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added a section on non-awkward MOS scales, added to the section on diatonic modes, other minor changes
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There are many possible 41edo scales. Those discussed here are those with at least 5 notes, and which have a plain perfect 5th from the tonic. Scales that are awkward to play on the Kite guitar are avoided. An '''awkward''' scale has a step which requires a jump of more than four frets. Thus plain minor 2nds and plain/mid 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, 2 upward and 1 downward. Any scale which doesn't have exactly three upward hops per octave will be awkward, because the downward hop will always be at least 6 frets, and usually 7 or more. Almost every scale with a low prime limit and/or a low odd limit is not awkward.  
There are many possible 41edo scales. Those discussed here are those with at least 5 notes, and which have a plain perfect 5th from the tonic. Scales that are awkward to play on the Kite guitar are avoided. An '''awkward''' scale has a step which requires a jump of more than four frets. Thus plain minor 2nds and plain/mid 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, 2 upward and 1 downward. Any scale which doesn't have exactly three upward hops per octave will be awkward, because the downward hop will always be at least 6 frets, and usually 7 or more. Almost every scale with a low prime limit and/or a low odd limit is not awkward.  


[[MOS scale|MOS (moment of symmetry) scales]] have only two step sizes, with the less frequent steps evenly distributed throughout the scale. MOS scales are an important part of microtonal scale theory. But almost every 41-edo MOS scale with a perfect 5th is awkward. The only exception is scales from the [[Magic|Laquinyo]] temperament, which have a small step of only one fret. They have either a very lopsided L/s ratio or more than 12 notes. They are discussed further in the Nineteen-tone section.  
[[MOS scale|MOS (moment of symmetry) scales]] have only two step sizes, with the less frequent steps evenly distributed throughout the scale. MOS scales are an important part of microtonal scale theory. But almost every 41-edo MOS scale with a perfect 5th is awkward. The only exception is scales from the [[Magic|Laquinyo]] temperament, which have a small step of only one fret. They have either a very lopsided L/s ratio or more than 12 notes. They are discussed further in the Nineteen-tone section. See also the Checkerboard scale in the Eleven-tone section.  


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 [[Essential tempering commas|innate comma]] which 41edo does not temper out. Thus many Kite Guitar scales have '''dual''' notes, meaning a note may vary by 1 edostep, in order to avoid a wolf 5th. A scale with a dual note or two is called a '''fluid''' scale. In the tables below, a note that may be either a M2 or a vM2 is indicated by (v)M2.   
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 [[Essential tempering commas|innate comma]] which 41edo does not temper out. Thus many Kite Guitar scales have '''dual''' notes, meaning a note may vary by 1 edostep, in order to avoid a wolf 5th. A scale with a dual note or two is called a '''fluid''' scale. In the tables below, a note that may be either a M2 or a vM2 is indicated by (v)M2.   
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|}
|}
=== The seven diatonic modes ===
=== The seven diatonic modes ===
Generalizing major and minor to 41edo is fairly straightforward. The dorian and locrian modes don't translate well. The other five ya modes are formed from this collection of notes:
Generalizing major and minor to 41edo is fairly straightforward. The 3rd, 6th and 7th are all grouped together on on end of the genchain of 5ths, and upping or downing them only breaks the genchain of 5ths once. Hence there is only one wolf 5th, and only one note becomes dual to avoid it. But with the other 5 modes, the chain gets broken twice, and there are two wolf 5ths, and two dual notes. The dual notes are chosen to get six triads with a P5. The scales are all yaza except where noted.
<tt>
{| class="wikitable center-all"
   D ----- A ----- E ----- B
|+
     \    / \    / \    / \
!
     \  /  \  /  \  /  \
!name
       \ /    \ /    \ /    \
! colspan="8" |scale
       ^F ---- ^C ---- ^G ---- ^D
!as chains of 5ths
</tt>Five of the seven za modes are formed from this collection:
!edosteps
<tt>
!step sizes
     ------- ------- -------
!step count
     \    / \    / \    / \
!moves
     \  /  \  /  \  /  \
|-
   vF  \ / vC  \ / vG  \ / vD  \
!
       D ----- A ----- E ----- B
!downlydian
</tt>In both cases, the D is dual. But the two dorian scales and the two locrian scales are not from these lattices, and are not actually modes of the other scales.
|P1
To be consistent, the two dorian scales should have a dual tonic. To avoid this, and to provide all six triads, there are ''two'' dual notes. Note that the 6th of the <u>up</u>dorian scale can be <u>downed</u>. Note that this dual-ness affects the step sizes, and 74<u>67</u>-<u>74</u>6 can become 74<u>67</u>-<u>65</u>6. Thus the moves vary.
|M2
 
