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 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

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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.

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.

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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==Non-awkward MOS scales ==

See the discussion at [[Kite Giedraitis's Categorizations of 41edo Scales]]. It also discusses the many non-octave MOS scales. Checkerboard[11] is discussed in the eleven-tone section. It can be thought of as every other note of Laquinyo. ~~Tritriyo~~ is ~~likewise~~ every fourth note.

See the discussion at [[Kite Giedraitis's Categorizations of 41edo Scales]]. It also discusses the many non-octave MOS scales. Checkerboard[11] is discussed in the eleven-tone section. It can be thought of as every other note of the Laquinyo genchain. Likewise, the 41edo smitonic scale, based on an ^m3 generator, is every fourth note of the Laquinyo genchain, and the Pythagorean pentatonic is every fifth note. Other MOS scales derived from the ^m3 generator are more awkward to play.

{| class="wikitable"

|+non-awkward MOS scales

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!notes

|-

|~~Tritriyo~~

|[[Smitonic]]

|(P8, ccP4/9)

|11\41

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| +1, -5

|-

| rowspan="3" |Checkerboard

| rowspan="3" |Checkerboard or Laquinyo

or Laquinyo

wawa

| rowspan="3" |(P8, cm7/5)

@@ Line 1,660: / Line 1,660: @@
 ===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 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
@@ Line 1,666: / Line 1,666: @@
 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.
+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.
 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'''.
@@ Line 1,963: / Line 1,963: @@
 ==Non-awkward MOS scales ==
-See the discussion at [[Kite Giedraitis's Categorizations of 41edo Scales]]. It also discusses the many non-octave MOS scales. Checkerboard[11] is discussed in the eleven-tone section. It  can be thought of as every other note of Laquinyo. Tritriyo is likewise every fourth note.
+See the discussion at [[Kite Giedraitis's Categorizations of 41edo Scales]]. It also discusses the many non-octave MOS scales. Checkerboard[11] is discussed in the eleven-tone section. It  can be thought of as every other note of the Laquinyo genchain. Likewise, the 41edo smitonic scale, based on an ^m3 generator, is every fourth note of the Laquinyo genchain, and the Pythagorean pentatonic is every fifth note. Other MOS scales derived from the ^m3 generator are more awkward to play.
 {| class="wikitable"
 |+non-awkward MOS scales
@@ Line 1,975: / Line 1,975: @@
 !notes
 |-
-|Tritriyo
+|[[Smitonic]]
 |(P8, ccP4/9)
 |11\41
@@ Line 2,015: / Line 2,015: @@
 | +1, -5
 |-
-| rowspan="3" |Checkerboard
+| rowspan="3" |Checkerboard or Laquinyo
-or Laquinyo
 wawa
 | rowspan="3" |(P8, cm7/5)