11L 1s

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←10L 1s11L 1s12L 1s→
↙10L 2s↓11L 2s 12L 2s↘
Brightest mode LLLLLLLLLLLs
Period 2/1
Range for bright generator 1\12 (100¢) to 1\11 (109.1¢)
Range for dark generator 10\11 (1090.9¢) to 11\12 (1100¢)
Parent MOS 1L 10s
Sister MOS 1L 11s
Daughter MOSes 12L 11s, 11L 12s
Equal tunings
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¢)
Brightest-mode tunings on xenpaper
Supersoft Soft Semisoft Basic Semihard Hard Superhard

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 (in steps of edo) Cents Step ratio Comments
(Every tuning produces a proper scale)
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