|vM3
To be consistent, the two locrian scales 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 dual as well as the 3rd. Again, this dual-ness affects the step sizes and the moves.
|(v)A4
{| class="wikitable center-all"
|P5
|+
|(◇)vM6
!subgroup
|vM7
!name
|P8
! colspan="8" |scale
|P15M26 vM637vA4 A4
!as chains of 5ths
|76<u>83</u>-<u>67</u>4
!edosteps
| rowspan="2" |8 7 6 4 3
!step sizes
 
!step count
L/s = 2.66
!moves
| rowspan="2" |3L 2M 2s
 
or 5L 2s
|  +3, +2, -3
|-
!
!downmajor (ya)
|P1
|(v)M2
|vM3
|P4
|P5
|vM6
|vM7
|P8
|P415M2 vM2637
|<u>76</u>47-674
|
|-
!
!downmixolydian
|P1
|(v)M2
|vM3
|P4
|P5
|vM6
|(◇)vm7
|P8
|vm7 m7P415M2 vM263
|<u>76</u>47-6<u>38</u>
|
|
|
|-
!
!updorian
|P1
|M2
|^m3
|(^)4
|P5
|(◇)^M6
|^m7
|P8
|^m37^4 P415M26 ^M6
|74<u>67</u>-<u>83</u>6
|
|
|
|-
!
!upminor (ya)
|P1
|M2
|^m3
|(^)4
|P5
|^m6
|^m7
|P8
|^m637^4 P415M2
|74<u>67</u>-476
|
|
|
|-
!
!upphrygian
|P1
|(^)m2
|^m3
|P4
|P5
|^m6
|(◇)^m7
|P8
|m2 ^m2637 m7P415
|<u>38</u>67-4<u>76</u>
|
|
|
|-
!
!uplocrian
|P1
|(^)m2
|^m3
|P4
|d5
|^m6
|(◇)^m7
|P8
|d5m2 ^m2637 m7P41
|<u>38</u>63-8<u>76</u>
|8 7 6 4 3
|varies
|varies
|-
!
!uplydian
|P1
|M2
|^M3
|(^)A4
|P5
|(◇)^M6
|^M7
|P8
|P15M26 ^M637^A4 A4
|78<u>63</u>-<u>87</u>2
|8 7 2
L/s = 4
|2L 3M 2s
 
or 5L 2s
|  +4, +1, -3
|-
!
!upmajor (za)
|P1
|(^)M2
|^M3
|P4
|P5
|^M6
|^M7
|P8
|P415M2 ^M2637
|<u>78</u>27-872
|
|
|
|-
!
!upmixolydian
|P1
|(^)M2
|^M3
|P4
|P5
|^M6
|(◇)^m7
|P8
|m7P4152 ^M263
|<u>78</u>27-8<u>36</u>
|
|
|
|-
!
!downminor (za)
|P1
|M2
|vm3
|(v)4
|P5
|vm6
|vm7
|P8
|vm637v4 P415M2
|72<u>87</u>-278
|
|
|
|-
!
!downphrygian
|P1
|(v)m2
|vm3
|P4
|P5
|vm6
|(◇)vm7
|P8
|m2 vm2637 m7P415
|<u>36</u>87-2<u>78</u>
|
|
|
|-
!yaza
!downdorian
|P1
|M2
|vm3
|(v)4
|P5
|(◇)vM6
|vm7
|P8
|vm37v4 P415M26 vM6
|72<u>87</u>-<u>72</u>8
|8 7 (6) (3) 2
|varies
|varies
|-
!"
!downlocrian
|P1
|vm2
|(v)m3
|P4
|(v)d5
|vm6
|m7
|P8
|d5 vd5vm263 m37P41
|2<u>87</u> <u>3-6</u>87
|"
|varies
|varies
|}
Whereas the upped/downed major and minor modes have only three step sizes, the other modes have five (8 7 6 4 3 or 8 7 6 3 2). The L/s ratio is very large, 2.66 or 4. Furthermore, the dual-ness affects the step sizes, and the moves can vary. It's possible to make the scales more uniform. They mostly become either ya or za. The dorian and locrian modes don't work well. The other five ya modes are formed from this collection of notes:
 
