10L 5s

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↖ 9L 4s ↑10L 4s 11L 4s ↗
← 9L 5s10L 5s 11L 5s →
↙ 9L 6s ↓10L 6s 11L 6s ↘
┌╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬┐
│║║│║║│║║│║║│║║││
│││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLLsLLsLLsLLs
sLLsLLsLLsLLsLL
Equave 2/1 (1200.0¢)
Period 1\5 (240.0¢)
Generator size
Bright 1\15 to 1\10 (80.0¢ to 120.0¢)
Dark 1\10 to 2\15 (120.0¢ to 160.0¢)
TAMNAMS information
Descends from 5L 5s (pentawood)
Required step ratio range 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 5L 5s
Sister 5L 10s
Daughters 15L 10s, 10L 15s
Neutralized 5L 10s
2-Flought 25L 5s, 10L 20s
Equal tunings
Equalized (L:s = 1:1) 1\15 (80.0¢)
Supersoft (L:s = 4:3) 4\55 (87.3¢)
Soft (L:s = 3:2) 3\40 (90.0¢)
Semisoft (L:s = 5:3) 5\65 (92.3¢)
Basic (L:s = 2:1) 2\25 (96.0¢)
Semihard (L:s = 5:2) 5\60 (100.0¢)
Hard (L:s = 3:1) 3\35 (102.9¢)
Superhard (L:s = 4:1) 4\45 (106.7¢)
Collapsed (L:s = 1:0) 1\10 (120.0¢)

10L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 5 small steps, with a period of 2 large steps and 1 small step that repeats every 240.0¢, or 5 times every octave. 10L 5s is a child scale of 5L 5s, expanding it by 5 tones. Generators that produce this scale range from 80¢ to 120¢, or from 120¢ to 160¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

Modes

Modes of 10L 5s
UDP Rotational order Step pattern
10|0(5) 1 LLsLLsLLsLLsLLs
5|5(5) 2 LsLLsLLsLLsLLsL
0|10(5) 3 sLLsLLsLLsLLsLL

Scale tree

Scale Tree and Tuning Spectrum of 10L 5s
Generator(edo) Cents Step Ratio Comments(always proper)
Bright Dark L:s Hardness
1\15 80.000 160.000 1:1 1.000 Equalized 10L 5s
6\85 84.706 155.294 6:5 1.200
5\70 85.714 154.286 5:4 1.250
9\125 86.400 153.600 9:7 1.286
4\55 87.273 152.727 4:3 1.333 Supersoft 10L 5s
11\150 88.000 152.000 11:8 1.375
7\95 88.421 151.579 7:5 1.400
10\135 88.889 151.111 10:7 1.429
3\40 90.000 150.000 3:2 1.500 Soft 10L 5s
11\145 91.034 148.966 11:7 1.571
8\105 91.429 148.571 8:5 1.600
13\170 91.765 148.235 13:8 1.625
5\65 92.308 147.692 5:3 1.667 Semisoft 10L 5s
12\155 92.903 147.097 12:7 1.714
7\90 93.333 146.667 7:4 1.750
9\115 93.913 146.087 9:5 1.800
2\25 96.000 144.000 2:1 2.000 Basic 10L 5s
9\110 98.182 141.818 9:4 2.250
7\85 98.824 141.176 7:3 2.333
12\145 99.310 140.690 12:5 2.400
5\60 100.000 140.000 5:2 2.500 Semihard 10L 5s
13\155 100.645 139.355 13:5 2.600
8\95 101.053 138.947 8:3 2.667
11\130 101.538 138.462 11:4 2.750
3\35 102.857 137.143 3:1 3.000 Hard 10L 5s
10\115 104.348 135.652 10:3 3.333
7\80 105.000 135.000 7:2 3.500
11\125 105.600 134.400 11:3 3.667
4\45 106.667 133.333 4:1 4.000 Superhard 10L 5s
9\100 108.000 132.000 9:2 4.500
5\55 109.091 130.909 5:1 5.000
6\65 110.769 129.231 6:1 6.000
1\10 120.000 120.000 1:0 → ∞ Collapsed 10L 5s
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