15L 5s

15L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 5 small steps, with a period of 3 large steps and 1 small step that repeats every 240.0 ¢, or 5 times every octave. 15L 5s is a grandchild scale of 5L 5s, expanding it by 10 tones. Generators that produce this scale range from 60 ¢ to 80 ¢, or from 160 ¢ to 180 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

↖ 14L 4s	↑ 15L 4s	16L 4s ↗
← 14L 5s	15L 5s	16L 5s →
↙ 14L 6s	↓ 15L 6s	16L 6s ↘

Scale structure
Step pattern	LLLsLLLsLLLsLLLsLLLs sLLLsLLLsLLLsLLLsLLL
Equave	2/1 (1200.0 ¢)
Period	1\5 (240.0 ¢)
Generator size
Bright	1\20 to 1\15 (60.0 ¢ to 80.0 ¢)
Dark	2\15 to 3\20 (160.0 ¢ to 180.0 ¢)
TAMNAMS information
Related to	5L 5s (pentawood)
With tunings	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	5L 10s
Sister	5L 15s
Daughters	20L 15s, 15L 20s
Neutralized	10L 10s
2-Flought	35L 5s, 15L 25s
Equal tunings
Equalized (L:s = 1:1)	1\20 (60.0 ¢)
Supersoft (L:s = 4:3)	4\75 (64.0 ¢)
Soft (L:s = 3:2)	3\55 (65.5 ¢)
Semisoft (L:s = 5:3)	5\90 (66.7 ¢)
Basic (L:s = 2:1)	2\35 (68.6 ¢)
Semihard (L:s = 5:2)	5\85 (70.6 ¢)
Hard (L:s = 3:1)	3\50 (72.0 ¢)
Superhard (L:s = 4:1)	4\65 (73.8 ¢)
Collapsed (L:s = 1:0)	1\15 (80.0 ¢)
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Modes

Modes of 15L 5s

UDP	Cyclic order	Step pattern
15|0(5)	1	LLLsLLLsLLLsLLLsLLLs
10|5(5)	2	LLsLLLsLLLsLLLsLLLsL
5|10(5)	3	LsLLLsLLLsLLLsLLLsLL
0|15(5)	4	sLLLsLLLsLLLsLLLsLLL

Intervals

Intervals of 15L 5s

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 60.0 ¢
	Perfect 1-mosstep	P1ms	L	60.0 ¢ to 80.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	80.0 ¢ to 120.0 ¢
	Major 2-mosstep	M2ms	2L	120.0 ¢ to 160.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	160.0 ¢ to 180.0 ¢
	Augmented 3-mosstep	A3ms	3L	180.0 ¢ to 240.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	240.0 ¢
5-mosstep	Diminished 5-mosstep	d5ms	3L + 2s	240.0 ¢ to 300.0 ¢
	Perfect 5-mosstep	P5ms	4L + s	300.0 ¢ to 320.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	320.0 ¢ to 360.0 ¢
	Major 6-mosstep	M6ms	5L + s	360.0 ¢ to 400.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	5L + 2s	400.0 ¢ to 420.0 ¢
	Augmented 7-mosstep	A7ms	6L + s	420.0 ¢ to 480.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	6L + 2s	480.0 ¢
9-mosstep	Diminished 9-mosstep	d9ms	6L + 3s	480.0 ¢ to 540.0 ¢
	Perfect 9-mosstep	P9ms	7L + 2s	540.0 ¢ to 560.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	560.0 ¢ to 600.0 ¢
	Major 10-mosstep	M10ms	8L + 2s	600.0 ¢ to 640.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	8L + 3s	640.0 ¢ to 660.0 ¢
	Augmented 11-mosstep	A11ms	9L + 2s	660.0 ¢ to 720.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	9L + 3s	720.0 ¢
13-mosstep	Diminished 13-mosstep	d13ms	9L + 4s	720.0 ¢ to 780.0 ¢
	Perfect 13-mosstep	P13ms	10L + 3s	780.0 ¢ to 800.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	10L + 4s	800.0 ¢ to 840.0 ¢
	Major 14-mosstep	M14ms	11L + 3s	840.0 ¢ to 880.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	11L + 4s	880.0 ¢ to 900.0 ¢
	Augmented 15-mosstep	A15ms	12L + 3s	900.0 ¢ to 960.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	12L + 4s	960.0 ¢
17-mosstep	Diminished 17-mosstep	d17ms	12L + 5s	960.0 ¢ to 1020.0 ¢
	Perfect 17-mosstep	P17ms	13L + 4s	1020.0 ¢ to 1040.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	13L + 5s	1040.0 ¢ to 1080.0 ¢
	Major 18-mosstep	M18ms	14L + 4s	1080.0 ¢ to 1120.0 ¢
19-mosstep	Perfect 19-mosstep	P19ms	14L + 5s	1120.0 ¢ to 1140.0 ¢
	Augmented 19-mosstep	A19ms	15L + 4s	1140.0 ¢ to 1200.0 ¢
20-mosstep	Perfect 20-mosstep	P20ms	15L + 5s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 15L 5s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\20						60.000	180.000	1:1	1.000	Equalized 15L 5s
					6\115	62.609	177.391	6:5	1.200
				5\95		63.158	176.842	5:4	1.250
					9\170	63.529	176.471	9:7	1.286
			4\75			64.000	176.000	4:3	1.333	Supersoft 15L 5s
					11\205	64.390	175.610	11:8	1.375
				7\130		64.615	175.385	7:5	1.400
					10\185	64.865	175.135	10:7	1.429
		3\55				65.455	174.545	3:2	1.500	Soft 15L 5s
					11\200	66.000	174.000	11:7	1.571
				8\145		66.207	173.793	8:5	1.600
					13\235	66.383	173.617	13:8	1.625
			5\90			66.667	173.333	5:3	1.667	Semisoft 15L 5s
					12\215	66.977	173.023	12:7	1.714
				7\125		67.200	172.800	7:4	1.750
					9\160	67.500	172.500	9:5	1.800
	2\35					68.571	171.429	2:1	2.000	Basic 15L 5s
					9\155	69.677	170.323	9:4	2.250
				7\120		70.000	170.000	7:3	2.333
					12\205	70.244	169.756	12:5	2.400
			5\85			70.588	169.412	5:2	2.500	Semihard 15L 5s
					13\220	70.909	169.091	13:5	2.600
				8\135		71.111	168.889	8:3	2.667
					11\185	71.351	168.649	11:4	2.750
		3\50				72.000	168.000	3:1	3.000	Hard 15L 5s
					10\165	72.727	167.273	10:3	3.333
				7\115		73.043	166.957	7:2	3.500
					11\180	73.333	166.667	11:3	3.667
			4\65			73.846	166.154	4:1	4.000	Superhard 15L 5s
					9\145	74.483	165.517	9:2	4.500
				5\80		75.000	165.000	5:1	5.000
					6\95	75.789	164.211	6:1	6.000
1\15						80.000	160.000	1:0	→ ∞	Collapsed 15L 5s

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