   D ----- A ----- E ----- B
     \    / \    / \    / \
     \  /  \  /  \  /  \
       \ /    \ /    \ /    \
       ^F ---- ^C ---- ^G ---- ^D
</tt>Five of the seven za modes are formed from this collection:
<tt>
     ------- ------- -------
     \    / \    / \    / \
     \  /  \  /  \  /  \
   vF  \ / vC  \ / vG  \ / vD  \
       D ----- A ----- E ----- B
In both cases, the D is dual. 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 dual tonic. To avoid this, and to provide all six triads, there are ''two'' dual notes. Note that the 6th of the <u>up</u>dorian scale can be <u>downed</u>. Note that this dual-ness affects the step sizes, and 74<u>67</u>-<u>74</u>6 can become 74<u>67</u>-<u>65</u>6. Thus the moves vary.
 
To be consistent, the two locrian scales 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 dual as well as the 3rd. Again, this dual-ness affects the step sizes and the moves.
{| class="wikitable center-all"
|+
!subgroup
!name
! colspan="8" |scale
!as chains of 5ths
!edosteps
!step sizes
!step count
!moves
|-
! rowspan="5" |ya
(2.3.5)
!downlydian
|P1
|M2
|vM3
|vA4
|P5
|(v)M6
|vM7
|P8
|P15M26 vM637vA4
|7674-<u>76</u>4
| rowspan="5" |7 6 4
 
L/s = 1.75
| rowspan="5" |3L 2M 2s
 
or 5L 2s
| rowspan="5" | +3, +2, -3
|-
!downmajor
|P1
|(v)M2
|vM3
|P4
|P5
|vM6
|vM7
|P8
|P415M2 vM2637
|<u>76</u>47-674
|-
!downmixolydian
|P1
|vM2
|vM3
|P4
|(v)5
|vM6
|m7
|P8
|m7P415 v5vM263
|674<u>7-6</u>47
|-
|-
! rowspan="5" |ya
!upminor
(2.3.5)
!downlydian
|P1
|P1
|M2
|M2
|vM3
|^m3
|vA4
|(^)4
|P5
|P5
|(v)M6
|^m6
|vM7
|^m7
|P8
|P8
|P15M26 vM637vA4
|^m637^4 P415M2
|7674-<u>76</u>4
|74<u>67</u>-476
| rowspan="5" |7 6 4
 
