Kite Guitar Scales: Difference between revisions

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

~~The [[Color notation~~/~~Temperament Names|color 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.

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.

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 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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 M3 ~6 m2 ^4 vm7 M2 ~5 vM7 ^m3 vm6 '''<u>P1</u>''' ^M3 vM6 ^m2 ~4 m7 ^M2 v5 M7 ~3 m6
-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.
+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.
+Checkerboard[5] and Checkerboard[8] are also MOS scales, with L/s ratios of 2.75 and 1.75 respectively.
 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'''.