11L 4s

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↖10L 3s ↑11L 3s 12L 3s↗
←10L 4s11L 4s 12L 4s→
↙10L 5s ↓11L 5s 12L 5s↘
┌╥╥╥┬╥╥╥┬╥╥╥┬╥╥┬┐
│║║║│║║║│║║║│║║││
│││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLLsLLLsLLs
sLLsLLLsLLLsLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 4\15 to 3\11 (320.0¢ to 327.3¢)
Dark 8\11 to 11\15 (872.7¢ to 880.0¢)
TAMNAMS information
Descends from 4L 3s (smitonic)
Required step ratio range 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 4L 7s
Sister 4L 11s
Daughters 15L 11s, 11L 15s
Neutralized 7L 8s
Equal tunings
Equalized (L:s = 1:1) 4\15 (320.0¢)
Supersoft (L:s = 4:3) 15\56 (321.4¢)
Soft (L:s = 3:2) 11\41 (322.0¢)
Semisoft (L:s = 5:3) 18\67 (322.4¢)
Basic (L:s = 2:1) 7\26 (323.1¢)
Semihard (L:s = 5:2) 17\63 (323.8¢)
Hard (L:s = 3:1) 10\37 (324.3¢)
Superhard (L:s = 4:1) 13\48 (325.0¢)
Collapsed (L:s = 1:0) 3\11 (327.3¢)

11L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 11 large steps and 4 small steps, repeating every octave. 11L 4s is a grandchild scale of 4L 3s, expanding it by 8 tones. Generators that produce this scale range from 320¢ to 327.3¢, or from 872.7¢ to 880¢.

The bright generator represents a minor third slightly sharp of 6/5 (315.6¢). At its harmonic entropy minimum, the octave-reduced 7th harmonic (about 968¢) equals 3 of these generators.

Modes

Modes of 11L 4s
UDP Rotational order Step pattern
14|0 1 LLLsLLLsLLLsLLs
13|1 5 LLLsLLLsLLsLLLs
12|2 9 LLLsLLsLLLsLLLs
11|3 13 LLsLLLsLLLsLLLs
10|4 2 LLsLLLsLLLsLLsL
9|5 6 LLsLLLsLLsLLLsL
8|6 10 LLsLLsLLLsLLLsL
7|7 14 LsLLLsLLLsLLLsL
6|8 3 LsLLLsLLLsLLsLL
5|9 7 LsLLLsLLsLLLsLL
4|10 11 LsLLsLLLsLLLsLL
3|11 15 sLLLsLLLsLLLsLL
2|12 4 sLLLsLLLsLLsLLL
1|13 8 sLLLsLLsLLLsLLL
0|14 12 sLLsLLLsLLLsLLL

Scale tree

Scale Tree and Tuning Spectrum of 11L 4s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
4\15 320.000 880.000 1:1 1.000 Equalized 11L 4s
23\86 320.930 879.070 6:5 1.200
19\71 321.127 878.873 5:4 1.250
34\127 321.260 878.740 9:7 1.286
15\56 321.429 878.571 4:3 1.333 Supersoft 11L 4s
41\153 321.569 878.431 11:8 1.375
26\97 321.649 878.351 7:5 1.400
37\138 321.739 878.261 10:7 1.429
11\41 321.951 878.049 3:2 1.500 Soft 11L 4s
40\149 322.148 877.852 11:7 1.571
29\108 322.222 877.778 8:5 1.600
47\175 322.286 877.714 13:8 1.625
18\67 322.388 877.612 5:3 1.667 Semisoft 11L 4s
43\160 322.500 877.500 12:7 1.714
25\93 322.581 877.419 7:4 1.750
32\119 322.689 877.311 9:5 1.800
7\26 323.077 876.923 2:1 2.000 Basic 11L 4s
Scales with tunings softer than this are proper
31\115 323.478 876.522 9:4 2.250
24\89 323.596 876.404 7:3 2.333
41\152 323.684 876.316 12:5 2.400
17\63 323.810 876.190 5:2 2.500 Semihard 11L 4s
44\163 323.926 876.074 13:5 2.600
27\100 324.000 876.000 8:3 2.667
37\137 324.088 875.912 11:4 2.750
10\37 324.324 875.676 3:1 3.000 Hard 11L 4s
33\122 324.590 875.410 10:3 3.333
23\85 324.706 875.294 7:2 3.500
36\133 324.812 875.188 11:3 3.667
13\48 325.000 875.000 4:1 4.000 Superhard 11L 4s
29\107 325.234 874.766 9:2 4.500
16\59 325.424 874.576 5:1 5.000
19\70 325.714 874.286 6:1 6.000
3\11 327.273 872.727 1:0 → ∞ Collapsed 11L 4s