15L 7s

↖ 14L 6s	↑ 15L 6s	16L 6s ↗
← 14L 7s	15L 7s	16L 7s →
↙ 14L 8s	↓ 15L 8s	16L 8s ↘

┌╥╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬┐ │║║║│║║│║║│║║│║║│║║│║║││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLsLLsLLsLLsLLsLLsLLs sLLsLLsLLsLLsLLsLLsLLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	19\22 to 13\15 (1036.4¢ to 1040.0¢)
Dark	2\15 to 3\22 (160.0¢ to 163.6¢)
TAMNAMS information
Descends from	7L 1s (pine)
Ancestor's step ratio range	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	7L 8s
Sister	7L 15s
Daughters	22L 15s, 15L 22s
Neutralized	8L 14s
2-Flought	37L 7s, 15L 29s
Equal tunings
Equalized (L:s = 1:1)	19\22 (1036.4¢)
Supersoft (L:s = 4:3)	70\81 (1037.0¢)
Soft (L:s = 3:2)	51\59 (1037.3¢)
Semisoft (L:s = 5:3)	83\96 (1037.5¢)
Basic (L:s = 2:1)	32\37 (1037.8¢)
Semihard (L:s = 5:2)	77\89 (1038.2¢)
Hard (L:s = 3:1)	45\52 (1038.5¢)
Superhard (L:s = 4:1)	58\67 (1038.8¢)
Collapsed (L:s = 1:0)	13\15 (1040.0¢)

15L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 7 small steps, repeating every octave. 15L 7s is a grandchild scale of 7L 1s, expanding it by 14 tones. Generators that produce this scale range from 1036.4¢ to 1040¢, or from 160¢ to 163.6¢.

Modes

Modes of 15L 7s

UDP	Cyclic order	Step pattern
21|0	1	LLLsLLsLLsLLsLLsLLsLLs
20|1	20	LLsLLLsLLsLLsLLsLLsLLs
19|2	17	LLsLLsLLLsLLsLLsLLsLLs
18|3	14	LLsLLsLLsLLLsLLsLLsLLs
17|4	11	LLsLLsLLsLLsLLLsLLsLLs
16|5	8	LLsLLsLLsLLsLLsLLLsLLs
15|6	5	LLsLLsLLsLLsLLsLLsLLLs
14|7	2	LLsLLsLLsLLsLLsLLsLLsL
13|8	21	LsLLLsLLsLLsLLsLLsLLsL
12|9	18	LsLLsLLLsLLsLLsLLsLLsL
11|10	15	LsLLsLLsLLLsLLsLLsLLsL
10|11	12	LsLLsLLsLLsLLLsLLsLLsL
9|12	9	LsLLsLLsLLsLLsLLLsLLsL
8|13	6	LsLLsLLsLLsLLsLLsLLLsL
7|14	3	LsLLsLLsLLsLLsLLsLLsLL
6|15	22	sLLLsLLsLLsLLsLLsLLsLL
5|16	19	sLLsLLLsLLsLLsLLsLLsLL
4|17	16	sLLsLLsLLLsLLsLLsLLsLL
3|18	13	sLLsLLsLLsLLLsLLsLLsLL
2|19	10	sLLsLLsLLsLLsLLLsLLsLL
1|20	7	sLLsLLsLLsLLsLLsLLLsLL
0|21	4	sLLsLLsLLsLLsLLsLLsLLL

