5L 15s

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

Scale structure
Step pattern	LsssLsssLsssLsssLsss sssLsssLsssLsssLsssL
Equave	2/1 (1200.0 ¢)
Period	1\5 (240.0 ¢)
Generator size
Bright	3\20 to 1\5 (180.0 ¢ to 240.0 ¢)
Dark	0\5 to 1\20 (0.0 ¢ to 60.0 ¢)
TAMNAMS information
Related to	5L 5s (pentawood)
With tunings	3:1 to 1:0 (hard)
Related MOS scales
Parent	5L 10s
Sister	15L 5s
Daughters	20L 5s, 5L 20s
Neutralized	10L 10s
2-Flought	25L 15s, 5L 35s
Equal tunings
Equalized (L:s = 1:1)	3\20 (180.0 ¢)
Supersoft (L:s = 4:3)	10\65 (184.6 ¢)
Soft (L:s = 3:2)	7\45 (186.7 ¢)
Semisoft (L:s = 5:3)	11\70 (188.6 ¢)
Basic (L:s = 2:1)	4\25 (192.0 ¢)
Semihard (L:s = 5:2)	9\55 (196.4 ¢)
Hard (L:s = 3:1)	5\30 (200.0 ¢)
Superhard (L:s = 4:1)	6\35 (205.7 ¢)
Collapsed (L:s = 1:0)	1\5 (240.0 ¢)
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5L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 15 small steps, with a period of 1 large step and 3 small steps that repeats every 240.0 ¢, or 5 times every octave. 5L 15s is a grandchild scale of 5L 5s, expanding it by 10 tones. Generators that produce this scale range from 180 ¢ to 240 ¢, or from 0 ¢ to 60 ¢.

Modes

Modes of 5L 15s

UDP	Cyclic order	Step pattern
15|0(5)	1	LsssLsssLsssLsssLsss
10|5(5)	4	sLsssLsssLsssLsssLss
5|10(5)	3	ssLsssLsssLsssLsssLs
0|15(5)	2	sssLsssLsssLsssLsssL

Intervals

Intervals of 5L 15s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Perfect 1-mosstep	P1ms	s	0.0 ¢ to 60.0 ¢
	Augmented 1-mosstep	A1ms	L	60.0 ¢ to 240.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 120.0 ¢
	Major 2-mosstep	M2ms	L + s	120.0 ¢ to 240.0 ¢
3-mosstep	Diminished 3-mosstep	d3ms	3s	0.0 ¢ to 180.0 ¢
	Perfect 3-mosstep	P3ms	L + 2s	180.0 ¢ to 240.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	L + 3s	240.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	L + 4s	240.0 ¢ to 300.0 ¢
	Augmented 5-mosstep	A5ms	2L + 3s	300.0 ¢ to 480.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	240.0 ¢ to 360.0 ¢
	Major 6-mosstep	M6ms	2L + 4s	360.0 ¢ to 480.0 ¢
7-mosstep	Diminished 7-mosstep	d7ms	L + 6s	240.0 ¢ to 420.0 ¢
	Perfect 7-mosstep	P7ms	2L + 5s	420.0 ¢ to 480.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	2L + 6s	480.0 ¢
9-mosstep	Perfect 9-mosstep	P9ms	2L + 7s	480.0 ¢ to 540.0 ¢
	Augmented 9-mosstep	A9ms	3L + 6s	540.0 ¢ to 720.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	2L + 8s	480.0 ¢ to 600.0 ¢
	Major 10-mosstep	M10ms	3L + 7s	600.0 ¢ to 720.0 ¢
11-mosstep	Diminished 11-mosstep	d11ms	2L + 9s	480.0 ¢ to 660.0 ¢
	Perfect 11-mosstep	P11ms	3L + 8s	660.0 ¢ to 720.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	3L + 9s	720.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	3L + 10s	720.0 ¢ to 780.0 ¢
	Augmented 13-mosstep	A13ms	4L + 9s	780.0 ¢ to 960.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	3L + 11s	720.0 ¢ to 840.0 ¢
	Major 14-mosstep	M14ms	4L + 10s	840.0 ¢ to 960.0 ¢
15-mosstep	Diminished 15-mosstep	d15ms	3L + 12s	720.0 ¢ to 900.0 ¢
	Perfect 15-mosstep	P15ms	4L + 11s	900.0 ¢ to 960.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	4L + 12s	960.0 ¢
17-mosstep	Perfect 17-mosstep	P17ms	4L + 13s	960.0 ¢ to 1020.0 ¢
	Augmented 17-mosstep	A17ms	5L + 12s	1020.0 ¢ to 1200.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	4L + 14s	960.0 ¢ to 1080.0 ¢
	Major 18-mosstep	M18ms	5L + 13s	1080.0 ¢ to 1200.0 ¢
19-mosstep	Diminished 19-mosstep	d19ms	4L + 15s	960.0 ¢ to 1140.0 ¢
	Perfect 19-mosstep	P19ms	5L + 14s	1140.0 ¢ to 1200.0 ¢
20-mosstep	Perfect 20-mosstep	P20ms	5L + 15s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 5L 15s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\20						180.000	60.000	1:1	1.000	Equalized 5L 15s
					16\105	182.857	57.143	6:5	1.200
				13\85		183.529	56.471	5:4	1.250
					23\150	184.000	56.000	9:7	1.286
			10\65			184.615	55.385	4:3	1.333	Supersoft 5L 15s
					27\175	185.143	54.857	11:8	1.375
				17\110		185.455	54.545	7:5	1.400
					24\155	185.806	54.194	10:7	1.429
		7\45				186.667	53.333	3:2	1.500	Soft 5L 15s
					25\160	187.500	52.500	11:7	1.571
				18\115		187.826	52.174	8:5	1.600
					29\185	188.108	51.892	13:8	1.625
			11\70			188.571	51.429	5:3	1.667	Semisoft 5L 15s
					26\165	189.091	50.909	12:7	1.714
				15\95		189.474	50.526	7:4	1.750
					19\120	190.000	50.000	9:5	1.800
	4\25					192.000	48.000	2:1	2.000	Basic 5L 15s Scales with tunings softer than this are proper
					17\105	194.286	45.714	9:4	2.250
				13\80		195.000	45.000	7:3	2.333
					22\135	195.556	44.444	12:5	2.400
			9\55			196.364	43.636	5:2	2.500	Semihard 5L 15s
					23\140	197.143	42.857	13:5	2.600
				14\85		197.647	42.353	8:3	2.667
					19\115	198.261	41.739	11:4	2.750
		5\30				200.000	40.000	3:1	3.000	Hard 5L 15s
					16\95	202.105	37.895	10:3	3.333
				11\65		203.077	36.923	7:2	3.500
					17\100	204.000	36.000	11:3	3.667
			6\35			205.714	34.286	4:1	4.000	Superhard 5L 15s
					13\75	208.000	32.000	9:2	4.500
				7\40		210.000	30.000	5:1	5.000
					8\45	213.333	26.667	6:1	6.000
1\5						240.000	0.000	1:0	→ ∞	Collapsed 5L 15s

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