful, because if you've already found vDb on your instrument, and you see ^^C or vvC# on the score, you know what to play.

arrows frets interval equivalence
1 half a fret a quarter-sharp/flat or a desc. dim 2nd ^C = B#
2 1 fret half a sharp/flat ^^C = vvC#
3 1.5 frets a minor 2nd ^^^C = Db
4 2 frets 1 sharp/flat = an augmented unison ^^^^C = C#

Since a minor 2nd and an augmented unison add up to a major 2nd, there are 7 arrows from C to D. In this table, the plain notes are bolded.

0 1 2 3 4 5 6 7
C ^C ^^C = vvC# vC# C# ^C# ^^C#
vvDb vDb Db ^Db ^^Db = vvD vD D

The interval from C# to Db is a diminished 2nd. Since this interval is 0¢ in 12-equal, musicians don't think about it much. But in 41-equal, a diminished 2nd is actually -30¢, and a descending dim 2nd = 1 arrow.

In 12-equal, there are 3 "versions" of a note, for example Db, D and D# (not counting the occasional Dbb or D##). In 41-equal, there are 15 versions, running from vvDb to ^^D# (counting ^^Db and vvD separately even though they are the same note, likewise with ^^D and vvD#).

^^Db ^^D ^^D#
^Db ^D ^D#
Db D D#
vDb vD vD#
vvDb vvD vvD#

So how exactly would a vocalist or violinist or trombonist tune a precise number of cents sharp or flat? It helps to borrow a Kite guitar and familiarize oneself with the sound of the various intervals. It also helps to understand just intonation. See the "What it is -- long explanation" page for an overview.

In practice, use the ups and downs as a rough guide, then listen to the other parts and try to blend. For example, the downmajor 3rd from D to vF# is 380¢, very close to the just intonation 5/4 of 386¢. So to play vF# over a D, one simply flattens the 12-equal F# until the interference beats go away. But wait, should the 3rd be 380¢ or 386¢? In general, deviating slightly from 41-equal is fine, if it makes the chord smoother. The just harmonic 7th is only 3¢ sharp of the 41-equal downminor 7th, so such deviation is even less of an issue.

Beware, not all composers use simple just intonation ratios in their harmonies!