L/s = 1.75
| rowspan="5" |3L 2M 2s
 
or 5L 2s
| rowspan="5" | +3, +2, -3
|-
|-
!downmajor
!upphrygian
|P1
|P1
|(v)M2
|^m2
|vM3
|^m3
|P4
|P4
|P5
|P5
|vM6
|^m6
|vM7
|(^)m7
|P8
|P8
|P415M2 vM2637
|^m2637 m7P415
|<u>76</u>47-674
|4767-4<u>67</u>
|-
|-
!downmixolydian
!"
|P1
!updorian
|vM2
|vM3
|P4
|(v)5
|vM6
|m7
|P8
|m7P415 v5vM263
|674<u>7-6</u>47
|-
!upminor
|P1
|P1
|M2
|M2
Line 565: Line 832:
|(^)4
|(^)4
|P5
|P5
|^m6
|(v)M6
|^m7
|^m7
|P8
|P8
|^m637^4 P415M2
|^m37^4 P415M26 vM6
|74<u>67</u>-476
|74<u>67</u>-<u>74</u>6
|7 6 (5) 4
|varies
|varies
|-
|-
!upphrygian
!"
!uplocrian
|P1
|P1
|^m2
|^m2
|^m3
|(^)m3
|P4
|P4
|P5
|(^)d5
|^m6
|^m6
|(^)m7
|m7
|P8
|P8
|^m2637 m7P415
|d5 ^d5^m263 m37P41
|4767-4<u>67</u>
|4<u>67</u> <u>3-8</u>67
|(8) 7 6 4 (3)
|varies
|varies
|-
|-
!"
! rowspan="5" |za
!updorian
(2.3.7)
!uplydian
|P1
|P1
|M2
|M2
|^m3
|^M3
|(^)4
|^A4
|P5
|P5
|(v)M6
|(^)M6
|^m7
|^M7
|P8
|P8
|^m37^4 P415M26 vM6
|P15M26 ^M637^A4
|74<u>67</u>-<u>74</u>6
|7872-<u>78</u>2
|7 6 (5) 4
| rowspan="5" |8 7 2
|varies
L/s = 4
|varies
| rowspan="5" |2L 3M 2s
 
or 5L 2s
| rowspan="5" | +4, +1, -3
|-
|-
!"
!upmajor
!uplocrian
|P1
|P1
|^m2
|(^)M2
|(^)m3
|^M3
|P4
|P4
|(^)d5
|P5
|^m6
|^M6
|m7
|^M7
|P8
|P8
|d5 ^d5^m263 m37P41
|P415M2 ^M2637
|4<u>67</u> <u>3-8</u>67
|<u>78</u>27-872
|(8) 7 6 4 (3)
|-
|varies
!upmixolydian
|varies
|P1
|^M2
|^M3
|P4
|(^)5
|^M6
|m7
|P8
|m7P415 ^5^M263
|872<u>7-8</u>27
|-
|-
! rowspan="5" |za
!downminor
(2.3.7)
!uplydian
|P1
|P1
|M2
|M2
|^M3
|vm3
|^A4
|(v)4
|P5
|P5
|(^)M6
|vm6
|^M7
|vm7
|P8
|P8
|P15M26 ^M637^A4
|vm637v4 P415M2
|7872-<u>78</u>2
|72<u>87</u>-278
| rowspan="5" |8 7 2
L/s = 4
| rowspan="5" |2L 3M 2s
 
or 5L 2s
| rowspan="5" | +4, +1, -3
|-
|-
!upmajor
!downphrygian
|P1
|P1
|(^)M2
|vm2
|^M3
|vm3
|P4
|P4
|P5
|P5
|^M6
|vm6
|^M7
|(v)m7
|P8
|P8
|P415M2 ^M2637
|vm2637 m7P415
|<u>78</u>27-872
|2787-2<u>87</u>
|-
|-
!upmixolydian
!yaza
!downdorian
|P1
|P1
|^M2
|M2
|^M3
|vm3
|P4
|(^)5
|^M6
|m7
|P8
|m7P415 ^5^M263
|872<u>7-8</u>27
|-
!downminor
|P1
|M2
|vm3
|(v)4
|(v)4
|P5
|P5
|vm6
|(v)M6
|vm7
|vm7
|P8
|P8
|vm637v4 P415M2
|vm37v4 P415M26 vM6
|72<u>87</u>-278
|72<u>87</u>-<u>72</u>8
|8 7 (6) (3) 2
|varies
|varies
|-
|-
!downphrygian
!"
!downlocrian
|P1
|P1
|vm2
|vm2
|vm3
|(v)m3
|P4
|P4
|P5
|(v)d5
|vm6
|vm6
|(v)m7
|m7
|P8
|P8
|vm2637 m7P415
|d5 vd5vm263 m37P41
|2787-2<u>87</u>
|2<u>87</u> <u>3-6</u>87
|-
|"
!yaza
!downdorian
|P1
|M2
|vm3
|(v)4
|P5
|(v)M6
|vm7
|P8
|vm37v4 P415M26 vM6
|72<u>87</u>-<u>72</u>8
|8 7 (6) (3) 2
|varies
|varies
|varies
|varies
|-
|}
!"
== Near-equidistant Scales ==
!downlocrian
Certain Asian music uses very "lopsided" scales such as P1 M3 P4 P5 M7 P8 (SE Asia) and P1 M2 m3 P5 m6 P8 (Japan). While there is a certain charm to these, scales with equal or roughly equal sizes are also attractive. The only such 12edo scales are the whole tone scale and the full 12-note gamut. Since 41 is a prime number, it has no strictly equal scales. But there are many nearly-equal scales, or near-edos.   
|P1
 
