16L 3s
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Scale structure
Step pattern
LLLLLLsLLLLLsLLLLLs
sLLLLLsLLLLLsLLLLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
13\19 to 11\16 (821.1¢ to 825.0¢)
Dark
5\16 to 6\19 (375.0¢ to 378.9¢)
TAMNAMS information
Descends from
3L 7s (sephiroid)
Required step ratio range
3:1 to 4:1 (parahard)
Related MOS scales
Parent
3L 13s
Sister
3L 16s
Daughters
19L 16s
16L 19s
Equal tunings
Equalized (L:s = 1:1)
13\19 (821.1¢)
Supersoft (L:s = 4:3)
50\73 (821.9¢)
Soft (L:s = 3:2)
37\54 (822.2¢)
Semisoft (L:s = 5:3)
61\89 (822.5¢)
Basic (L:s = 2:1)
24\35 (822.9¢)
Semihard (L:s = 5:2)
59\86 (823.3¢)
Hard (L:s = 3:1)
35\51 (823.5¢)
Superhard (L:s = 4:1)
46\67 (823.9¢)
Collapsed (L:s = 1:0)
11\16 (825.0¢)
| ↖15L 2s | ↑16L 2s | 17L 2s↗ |
| ←15L 3s | 16L 3s | 17L 3s→ |
| ↙15L 4s | ↓16L 4s | 17L 4s↘ |
┌╥╥╥╥╥╥┬╥╥╥╥╥┬╥╥╥╥╥┬┐ │║║║║║║│║║║║║│║║║║║││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLLsLLLLLsLLLLLL
16L 19s
16L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 16 large steps and 3 small steps, repeating every octave. 16L 3s is a great-grandchild scale of 3L 7s, expanding it by 9 tones. Generators that produce this scale range from 821.1¢ to 825¢, or from 375¢ to 378.9¢.
| Generator (edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 13\19 | 821.053 | 378.947 | 1:1 | 1.000 | Equalized 16L 3s | |||||
| 76\111 | 821.622 | 378.378 | 6:5 | 1.200 | ||||||
| 63\92 | 821.739 | 378.261 | 5:4 | 1.250 | ||||||
| 113\165 | 821.818 | 378.182 | 9:7 | 1.286 | ||||||
| 50\73 | 821.918 | 378.082 | 4:3 | 1.333 | Supersoft 16L 3s | |||||
| 137\200 | 822.000 | 378.000 | 11:8 | 1.375 | ||||||
| 87\127 | 822.047 | 377.953 | 7:5 | 1.400 | ||||||
| 124\181 | 822.099 | 377.901 | 10:7 | 1.429 | ||||||
| 37\54 | 822.222 | 377.778 | 3:2 | 1.500 | Soft 16L 3s | |||||
| 135\197 | 822.335 | 377.665 | 11:7 | 1.571 | ||||||
| 98\143 | 822.378 | 377.622 | 8:5 | 1.600 | ||||||
| 159\232 | 822.414 | 377.586 | 13:8 | 1.625 | ||||||
| 61\89 | 822.472 | 377.528 | 5:3 | 1.667 | Semisoft 16L 3s | |||||
| 146\213 | 822.535 | 377.465 | 12:7 | 1.714 | ||||||
| 85\124 | 822.581 | 377.419 | 7:4 | 1.750 | ||||||
| 109\159 | 822.642 | 377.358 | 9:5 | 1.800 | ||||||
| 24\35 | 822.857 | 377.143 | 2:1 | 2.000 | Basic 16L 3s Scales with tunings softer than this are proper | |||||
| 107\156 | 823.077 | 376.923 | 9:4 | 2.250 | ||||||
| 83\121 | 823.140 | 376.860 | 7:3 | 2.333 | ||||||
| 142\207 | 823.188 | 376.812 | 12:5 | 2.400 | ||||||
| 59\86 | 823.256 | 376.744 | 5:2 | 2.500 | Semihard 16L 3s | |||||
| 153\223 | 823.318 | 376.682 | 13:5 | 2.600 | ||||||
| 94\137 | 823.358 | 376.642 | 8:3 | 2.667 | ||||||
| 129\188 | 823.404 | 376.596 | 11:4 | 2.750 | ||||||
| 35\51 | 823.529 | 376.471 | 3:1 | 3.000 | Hard 16L 3s | |||||
| 116\169 | 823.669 | 376.331 | 10:3 | 3.333 | ||||||
| 81\118 | 823.729 | 376.271 | 7:2 | 3.500 | ||||||
| 127\185 | 823.784 | 376.216 | 11:3 | 3.667 | ||||||
| 46\67 | 823.881 | 376.119 | 4:1 | 4.000 | Superhard 16L 3s | |||||
| 103\150 | 824.000 | 376.000 | 9:2 | 4.500 | ||||||
| 57\83 | 824.096 | 375.904 | 5:1 | 5.000 | ||||||
| 68\99 | 824.242 | 375.758 | 6:1 | 6.000 | ||||||
| 11\16 | 825.000 | 375.000 | 1:0 | → ∞ | Collapsed 16L 3s | |||||
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