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Kite Guitar chord shapes (downmajor tuning): Difference between revisions

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→Sixth chords: added fingering for hi-3-5 vm6 chord
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!downminor-6
!downminor-6
|-
|-
!example, with homonym
!example, with homonym(s)
!C^6 = ^Avm7
!C^6 = ^Avm7
!Cv6 = vA^m7
!Cv6 = vA^m7
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(C^m6,11 = F^9)
(C^m6,11 = F^9)
!Cvm6 = vA^m7(b5)
!Cvm6 = vA^m7(b5)
= Fv9noR
|-
|-
!example notes
!example notes
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1 . 4 (2) 3 1
1 . 4 (2) 3 1
|1 . 4 (2) 1 1
|1 . 4 (2) 1 1
|???
|T . 4 (3) 1 2
(T = thumb)
|}
|}


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!downmaj9down#11
!downmaj9down#11
|-
|-
! rowspan="2" |example
!example w homonym
!Cv,7no5 = Bb2(b5)
!Cv,7no5 = Bb2(b5)
!CvM7(4) = F2,b5
!CvM7(4) = F2,b5
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!CvM9,v#11
!CvM9,v#11
|-
|-
!example notes
!C vE Bb
!C vE Bb
!C F G vB
!C F G vB
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In addition, there are unconventional scales like the whole tone, diminished and Tcherepnin scales. But these are much less common, because they don't map to a compact shape in the JI lattice. (See "Convexity and the well-formedness of musical objects", Aline Honingh and Rens Bod, Journal of New Music Research, 2005.)
In addition, there are unconventional scales like the whole tone, diminished and Tcherepnin scales. But these are much less common, because they don't map to a compact shape in the JI lattice. (See "Convexity and the well-formedness of musical objects", Aline Honingh and Rens Bod, Journal of New Music Research, 2005.)


==== 41-edo scales ====
==== Prime subgroups ====
41-edo has an enormous variety of scales. There are many thousands of unconventional scales, but we will focus on the ones that map compactly to the JI lattice. These are scales that contain numerous perfect 5ths.
Imperfect degrees in 12-edo have two qualities, major and minor, and each one implies two [[Color notation|colors]].
 
{| class="wikitable" style="text-align:center;"
Imperfect degrees in 12-edo have two qualities, major and minor. In 41-edo, there are 7 qualities, and each one implies a color.
!quality
| colspan="2" |minor
| colspan="2" |major
|-
!color
|4thwd wa
|gu
|yo
|5thwd wa
|-
!prime
|3-under
|5-under
|5-over
|3-over
|}
12-edo accurately represents only primes 2, 3 and 5 (as well as 17 and 19, and various other higher primes). 41-edo accurately represents primes 7, 11 and 13 as well. There are 7 qualities:
{| class="wikitable" style="text-align:center;"
{| class="wikitable" style="text-align:center;"
!quality
!quality
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|7-under
|7-under
|}
|}
Two notes a perfect fifth apart generally have the same quality. So compact scales use only a few qualities, and thus a small prime subgroup. In [[color notation]], these subgroups are named wa = 2.3, ya = 2.3.5, za = 2.3.7, and ila = 2.3.11. 41-edo doesn't distinguish between the ila subgroup and the tha subgroup 2.3.13, so tha is lumped in with ila.
In [[color notation]], these subgroups are named wa = 2.3, ya = 2.3.5, za = 2.3.7, and ila = 2.3.11. 41-edo doesn't distinguish between the ila subgroup and the tha subgroup 2.3.13, so tha is lumped in with ila.
 
==== 41-edo scales ====
41-edo has an enormous variety of scales. There are many thousands of unconventional scales, but we will focus on the ones that map compactly to the JI lattice. These are scales that contain numerous perfect 5ths. Two notes a perfect fifth apart generally have the same quality. So compact scales use only a few qualities, and thus a small prime subgroup. 


