2L 15s

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

┌╥┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┬┐ │║│││││││║│││││││││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsssssssLssssssss ssssssssLsssssssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	8\17 to 1\2 (564.7¢ to 600.0¢)
Dark	1\2 to 9\17 (600.0¢ to 635.3¢)
TAMNAMS information
Descends from	2L 7s (balzano)
Ancestor's step ratio range	5:1 to 1:0
Related MOS scales
Parent	2L 13s
Sister	15L 2s
Daughters	17L 2s, 2L 17s
Neutralized	4L 13s
2-Flought	19L 15s, 2L 32s
Equal tunings
Equalized (L:s = 1:1)	8\17 (564.7¢)
Supersoft (L:s = 4:3)	25\53 (566.0¢)
Soft (L:s = 3:2)	17\36 (566.7¢)
Semisoft (L:s = 5:3)	26\55 (567.3¢)
Basic (L:s = 2:1)	9\19 (568.4¢)
Semihard (L:s = 5:2)	19\40 (570.0¢)
Hard (L:s = 3:1)	10\21 (571.4¢)
Superhard (L:s = 4:1)	11\23 (573.9¢)
Collapsed (L:s = 1:0)	1\2 (600.0¢)

2L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 15 small steps, repeating every octave. 2L 15s is related to 2L 7s, expanding it by 8 tones. Generators that produce this scale range from 564.7¢ to 600¢, or from 600¢ to 635.3¢.

Modes

Modes of 2L 15s

UDP	Cyclic order	Step pattern
16|0	1	LsssssssLssssssss
15|1	9	LssssssssLsssssss
14|2	17	sLsssssssLsssssss
13|3	8	sLssssssssLssssss
12|4	16	ssLsssssssLssssss
11|5	7	ssLssssssssLsssss
10|6	15	sssLsssssssLsssss
9|7	6	sssLssssssssLssss
8|8	14	ssssLsssssssLssss
7|9	5	ssssLssssssssLsss
6|10	13	sssssLsssssssLsss
5|11	4	sssssLssssssssLss
4|12	12	ssssssLsssssssLss
3|13	3	ssssssLssssssssLs
2|14	11	sssssssLsssssssLs
1|15	2	sssssssLssssssssL
0|16	10	ssssssssLsssssssL

Intervals

Intervals of 2L 15s

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 600.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 141.2¢
	Major 2-mosstep	M2ms	L + s	141.2¢ to 600.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 211.8¢
	Major 3-mosstep	M3ms	L + 2s	211.8¢ to 600.0¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0¢ to 282.4¢
	Major 4-mosstep	M4ms	L + 3s	282.4¢ to 600.0¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0¢ to 352.9¢
	Major 5-mosstep	M5ms	L + 4s	352.9¢ to 600.0¢
6-mosstep	Minor 6-mosstep	m6ms	6s	0.0¢ to 423.5¢
	Major 6-mosstep	M6ms	L + 5s	423.5¢ to 600.0¢
7-mosstep	Minor 7-mosstep	m7ms	7s	0.0¢ to 494.1¢
	Major 7-mosstep	M7ms	L + 6s	494.1¢ to 600.0¢
8-mosstep	Diminished 8-mosstep	d8ms	8s	0.0¢ to 564.7¢
	Perfect 8-mosstep	P8ms	L + 7s	564.7¢ to 600.0¢
9-mosstep	Perfect 9-mosstep	P9ms	L + 8s	600.0¢ to 635.3¢
	Augmented 9-mosstep	A9ms	2L + 7s	635.3¢ to 1200.0¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	600.0¢ to 705.9¢
	Major 10-mosstep	M10ms	2L + 8s	705.9¢ to 1200.0¢
11-mosstep	Minor 11-mosstep	m11ms	L + 10s	600.0¢ to 776.5¢
	Major 11-mosstep	M11ms	2L + 9s	776.5¢ to 1200.0¢
12-mosstep	Minor 12-mosstep	m12ms	L + 11s	600.0¢ to 847.1¢
	Major 12-mosstep	M12ms	2L + 10s	847.1¢ to 1200.0¢
13-mosstep	Minor 13-mosstep	m13ms	L + 12s	600.0¢ to 917.6¢
	Major 13-mosstep	M13ms	2L + 11s	917.6¢ to 1200.0¢
14-mosstep	Minor 14-mosstep	m14ms	L + 13s	600.0¢ to 988.2¢
	Major 14-mosstep	M14ms	2L + 12s	988.2¢ to 1200.0¢
15-mosstep	Minor 15-mosstep	m15ms	L + 14s	600.0¢ to 1058.8¢
	Major 15-mosstep	M15ms	2L + 13s	1058.8¢ to 1200.0¢
16-mosstep	Minor 16-mosstep	m16ms	L + 15s	600.0¢ to 1129.4¢
	Major 16-mosstep	M16ms	2L + 14s	1129.4¢ to 1200.0¢
17-mosstep	Perfect 17-mosstep	P17ms	2L + 15s	1200.0¢

Tuning spectrum

Todo: review Review entries from past page revision and enter them into the scale tree.

Triton / liese / progress range

Scale Tree and Tuning Spectrum of 2L 15s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
8\17						564.706	635.294	1:1	1.000	Equalized 2L 15s
					41\87	565.517	634.483	6:5	1.200
				33\70		565.714	634.286	5:4	1.250
					58\123	565.854	634.146	9:7	1.286
			25\53			566.038	633.962	4:3	1.333	Supersoft 2L 15s
					67\142	566.197	633.803	11:8	1.375
				42\89		566.292	633.708	7:5	1.400
					59\125	566.400	633.600	10:7	1.429
		17\36				566.667	633.333	3:2	1.500	Soft 2L 15s
					60\127	566.929	633.071	11:7	1.571
				43\91		567.033	632.967	8:5	1.600
					69\146	567.123	632.877	13:8	1.625
			26\55			567.273	632.727	5:3	1.667	Semisoft 2L 15s
					61\129	567.442	632.558	12:7	1.714
				35\74		567.568	632.432	7:4	1.750
					44\93	567.742	632.258	9:5	1.800
	9\19					568.421	631.579	2:1	2.000	Basic 2L 15s Scales with tunings softer than this are proper
					37\78	569.231	630.769	9:4	2.250
				28\59		569.492	630.508	7:3	2.333
					47\99	569.697	630.303	12:5	2.400
			19\40			570.000	630.000	5:2	2.500	Semihard 2L 15s
					48\101	570.297	629.703	13:5	2.600
				29\61		570.492	629.508	8:3	2.667
					39\82	570.732	629.268	11:4	2.750
		10\21				571.429	628.571	3:1	3.000	Hard 2L 15s
					31\65	572.308	627.692	10:3	3.333
				21\44		572.727	627.273	7:2	3.500
					32\67	573.134	626.866	11:3	3.667
			11\23			573.913	626.087	4:1	4.000	Superhard 2L 15s
					23\48	575.000	625.000	9:2	4.500
				12\25		576.000	624.000	5:1	5.000
					13\27	577.778	622.222	6:1	6.000
1\2						600.000	600.000	1:0	→ ∞	Collapsed 2L 15s

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