Reference table of 41-equal pitches
C anchor G anchor D anchor A anchor E anchor
C C +0¢ C -2¢ C -5¢ C -7¢ C -10¢ C
^C C +29¢ C +27¢ C +24¢ C +22¢ C +20¢ ^C
^^C / vvC# / vDb C# -41¢ C# -44¢ C# -46¢ C# -49¢ C +49¢ ^^C / vvC# / vDb
vC# / Db C# -12¢ C# -15¢ C# -17¢ C# -20¢ C# -22¢ vC# / Db
#C / ^Db C# +17¢ C# +15¢ C# +12¢ C# +10¢ C# +7¢ #C / ^Db
^C# / ^^Db / vvD C# +46¢ C# +44¢ C# +41¢ C# +39¢ C# +37¢ ^C# / ^^Db / vvD
vD D -24¢ D -27¢ D -29¢ D -32¢ D -34¢ vD
D D +5¢ D +2¢ D +0¢ D -2¢ D -5¢ D
^D D +34¢ D +32¢ D +29¢ D +27¢ D +24¢ ^D
^^D / vvD# / vEb Eb -37¢ Eb -39¢ Eb -41¢ Eb -44¢ Eb -46¢ ^^D / vvD# / vEb
vD# / Eb Eb -7¢ Eb -10¢ Eb -12¢ Eb -15¢ Eb -17¢ vD# / Eb
D# / ^Eb Eb +22¢ Eb +20¢ Eb +17¢ Eb +15¢ Eb +12¢ D# / ^Eb
^D# / ^^Eb / vvE E -49¢ Eb +49¢ Eb +46¢ Eb +44¢ Eb +41¢ ^D# / ^^Eb / vvE
vE E -20¢ E -22¢ E -24¢ E -27¢ E -29¢ vE
E E +10¢ E +7¢ E +5¢ E +2¢ E +0¢ E
^E / vvF E +39¢ E +37¢ E +34¢ E +32¢ E +29¢ ^E / vvF
^^E / vF F -32¢ F -34¢ F -37¢ F -39¢ F -41¢ ^^E / vF
F F -2¢ F -5¢ F -7¢ F -10¢ F -12¢ F
^F F +27¢ F +24¢ F +22¢ F +20¢ F +17¢ ^F
^^F / vvF# / vGb F# -44¢ F# -46¢ F# -49¢ F +49¢ F +46¢ ^^F / vvF# / vGb
vF# / Gb F# -15¢ F# -17¢ F# -20¢ F# -22¢ F# -24¢ vF# / Gb
#F / ^Gb F# +15¢ F# +12¢ F# +10¢ F# +7¢ F# +5¢ #F / ^Gb
^F# / ^^Gb / vvG F# +44¢ F# +41¢ F# +39¢ F# +37¢ F# +34¢ ^F# / ^^Gb / vvG
vG G -27¢ G -29¢ G -32¢ G -34¢ G -37¢ vG
G G +2¢ G +0¢ G -2¢ G -5¢ G -7¢ G
^G G +32¢ G +29¢ G +27¢ G +24¢ G +22¢ ^G
^^G / vvG# / vAb G# -39¢ G# -41¢ G# -44¢ G# -46¢ G# -49¢ ^^G / vvG# / vAb
vG# / Ab G# -10¢ G# -12¢ G# -15¢ G# -17¢ G# -20¢ vG# / Ab
#G / ^Ab G# +20¢ G# +17¢ G# +15¢ G# +12¢ G# +10¢ #G / ^Ab
^G# / ^^Ab / vvA G# +49¢ G# +46¢ G# +44¢ G# +41¢ G# +39¢ ^G# / ^^Ab / vvA
vA A -22¢ A -24¢ A -27¢ A -29¢ A -32¢ vA
A A +7¢ A +5¢ A +2¢ A +0¢ A -2¢ A
^A A +37¢ A +34¢ A +32¢ A +29¢ A +27¢ ^A
^^A / vvA# / vBb Bb -34¢ Bb -37¢ Bb -39¢ Bb -41¢ Bb -44¢ ^^A / vvA# / vBb
vA# / Bb Bb -5¢ Bb -7¢ Bb -10¢ Bb -12¢ Bb -15¢ vA# / Bb
A# / ^Bb Bb +24¢ Bb +22¢ Bb +20¢ Bb +17¢ Bb +15¢ A# / ^Bb
^A# / ^^Bb / vvB B -46¢ B -49¢ Bb +49¢ Bb +46¢ Bb +44¢ ^A# / ^^Bb / vvB
vB B -17¢ B -20¢ B -22¢ B -24¢ B -27¢ vB
B B +12¢ B +10¢ B +7¢ B +5¢ B +2¢ B
^B / vvC B +41¢ B +39¢ B +37¢ B +34¢ B +32¢ ^B / vvC
^^B / vC C -29¢ C -32¢ C -34¢ C -37¢ C -39¢ ^^B / vC
C C +0¢ C -2¢ C -5¢ C -7¢ C -10¢ C
C anchor G anchor D anchor A anchor E anchor

See also: Ups and downs notation

Scales and key signatures

Any scale without arrows is just as one would expect. D minor is still D E F G A Bb C D. Adding up or down to the scale name alters the 3rd, 6th and 7th. Thus D upminor is D E ^F G A ^Bb ^C D. If the tonic has an arrow, it's added to every note: vD upminor = vD vE F vG vA Bb C vD.

The key signature is divided into two regions. The sharp/flat region is as usual, except it can also have double-sharps or double-flats (e.g. Db minor has Bbb). The arrow region consists of up to two stacks, a quadruple stack for the tonic, 2nd 4th and 5th, and/or a triple stack for the 3rd, 6th and 7th.

