3L 9s

Todo: review Adopt scale tree template, review entries

↖ 2L 8s	↑ 3L 8s	4L 8s ↗
← 2L 9s	3L 9s	4L 9s →
↙ 2L 10s	↓ 3L 10s	4L 10s ↘

┌╥┬┬┬╥┬┬┬╥┬┬┬┐ │║│││║│││║││││ ││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsssLsssLsss sssLsssLsssL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	3\12 to 1\3 (300.0 ¢ to 400.0 ¢)
Dark	0\3 to 1\12 (0.0 ¢ to 100.0 ¢)
TAMNAMS information
Related to	3L 6s (tcherepnin)
With tunings	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	3L 6s
Sister	9L 3s
Daughters	12L 3s, 3L 12s
Neutralized	6L 6s
2-Flought	15L 9s, 3L 21s
Equal tunings
Equalized (L:s = 1:1)	3\12 (300.0 ¢)
Supersoft (L:s = 4:3)	10\39 (307.7 ¢)
Soft (L:s = 3:2)	7\27 (311.1 ¢)
Semisoft (L:s = 5:3)	11\42 (314.3 ¢)
Basic (L:s = 2:1)	4\15 (320.0 ¢)
Semihard (L:s = 5:2)	9\33 (327.3 ¢)
Hard (L:s = 3:1)	5\18 (333.3 ¢)
Superhard (L:s = 4:1)	6\21 (342.9 ¢)
Collapsed (L:s = 1:0)	1\3 (400.0 ¢)

3L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 9 small steps, with a period of 1 large step and 3 small steps that repeats every 400.0 ¢, or 3 times every octave. 3L 9s is a child scale of 3L 6s, expanding it by 3 tones. Generators that produce this scale range from 300 ¢ to 400 ¢, or from 0 ¢ to 100 ¢. This MOS represents, among other chromatic scales, that of the Augene temperament.

Modes

Modes of 3L 9s

UDP	Cyclic order	Step pattern
9|0(3)	1	LsssLsssLsss
6|3(3)	4	sLsssLsssLss
3|6(3)	3	ssLsssLsssLs
0|9(3)	2	sssLsssLsssL

Scale tree

Generator ranges:

• Chroma-positive generator: 300 cents (3\12) to 400 cents (1\3)
• Chroma-negative generator: 0 cents (0\3) to 100 cents (1\12)

Small step (chroma-negative generator)						Cents	L	s	L/s	Comments
1\12						100.000	1	1	1.000
					5\63	95.238	6	5	1.200	Misty/fog
				4\51		94.118	5	4	1.250
					7\90	93.333	9	7	1.286
			3\39			92.308	4	3	1.333
					8\105	91.429	11	8	1.375
				5\66		90.909	7	5	1.400
					7\93	90.323	10	7	1.429
		2\27				88.889	3	2	1.500	Augene is around here
					7\96	87.500	11	7	1.571
				5\69		86.957	8	5	1.600
					8\111	86.486	13	8	1.625	Golden augene (86.6169¢)
			3\42			85.714	5	3	1.667
					7\99	84.848	12	7	1.714
				4\57		84.211	7	4	1.750
					5\72	83.333	9	5	1.800
	1\15					80.000	2	1	2.000	Basic 3L 9s (Generators larger than this are proper)
					4\63	76.190	9	4	2.250
				3\48		75.000	7	3	2.333
					5\81	74.074	12	5	2.400
			2\33			72.727	5	2	2.500	Inflated is around here
					5\84	71.429	13	5	2.600	Golden inflated (71.1993¢)
				3\51		70.588	8	3	2.667
					4\69	69.565	11	4	2.750
		1\18				66.667	3	1	3.000
					3\57	63.158	10	3	3.333
				2\39		61.538	7	2	3.500
					3\60	60.000	11	3	3.667
			1\21			57.143	4	1	4.000
					2\45	53.333	9	2	4.500
				1\24		50.000	5	1	5.000
					1\27	44.444	6	1	6.000	Hemiaug
0\3						0	1	0	→ inf