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Kite Guitar Scales: Difference between revisions

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autopatrolled, Sysops
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adding equiheptatonic and decatonic, a work in progress
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Every pentatonic scale has 5 modes, but only those modes with a non-fuzzy 5th are listed.  
Every pentatonic scale has 5 modes, but only those modes with a non-fuzzy 5th are listed.  
=== Major and minor scales ===
=== Major and minor scales ===
The za scales are nearly [[5-edo|equipentatonic]], dividing the P4 into two nearly equal steps of ^M2 and vm3 (8 and 9).
{| class="wikitable left-9 center-all"
{| class="wikitable left-9 center-all"
|+
|+
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|P8
|P8
|18/(18:16:'''15''':14:13:12:11:10)
|18/(18:16:'''15''':14:13:12:11:10)
| rowspan="2" |^m2, ~2, vM2, M2, ^M2
| rowspan="2" |"
| rowspan="2" |4 5 6 7 8
| rowspan="2" |"
|-
|-
!subharmonic minor
!subharmonic minor
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=== The seven modes ===
=== The seven modes ===
Generalizing the 7 modes to 41edo is tricky. Five of the seven ya modes are formed from this collection of notes:
Generalizing the seven modes to 41edo is tricky. Five of the seven ya modes are formed from this collection of notes:
<tt>
<tt>
   D ----- A ----- E ----- B
   D ----- A ----- E ----- B
Line 267: Line 268:
       \ /    \ /    \ /    \
       \ /    \ /    \ /    \
       ^F ---- ^C ---- ^G ---- ^D
       ^F ---- ^C ---- ^G ---- ^D
</tt>
</tt>
Five of the seven za modes are formed from this collection:
Five of the seven za modes are formed from this collection:
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   vF  \ / vC  \ / vG  \ / vD  \
   vF  \ / vC  \ / vG  \ / vD  \
       D ----- A ----- E ----- B
       D ----- A ----- E ----- B
</tt>
</tt>
In both cases, the D is fuzzy. But the two dorian scales and the two locrian scales are not from these lattices, and are not actually modes of the other scales.  
In both cases, the D is fuzzy. But the two dorian scales and the two locrian scales are not from these lattices, and are not actually modes of the other scales.


To be consistent, the two dorian scales should have a fuzzy tonic. To avoid this, and to provide all six triads, there are ''two'' fuzzy notes. Note that the 6th of the <u>up</u>dorian scale can be <u>down</u>ed.
To be consistent, the two dorian scales should have a fuzzy tonic. To avoid this, and to provide all six triads, there are ''two'' fuzzy notes. Note that the 6th of the <u>up</u>dorian scale can be <u>downed</u>.