In practice, 41-edo scales tend to be "fuzzy", meaning that one or two scale notes may sometimes shift by an edostep. For example, a major scale may contain both a M2 and a vM2, and use whichever one is required by the harmony at the moment.
In practice, 41-edo scales tend to be "fuzzy", meaning that one or two scale notes may sometimes shift by an edostep. For example, a major scale may contain both a M2 and a vM2, and use whichever one is required by the harmony at the moment.
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| colspan="4" |12 5 7 12 5
| colspan="4" |12 5 7 12 5
|}
|}
The za scale is the most equally distributed, thus arguably the most pentatonic-friendly of the subgroups. In contrast, ya pentatonic has steps... '''''[needs work]'''''
A scale needn't have every single step size on the list in order to be in the category, just most of them. In practice, a non-wa pentatonic scale will often lack a m3 step, as in the examples. But a fuzzy pentatonic scale often will have a m3, e.g. C D vE G vA/A C. Ya and za scales generally contain a wolf 5th (either an ^5 or a v5), and would often become fuzzy to avoid the wolf.  
A scale needn't have every single step size on the list in order to be in the category, just most of them. In practice, a non-wa pentatonic scale will often lack a m3 step, as in the examples. But a fuzzy pentatonic scale often will have a m3, e.g. C D vE G vA/A C. Ya and za scales generally contain a wolf 5th (either an ^5 or a v5), and would often become fuzzy to avoid the wolf.  


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| colspan="8" |11/12 6/5 7 9 8
| colspan="8" |11/12 6/5 7 9 8
|}
|}
There are four basic categories of diatonic scales. In practice, a non-wa scale will often lack a m2 step, unless it's fuzzy. The ya and za diatonic scales have wolf 5ths, and thus tend to be fuzzy.  
There are four basic categories of diatonic scales. In practice, a non-wa scale will often lack a m2 step, unless it's fuzzy. The ya and za diatonic scales have wolf 5ths, and thus tend to be fuzzy. The ila scale is the most equally distributed, thus arguably the most diatonic-friendly. Ya is also fairly equal.  
{| class="wikitable" style="text-align:center;"
{| class="wikitable" style="text-align:center;"
!scale type -->
!scale type -->
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| colspan="7" |7 6 6 5 5 4 8  (harmonics 8-14)
| colspan="7" |7 6 6 5 5 4 8  (harmonics 8-14)
|}
|}
Most 41-edo intervals suggest a specific ratio, but those only a few edosteps wide don't. Thus the remaining categories don't imply any prime subgroups. On the Kite guitar, playing a run of notes one fret apart inherits the term "chromatic" from 12-edo. 12-edo's chromaticism, which translates to runs played on every other fret, is called dodecatonic. Microtonal scales differ from fuzzy scales in having many sequential ^1 intervals.
Most 41-edo intervals suggest a specific ratio, but those only a few edosteps wide don't. Thus the remaining categories don't imply any prime subgroups. On the Kite guitar, playing a run of notes one fret apart inherits the term "chromatic" from 12-edo. 12-edo's chromaticism, which translates to runs played on every other fret, is called dodecatonic. It's a bit of a misnomer, because a scale with 10 or 11 notes might 'feel" dodecatonic. Microtonal scales differ from fuzzy scales in having many sequential ^1 intervals.
{| class="wikitable" style="text-align:center;"
{| class="wikitable" style="text-align:center;"
!scale type -->
!scale type -->
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| colspan="2" |2 2 2 1 1 1 2...
| colspan="2" |2 2 2 1 1 1 2...
|}
|}
Scales with edosteps of 2, 3 and 4 are dodecatonic/chromatic, and those of 1, 2 and 3 are chromatic/microtonal.  
On the Kite guitar, going up an "even" interval (one that has an even number of edosteps) keeps one on the same string, and an "odd" one takes you to the next string. An octave spans 3 strings, thus a scale often has only 3 odd intervals. The exceptions are generally either fuzzy or awkward to play. The latter include wa, ila and zala diatonic, and microtonal scales with many ^1 steps.
 
