16L 4s

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↖ 15L 3s ↑ 16L 3s 17L 3s ↗
← 15L 4s 16L 4s 17L 4s →
↙ 15L 5s ↓ 16L 5s 17L 5s ↘
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Scale structure
Step pattern LLLLsLLLLsLLLLsLLLLs
sLLLLsLLLLsLLLLsLLLL
Equave 2/1 (1200.0¢)
Period 1\4 (300.0¢)
Generator size
Bright 1\20 to 1\16 (60.0¢ to 75.0¢)
Dark 3\16 to 4\20 (225.0¢ to 240.0¢)
TAMNAMS information
Descends from 4L 4s (tetrawood)
Ancestor's step ratio range 3:1 to 4:1 (parahard)
Related MOS scales
Parent 4L 12s
Sister 4L 16s
Daughters 20L 16s, 16L 20s
Neutralized 12L 8s
2-Flought 36L 4s, 16L 24s
Equal tunings
Equalized (L:s = 1:1) 1\20 (60.0¢)
Supersoft (L:s = 4:3) 4\76 (63.2¢)
Soft (L:s = 3:2) 3\56 (64.3¢)
Semisoft (L:s = 5:3) 5\92 (65.2¢)
Basic (L:s = 2:1) 2\36 (66.7¢)
Semihard (L:s = 5:2) 5\88 (68.2¢)
Hard (L:s = 3:1) 3\52 (69.2¢)
Superhard (L:s = 4:1) 4\68 (70.6¢)
Collapsed (L:s = 1:0) 1\16 (75.0¢)

16L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 16 large steps and 4 small steps, with a period of 4 large steps and 1 small step that repeats every 300.0¢, or 4 times every octave. 16L 4s is a great-grandchild scale of 4L 4s, expanding it by 12 tones. Generators that produce this scale range from 60¢ to 75¢, or from 225¢ to 240¢. 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 16L 4s
UDP Cyclic
order
Step
pattern
16|0(4) 1 LLLLsLLLLsLLLLsLLLLs
12|4(4) 2 LLLsLLLLsLLLLsLLLLsL
8|8(4) 3 LLsLLLLsLLLLsLLLLsLL
4|12(4) 4 LsLLLLsLLLLsLLLLsLLL
0|16(4) 5 sLLLLsLLLLsLLLLsLLLL

Scale tree

Scale Tree and Tuning Spectrum of 16L 4s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\20 60.000 240.000 1:1 1.000 Equalized 16L 4s
6\116 62.069 237.931 6:5 1.200
5\96 62.500 237.500 5:4 1.250
9\172 62.791 237.209 9:7 1.286
4\76 63.158 236.842 4:3 1.333 Supersoft 16L 4s
11\208 63.462 236.538 11:8 1.375
7\132 63.636 236.364 7:5 1.400
10\188 63.830 236.170 10:7 1.429
3\56 64.286 235.714 3:2 1.500 Soft 16L 4s
11\204 64.706 235.294 11:7 1.571
8\148 64.865 235.135 8:5 1.600
13\240 65.000 235.000 13:8 1.625
5\92 65.217 234.783 5:3 1.667 Semisoft 16L 4s
12\220 65.455 234.545 12:7 1.714
7\128 65.625 234.375 7:4 1.750
9\164 65.854 234.146 9:5 1.800
2\36 66.667 233.333 2:1 2.000 Basic 16L 4s
9\160 67.500 232.500 9:4 2.250
7\124 67.742 232.258 7:3 2.333
12\212 67.925 232.075 12:5 2.400
5\88 68.182 231.818 5:2 2.500 Semihard 16L 4s
13\228 68.421 231.579 13:5 2.600
8\140 68.571 231.429 8:3 2.667
11\192 68.750 231.250 11:4 2.750
3\52 69.231 230.769 3:1 3.000 Hard 16L 4s
10\172 69.767 230.233 10:3 3.333
7\120 70.000 230.000 7:2 3.500
11\188 70.213 229.787 11:3 3.667
4\68 70.588 229.412 4:1 4.000 Superhard 16L 4s
9\152 71.053 228.947 9:2 4.500
5\84 71.429 228.571 5:1 5.000
6\100 72.000 228.000 6:1 6.000
1\16 75.000 225.000 1:0 → ∞ Collapsed 16L 4s