To be consistent, the uplocrian or downlocrian scale should have an upflat or downflat 5th. To get a plain flat 5th, and thus a more consonant 5:6:7 or 7/(7:6:5) tonic triad, the 5th is fuzzy as well as the 3rd.
To be consistent, the uplocrian or downlocrian scale should have an upflat or downflat 5th. To get a plain flat 5th, and thus a more consonant 5:6:7 or 7/(7:6:5) tonic triad, the 5th is fuzzy as well as the 3rd.
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|vm2, m2, vM2, M2, ^M2
|vm2, m2, vM2, M2, ^M2
|2 3 6 7 8
|2 3 6 7 8
|}
=== Near-equiheptatonic scales ===
These are a cross between the usual modes and the harmonic or subharmonic scales. Obviously they are reminiscent of 7-edo. The 4th is divided into three nearly equal steps of two vM2's and a ~2 (6 6 5), thus it's also reminiscent of the third-4th [[pergen]] and the [[Porcupine|Triyo]] temperament.
The smallest step of the upminor or downmajor scale is widened by 1 edostep to a mid-2nd.
As can be seen from [[:File:41-edo spiral.png|this picture]], the upminor scale falls on two arms of the 41edo spiral of 5ths. Only 1 fuzzy note is needed to avoid wolf fifths. But the 
mid-downmajor - 7 6 6 5 - 6 6 5 --> 6 5 7 6 - 6 5 6 = vM2 ^m3
mid-upminor - 5667-566 --> mid = 6675-665
6657 = P1  vM2    ~3  P4    P5
6567 = P1  vM2  ^m3  P4  P5
5667 = P1  ~2    ^m3  P4  P5
7665 = P1  M2  ^m3    ~4  P5
6765 = P1  vM2  ^m3  ~4  P5
6675 = P1  vM2    ~3    ~4  P5
665 = P5  vM6    ~7  P8
656 = P5  vM6  ^m7  P8
566 = P5  ~6    ^m7  P8
{| class="wikitable center-all"
!subgroup
!name
! colspan="8" |scale
!as edosteps
!as (sub)harmonic series fragments
!as chain of 5ths
! colspan="2" |step sizes
|-
! rowspan="2" |yala
(2.3.5.11)
!mid-major
|P1
|M2
|vM3
|~4
|P5
|vM6
|~7
|P8
|7665-665
|(8:9:10:11:12)/8 + (9:10:11:12)/6
|P152  vM63  ~74
| rowspan="2" |~2, vM2, M2
| rowspan="2" |5 6 7
|-
!mid?
|P1
|vM2
|~3
|P4
|P5
|vM6
|~7
|P8
|6657-665
|(9:10:11:12)/9 + (8:9:10:11:12)/6
|P415  vM26  ~37
|-
! rowspan="2" |"
!mid-minor
|P1
|~2
|^m3
|P4
|P5
|~6
|^m7
|P8
|5667-566
|12/(12:11:10:9:8) + 18/(12:11:10:9)
|~26  ^m37  P415
| rowspan="2" |"
| rowspan="2" |"
|-
!?
|P1
|vM2
|~3
|~4
|P5
|vM6
|~7
|P8
|6675-665
|
|P15  vM26  ~374
|-
! rowspan="2" |"
!?
|P1
|vM2
|vM3
|~4
|P5
|vM6
|~7
|P8
|6765-665
|
|P15  vM263  ~74
| rowspan="2" |"
| rowspan="2" |"
|-
!?
|P1
|vM2
|^m3
|P4
|P5
|vM6
|^m7
|P8
|6567-656
|
|^m37  P415 vM26
|}
== Decatonic - Ten is the New Twelve ==
"The Flight of the Bumblebee" has simple 5-limit triads, but a scale that is clearly dodecatonic. The evenly-spaced 12edo scale is quite fitting for this piece. How would this piece translate to the Kite guitar? Poorly, because the scale would be either very uneven (steps of 2, 3 and 4, L/s ratio of 2), or very awkward to play (all plain notes, lots of jumping between strings).
Is there an easily playable chromatic-sounding scale with nearly even steps? We need three odd numbers and the rest even. If the even number is 6 or 8, we get the equiheptatonic (41/6 is about 7) or equipentatonic (41/8 is about 5) scales. The obvious answer is 4, which makes a decatonic scale.
{| class="wikitable center-all"
!subgroup
!name
! colspan="11" |scale
!as edosteps
!as a chord
! colspan="2" |step sizes
|-
! rowspan="2" |yalaza
(2.3.5.7.11)
!twin downminor pentatonic #1
|P1
|~2
|vm3
|vM3
|(v)4
|d5
|P5
|~6
|vm7
|vM7
|P8
|5444-34-5444
|12:13:14:15:16
| rowspan="2" |m2, ^m2, ~2
| rowspan="2" |3 4 5
|-
!twin downminor pentatonic #2
|P1
|^m2
|vm3
|vM3
|(v)4
|A4
|P5
|^m6
|vm7
|vM7
|P8
|4544-43-4544
|
|-
! rowspan="2" |"
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