4L 10s

↖ 3L 9s	↑ 4L 9s	5L 9s ↗
← 3L 10s	4L 10s	5L 10s →
↙ 3L 11s	↓ 4L 11s	5L 11s ↘

┌╥┬┬╥┬┬┬╥┬┬╥┬┬┬┐ │║││║│││║││║││││ ││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssLsssLssLsss sssLssLsssLssL
Equave	2/1 (1200.0 ¢)
Period	1\2 (600.0 ¢)
Generator size
Bright	3\14 to 1\4 (257.1 ¢ to 300.0 ¢)
Dark	1\4 to 4\14 (300.0 ¢ to 342.9 ¢)
TAMNAMS information
Related to	4L 6s (lime)
With tunings	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	4L 6s
Sister	10L 4s
Daughters	14L 4s, 4L 14s
Neutralized	8L 6s
2-Flought	18L 10s, 4L 24s
Equal tunings
Equalized (L:s = 1:1)	3\14 (257.1 ¢)
Supersoft (L:s = 4:3)	10\46 (260.9 ¢)
Soft (L:s = 3:2)	7\32 (262.5 ¢)
Semisoft (L:s = 5:3)	11\50 (264.0 ¢)
Basic (L:s = 2:1)	4\18 (266.7 ¢)
Semihard (L:s = 5:2)	9\40 (270.0 ¢)
Hard (L:s = 3:1)	5\22 (272.7 ¢)
Superhard (L:s = 4:1)	6\26 (276.9 ¢)
Collapsed (L:s = 1:0)	1\4 (300.0 ¢)

4L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 10 small steps, with a period of 2 large steps and 5 small steps that repeats every 600.0 ¢, or twice every octave. 4L 10s is a child scale of 4L 6s, expanding it by 4 tones. Generators that produce this scale range from 257.1 ¢ to 300 ¢, or from 300 ¢ to 342.9 ¢.

The generator range puts a minor third (300 to 342.857 cents) -1 generator away from the period and 38edo almost exactly at the harmonic entropy minimum for its pattern.

Modes

Modes of 4L 10s

UDP	Cyclic order	Step pattern
12|0(2)	1	LssLsssLssLsss
10|2(2)	4	LsssLssLsssLss
8|4(2)	7	sLssLsssLssLss
6|6(2)	3	sLsssLssLsssLs
4|8(2)	6	ssLssLsssLssLs
2|10(2)	2	ssLsssLssLsssL
0|12(2)	5	sssLssLsssLssL

Intervals

Intervals of 4L 10s

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 85.7 ¢
	Major 1-mosstep	M1ms	L	85.7 ¢ to 300.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 171.4 ¢
	Major 2-mosstep	M2ms	L + s	171.4 ¢ to 300.0 ¢
3-mosstep	Diminished 3-mosstep	d3ms	3s	0.0 ¢ to 257.1 ¢
	Perfect 3-mosstep	P3ms	L + 2s	257.1 ¢ to 300.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	L + 3s	300.0 ¢ to 342.9 ¢
	Augmented 4-mosstep	A4ms	2L + 2s	342.9 ¢ to 600.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	300.0 ¢ to 428.6 ¢
	Major 5-mosstep	M5ms	2L + 3s	428.6 ¢ to 600.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	300.0 ¢ to 514.3 ¢
	Major 6-mosstep	M6ms	2L + 4s	514.3 ¢ to 600.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	2L + 5s	600.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	600.0 ¢ to 685.7 ¢
	Major 8-mosstep	M8ms	3L + 5s	685.7 ¢ to 900.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	600.0 ¢ to 771.4 ¢
	Major 9-mosstep	M9ms	3L + 6s	771.4 ¢ to 900.0 ¢
10-mosstep	Diminished 10-mosstep	d10ms	2L + 8s	600.0 ¢ to 857.1 ¢
	Perfect 10-mosstep	P10ms	3L + 7s	857.1 ¢ to 900.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	3L + 8s	900.0 ¢ to 942.9 ¢
	Augmented 11-mosstep	A11ms	4L + 7s	942.9 ¢ to 1200.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	3L + 9s	900.0 ¢ to 1028.6 ¢
	Major 12-mosstep	M12ms	4L + 8s	1028.6 ¢ to 1200.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	3L + 10s	900.0 ¢ to 1114.3 ¢
	Major 13-mosstep	M13ms	4L + 9s	1114.3 ¢ to 1200.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	4L + 10s	1200.0 ¢