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Kite Guitar Scales: Difference between revisions

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=== Major and minor scales ===
=== Major and minor scales ===
See below for modes of these scales.  
The two ya scales are only modes of each other if the dual notes are included. Same with the two za scales. See below for the other 5 modes (dorian, lydian, etc).  
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=== The seven diatonic modes ===
=== The seven diatonic modes ===
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 five modes, the chain gets broken twice, and there are two wolf 5ths, and two dual notes. The dual notes are chosen to get six similar triads with a P5. The scales are all yaza except where noted.
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 five modes, the chain gets broken twice, and there are two wolf 5ths, and two dual notes. The dual notes are chosen to get six similar triads with a P5. The scales are all yaza except where noted. Most of these scales are not actually modes of each other.
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the seven diatonic modes
!name
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! colspan="8" |scale
! colspan="8" |scale
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|(4)
|(4)
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Whereas the major and minor modes have only 3 step sizes, the other modes have 5. 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:
Whereas the major and minor modes have only 3 step sizes, the other modes have 5. Furthermore, the dual-ness affects the step sizes, and the moves can vary. It's possible to make the scales more uniform. They mostly have only 3 step sizes. They mostly become either ya or za. They mostly become modes of each other. The dorian and locrian modes are somewhat problematic.  
 
Five of the seven ya modes (all but dorian and locrian) are formed from this collection of notes:


   D ----- A ----- E ----- B
   D ----- A ----- E ----- B
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the seven diatonic modes, alternate versions
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===Pentatonic (2L 2s 1xs)===
===Pentatonic (2L 2s 1xs)===
We've already seen how the upmajor and downminor pentatonic scales are nearly equi-pentatonic. See also Checkerboard[5] in the eleven-tone section.
We've already seen how the upmajor and downminor pentatonic scales are nearly equi-pentatonic.


===Hexatonic (whole tone) (1XL 3L 2s)===
===Hexatonic (whole tone) (1XL 3L 2s)===
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|5654-6564
|5654-6564
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See also Checkerboard[8] in the eleven-tone section.
===Dodecatonic (twelve-tone) (7L 3m 2s)===
===Dodecatonic (twelve-tone) (7L 3m 2s)===
"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, nicely evoking the random movements of flying insects. How would this piece translate to the Kite Guitar? Poorly, because the scale would be either very awkward to play (all plain notes, lots of hopping between strings), or very uneven, with an L/s ratio of at least 2.  
"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, nicely evoking the random movements of flying insects. How would this piece translate to the Kite Guitar? Poorly, because the scale would be either very awkward to play (all plain notes, lots of hopping between strings), or very uneven, with an L/s ratio of at least 2.  
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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 containing all 11 modes runs from -10 generators to +10:
This scale 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]] and therefore doesn't needing a 3rd step size or a 3rd move. It's 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|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.
The [[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 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'''.
11 generators add up to 4 octaves 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'''.
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*3 steps = minorish 3rd = 322¢ or 351¢
*3 steps = minorish 3rd = 322¢ or 351¢
*4 steps = majorish 3rd = 410¢ or 439¢
*4 steps = majorish 3rd = 410¢ or 439¢
*5 steps = middish 4th = 527¢ or 566¢
*5 steps = middish 4th = 527¢ or 556¢
*6 steps = middish 5th = 644¢ or 673¢
*6 steps = middish 5th = 644¢ or 673¢


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==Non-awkward MOS scales ==
==Non-awkward MOS scales ==
See the discussion at [[Kite Giedraitis's Categorizations of 41edo Scales]].
See the discussion at [[Kite Giedraitis's Categorizations of 41edo Scales]]. Checkerboard[11] is discussed in the eleven-tone section.
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|+non-awkward MOS scales
|+non-awkward MOS scales
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|8 3
|8 3
| +4, -5
| +4, -5
| no 4ths or 5ths
| no perfect 4ths or 5ths
|-
|-
| rowspan="5" |Laquinyo
| rowspan="5" |Laquinyo
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|11 4
|11 4
| +2, -1
| +2, -1
| rowspan="3" | no 4ths or 5ths
| rowspan="3" | no perfect 4ths or 5ths
|-
|-
|8 = 3L 5s
|8 = 3L 5s
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