15L 2s

↖ 14L 1s	↑ 15L 1s	16L 1s ↗
← 14L 2s	15L 2s	16L 2s →
↙ 14L 3s	↓ 15L 3s	16L 3s ↘

┌╥╥╥╥╥╥╥╥┬╥╥╥╥╥╥╥┬┐ │║║║║║║║║│║║║║║║║││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLLLLsLLLLLLLs sLLLLLLLsLLLLLLLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	9\17 to 8\15 (635.3¢ to 640.0¢)
Dark	7\15 to 8\17 (560.0¢ to 564.7¢)
TAMNAMS information
Descends from	2L 7s (balzano)
Ancestor's step ratio range	4:1 to 5:1
Related MOS scales
Parent	2L 13s
Sister	2L 15s
Daughters	17L 15s, 15L 17s
Neutralized	13L 4s
2-Flought	32L 2s, 15L 19s
Equal tunings
Equalized (L:s = 1:1)	9\17 (635.3¢)
Supersoft (L:s = 4:3)	35\66 (636.4¢)
Soft (L:s = 3:2)	26\49 (636.7¢)
Semisoft (L:s = 5:3)	43\81 (637.0¢)
Basic (L:s = 2:1)	17\32 (637.5¢)
Semihard (L:s = 5:2)	42\79 (638.0¢)
Hard (L:s = 3:1)	25\47 (638.3¢)
Superhard (L:s = 4:1)	33\62 (638.7¢)
Collapsed (L:s = 1:0)	8\15 (640.0¢)

15L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 2 small steps, repeating every octave. 15L 2s is related to 2L 7s, expanding it by 8 tones. Generators that produce this scale range from 635.3¢ to 640¢, or from 560¢ to 564.7¢.

Modes

Modes of 15L 2s

UDP	Cyclic order	Step pattern
16|0	1	LLLLLLLLsLLLLLLLs
15|1	10	LLLLLLLsLLLLLLLLs
14|2	2	LLLLLLLsLLLLLLLsL
13|3	11	LLLLLLsLLLLLLLLsL
12|4	3	LLLLLLsLLLLLLLsLL
11|5	12	LLLLLsLLLLLLLLsLL
10|6	4	LLLLLsLLLLLLLsLLL
9|7	13	LLLLsLLLLLLLLsLLL
8|8	5	LLLLsLLLLLLLsLLLL
7|9	14	LLLsLLLLLLLLsLLLL
6|10	6	LLLsLLLLLLLsLLLLL
5|11	15	LLsLLLLLLLLsLLLLL
4|12	7	LLsLLLLLLLsLLLLLL
3|13	16	LsLLLLLLLLsLLLLLL
2|14	8	LsLLLLLLLsLLLLLLL
1|15	17	sLLLLLLLLsLLLLLLL
0|16	9	sLLLLLLLsLLLLLLLL

Intervals

Intervals of 15L 2s

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 70.6¢
	Major 1-mosstep	M1ms	L	70.6¢ to 80.0¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	80.0¢ to 141.2¢
	Major 2-mosstep	M2ms	2L	141.2¢ to 160.0¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	160.0¢ to 211.8¢
	Major 3-mosstep	M3ms	3L	211.8¢ to 240.0¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	240.0¢ to 282.4¢
	Major 4-mosstep	M4ms	4L	282.4¢ to 320.0¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	320.0¢ to 352.9¢
	Major 5-mosstep	M5ms	5L	352.9¢ to 400.0¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	400.0¢ to 423.5¢
	Major 6-mosstep	M6ms	6L	423.5¢ to 480.0¢
7-mosstep	Minor 7-mosstep	m7ms	6L + s	480.0¢ to 494.1¢
	Major 7-mosstep	M7ms	7L	494.1¢ to 560.0¢
8-mosstep	Perfect 8-mosstep	P8ms	7L + s	560.0¢ to 564.7¢
	Augmented 8-mosstep	A8ms	8L	564.7¢ to 640.0¢
9-mosstep	Diminished 9-mosstep	d9ms	7L + 2s	560.0¢ to 635.3¢
	Perfect 9-mosstep	P9ms	8L + s	635.3¢ to 640.0¢
10-mosstep	Minor 10-mosstep	m10ms	8L + 2s	640.0¢ to 705.9¢
	Major 10-mosstep	M10ms	9L + s	705.9¢ to 720.0¢
11-mosstep	Minor 11-mosstep	m11ms	9L + 2s	720.0¢ to 776.5¢
	Major 11-mosstep	M11ms	10L + s	776.5¢ to 800.0¢
12-mosstep	Minor 12-mosstep	m12ms	10L + 2s	800.0¢ to 847.1¢
	Major 12-mosstep	M12ms	11L + s	847.1¢ to 880.0¢
13-mosstep	Minor 13-mosstep	m13ms	11L + 2s	880.0¢ to 917.6¢
	Major 13-mosstep	M13ms	12L + s	917.6¢ to 960.0¢
14-mosstep	Minor 14-mosstep	m14ms	12L + 2s	960.0¢ to 988.2¢
	Major 14-mosstep	M14ms	13L + s	988.2¢ to 1040.0¢
15-mosstep	Minor 15-mosstep	m15ms	13L + 2s	1040.0¢ to 1058.8¢
	Major 15-mosstep	M15ms	14L + s	1058.8¢ to 1120.0¢
16-mosstep	Minor 16-mosstep	m16ms	14L + 2s	1120.0¢ to 1129.4¢
	Major 16-mosstep	M16ms	15L + s	1129.4¢ to 1200.0¢
17-mosstep	Perfect 17-mosstep	P17ms	15L + 2s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 15L 2s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
9\17						635.294	564.706	1:1	1.000	Equalized 15L 2s
					53\100	636.000	564.000	6:5	1.200
				44\83		636.145	563.855	5:4	1.250
					79\149	636.242	563.758	9:7	1.286
			35\66			636.364	563.636	4:3	1.333	Supersoft 15L 2s
					96\181	636.464	563.536	11:8	1.375
				61\115		636.522	563.478	7:5	1.400
					87\164	636.585	563.415	10:7	1.429
		26\49				636.735	563.265	3:2	1.500	Soft 15L 2s
					95\179	636.872	563.128	11:7	1.571
				69\130		636.923	563.077	8:5	1.600
					112\211	636.967	563.033	13:8	1.625
			43\81			637.037	562.963	5:3	1.667	Semisoft 15L 2s
					103\194	637.113	562.887	12:7	1.714
				60\113		637.168	562.832	7:4	1.750
					77\145	637.241	562.759	9:5	1.800
	17\32					637.500	562.500	2:1	2.000	Basic 15L 2s Scales with tunings softer than this are proper
					76\143	637.762	562.238	9:4	2.250
				59\111		637.838	562.162	7:3	2.333
					101\190	637.895	562.105	12:5	2.400
			42\79			637.975	562.025	5:2	2.500	Semihard 15L 2s
					109\205	638.049	561.951	13:5	2.600
				67\126		638.095	561.905	8:3	2.667
					92\173	638.150	561.850	11:4	2.750
		25\47				638.298	561.702	3:1	3.000	Hard 15L 2s
					83\156	638.462	561.538	10:3	3.333
				58\109		638.532	561.468	7:2	3.500
					91\171	638.596	561.404	11:3	3.667
			33\62			638.710	561.290	4:1	4.000	Superhard 15L 2s
					74\139	638.849	561.151	9:2	4.500
				41\77		638.961	561.039	5:1	5.000
					49\92	639.130	560.870	6:1	6.000
8\15						640.000	560.000	1:0	→ ∞	Collapsed 15L 2s

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