From this we can deduce that chromatic scales are often 19 tones, and microtonal ones are often 22. We can also deduce that a dodecatonic scale usually has two vm2's. If there are more vm2's, the scale is dodecatonic/chromatic. Scales of 1, 2 and 3 edosteps are chromatic/microtonal.


=== Harmonic scales ===
=== Harmonic scales ===
In Western music, harmonies often require notes that the melody doesn't. For example, "Auld Lang Syne" has a pentatonic melody but diatonic harmonies. Often the melody is diatonic but the harmonies are at least somewhat chromatic. The score will have accidentals in the piano part but not the vocal part.
In Western music, harmonies often require notes that the melody doesn't. For example, "Auld Lang Syne" has a pentatonic melody but diatonic harmonies. Often the melody is diatonic but the harmonies are at least somewhat chromatic. The score will have accidentals in the piano part but not the vocal part. The scale used by the melody is the melodic scale, and the one used to construct chords is the harmonic scale. 


41-edo allows 7-limit harmonies, which are almost never diatonic, and tend to be dodecatonic.  
In 12-edo, a song is generally in a major or minor key, and uses a major or minor scale. A 5-limit piece in 41-edo often is as well. But unlike 12-edo, 41-edo allows the use of 7-limit chords such as 4:5:6:7. If this is one's tonic chord, both major and minor are used simultaneously. A simple Iv7 - IVv7 progression has both a downmajor 3rd and a downminor 3rd. Clearly the major/minor duality no longer applies. Instead, there is an up/down duality.   
 
For 5-limit scales, one chooses a 7-note subset of the 12 notes, and lets the imperfect degrees be either major or minor, or some combination. For 7-limit scales, choose a 12-note subset, and let all but the tonic, 4th and 5th be either upped or downed. (The M2 and m7 may also be plain.) Combining upped and downed intervals in a 41-edo scale creates double-up and double-down intervals, i.e. mid intervals. This increases the odd limit and/or the prime limit, so scales tend not to mix up and down.
 
Harmonic scales aren't played sequentially to create melodies, and having more than 3 odd intervals isn't awkward. Often a harmonic scale is fuzzy, and uses pitch shifts of one edostep. Such a scale would be classified as diatonic/microtonal or decatonic/microtonal.


otonal (yo and zo): P1  vm2  vM2/M2  vm3  vM3  P4  d5  P5  vm6  vM6  vm7/m7  vM7  P8
otonal (yo and zo): P1  vm2  vM2/M2  vm3  vM3  P4  d5  P5  vm6  vM6  vm7/m7  vM7  P8


scale steps:      vm2  A1/~2  vm2/m2  A1  ^m2  m2  A1  vm2  A1  m2/^m2  m2/A1  ^m2  =  2  4/5  2/3  4  4  3  4  2  4  3/4  3/4  4
scale steps:      vm2  A1/~2  vm2/m2  A1  ^m2  m2  A1  vm2  A1  m2/^m2  m2/A1  ^m2  =  2  4/5  2/3  4  4  3  4  2  4  3/4  3/4  4
In 12-edo, a song is generally in a major or minor key, and uses a major or minor scale. 41-edo allows the use of 7-limit chords such as 4:5:6:7. If this is one's tonic chord, both major and minor are used simultaneously. A simple Iv7 - IVv7 progression has both a downmajor and a downminor 3rd. Clearly the major/minor duality no longer applies. Instead, there is an up/down duality.
12-edo scales: choose a 7-note subset, and let the imperfect degrees be either major or minor, or some combination
41-edo scales: choose a 12-note subset, and let all but the tonic, 4th and 5th be either upped or downed.
12-edo: implies a ya subgroup
41-edo: implies both ya and za, and even ila
ya implies heptatonic, za implies pentatonic


ya: 5-over maps to major, so major is more otonal than minor, and for a scale using A B C D E F G, C is the obvious tonic.
ya: 5-over maps to major, so major is more otonal than minor, and for a scale using A B C D E F G, C is the obvious tonic.
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