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 generator for its harmonic entropy minimum is the cube root of 8/5.

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

Scale tree

2/9					266.667
				11/49	269.388
			9/40		270
				16/71	270.423
		7/31			270.968
				19/84	271.429
			12/53		271.698
				17/75	272
	5/22				272.727
				18/79	273.418
			13/57		273.684
				21/92	273.913
		8/35			274.286
				19/83	274.699
			11/48		275
				14/61	275.410
3/13					276.923

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