D up-D down-D
major

D E F# G A B C# D

^D ^E ^F# ^G ^A ^B ^C# ^D

vD vE vF# vG vA vB vC# vD

downmajor

D E vF# G A vB vC# D

^D ^E F# ^G ^A B C# ^D

vD vE vvF# vG vA vvB vvC# vD

minor

D E F G A Bb C D

^D ^E ^F ^G ^A ^Bb ^C ^D

vD vE vF vG vA vBb vC vD

upminor

D E ^F G A ^Bb ^C D

^D ^E ^^F ^G ^A ^^Bb ^^C ^D

vD vE F vG vA Bb C vD

Upmajor and downminor work similarly.

Both stacks always have the exact same shape. The only differences are whether the arrows point up or down, and whether they are single or double. The lowest arrow in the quadruple stack always indicates the tonic. The triple stack's lowest arrow indicates the 3rd, and its highest arrow indicates the 7th. Thus it's quite easy to deduce the tonic. Note that C downmajor and vA upminor have slightly different key signatures. The former has plain D and the latter has down D.

See also: Kite's Thoughts on 41edo Note Names and Key Signatures

Cancelling rules

Arrows behave just like accidentals. If a middle-C on the score has an up, any middle-Cs following it in the same measure inherit that up. Any C in another octave does not. If an up-C is followed by a down-C, the down-arrow cancels the up-arrow.

But what happens when accidentals are mixed with arrows? What if the key signature makes that upped C be sharp? Or what if there is a C with a sharp just before the upped C? Does the up-arrow override or "cancel" the sharp? And what if an upped C is followed by a sharpened C?

There are several possible ways to handle this issue. The default is the simplest way, to explicitly specify both arrows and accidentals every time. Thus any accidental or arrow cancels any previous ones.

explicit accidentals & arrows
start with

this

turn it into this
C ^C ^^C C# ^C# ^^C#
C ^♮ ^^♮ # ^# ^^#
^C ♮ ^^♮ # ^# ^^#
^^C ♮ ^♮ # ^# ^^#
C# ♮ ^♮ ^^♮ ^# ^^#
^C# ♮ ^♮ ^^♮ # ^^#
^^C# ♮ ^♮ ^^♮ # ^#

Another approach allows arrows to appear alone. Accidentals cancel arrows, but arrows don't cancel accidentals.

accidentals cancels arrows
start with

this

turn it into this
C ^C ^^C C# ^C# ^^C#
C ^ ^^ # ^# ^^#
^C ♮ ^^ # ^# ^^#
^^C ♮ ^ # ^# ^^#
C# ♮ ^♮ ^^♮ ^ ^^
^C# ♮ ^♮ ^^♮ # ^^
^^C# ♮ ^♮ ^^♮ # ^

A 3rd approach has arrows and accidentals behave independently of each other, and not cancel each other. This approach is always indicated at the top of the score. Remember the 15 versions of D?

^^Db ^^D ^^D#
^Db ^D ^D#
Db D D#
vDb vD vD#
vvDb vvD vvD#

Adding an accidental moves you sideways. Adding an arrow moves you up or down. Thus a sharpened D followed by a downed D is vD#. This approach requires the plain sign ◇ (mnemonic: it looks like an up and a down fused together), which is analogous to a natural sign.

no cancellations
start with

this

turn it into this
C ^C ^^C C# ^C# ^^C#
C ^ ^^ # ^# ^^#
^C ◇ ^^ ◇# # ^^#
^^C ◇ ^ ◇# ^# #
C# ♮ ^♮ ^^♮ ^ ^^
^C# ◇♮ ♮ ^^♮ ◇ ^^
^^C# ◇♮ ^♮ ♮ ◇ ^

This approach often minimizes clutter greatly because of how 41edo works. The key of D downmajor has vC#. Of all the various C-naturals, often the most likely one is vC.

See also: Kite's Thoughts on 41edo Note Names and Key Signatures

Interval names

Intervals also use arrows. If D is 0¢ and E is +5¢, a major 2nd is 205¢, so an upmajor 2nd must be about 235¢.

This table lists all the intervals. There are 7 versions of every scale degree: 3 major versions, 3 minor versions, and a mid version midway between major and minor (e.g. ~2). The 7 fourths overlap with the 7 fifths, making 4 tritones. There are only 3 versions of the octave. Just like the notes, most intervals have alternate names. A few are shown here, e.g. aug unisons and aug 5ths.