|vm2
|(v)m3
|P4
|(v)d5
|vm6
|m7
|P8
|d5 vd5vm263 m37P41
|2<u>87</u> <u>3-6</u>87
|"
|varies
|varies
|}
It would also be possible to define the modes based on the harmonic and subharmonic scales. For example, the downmixolydian scale could be P1 M2 vM3 P4 P5 vM6 vm7 P8, which contains a 4:5:6:7:9 chord. But this scale has two wolf 5ths.
 
== Near-equidistant Scales ==
Certain Asian music uses very "lopsided" scales such as P1 M3 P4 P5 M7 P8 (SE Asia) and P1 M2 m3 P5 m6 P8 (Japan). While there is a certain charm to these, scales with equal or roughly equal sizes are also attractive. The only such 12edo scales are the whole tone scale and the full 12-note gamut. Since 41 is a prime number, it has no strictly equal scales. But there are many nearly-equal scales, or near-edos.   
 
If N goes into 41 X times with a remainder of Y, then the near-N-edo scale has steps YL and (N-Y)s, where L=X+1 and s=X. This near-N-edo scale is altered slightly so that there are only 3 odd numbers, and the rest are even. This avoids an awkward scale and also tends to make the intervals well tuned. For example, the unaltered whole-tone scale would have thirds of mostly 14/11 (plain M3) with some 5/4, but the the altered one has thirds of mostly 5/4 with some 9/7.   
If N goes into 41 X times with a remainder of Y, then the near-N-edo scale has steps YL and (N-Y)s, where L=X+1 and s=X. This near-N-edo scale is altered slightly so that there are only 3 odd numbers, and the rest are even. This avoids an awkward scale and also tends to make the intervals well tuned. For example, the unaltered whole-tone scale would have thirds of mostly 14/11 (plain M3) with some 5/4, but the the altered one has thirds of mostly 5/4 with some 9/7.   


Line 825: Line 1,065:


=== Tritonic and Tetratonic ===
=== Tritonic and Tetratonic ===
Tritonic scales are augmented triads. The moves are -0 and --1, meaning same fret up 1 string, and up 1 fret up 1 string. Tetratonic scales are dim6/dim7 tetrads. Both augmented and dim6/dim7 chords are discussed on the [[Kite Guitar Chord Shapes (downmajor tuning)|chords page]].
Tritonic scales are augmented triads. Both moves hop strings, hence have a negative sign. The moves are -0 and --1, meaning same fret up 1 string, and up 1 fret up 1 string.  
 
Tetratonic scales are dim6/dim7 tetrads.  
 
Both augmented and dim6/dim7 chords are discussed on the [[Kite Guitar Chord Shapes (downmajor tuning)|chords page]].


=== Pentatonic (2L 2s 1xs) ===
=== Pentatonic (2L 2s 1xs) ===
We've already seen how the upmajor and downminor pentatonic scales are nearly equi-pentatonic.
We've already seen how the upmajor and downminor pentatonic scales are nearly equi-pentatonic. See also Checkerboard[5] in the eleven-tone section.


=== Hexatonic (whole tone) (1XL 3L 2s) ===
=== Hexatonic (whole tone) (1XL 3L 2s) ===
Line 1,125: Line 1,369:
|5654-6564
|5654-6564
|}
|}
See also Checkerboard[8] in the eleven-tone section.