Intervals

Intervals of 15L 7s

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 54.5¢
	Major 1-mosstep	M1ms	L	54.5¢ to 80.0¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	80.0¢ to 109.1¢
	Major 2-mosstep	M2ms	2L	109.1¢ to 160.0¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	160.0¢ to 163.6¢
	Augmented 3-mosstep	A3ms	3L	163.6¢ to 240.0¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	160.0¢ to 218.2¢
	Major 4-mosstep	M4ms	3L + s	218.2¢ to 240.0¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	240.0¢ to 272.7¢
	Major 5-mosstep	M5ms	4L + s	272.7¢ to 320.0¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	320.0¢ to 327.3¢
	Major 6-mosstep	M6ms	5L + s	327.3¢ to 400.0¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	320.0¢ to 381.8¢
	Major 7-mosstep	M7ms	5L + 2s	381.8¢ to 400.0¢
8-mosstep	Minor 8-mosstep	m8ms	5L + 3s	400.0¢ to 436.4¢
	Major 8-mosstep	M8ms	6L + 2s	436.4¢ to 480.0¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	480.0¢ to 490.9¢
	Major 9-mosstep	M9ms	7L + 2s	490.9¢ to 560.0¢
10-mosstep	Minor 10-mosstep	m10ms	6L + 4s	480.0¢ to 545.5¢
	Major 10-mosstep	M10ms	7L + 3s	545.5¢ to 560.0¢
11-mosstep	Minor 11-mosstep	m11ms	7L + 4s	560.0¢ to 600.0¢
	Major 11-mosstep	M11ms	8L + 3s	600.0¢ to 640.0¢
12-mosstep	Minor 12-mosstep	m12ms	8L + 4s	640.0¢ to 654.5¢
	Major 12-mosstep	M12ms	9L + 3s	654.5¢ to 720.0¢
13-mosstep	Minor 13-mosstep	m13ms	8L + 5s	640.0¢ to 709.1¢
	Major 13-mosstep	M13ms	9L + 4s	709.1¢ to 720.0¢
14-mosstep	Minor 14-mosstep	m14ms	9L + 5s	720.0¢ to 763.6¢
	Major 14-mosstep	M14ms	10L + 4s	763.6¢ to 800.0¢
15-mosstep	Minor 15-mosstep	m15ms	10L + 5s	800.0¢ to 818.2¢
	Major 15-mosstep	M15ms	11L + 4s	818.2¢ to 880.0¢
16-mosstep	Minor 16-mosstep	m16ms	10L + 6s	800.0¢ to 872.7¢
	Major 16-mosstep	M16ms	11L + 5s	872.7¢ to 880.0¢
17-mosstep	Minor 17-mosstep	m17ms	11L + 6s	880.0¢ to 927.3¢
	Major 17-mosstep	M17ms	12L + 5s	927.3¢ to 960.0¢
18-mosstep	Minor 18-mosstep	m18ms	12L + 6s	960.0¢ to 981.8¢
	Major 18-mosstep	M18ms	13L + 5s	981.8¢ to 1040.0¢
19-mosstep	Diminished 19-mosstep	d19ms	12L + 7s	960.0¢ to 1036.4¢
	Perfect 19-mosstep	P19ms	13L + 6s	1036.4¢ to 1040.0¢
20-mosstep	Minor 20-mosstep	m20ms	13L + 7s	1040.0¢ to 1090.9¢
	Major 20-mosstep	M20ms	14L + 6s	1090.9¢ to 1120.0¢
21-mosstep	Minor 21-mosstep	m21ms	14L + 7s	1120.0¢ to 1145.5¢
	Major 21-mosstep	M21ms	15L + 6s	1145.5¢ to 1200.0¢
22-mosstep	Perfect 22-mosstep	P22ms	15L + 7s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 15L 7s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
19\22						1036.364	163.636	1:1	1.000	Equalized 15L 7s
					108\125	1036.800	163.200	6:5	1.200
				89\103		1036.893	163.107	5:4	1.250
					159\184	1036.957	163.043	9:7	1.286
			70\81			1037.037	162.963	4:3	1.333	Supersoft 15L 7s
					191\221	1037.104	162.896	11:8	1.375
				121\140		1037.143	162.857	7:5	1.400
					172\199	1037.186	162.814	10:7	1.429
		51\59				1037.288	162.712	3:2	1.500	Soft 15L 7s
					185\214	1037.383	162.617	11:7	1.571
				134\155		1037.419	162.581	8:5	1.600
					217\251	1037.450	162.550	13:8	1.625
			83\96			1037.500	162.500	5:3	1.667	Semisoft 15L 7s
					198\229	1037.555	162.445	12:7	1.714
				115\133		1037.594	162.406	7:4	1.750
					147\170	1037.647	162.353	9:5	1.800
	32\37					1037.838	162.162	2:1	2.000	Basic 15L 7s Scales with tunings softer than this are proper
					141\163	1038.037	161.963	9:4	2.250
				109\126		1038.095	161.905	7:3	2.333
					186\215	1038.140	161.860	12:5	2.400
			77\89			1038.202	161.798	5:2	2.500	Semihard 15L 7s
					199\230	1038.261	161.739	13:5	2.600
				122\141		1038.298	161.702	8:3	2.667
					167\193	1038.342	161.658	11:4	2.750
		45\52				1038.462	161.538	3:1	3.000	Hard 15L 7s
					148\171	1038.596	161.404	10:3	3.333
				103\119		1038.655	161.345	7:2	3.500
					161\186	1038.710	161.290	11:3	3.667
			58\67			1038.806	161.194	4:1	4.000	Superhard 15L 7s
					129\149	1038.926	161.074	9:2	4.500
				71\82		1039.024	160.976	5:1	5.000
					84\97	1039.175	160.825	6:1	6.000
13\15						1040.000	160.000	1:0	→ ∞	Collapsed 15L 7s

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