4L 9s

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

┌╥┬┬╥┬┬╥┬┬╥┬┬┬┐ │║││║││║││║││││ │││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssLssLssLsss sssLssLssLssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	3\13 to 1\4 (276.9 ¢ to 300.0 ¢)
Dark	3\4 to 10\13 (900.0 ¢ to 923.1 ¢)
TAMNAMS information
Related to	4L 5s (gramitonic)
With tunings	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	4L 5s
Sister	9L 4s
Daughters	13L 4s, 4L 13s
Neutralized	8L 5s
2-Flought	17L 9s, 4L 22s
Equal tunings
Equalized (L:s = 1:1)	3\13 (276.9 ¢)
Supersoft (L:s = 4:3)	10\43 (279.1 ¢)
Soft (L:s = 3:2)	7\30 (280.0 ¢)
Semisoft (L:s = 5:3)	11\47 (280.9 ¢)
Basic (L:s = 2:1)	4\17 (282.4 ¢)
Semihard (L:s = 5:2)	9\38 (284.2 ¢)
Hard (L:s = 3:1)	5\21 (285.7 ¢)
Superhard (L:s = 4:1)	6\25 (288.0 ¢)
Collapsed (L:s = 1:0)	1\4 (300.0 ¢)

4L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 9 small steps, repeating every octave. 4L 9s is a child scale of 4L 5s, expanding it by 4 tones. Generators that produce this scale range from 276.9 ¢ to 300 ¢, or from 900 ¢ to 923.1 ¢.

4L 9s represents chromatic scales of Huxley, Lovecraft, gariberttet and subklei temperaments. The harmonic entropy minimum for this pattern maps +2, +3, and +5 bright generators to 7/5, 5/3 and 7/3, respectively.

Modes

Modes of 4L 9s

UDP	Cyclic order	Step pattern
12|0	1	LssLssLssLsss
11|1	4	LssLssLsssLss
10|2	7	LssLsssLssLss
9|3	10	LsssLssLssLss
8|4	13	sLssLssLssLss
7|5	3	sLssLssLsssLs
6|6	6	sLssLsssLssLs
5|7	9	sLsssLssLssLs
4|8	12	ssLssLssLssLs
3|9	2	ssLssLssLsssL
2|10	5	ssLssLsssLssL
1|11	8	ssLsssLssLssL
0|12	11	sssLssLssLssL

Intervals

Intervals of 4L 9s

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 300.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 184.6 ¢
	Major 2-mosstep	M2ms	L + s	184.6 ¢ to 300.0 ¢
3-mosstep	Diminished 3-mosstep	d3ms	3s	0.0 ¢ to 276.9 ¢
	Perfect 3-mosstep	P3ms	L + 2s	276.9 ¢ to 300.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	300.0 ¢ to 369.2 ¢
	Major 4-mosstep	M4ms	2L + 2s	369.2 ¢ to 600.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	300.0 ¢ to 461.5 ¢
	Major 5-mosstep	M5ms	2L + 3s	461.5 ¢ to 600.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	300.0 ¢ to 553.8 ¢
	Major 6-mosstep	M6ms	2L + 4s	553.8 ¢ to 600.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	600.0 ¢ to 646.2 ¢
	Major 7-mosstep	M7ms	3L + 4s	646.2 ¢ to 900.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	600.0 ¢ to 738.5 ¢
	Major 8-mosstep	M8ms	3L + 5s	738.5 ¢ to 900.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	600.0 ¢ to 830.8 ¢
	Major 9-mosstep	M9ms	3L + 6s	830.8 ¢ to 900.0 ¢
10-mosstep	Perfect 10-mosstep	P10ms	3L + 7s	900.0 ¢ to 923.1 ¢
	Augmented 10-mosstep	A10ms	4L + 6s	923.1 ¢ to 1200.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	3L + 8s	900.0 ¢ to 1015.4 ¢
	Major 11-mosstep	M11ms	4L + 7s	1015.4 ¢ to 1200.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	3L + 9s	900.0 ¢ to 1107.7 ¢
	Major 12-mosstep	M12ms	4L + 8s	1107.7 ¢ to 1200.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	4L + 9s	1200.0 ¢