11L 1s

←10L 1s	11L 1s	12L 1s→
↙10L 2s	↓11L 2s	12L 2s↘

┌╥╥╥╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║║║║││ ││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLLLLLLLs sLLLLLLLLLLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	1\12 to 1\11 (100.0¢ to 109.1¢)
Dark	10\11 to 11\12 (1090.9¢ to 1100.0¢)
TAMNAMS information
Descends from	1L 9s (antisinatonic)
Required step ratio range	2:1 to 3:1 (hypohard)
Related MOS scales
Parent	1L 10s
Sister	1L 11s
Daughters	12L 11s 11L 12s
Equal tunings
Equalized (L:s = 1:1)	1\12 (100.0¢)
Supersoft (L:s = 4:3)	4\47 (102.1¢)
Soft (L:s = 3:2)	3\35 (102.9¢)
Semisoft (L:s = 5:3)	5\58 (103.4¢)
Basic (L:s = 2:1)	2\23 (104.3¢)
Semihard (L:s = 5:2)	5\57 (105.3¢)
Hard (L:s = 3:1)	3\34 (105.9¢)
Superhard (L:s = 4:1)	4\45 (106.7¢)
Collapsed (L:s = 1:0)	1\11 (109.1¢)

11L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 11 large steps and 1 small step, repeating every octave. 11L 1s is a grandchild scale of 1L 9s, expanding it by 2 tones. Generators that produce this scale range from 100¢ to 109.1¢, or from 1090.9¢ to 1100¢. Scales of this form are always proper because there is only one small step.

The 11L 1s MOS scale, with its diatonic minor second generator, is the dodecatonic scale of ripple (9:8 = +2 generators-6:5 = +3 generators) temperaments. However, it feels markedly more hendecatonic to listeners used to the equally divided chromatic scale because of its unbroken chain of eleven equal steps–never mind that the 12th degree is actually less than the octave. This hendecatonic feel is especially pronounced above 2\23, where the octave feels like a comma shift of the 12th degree rather than an independent note.

Modes

Modes of 11L 1s

UDP	Rotational order	Step pattern
11|0	1	LLLLLLLLLLLs
10|1	2	LLLLLLLLLLsL
9|2	3	LLLLLLLLLsLL
8|3	4	LLLLLLLLsLLL
7|4	5	LLLLLLLsLLLL
6|5	6	LLLLLLsLLLLL
5|6	7	LLLLLsLLLLLL
4|7	8	LLLLsLLLLLLL
3|8	9	LLLsLLLLLLLL
2|9	10	LLsLLLLLLLLL
1|10	11	LsLLLLLLLLLL
0|11	12	sLLLLLLLLLLL

Scale tree

Scale Tree and Tuning Spectrum of 11L 1s

Generator(edo)						Cents		Step Ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\12						100.000	1100.000	1:1	1.000	Equalized 11L 1s Ripple (100.838¢)
					6\71	101.408	1098.592	6:5	1.200
				5\59		101.695	1098.305	5:4	1.250
					9\106	101.887	1098.113	9:7	1.286
			4\47			102.128	1097.872	4:3	1.333	Supersoft 11L 1s
					11\129	102.326	1097.674	11:8	1.375
				7\82		102.439	1097.561	7:5	1.400
					10\117	102.564	1097.436	10:7	1.429
		3\35				102.857	1097.143	3:2	1.500	Soft 11L 1s
					11\128	103.125	1096.875	11:7	1.571
				8\93		103.226	1096.774	8:5	1.600
					13\151	103.311	1096.689	13:8	1.625
			5\58			103.448	1096.552	5:3	1.667	Semisoft 11L 1s
					12\139	103.597	1096.403	12:7	1.714
				7\81		103.704	1096.296	7:4	1.750
					9\104	103.846	1096.154	9:5	1.800
	2\23					104.348	1095.652	2:1	2.000	Basic 11L 1s
					9\103	104.854	1095.146	9:4	2.250
				7\80		105.000	1095.000	7:3	2.333
					12\137	105.109	1094.891	12:5	2.400
			5\57			105.263	1094.737	5:2	2.500	Semihard 11L 1s
					13\148	105.405	1094.595	13:5	2.600
				8\91		105.495	1094.505	8:3	2.667
					11\125	105.600	1094.400	11:4	2.750
		3\34				105.882	1094.118	3:1	3.000	Hard 11L 1s
					10\113	106.195	1093.805	10:3	3.333
				7\79		106.329	1093.671	7:2	3.500
					11\124	106.452	1093.548	11:3	3.667
			4\45			106.667	1093.333	4:1	4.000	Superhard 11L 1s
					9\101	106.931	1093.069	9:2	4.500
				5\56		107.143	1092.857	5:1	5.000
					6\67	107.463	1092.537	6:1	6.000
1\11						109.091	1090.909	1:0	→ ∞	Collapsed 11L 1s