11 basic frequency ratios are shown. There are 8 familiar ones that should "lock" right away, and 3 others (7/6, 7/5 and 7/4) that will lock with a little practice. "7/6 -3¢" means that the downminor 3rd is 3¢ flat of 7/6, and one should sharpen it by 3¢ to tune it exactly. There are many more ratios, enough to fill the whole column!

cents ratio degree name alternate name
0 0¢ 1/1 1sns P1 perfect 1sn ^d2 updim 2nd
1 29 ^1 aug 1sn vvm2 dudminor 2nd
2 59 2nds vm2 downminor 2nd ^^1 / vvA1 dup 1sn
3 88 m2 minor 2nd vA1 downaug 1sn
4 117 ^m2 upminor 2nd A1 aug 1sn
5 146 ~2 mid 2nd ^A1 upaug 1sn
6 176 vM2 downmajor 2nd
7 205 M2 major 2nd
8 234 ^M2 upmajor 2nd
9 263 7/6 -3¢ 3rds vm3 downminor 3rd
10 293 m3 minor 3rd
11 322 6/5 +6¢ ^m3 upminor 3rd
12 351 ~3 mid 3rd
13 380 5/4 -6¢ vM3 downmajor 3rd
14 410 M3 major 3rd
15 439 ^M3 upmajor 3rd
16 468 4ths v4 down 4th
17 498 4/3 P4 perfect 4th
18 527 ^4 up 4th
19 556 tritones ~4 mid 4th vd5 downdim 5th
20 585 7/5 +3¢ vA4 downaug 4th d5 dim 5th
21 615 A4 aug 4th ^d5 updim 5th
22 644 ^A4 upaug 4th ~5 mid 5th
23 673 5ths v5 down 5th
24 702 3/2 P5 perfect 5th
25 732 ^5 up 5th
26 761 6ths vm6 downminor 6th ^^5 / vvA5 dup 5th
27 790 m6 minor 6th vA5 downaug 5th
28 820 8/5 +6¢ ^m6 upminor 6th A5 aug 5th
29 849 ~6 mid 6th ^A5 upaug 5th
30 878 5/3 -6¢ vM6 downmajor 6th
31 907 M6 major 6th
32 937 ^M6 upmajor 6th
33 966 7/4 -3¢ 7ths vm7 downminor 7th
34 995 m7 minor 7th
35 1024 ^m7 upminor 7th
36 1054 ~7 mid 7th
37 1083 vM7 downmajor 7th
38 1112 M7 major 7th
39 1141 ^M7 upmajor 7th
40 1171 8ves v8 down 8ve
41 1200 2/1 P8 8ve

Chord names

Any chord name without arrows is as expected. Cm7 is still C Eb G Bb. But in practice most chords have arrows in them. An arrow between the chord root and the chord type (e.g. C^m7) raises or lowers the 3rd, and also the 6th, 7th or 11th, if present. Thus C down-seven is the usual C7 chord with the 3rd and 7th downed: Cv7 = C vE G vBb. Mnemonic: every other note of a stacked-3rds chord with a 6th below the root is affected: 6th - root - 3rd - 5th - 7th - 9th - 11th - 13th. Note that the 6th is affected, but the 13th is not.

If the 3rd is downed but the minor 7th is not, the chord is named C-down add7, written Cv,7. The comma before the 7 means "add".

Analogous to M and m, "a" means augmented and "d" means diminished. Thus C^a = C ^E G# and Bvd7 = B vD F vAb. Half-diminished chords are named as dim add7 chords. For example, C ^Eb Gb ^Bb is C updim up-7, written C^d^7.

Alterations are enclosed in parentheses, additions never are. For example Cv(vv#5) is C vE vvG#.

Chord roots often have arrows. The arrows add up and cancel out as expected. Thus vA^m = vA C vE, and vAvm = vA vvC vE.

See also:

The circle of fifths

These charts show the notes and intervals of 12-equal as a circle of 5ths.



But in 41-equal, G# ≠ Ab, the circle of fifths opens up into a spiral. Because this spiral is really a circle of 41 fifths, the innermost and outermost few notes are duplicates. In the 2nd chart, "-ish" means ±1 arrow.

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