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Kite Guitar Scales: Difference between revisions

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== Overview ==
== Overview ==


There are many possible scales. Those listed here are select ones with a low prime limit and/or a low odd limit.  
There are many possible 41edo scales. Those discussed here are those which are not awkward to play on the Kite guitar. An awkward scale has a step which requires a jump of more than four frets. Thus plain minor 2nds and 3rds are avoided. A scale naturally hops from one string to the next as it goes up or down. Unlike other guitars, the Kite guitar doesn't let one hop freely. For example, the 3-limit scale fragment P1 M2 M3 P4 requires 3 hops. Any scale which doesn't have exactly three hops per octave is awkward. All pentatonic, hexatonic and heptatonic MOS scales are awkward. However every scale with a low prime limit and/or a low odd limit is not awkward.  


Every scale can be thought of as a chord, e.g. the 12edo major pentatonic scale is a 6add9 pentad. Many pentads and heptads have an innate comma which 41edo does not temper out. Thus many Kite Guitar scales are "fuzzy", meaning a scale degree may vary by 1 edostep. In the tables below, a note that may be either a M2 or a vM2 is indicated by (v)M2. In general, major scales have a fuzzy 2nd and minor scales have a fuzzy 4th. But the chord progression may make other degrees fuzzy. For example, Iv - IVv - Vv7 - Iv requires a fuzzy 4th.
Every scale can be thought of as a chord, e.g. the 12edo major pentatonic scale is a 6add9 pentad. Many pentads and heptads have an innate comma which 41edo does not temper out. Thus many Kite Guitar scales are "fuzzy", meaning a scale degree may vary by 1 edostep. In the tables below, a note that may be either a M2 or a vM2 is indicated by (v)M2. In general, major scales have a fuzzy 2nd and minor scales have a fuzzy 4th. But the chord progression may make other degrees fuzzy. For example, Iv - IVv - Vv7 - Iv requires a fuzzy 4th.
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=== Harmonic and subharmonic scales ===
=== Harmonic and subharmonic scales ===
These are named after the triad implied by the 3rd and 5th, minus the up or down. Note that the harmonic ''major'' scale contains a ''minor'' 7th, and the harmonic ''minor'' scale contains a ''major'' 6th. Likewise with the subharmajor and subharminor scales. A harmonic diminished pentatonic scale would be P1 ^m3 d5 ^m6 ^m7 P8 = 5:6:7:8:9. But it's not very plausible, and would be heard as one of the other modes.
These are named after the triad implied by the 3rd and 5th, minus the up or down. Note that the harmonic ''major'' scale contains a down''minor'' 7th, and the harmonic ''minor'' scale contains a down''major'' 6th. Likewise with the subharmajor and subharminor scales. A harmonic diminished pentatonic scale would be P1 ^m3 d5 ^m6 ^m7 P8 = 5:6:7:8:9. But it's not very plausible, and would be heard as one of the other modes.  
{| class="wikitable left-9 center-all"
{| class="wikitable left-9 center-all"
|+
|+
!subgroup
!subgroup
!name
!name
!nickname
! colspan="6" |scale
! colspan="6" |scale
!as a chord
!as a chord
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(2.3.5.7)
(2.3.5.7)
!harmonic major
!harmonic major
!harmajor
|P1
|P1
|M2
|M2
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|-
|-
!harmonic minor
!harmonic minor
!harminor
|P1
|P1
|vm3
|vm3
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! rowspan="3" |"
! rowspan="3" |"
!subharmonic major
!subharmonic major
!subharmajor
|P1
|P1
|M2
|M2
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|-
|-
!subharmonic minor
!subharmonic minor
!subharminor
|P1
|P1
|^m3
|^m3
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|-
|-
!subharmonic diminished
!subharmonic diminished
!subhardim
|P1
|P1
|vm3
|vm3
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| style="text-align: left" |vm7(b5),vm6 = 14/(14:12:10:9:8)
| style="text-align: left" |vm7(b5),vm6 = 14/(14:12:10:9:8)
|}
|}
All five of these scales are "anti-MOS" in the sense that each scale step has a unique size.


== Heptatonic Scales ==
== Heptatonic Scales ==
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=== Harmonic and subharmonic scales ===
=== Harmonic and subharmonic scales ===
These all have the same prime subgroup, yazalatha (2.3.5.7.11.13). They use harmonics 7-14. Adding the 15th harmonic (the '''bolded''' note) makes an octotonic scale that uses harmonics 8-16. Again, the scales are named after the triad implied by the 3rd and 5th, minus the up or down. If there are two 3rds, the unbolded one is used. Each scale contains the similarly-named pentatonic scale, e.g. the harmajor scale contains the harmajor pentatonic scale.  
These all have the same prime subgroup, yazalatha (2.3.5.7.11.13). They use harmonics 7-14. Adding the 15th harmonic (the '''bolded''' note) makes an octotonic scale that uses harmonics 8-16. Again, the scales are named after the triad implied by the 3rd and 5th, minus the up or down. If there are two 3rds, the unbolded one is used. Each scale contains the similarly-named pentatonic scale, e.g. the harmajor scale contains the harmajor pentatonic scale. Subhardim = 14/(14:13:12:11:10:9:8) is a theoretical possibility.  
{| class="wikitable left-11 center-all"
{| class="wikitable left-11 center-all"
|+
|+
!
!name
!nickname
! colspan="9" |scale
! colspan="9" |scale
!as a chord
!as a chord
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|-
|-
!harmonic major
!harmonic major
!harmajor
|P1
|P1
|M2
|M2
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|-
|-
!harmonic minor
!harmonic minor
!harminor
|P1
|P1
|~2
|~2
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|-
|-
!subharmonic major
!subharmonic major
!subharmajor
|P1
|P1
|M2
|M2
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|-
|-
!subharmonic minor
!subharmonic minor
!subharminor
|P1
|P1
|~2
|~2
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| style="text-align: left" |24/(24:22:20:18:16:'''15''':14:13)
| style="text-align: left" |24/(24:22:20:18:16:'''15''':14:13)
|}
|}
One of the hallmarks of harmonic and subharmonic scales is that each step has a unique size. Unfortunately, in 41edo, these scales do not have unique step sizes. The heptatonic scales run 8 7 6 6 5 5 4. The octotonic step sizes are worse, 7 6 6 5 5 4 4 4. Only the pentatonic scales have unique step sizes.
One of the hallmarks of harmonic and subharmonic scales is that each step has a unique size. Unfortunately, in 41edo, these scales do not have unique step sizes. The heptatonic scales run 8 7 6 6 5 5 4. The octotonic step sizes are worse, 7 6 6 5 5 4 4 4. Only the "anti-MOS" pentatonic scales have unique step sizes.