=== Dodecatonic (twelve-tone) (7L 3m 2s) ===
=== Dodecatonic (twelve-tone) (7L 3m 2s) ===
Line 1,203: Line 1,448:


=== Decatonic - the semitonal scale or twin pentatonic scale (2L 7s 1xs) ===
=== Decatonic - the semitonal scale or twin pentatonic scale (2L 7s 1xs) ===
Is there an easily playable chromatic-sounding scale with nearly equal steps? One such is the decatonic scale. The precise term for these scales is not chromatic but '''semitonal''', because the steps are roughly the size of a 12edo semitone. '''Chromatic''' includes semitonal, trientonal/fretwise, and microtonal. '''Trientonal''' refers to movement by a single fret, see the section on 19-tone scales. '''Microtonal''' refers to movement by a half-fret, see the final section.
Is there an easily playable chromatic-sounding scale with nearly equal steps? One such is the decatonic scale. The precise term for these scales is not chromatic but '''semitonal''', because the steps are roughly the size of a 12edo semitone. '''Trientonal''' ("by third-tones") or '''fretwise''' refers to movement by a single fret, see the section on 19-tone scales. '''Microtonal''' refers to movement by a half-fret, see the final section. '''Chromatic''' includes semitonal, trientonal/fretwise, and microtonal.  


If the steps are nearly equal, it follows that every other note will make a nearly-equal pentatonic scale. Thus these scales consist of two intertwined za pentatonic scales. If we further require that the two scales be either upmajor or downminor, there are only 3 such scales, each with two primary modes. The modes are named after the "one" of the non-tonic scale, similar to how octotonic scales are named.
If the steps are nearly equal, it follows that every other note will make a nearly-equal pentatonic scale. Thus these scales consist of two intertwined za pentatonic scales. If we further require that the two scales be either upmajor or downminor, there are only 3 such scales, each with two primary modes. The modes are named after the "one" of the non-tonic scale, similar to how octotonic scales are named.
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=== Eleven-tone - The checkerboard scale (8L 3s) ===
=== Eleven-tone - The checkerboard scale (8L 3s) ===
This scale is notable for not needing a 3rd step size or a 3rd move. It gets its name from the fact that it uses every other fret of each string, and each string's notes are offset by one fret from the neighboring strings. Thus the scale chart looks like an actual checkerboard. It's a [[MOS scale]] generated by the ^M3, which is 15\41. The complete genchain runs from -10 generators to +10:
This scale is notable for not needing a 3rd step size or a 3rd move. It gets its name from the fact that it uses every other fret of each string, and each string's notes are offset by one fret from the neighboring strings. Thus the scale chart looks like an actual checkerboard. It's a [[MOS scale]] generated by the ^M3, which is 15\41. The complete genchain containing all 11 modes runs from -10 generators to +10:


M3 ~6 m2 ^4 vm7 M2 ~5 vM7 ^m3 vm6 '''<u>P1</u>''' ^M3 vM6 ^m2 ~4 m7 ^M2 v5 M7 ~3 m6
M3 ~6 m2 ^4 vm7 M2 ~5 vM7 ^m3 vm6 '''<u>P1</u>''' ^M3 vM6 ^m2 ~4 m7 ^M2 v5 M7 ~3 m6


The official [[Color notation/Temperament Names|name]] for this temperament is Sasa-tritribizo, with an extremely complex [[pergen]] (P8, c⁶P5/18). Better to call it checkerboard! Checkerboard[5] and Checkerboard[8] are also MOS scales, with L/s ratios of 2.75 and 1.75 respectively.
The official [[Color notation/Temperament Names|color name]] for this temperament is Sasa-tritribizo, with an extremely complex [[pergen]] (P8, c<sup>6</sup>P5/18). Better to call it checkerboard! Checkerboard[5] and Checkerboard[8] are also MOS scales, with L/s ratios of 2.75 and 1.75 respectively.


