9L 3s

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

┌╥╥╥┬╥╥╥┬╥╥╥┬┐ │║║║│║║║│║║║││ ││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLsLLLsLLLs sLLLsLLLsLLL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	1\12 to 1\9 (100.0 ¢ to 133.3 ¢)
Dark	2\9 to 3\12 (266.7 ¢ to 300.0 ¢)
TAMNAMS information
Related to	3L 6s (tcherepnin)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	3L 6s
Sister	3L 9s
Daughters	12L 9s, 9L 12s
Neutralized	6L 6s
2-Flought	21L 3s, 9L 15s
Equal tunings
Equalized (L:s = 1:1)	1\12 (100.0 ¢)
Supersoft (L:s = 4:3)	4\45 (106.7 ¢)
Soft (L:s = 3:2)	3\33 (109.1 ¢)
Semisoft (L:s = 5:3)	5\54 (111.1 ¢)
Basic (L:s = 2:1)	2\21 (114.3 ¢)
Semihard (L:s = 5:2)	5\51 (117.6 ¢)
Hard (L:s = 3:1)	3\30 (120.0 ¢)
Superhard (L:s = 4:1)	4\39 (123.1 ¢)
Collapsed (L:s = 1:0)	1\9 (133.3 ¢)

9L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 3 small steps, with a period of 3 large steps and 1 small step that repeats every 400.0 ¢, or 3 times every octave. 9L 3s is a child scale of 3L 6s, expanding it by 3 tones. Generators that produce this scale range from 100 ¢ to 133.3 ¢, or from 266.7 ¢ to 300 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

9L 3s represents the chromatic scale of August temperament and its higher-limit extensions.

Modes

Modes of 9L 3s

UDP	Cyclic order	Step pattern
9|0(3)	1	LLLsLLLsLLLs
6|3(3)	2	LLsLLLsLLLsL
3|6(3)	3	LsLLLsLLLsLL
0|9(3)	4	sLLLsLLLsLLL

Intervals

Intervals of 9L 3s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Diminished 1-mosstep	d1ms	s	0.0 ¢ to 100.0 ¢
	Perfect 1-mosstep	P1ms	L	100.0 ¢ to 133.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	133.3 ¢ to 200.0 ¢
	Major 2-mosstep	M2ms	2L	200.0 ¢ to 266.7 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	266.7 ¢ to 300.0 ¢
	Augmented 3-mosstep	A3ms	3L	300.0 ¢ to 400.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	400.0 ¢
5-mosstep	Diminished 5-mosstep	d5ms	3L + 2s	400.0 ¢ to 500.0 ¢
	Perfect 5-mosstep	P5ms	4L + s	500.0 ¢ to 533.3 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	533.3 ¢ to 600.0 ¢
	Major 6-mosstep	M6ms	5L + s	600.0 ¢ to 666.7 ¢
7-mosstep	Perfect 7-mosstep	P7ms	5L + 2s	666.7 ¢ to 700.0 ¢
	Augmented 7-mosstep	A7ms	6L + s	700.0 ¢ to 800.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	6L + 2s	800.0 ¢
9-mosstep	Diminished 9-mosstep	d9ms	6L + 3s	800.0 ¢ to 900.0 ¢
	Perfect 9-mosstep	P9ms	7L + 2s	900.0 ¢ to 933.3 ¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	933.3 ¢ to 1000.0 ¢
	Major 10-mosstep	M10ms	8L + 2s	1000.0 ¢ to 1066.7 ¢
11-mosstep	Perfect 11-mosstep	P11ms	8L + 3s	1066.7 ¢ to 1100.0 ¢
	Augmented 11-mosstep	A11ms	9L + 2s	1100.0 ¢ to 1200.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	9L + 3s	1200.0 ¢

Scale tree

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