16L 3s

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↖15L 2s ↑16L 2s 17L 2s↗
←15L 3s16L 3s 17L 3s→
↙15L 4s ↓16L 4s 17L 4s↘
┌╥╥╥╥╥╥┬╥╥╥╥╥┬╥╥╥╥╥┬┐
│║║║║║║│║║║║║│║║║║║││
│││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLsLLLLLsLLLLLs
sLLLLLsLLLLLsLLLLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Step size ranges
Large 1\19 to 1\16 (63.2¢ to 75.0¢)
Small 0\16 to 1\19 (0.0¢ to 63.2¢)
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)
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¢)

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¢.


Scale tree and tuning spectrum of 16L 3s
Generator (in steps of 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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