=== The seven modes ===
=== The seven modes ===
Generalizing the seven modes to 41edo is tricky. Five of the seven ya modes are formed from this collection of notes:
Generalizing major and minor to 41edo is fairly straightforward. Some of the other modes are tricky. Five of the seven ya modes are formed from this collection of notes:
<tt>
<tt>
   D ----- A ----- E ----- B
   D ----- A ----- E ----- B
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<br>
</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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<br>
</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.
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These are a cross between the usual modes and the harmonic or subharmonic scales. Obviously they are reminiscent of [[7edo|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.  
These are a cross between the usual modes and the harmonic or subharmonic scales. Obviously they are reminiscent of [[7edo|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.
The two smallest steps of the upminor or downmajor scale are widened by 1 edostep to a mid-2nd.


As can be seen from [[:File:41-edo spiral.png|this picture]], the upminor scale occupies two arms of the 41edo spiral of 5ths. Only one fuzzy note is needed to avoid wolf fifths. But these scales occupy three arms, and would need two fuzzy notes.   
As can be seen from [[:File:41-edo spiral.png|this picture]], the upminor scale occupies two arms of the 41edo spiral of 5ths. Only one fuzzy note is needed to avoid wolf fifths. But these scales occupy three arms, and would need two fuzzy notes.   


mid-downmajor - 7 6 6 5 - 6 6 5 --> 6 5 7 6 - 6 5 6 = vM2 ^m3
"Middish-major" means a majorish scale that has a few mid notes.  
 
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"
{| class="wikitable center-all"
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! colspan="2" |step sizes
! colspan="2" |step sizes
|-
|-
! rowspan="2" |yala
! rowspan="3" |yala
(2.3.5.11)
(2.3.5.11)
!mid-major?
!middish-major
|P1
|P1
|M2
|(v)M2
|vM3
|vM3
|~4
|~4
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|7665-665
|7665-665
|(8:9:10:11:12)/8 + (9:10:11:12)/6
|(8:9:10:11:12)/8 + (9:10:11:12)/6
|P152  vM63 ~74
|P152  vM263 ~74
| rowspan="2" |~2, vM2, M2
| rowspan="3" |~2, vM2, M2
| rowspan="2" |5 6 7
| rowspan="3" |5 6 7
|-
|-
!mid?
!majorish-mid
|P1
|P1
|vM2
|vM2
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|(9:10:11:12)/9 + (8:9:10:11:12)/6
|(9:10:11:12)/9 + (8:9:10:11:12)/6
|P415  vM26  ~37
|P415  vM26  ~37
|-
!majorish-minor
|P1
|vM2
|^m3
|(^)4
|P5
|vM6
|^m7
|P8
|6567-656
|
|^m374  P415 vM26
|-
|-
! rowspan="2" |"
! rowspan="2" |"
!mid-minor?
!middish-minor
|P1
|P1
|~2
|~2
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|
|
|P15  vM26  ~374
|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
|}
|}


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|vM3
|vM3
|P4
|P4
|vA4/^d5
|A4/d5
|P5
|P5
|^m6
|^m6
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|vM7
|vM7
|P8
|P8
|^d5-^m2637  m7-P415-M2  vM2637-vA4
|A4-^m2637  m7-P415-M2  vM2637-d5
| rowspan="2" |vvA1, m2, ^m2, (~2)
| rowspan="2" |vvA1, m2, ^m2, (~2)
| rowspan="2" |2 3 4 (5)
| rowspan="2" |2 3 4 (5)
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|vM7
|vM7
|P8
|P8
|5444-34-5444
|544-434-5444
|12:13:14:15:16
|12:13:14:15:16
| rowspan="2" |m2, ^m2, ~2
| rowspan="2" |m2, ^m2, ~2
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|vM7
|vM7
|P8
|P8
|4544-43-4544
|454-443-4544
|
|
|-
|-
! rowspan="2" |"
! rowspan="2" |"
!
!
|P1
|m2
|M2
|^m3
|^M3
|d5
|P5
|
|
|
|
|
|
|
|
|
|344-454-4454
|
|
|
|
|
|
|
|
|
| rowspan="2" |"
| rowspan="2" |"
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