Kite Guitar Scales: Difference between revisions

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===Eleven-tone - The checkerboard scale (8L 3s)===

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:

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 need 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 '''P1''' ^M3 vM6 ^m2 ~4 m7 ^M2 v5 M7 ~3 m6

P4 and P5 do not appear here. P5 occurs at +18 ~9/7 generators, which ~~implies~~ the Sasa-tritribizo comma [5 -35 0 18> and the extremely complex [[pergen]] (P8, c6P5/18). However, one 3-limit interval occurs much sooner. 16/9 = m7 occurs at only +5 generators, meaning that this temperament can be considered to be the 2.9.15.7 [[Just intonation subgroup|subgroup]] with [[225/224]] & [[245/243]] vanishing. This implies the much simpler and hence much more useful pergen (P8, cm7/5). The [[Color notation/Temperament Names|color name]] is [[3125/3072|Laquinyo]] & [[225/224|Ruyoyo]] wawa, where "wawa" is a slangy term for using 9 not 3 in the subgroup. Adding prime 11 to the subgroup adds the [[100/99|Luyoyo]] comma to the name.

P4 and P5 do not appear here. Theoretically, P5 occurs at +18 ~9/7 generators, which would imply the Sasa-tritribizo comma [5 -35 0 18> and the extremely complex [[pergen]] (P8, c6P5/18). However, one 3-limit interval occurs much sooner. 16/9 = m7 occurs at only +5 generators, meaning that this temperament can be considered to be the 2.9.15.7 [[Just intonation subgroup|subgroup]] with [[225/224]] & [[245/243]] vanishing. This implies the much simpler and hence much more useful pergen (P8, cm7/5). The [[Color notation/Temperament Names|color name]] is [[3125/3072|Laquinyo]] & [[225/224|Ruyoyo]] wawa, where "wawa" is a slangy term for using 9 not 3 in the subgroup. Adding prime 11 to the subgroup adds the [[100/99|Luyoyo]] comma to the name.

Checkerboard[5] and Checkerboard[8] are also MOS scales, with L/s ratios of 2.75 and 1.75 respectively. Checkerboard[8] is the basis for the [[TAMNAMS]] name checkertonic for 3L 5s, whereas checkerboard[5] has the [[TAMNAMS|antipentic]] step pattern.

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 ===Eleven-tone - The checkerboard scale (8L 3s)===
-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:
+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 need 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
-P4 and P5 do not appear here. P5 occurs at +18 ~9/7 generators, which implies the Sasa-tritribizo comma [5 -35 0 18> and the extremely complex [[pergen]] (P8, c<sup>6</sup>P5/18). However, one 3-limit  interval occurs much sooner. 16/9 = m7 occurs at only +5 generators, meaning that this temperament can be considered to be the 2.9.15.7 [[Just intonation subgroup|subgroup]] with [[225/224]] & [[245/243]] vanishing. This implies the much simpler and hence much more useful pergen (P8, cm7/5). The [[Color notation/Temperament Names|color name]] is [[3125/3072|Laquinyo]] & [[225/224|Ruyoyo]] wawa, where "wawa" is a slangy term for using 9 not 3 in the subgroup. Adding prime 11 to the subgroup adds the [[100/99|Luyoyo]] comma to the name.
+P4 and P5 do not appear here. Theoretically, P5 occurs at +18 ~9/7 generators, which would imply the Sasa-tritribizo comma [5 -35 0 18> and the extremely complex [[pergen]] (P8, c<sup>6</sup>P5/18). However, one 3-limit interval occurs much sooner. 16/9 = m7 occurs at only +5 generators, meaning that this temperament can be considered to be the 2.9.15.7 [[Just intonation subgroup|subgroup]] with [[225/224]] & [[245/243]] vanishing. This implies the much simpler and hence much more useful pergen (P8, cm7/5). The [[Color notation/Temperament Names|color name]] is [[3125/3072|Laquinyo]] & [[225/224|Ruyoyo]] wawa, where "wawa" is a slangy term for using 9 not 3 in the subgroup. Adding prime 11 to the subgroup adds the [[100/99|Luyoyo]] comma to the name.
 Checkerboard[5] and Checkerboard[8] are also MOS scales, with L/s ratios of 2.75 and 1.75 respectively. Checkerboard[8] is the basis for the [[TAMNAMS]] name checkertonic for 3L 5s, whereas checkerboard[5] has the [[TAMNAMS|antipentic]] step pattern.