9L 4s

↖ 8L 3s	↑ 9L 3s	10L 3s ↗
← 8L 4s	9L 4s	10L 4s →
↙ 8L 5s	↓ 9L 5s	10L 5s ↘

┌╥╥╥┬╥╥┬╥╥┬╥╥┬┐ │║║║│║║│║║│║║││ │││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLsLLsLLsLLs sLLsLLsLLsLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	10\13 to 7\9 (923.1 ¢ to 933.3 ¢)
Dark	2\9 to 3\13 (266.7 ¢ to 276.9 ¢)
TAMNAMS information
Related to	4L 5s (gramitonic)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	4L 5s
Sister	4L 9s
Daughters	13L 9s, 9L 13s
Neutralized	5L 8s
2-Flought	22L 4s, 9L 17s
Equal tunings
Equalized (L:s = 1:1)	10\13 (923.1 ¢)
Supersoft (L:s = 4:3)	37\48 (925.0 ¢)
Soft (L:s = 3:2)	27\35 (925.7 ¢)
Semisoft (L:s = 5:3)	44\57 (926.3 ¢)
Basic (L:s = 2:1)	17\22 (927.3 ¢)
Semihard (L:s = 5:2)	41\53 (928.3 ¢)
Hard (L:s = 3:1)	24\31 (929.0 ¢)
Superhard (L:s = 4:1)	31\40 (930.0 ¢)
Collapsed (L:s = 1:0)	7\9 (933.3 ¢)

9L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 4 small steps, repeating every octave. 9L 4s is a child scale of 4L 5s, expanding it by 4 tones. Generators that produce this scale range from 923.1 ¢ to 933.3 ¢, or from 266.7 ¢ to 276.9 ¢.

It is the chromatic scale of Orwell temperament. The harmonic entropy minimum for this scale has three dark generators map to 8/5 (~813.6¢), where the generator is ~271.2¢.

Modes

Modes of 9L 4s

UDP	Cyclic order	Step pattern
12|0	1	LLLsLLsLLsLLs
11|1	11	LLsLLLsLLsLLs
10|2	8	LLsLLsLLLsLLs
9|3	5	LLsLLsLLsLLLs
8|4	2	LLsLLsLLsLLsL
7|5	12	LsLLLsLLsLLsL
6|6	9	LsLLsLLLsLLsL
5|7	6	LsLLsLLsLLLsL
4|8	3	LsLLsLLsLLsLL
3|9	13	sLLLsLLsLLsLL
2|10	10	sLLsLLLsLLsLL
1|11	7	sLLsLLsLLLsLL
0|12	4	sLLsLLsLLsLLL

Intervals

Intervals of 9L 4s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 92.3 ¢
	Major 1-mosstep	M1ms	L	92.3 ¢ to 133.3 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	133.3 ¢ to 184.6 ¢
	Major 2-mosstep	M2ms	2L	184.6 ¢ to 266.7 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	266.7 ¢ to 276.9 ¢
	Augmented 3-mosstep	A3ms	3L	276.9 ¢ to 400.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	266.7 ¢ to 369.2 ¢
	Major 4-mosstep	M4ms	3L + s	369.2 ¢ to 400.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	400.0 ¢ to 461.5 ¢
	Major 5-mosstep	M5ms	4L + s	461.5 ¢ to 533.3 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	533.3 ¢ to 553.8 ¢
	Major 6-mosstep	M6ms	5L + s	553.8 ¢ to 666.7 ¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	533.3 ¢ to 646.2 ¢
	Major 7-mosstep	M7ms	5L + 2s	646.2 ¢ to 666.7 ¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	666.7 ¢ to 738.5 ¢
	Major 8-mosstep	M8ms	6L + 2s	738.5 ¢ to 800.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	800.0 ¢ to 830.8 ¢
	Major 9-mosstep	M9ms	7L + 2s	830.8 ¢ to 933.3 ¢
10-mosstep	Diminished 10-mosstep	d10ms	6L + 4s	800.0 ¢ to 923.1 ¢
	Perfect 10-mosstep	P10ms	7L + 3s	923.1 ¢ to 933.3 ¢
11-mosstep	Minor 11-mosstep	m11ms	7L + 4s	933.3 ¢ to 1015.4 ¢
	Major 11-mosstep	M11ms	8L + 3s	1015.4 ¢ to 1066.7 ¢
12-mosstep	Minor 12-mosstep	m12ms	8L + 4s	1066.7 ¢ to 1107.7 ¢
	Major 12-mosstep	M12ms	9L + 3s	1107.7 ¢ to 1200.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	9L + 4s	1200.0 ¢