Kite Guitar Scales - Revision history

ArrowHead294 at 19:16, 13 March 2025

2025-03-13T19:16:31Z

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TallKite: /* 5L3s scales */ completed the table

2023-04-26T08:27:09Z

5L3s scales: completed the table

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TallKite: /* Other scales */

2023-04-20T23:11:37Z

Other scales

← Older revision		Revision as of 23:11, 20 April 2023
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	\|}		\|}

	== Other ~~Scales~~ ==		== Other scales ==

	=== 6L1s scales ===		=== 6L1s scales ===
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	To find the mode with the most notes in common, read the table from left to right, top to bottom. There are three series of 7 modes each:		To find the mode with the most notes in common, read the table from left to right, top to bottom. There are three series of 7 modes each:

	* down #1 <--> sym #1 <--> up #1 <--> down #2 <--> sym #2 <--> up #2 <--> down #3		* down #1 -- sym #1 -- up #1 -- down #2 -- sym #2 -- up #2 -- down #3
	* sym #3 <--> up #3 <--> down #4 <--> sym #4 <--> up #4 <--> down #5 <--> sym #5		* sym #3 -- up #3 -- down #4 -- sym #4 -- up #4 -- down #5 -- sym #5
	* up #5 <--> down #6 <--> sym #6 <--> up #6 <--> down #7 <--> sym #7 <--> up #7		* up #5 -- down #6 -- sym #6 -- up #6 -- down #7 -- sym #7 -- up #7

	=== 5L3s scales ===		=== 5L3s scales ===
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	* up pattern: 7 6 3 6 6 3 6 4		* up pattern: 7 6 3 6 6 3 6 4
	* down pattern: 6 6 3 6 7 4 6 3		* down pattern: 6 6 3 6 7 4 6 3
	* ??? pattern: 7 6 4 6 6 3 6 3		* ??? pattern: 6 7 4 6 6 3 6 3
	* ??? pattern: 6 6 4 7 6 3 6 3		* ??? pattern: 6 6 4 7 6 3 6 3
	The last two patterns have 4 notes on just one string.		The last two patterns have 4 notes on just one string.
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	\|+'''modes of 41edo's pseudo-5L3s (Kite guitar moves +3, -3, -5, +2)'''		\|+'''modes of 41edo's pseudo-5L3s (Kite guitar moves +3, -3, -5, +2)'''
	!		!
	!		!up
	!		!down
	!		!
	!		!

TallKite: major rewrite

2023-04-20T22:48:03Z

major rewrite

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AthiTrydhen: /* Archaeotonic scales */

2023-04-18T19:37:23Z

Archaeotonic scales

← Older revision		Revision as of 19:37, 18 April 2023
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	==== Archaeotonic scales ====		==== Archaeotonic scales ====
	41edo admits an [[archaeotonic]] scale with L = 6\41 (also the generator) and s = 5\41; this is also the closest that 41edo gets to 7edo. This scale isn't really awkward to play as a scale on the Kite guitar, though it slides up to the next rainbow zone. Scales approximating harder archaeotonic scales are possible, with the small step being 2, 3 ~~or 4~~ arrows and the large step 6, 7 ~~or 8~~ arrows.		41edo admits an [[archaeotonic]] scale with L = 6\41 (also the generator) and s = 5\41; this is also the closest that 41edo gets to 7edo. This scale isn't really awkward to play as a scale on the Kite guitar, though it slides up to the next rainbow zone. Scales approximating harder archaeotonic scales are possible, with the small step being 3 arrows and the large step 6 or 7 arrows.

	When the small step is 3 arrows, the most even-sounding scale would have two 7-arrow large steps and four 6-arrow large steps. To avoid three consecutive notes on different strings, we can choose between these patterns:		When the small step is 3 arrows, the most even-sounding scale would have two 7-arrow large steps and four 6-arrow large steps. To avoid three consecutive notes on different strings, we can choose between these patterns:

AthiTrydhen: /* Oneirotonic scales */

2023-04-18T19:36:25Z

Oneirotonic scales

← Older revision		Revision as of 19:36, 18 April 2023
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	41edo admits [[oneirotonic]] scales based on the 16\41 or 25\41 generator, but these can be tricky to play on the Kite guitar, since they have five odd-numbered steps rather than three as in the scales listed above. For example, the Celephaisian mode has the step size pattern 7 2 7 7 2 7 7 2. This can be modified (with the general effect of softening the scale) by using 3-arrow intervals (m2) and 4-arrow intervals (^m2 or A1) for the small steps. To balance these out, the large steps would have to be primarily 6-arrow (vM2). To get the general oneirotonic feel, a 7-arrow large step (M2) is preferred over a 5-arrow one (~2) in the event that a large step with an odd number of arrows is needed.		41edo admits [[oneirotonic]] scales based on the 16\41 or 25\41 generator, but these can be tricky to play on the Kite guitar, since they have five odd-numbered steps rather than three as in the scales listed above. For example, the Celephaisian mode has the step size pattern 7 2 7 7 2 7 7 2. This can be modified (with the general effect of softening the scale) by using 3-arrow intervals (m2) and 4-arrow intervals (^m2 or A1) for the small steps. To balance these out, the large steps would have to be primarily 6-arrow (vM2). To get the general oneirotonic feel, a 7-arrow large step (M2) is preferred over a 5-arrow one (~2) in the event that a large step with an odd number of arrows is needed.

