15L 3s

↖ 14L 2s	↑ 15L 2s	16L 2s ↗
← 14L 3s	15L 3s	16L 3s →
↙ 14L 4s	↓ 15L 4s	16L 4s ↘

┌╥╥╥╥╥┬╥╥╥╥╥┬╥╥╥╥╥┬┐ │║║║║║│║║║║║│║║║║║││ ││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLsLLLLLsLLLLLs sLLLLLsLLLLLsLLLLL
Equave	2/1 (1200.0 ¢)
Period	1\3 (400.0 ¢)
Generator size
Bright	1\18 to 1\15 (66.7 ¢ to 80.0 ¢)
Dark	4\15 to 5\18 (320.0 ¢ to 333.3 ¢)
TAMNAMS information
Related to	3L 6s (tcherepnin)
With tunings	3:1 to 4:1 (parahard)
Related MOS scales
Parent	3L 12s
Sister	3L 15s
Daughters	18L 15s, 15L 18s
Neutralized	12L 6s
2-Flought	33L 3s, 15L 21s
Equal tunings
Equalized (L:s = 1:1)	1\18 (66.7 ¢)
Supersoft (L:s = 4:3)	4\69 (69.6 ¢)
Soft (L:s = 3:2)	3\51 (70.6 ¢)
Semisoft (L:s = 5:3)	5\84 (71.4 ¢)
Basic (L:s = 2:1)	2\33 (72.7 ¢)
Semihard (L:s = 5:2)	5\81 (74.1 ¢)
Hard (L:s = 3:1)	3\48 (75.0 ¢)
Superhard (L:s = 4:1)	4\63 (76.2 ¢)
Collapsed (L:s = 1:0)	1\15 (80.0 ¢)

15L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 3 small steps, with a period of 5 large steps and 1 small step that repeats every 400.0 ¢, or 3 times every octave. 15L 3s is a great-grandchild scale of 3L 6s, expanding it by 9 tones. Generators that produce this scale range from 66.7 ¢ to 80 ¢, or from 320 ¢ to 333.3 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

Modes

Modes of 15L 3s

UDP	Cyclic order	Step pattern
15|0(3)	1	LLLLLsLLLLLsLLLLLs
12|3(3)	2	LLLLsLLLLLsLLLLLsL
9|6(3)	3	LLLsLLLLLsLLLLLsLL
6|9(3)	4	LLsLLLLLsLLLLLsLLL
3|12(3)	5	LsLLLLLsLLLLLsLLLL
0|15(3)	6	sLLLLLsLLLLLsLLLLL

Intervals

Intervals of 15L 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 66.7 ¢
	Perfect 1-mosstep	P1ms	L	66.7 ¢ to 80.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	80.0 ¢ to 133.3 ¢
	Major 2-mosstep	M2ms	2L	133.3 ¢ to 160.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	160.0 ¢ to 200.0 ¢
	Major 3-mosstep	M3ms	3L	200.0 ¢ to 240.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	240.0 ¢ to 266.7 ¢
	Major 4-mosstep	M4ms	4L	266.7 ¢ to 320.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	4L + s	320.0 ¢ to 333.3 ¢
	Augmented 5-mosstep	A5ms	5L	333.3 ¢ to 400.0 ¢
6-mosstep	Perfect 6-mosstep	P6ms	5L + s	400.0 ¢
7-mosstep	Diminished 7-mosstep	d7ms	5L + 2s	400.0 ¢ to 466.7 ¢
	Perfect 7-mosstep	P7ms	6L + s	466.7 ¢ to 480.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	480.0 ¢ to 533.3 ¢
	Major 8-mosstep	M8ms	7L + s	533.3 ¢ to 560.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	7L + 2s	560.0 ¢ to 600.0 ¢
	Major 9-mosstep	M9ms	8L + s	600.0 ¢ to 640.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	8L + 2s	640.0 ¢ to 666.7 ¢
	Major 10-mosstep	M10ms	9L + s	666.7 ¢ to 720.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	9L + 2s	720.0 ¢ to 733.3 ¢
	Augmented 11-mosstep	A11ms	10L + s	733.3 ¢ to 800.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	10L + 2s	800.0 ¢
13-mosstep	Diminished 13-mosstep	d13ms	10L + 3s	800.0 ¢ to 866.7 ¢
	Perfect 13-mosstep	P13ms	11L + 2s	866.7 ¢ to 880.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	11L + 3s	880.0 ¢ to 933.3 ¢
	Major 14-mosstep	M14ms	12L + 2s	933.3 ¢ to 960.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	12L + 3s	960.0 ¢ to 1000.0 ¢
	Major 15-mosstep	M15ms	13L + 2s	1000.0 ¢ to 1040.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	13L + 3s	1040.0 ¢ to 1066.7 ¢
	Major 16-mosstep	M16ms	14L + 2s	1066.7 ¢ to 1120.0 ¢
17-mosstep	Perfect 17-mosstep	P17ms	14L + 3s	1120.0 ¢ to 1133.3 ¢
	Augmented 17-mosstep	A17ms	15L + 2s	1133.3 ¢ to 1200.0 ¢
18-mosstep	Perfect 18-mosstep	P18ms	15L + 3s	1200.0 ¢

Scale tree

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