16L 4s
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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¢)
| ↖ 15L 3s | ↑ 16L 3s | 17L 3s ↗ |
| ← 15L 4s | 16L 4s | 17L 4s → |
| ↙ 15L 5s | ↓ 16L 5s | 17L 5s ↘ |
┌╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬┐ │║║║║│║║║║│║║║║│║║║║││ ││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLsLLLLsLLLLsLLLL
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
| 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
| 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 | |||||