# 15L 4s

 ↖ 14L 3s ↑15L 3s 16L 3s ↗ ← 14L 4s 15L 4s 16L 4s → ↙ 14L 5s ↓15L 5s 16L 5s ↘
```┌╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬╥╥╥┬┐
│║║║║│║║║║│║║║║│║║║││
│││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘```
Scale structure
Step pattern LLLLsLLLLsLLLLsLLLs
sLLLsLLLLsLLLLsLLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 5\19 to 4\15 (315.8¢ to 320.0¢)
Dark 11\15 to 14\19 (880.0¢ to 884.2¢)
TAMNAMS information
Descends from 4L 3s (smitonic)
Required step ratio range 3:1 to 4:1 (parahard)
Related MOS scales
Parent 4L 11s
Sister 4L 15s
Daughters 19L 15s, 15L 19s
Neutralized 11L 8s
2-Flought 34L 4s, 15L 23s
Equal tunings
Equalized (L:s = 1:1) 5\19 (315.8¢)
Supersoft (L:s = 4:3) 19\72 (316.7¢)
Soft (L:s = 3:2) 14\53 (317.0¢)
Semisoft (L:s = 5:3) 23\87 (317.2¢)
Basic (L:s = 2:1) 9\34 (317.6¢)
Semihard (L:s = 5:2) 22\83 (318.1¢)
Hard (L:s = 3:1) 13\49 (318.4¢)
Superhard (L:s = 4:1) 17\64 (318.8¢)
Collapsed (L:s = 1:0) 4\15 (320.0¢)

15L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 4 small steps, repeating every octave. 15L 4s is a great-grandchild scale of 4L 3s, expanding it by 12 tones. Generators that produce this scale range from 315.8¢ to 320¢, or from 880¢ to 884.2¢. It is notable as the MOS scale of Catakleismic[19].

## Scale tree

Scale Tree and Tuning Spectrum of 15L 4s
Bright Dark L:s Hardness
5\19 315.789 884.211 1:1 1.000 Equalized 15L 4s
29\110 316.364 883.636 6:5 1.200
24\91 316.484 883.516 5:4 1.250
43\163 316.564 883.436 9:7 1.286
19\72 316.667 883.333 4:3 1.333 Supersoft 15L 4s
52\197 316.751 883.249 11:8 1.375 Catakleismic
33\125 316.800 883.200 7:5 1.400
47\178 316.854 883.146 10:7 1.429
14\53 316.981 883.019 3:2 1.500 Soft 15L 4s
51\193 317.098 882.902 11:7 1.571
37\140 317.143 882.857 8:5 1.600
60\227 317.181 882.819 13:8 1.625
23\87 317.241 882.759 5:3 1.667 Semisoft 15L 4s
55\208 317.308 882.692 12:7 1.714
32\121 317.355 882.645 7:4 1.750
41\155 317.419 882.581 9:5 1.800
9\34 317.647 882.353 2:1 2.000 Basic 15L 4s
Scales with tunings softer than this are proper
40\151 317.881 882.119 9:4 2.250
31\117 317.949 882.051 7:3 2.333
53\200 318.000 882.000 12:5 2.400
22\83 318.072 881.928 5:2 2.500 Semihard 15L 4s
57\215 318.140 881.860 13:5 2.600
35\132 318.182 881.818 8:3 2.667
48\181 318.232 881.768 11:4 2.750
13\49 318.367 881.633 3:1 3.000 Hard 15L 4s
43\162 318.519 881.481 10:3 3.333
30\113 318.584 881.416 7:2 3.500
47\177 318.644 881.356 11:3 3.667
17\64 318.750 881.250 4:1 4.000 Superhard 15L 4s
38\143 318.881 881.119 9:2 4.500
21\79 318.987 881.013 5:1 5.000
25\94 319.149 880.851 6:1 6.000
4\15 320.000 880.000 1:0 → ∞ Collapsed 15L 4s