3L 11s

↖ 2L 10s	↑ 3L 10s	4L 10s ↗
← 2L 11s	3L 11s	4L 11s →
↙ 2L 12s	↓ 3L 12s	4L 12s ↘

Scale structure
Step pattern	LsssLssssLssss ssssLssssLsssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	9\14 to 2\3 (771.4 ¢ to 800.0 ¢)
Dark	1\3 to 5\14 (400.0 ¢ to 428.6 ¢)
TAMNAMS information
Related to	3L 5s (checkertonic)
With tunings	3:1 to 1:0 (hard)
Related MOS scales
Parent	3L 8s
Sister	11L 3s
Daughters	14L 3s, 3L 14s
Neutralized	6L 8s
2-Flought	17L 11s, 3L 25s
Equal tunings
Equalized (L:s = 1:1)	9\14 (771.4 ¢)
Supersoft (L:s = 4:3)	29\45 (773.3 ¢)
Soft (L:s = 3:2)	20\31 (774.2 ¢)
Semisoft (L:s = 5:3)	31\48 (775.0 ¢)
Basic (L:s = 2:1)	11\17 (776.5 ¢)
Semihard (L:s = 5:2)	24\37 (778.4 ¢)
Hard (L:s = 3:1)	13\20 (780.0 ¢)
Superhard (L:s = 4:1)	15\23 (782.6 ¢)
Collapsed (L:s = 1:0)	2\3 (800.0 ¢)
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3L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 11 small steps, repeating every octave. 3L 11s is a grandchild scale of 3L 5s, expanding it by 6 tones. Generators that produce this scale range from 771.4 ¢ to 800 ¢, or from 400 ¢ to 428.6 ¢.

Modes

Modes of 3L 11s

UDP	Cyclic order	Step pattern
13|0	1	LsssLssssLssss
12|1	10	LssssLsssLssss
11|2	5	LssssLssssLsss
10|3	14	sLsssLssssLsss
9|4	9	sLssssLsssLsss
8|5	4	sLssssLssssLss
7|6	13	ssLsssLssssLss
6|7	8	ssLssssLsssLss
5|8	3	ssLssssLssssLs
4|9	12	sssLsssLssssLs
3|10	7	sssLssssLsssLs
2|11	2	sssLssssLssssL
1|12	11	ssssLsssLssssL
0|13	6	ssssLssssLsssL

Intervals

Intervals of 3L 11s

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 85.7 ¢
	Major 1-mosstep	M1ms	L	85.7 ¢ to 400.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 171.4 ¢
	Major 2-mosstep	M2ms	L + s	171.4 ¢ to 400.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 257.1 ¢
	Major 3-mosstep	M3ms	L + 2s	257.1 ¢ to 400.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 342.9 ¢
	Major 4-mosstep	M4ms	L + 3s	342.9 ¢ to 400.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	L + 4s	400.0 ¢ to 428.6 ¢
	Augmented 5-mosstep	A5ms	2L + 3s	428.6 ¢ to 800.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	400.0 ¢ to 514.3 ¢
	Major 6-mosstep	M6ms	2L + 4s	514.3 ¢ to 800.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	400.0 ¢ to 600.0 ¢
	Major 7-mosstep	M7ms	2L + 5s	600.0 ¢ to 800.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	400.0 ¢ to 685.7 ¢
	Major 8-mosstep	M8ms	2L + 6s	685.7 ¢ to 800.0 ¢
9-mosstep	Diminished 9-mosstep	d9ms	L + 8s	400.0 ¢ to 771.4 ¢
	Perfect 9-mosstep	P9ms	2L + 7s	771.4 ¢ to 800.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	2L + 8s	800.0 ¢ to 857.1 ¢
	Major 10-mosstep	M10ms	3L + 7s	857.1 ¢ to 1200.0 ¢
11-mosstep	Minor 11-mosstep	m11ms	2L + 9s	800.0 ¢ to 942.9 ¢
	Major 11-mosstep	M11ms	3L + 8s	942.9 ¢ to 1200.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	2L + 10s	800.0 ¢ to 1028.6 ¢
	Major 12-mosstep	M12ms	3L + 9s	1028.6 ¢ to 1200.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	2L + 11s	800.0 ¢ to 1114.3 ¢
	Major 13-mosstep	M13ms	3L + 10s	1114.3 ¢ to 1200.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	3L + 11s	1200.0 ¢

Tuning spectrum

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

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 3L 11s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
9\14						771.429	428.571	1:1	1.000	Equalized 3L 11s
					47\73	772.603	427.397	6:5	1.200
				38\59		772.881	427.119	5:4	1.250
					67\104	773.077	426.923	9:7	1.286
			29\45			773.333	426.667	4:3	1.333	Supersoft 3L 11s
					78\121	773.554	426.446	11:8	1.375
				49\76		773.684	426.316	7:5	1.400
					69\107	773.832	426.168	10:7	1.429
		20\31				774.194	425.806	3:2	1.500	Soft 3L 11s
					71\110	774.545	425.455	11:7	1.571
				51\79		774.684	425.316	8:5	1.600
					82\127	774.803	425.197	13:8	1.625
			31\48			775.000	425.000	5:3	1.667	Semisoft 3L 11s
					73\113	775.221	424.779	12:7	1.714
				42\65		775.385	424.615	7:4	1.750
					53\82	775.610	424.390	9:5	1.800
	11\17					776.471	423.529	2:1	2.000	Basic 3L 11s Scales with tunings softer than this are proper
					46\71	777.465	422.535	9:4	2.250
				35\54		777.778	422.222	7:3	2.333
					59\91	778.022	421.978	12:5	2.400
			24\37			778.378	421.622	5:2	2.500	Semihard 3L 11s
					61\94	778.723	421.277	13:5	2.600
				37\57		778.947	421.053	8:3	2.667
					50\77	779.221	420.779	11:4	2.750
		13\20				780.000	420.000	3:1	3.000	Hard 3L 11s
					41\63	780.952	419.048	10:3	3.333
				28\43		781.395	418.605	7:2	3.500
					43\66	781.818	418.182	11:3	3.667
			15\23			782.609	417.391	4:1	4.000	Superhard 3L 11s
					32\49	783.673	416.327	9:2	4.500
				17\26		784.615	415.385	5:1	5.000
					19\29	786.207	413.793	6:1	6.000
2\3						800.000	400.000	1:0	→ ∞	Collapsed 3L 11s

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