3L 9s

↖ 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.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

MOS data is deprecated. Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

Scale tree

Scale tree and tuning spectrum of 3L 9s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\12						300.000	100.000	1:1	1.000	Equalized 3L 9s
					16\63	304.762	95.238	6:5	1.200	Misty/fog
				13\51		305.882	94.118	5:4	1.250
					23\90	306.667	93.333	9:7	1.286
			10\39			307.692	92.308	4:3	1.333	Supersoft 3L 9s
					27\105	308.571	91.429	11:8	1.375
				17\66		309.091	90.909	7:5	1.400
					24\93	309.677	90.323	10:7	1.429
		7\27				311.111	88.889	3:2	1.500	Soft 3L 9s Augene is around here
					25\96	312.500	87.500	11:7	1.571
				18\69		313.043	86.957	8:5	1.600
					29\111	313.514	86.486	13:8	1.625	Golden inflated (71.1993 ¢)
			11\42			314.286	85.714	5:3	1.667	Semisoft 3L 9s
					26\99	315.152	84.848	12:7	1.714
				15\57		315.789	84.211	7:4	1.750
					19\72	316.667	83.333	9:5	1.800
	4\15					320.000	80.000	2:1	2.000	Basic 3L 9s Scales with tunings softer than this are proper
					17\63	323.810	76.190	9:4	2.250
				13\48		325.000	75.000	7:3	2.333
					22\81	325.926	74.074	12:5	2.400
			9\33			327.273	72.727	5:2	2.500	Semihard 3L 9s Inflated is around here
					23\84	328.571	71.429	13:5	2.600
				14\51		329.412	70.588	8:3	2.667
					19\69	330.435	69.565	11:4	2.750
		5\18				333.333	66.667	3:1	3.000	Hard 3L 9s
					16\57	336.842	63.158	10:3	3.333
				11\39		338.462	61.538	7:2	3.500
					17\60	340.000	60.000	11:3	3.667
			6\21			342.857	57.143	4:1	4.000	Superhard 3L 9s
					13\45	346.667	53.333	9:2	4.500
				7\24		350.000	50.000	5:1	5.000
					8\27	355.556	44.444	6:1	6.000	Hemiaug
1\3						400.000	0.000	1:0	→ ∞	Collapsed 3L 9s