11 generators add up to an ^1, showing how very near 11-edo this scale is. 7 generators add up to a down-5th, thus all modes contain 4 down-5ths. The 11 modes of Checkerboard[11] are listed here in order from sharpest to flattest. The notes that differ from the neighboring modes are '''bolded'''.
11 generators add up to 4 8ves and an ^1, showing how very near 11-edo this scale is. 7 generators add up to a down-5th, thus all modes contain 4 down-5ths. The 11 modes of Checkerboard[11] are listed here in order from sharpest to flattest. The notes that differ from the neighboring modes are '''bolded'''.
{| class="wikitable center-all"
{| class="wikitable center-all"
!subgroup
!subgroup
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One can make a scale that's not very even, but still quite interesting, by using a smaller MOS, for example 13. This scale is 3 fretwise runs separated by 3 major 2nds.
One can make a scale that's not very even, but still quite interesting, by using a smaller MOS, for example 13. This scale is 3 fretwise runs separated by 3 major 2nds.
{| class="wikitable center-all"
{| class="wikitable center-all"
!name
!name
! colspan="14" |scale
! colspan="14" |scale
!edosteps
!edosteps
!step sizes
!step sizes
!step count
!step count
!moves
!moves
|-
!fretwise[13]
|P1
|vm2
|^m2
|^m3
|vM3
|^M3
|P4
|P5
|vm6
|^m6
|vM6
|^M6
|^M7
|P8
|2272-227-222272
|7 2, L/s = 3.5
|3L 10s
| +2, -3
|}
 
=== Microtonal scales ===
These scales use step sizes of 1 and 2 edosteps only. They are quite awkward to play, with much string-hopping and fret-leaping. If there are only 3 small steps, it is a 22-note MOS or MODMOS of Laquinyo.
 
== Non-awkward MOS scales ==
See the discussion at [[Kite Giedraitis's Categorizations of 41edo Scales]].
{| class="wikitable"
|+non-awkward MOS scales
!name
!pergen
! colspan="2" |generator
!MOS scales
!L & s
!moves
!notes
|-
|Tritriyo
|(P8, ccP4/9)
|11\41
|^m3
|7 = 4L 3s
|8 3
| +4, -5
|no 4ths or 5ths
|-
| rowspan="5" |Laquinyo
| rowspan="5" |(P8, P12/5)
| rowspan="5" |13\41
| rowspan="5" |vM3
|7 = 3L 4s
|11 2
| +1, -1
| rowspan="5" |fretwise scales
|-
|10 = 3L 7s
|9 2
| +1, -2
|-
|13 = 3L 10s
|7 2
| +1, -3
|-
|16 = 3L 13s
|5 2
| +1, -4
|-
|19 = 3L 16s
|3 2
| +1, -5
|-
| rowspan="3" |Checkerboard
| rowspan="3" |(P8, c<sup>6</sup>P5/18)
| rowspan="3" |15\41
| rowspan="3" |^M3
|5 = 3L 2s
|11 4
| +2, -1
| rowspan="3" |no 4ths or 5ths
|-
|8 = 3L 5s
|7 4
| +2, -3
|-
|11 = 8L 3s
|4 3
| +2, -5
|-
|-
!fretwise[13]
|Pythagorean
|P1
|(P8, P5)
|vm2
|17\41
|^m2
|^m3
|vM3
|^M3
|P4
|P4
|P5
|5 = 2L 3s
|vm6
|10 7
|^m6
| +5, -3
|vM6
|very close to 12-edo
|^M6
|^M7
|P8
|2272-227-222272
|7 2, L/s = 3.5
|3L 10s
| +2, -3
|}
|}
=== Microtonal scales ===
These scales use step sizes of 1 and 2 edosteps only. They are quite awkward to play, with much string-hopping and fret-leaping. If there are only 3 small steps, it is a 22-note MOS or MODMOS of Laquinyo.


[[Category:Kite Guitar]]
[[Category:Kite Guitar]]
Retrieved from "https://en.xen.wiki/w/Kite_Guitar_Scales"