	~~An example~~ of ~~a modification~~ to ~~Celephaisian is~~ 6 ~~4 7~~ 6 3 6 6 3. ~~Modifications~~ to ~~oneirotonic modes generally add a perfect fifth or a perfect fourth above~~ the ~~tonic~~ if ~~we want~~ the ~~steps with odd numbers~~ of ~~arrows to be roughly evenly distributed. One notable exception is 3~~ 6 4 7 6 3 6 6~~, a modification of Sarnathian and the eighth mode of the modified Celephaisian.~~		If all three small steps are 3-arrow, all the large steps have to contain an even number of arrows for the scale not to be awkward, which means there would have to be an 8-arrow large step, which can be placed anywhere in the scale. This gives rise to these three scale paradigms, not counting inversions or modes:

			* 8 3 6 6 3 6 6 3 (inversionally symmetric)
			* 6 3 8 6 3 6 6 3
			* 6 3 6 8 3 6 6 3

			Alternatively, one of the small steps can be 4-arrow. It's easiest to spread out the odd numbered steps if the 4-arrow step isn't right in the middle of the scale, hence these possibilities:

			* uponeirotonic: 6 4 7 6 3 6 6 3
			* downoneirotonic: 6 3 6 6 3 6 7 4

	=== Enneatonic (nine-tone) ===		=== Enneatonic (nine-tone) ===

AthiTrydhen: /* Archaeotonic scales */

2023-04-18T19:24:54Z

Archaeotonic scales

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 ==== Archaeotonic scales ====
-edo admits an [[archaeotonic]] scale with L = 6\41 (also the generator) and s = 5\41; this is also the closest that 41edo gets to 7edo. This scale isn't really awkward to play as a scale on the Kite guitar, though it slides up to the next rainbow zone. Scales approximating harder archaeotonic scales are possible, with the small step being 2, 3 or 4 arrows and the large step 6, 7 or 8 arrows. An example is 6 7 6 6 7 6 3, which doesn't slide up the fretboard. As is typical of hard archaeotonic scales, this scale lacks perfect fourths and fifths.
+edo admits an [[archaeotonic]] scale with L = 6\41 (also the generator) and s = 5\41; this is also the closest that 41edo gets to 7edo. This scale isn't really awkward to play as a scale on the Kite guitar, though it slides up to the next rainbow zone. Scales approximating harder archaeotonic scales are possible, with the small step being 2, 3 or 4 arrows and the large step 6, 7 or 8 arrows.
 ===Octotonic (3L 3m 2s)===

AthiTrydhen: /* Eleven-tone - The checkerboard scale (8L 3s) */

2023-04-18T07:37:41Z

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

← Older revision		Revision as of 07:37, 18 April 2023
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	===Eleven-tone - The checkerboard scale (8L 3s)===		===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		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.		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.

AthiTrydhen: /* Archaeotonic scales */

2023-04-18T07:32:41Z

Archaeotonic scales

← Older revision		Revision as of 07:32, 18 April 2023
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	==== Archaeotonic scales ====		==== Archaeotonic scales ====
	41edo admits an [[archaeotonic]] scale with L = 6\41 (also the generator) and s = 5\41; this is also the closest that 41edo gets to 7edo. This scale isn't really awkward to play as a scale on the Kite guitar, though it slides up to the next rainbow zone. Scales approximating harder archaeotonic scales are possible, with the small step being 2, 3 or 4 arrows and the large step 6, 7 or 8 arrows. An example is 6 7 6 6 7 6 3, which doesn't slide up the fretboard.		41edo admits an [[archaeotonic]] scale with L = 6\41 (also the generator) and s = 5\41; this is also the closest that 41edo gets to 7edo. This scale isn't really awkward to play as a scale on the Kite guitar, though it slides up to the next rainbow zone. Scales approximating harder archaeotonic scales are possible, with the small step being 2, 3 or 4 arrows and the large step 6, 7 or 8 arrows. An example is 6 7 6 6 7 6 3, which doesn't slide up the fretboard. As is typical of hard archaeotonic scales, this scale lacks perfect fourths and fifths.

	===Octotonic (3L 3m 2s)===		===Octotonic (3L 3m 2s)===

AthiTrydhen: /* Archaeotonic scales */ melodies can get awkward

2023-04-18T07:31:37Z

Archaeotonic scales: melodies can get awkward

← Older revision		Revision as of 07:31, 18 April 2023
Line 1,283:		Line 1,283:

	==== Archaeotonic scales ====		==== Archaeotonic scales ====
	41edo admits an [[archaeotonic]] scale with L = 6\41 (also the generator) and s = 5\41; this is also the closest that 41edo gets to 7edo. This scale isn't really awkward to play, though it slides up to the next rainbow zone. Scales approximating harder archaeotonic scales are possible, with the small step being 2, 3 or 4 arrows and the large step 6, 7 or 8 arrows. An example is 6 7 6 6 7 6 3, which doesn't slide up the fretboard.		41edo admits an [[archaeotonic]] scale with L = 6\41 (also the generator) and s = 5\41; this is also the closest that 41edo gets to 7edo. This scale isn't really awkward to play as a scale on the Kite guitar, though it slides up to the next rainbow zone. Scales approximating harder archaeotonic scales are possible, with the small step being 2, 3 or 4 arrows and the large step 6, 7 or 8 arrows. An example is 6 7 6 6 7 6 3, which doesn't slide up the fretboard.

	===Octotonic (3L 3m 2s)===		===Octotonic (3L 3m 2s)===