16L 5s
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Scale structure
Step pattern
LLLLsLLLsLLLsLLLsLLLs
sLLLsLLLsLLLsLLLsLLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
17\21 to 13\16 (971.4¢ to 975.0¢)
Dark
3\16 to 4\21 (225.0¢ to 228.6¢)
TAMNAMS information
Descends from
5L 1s (machinoid)
Ancestor's step ratio range
3:1 to 4:1 (parahard)
Related MOS scales
Parent
5L 11s
Sister
5L 16s
Daughters
21L 16s, 16L 21s
Neutralized
11L 10s
2-Flought
37L 5s, 16L 26s
Equal tunings
Equalized (L:s = 1:1)
17\21 (971.4¢)
Supersoft (L:s = 4:3)
64\79 (972.2¢)
Soft (L:s = 3:2)
47\58 (972.4¢)
Semisoft (L:s = 5:3)
77\95 (972.6¢)
Basic (L:s = 2:1)
30\37 (973.0¢)
Semihard (L:s = 5:2)
73\90 (973.3¢)
Hard (L:s = 3:1)
43\53 (973.6¢)
Superhard (L:s = 4:1)
56\69 (973.9¢)
Collapsed (L:s = 1:0)
13\16 (975.0¢)
↖ 15L 4s | ↑ 16L 4s | 17L 4s ↗ |
← 15L 5s | 16L 5s | 17L 5s → |
↙ 15L 6s | ↓ 16L 6s | 17L 6s ↘ |
┌╥╥╥╥┬╥╥╥┬╥╥╥┬╥╥╥┬╥╥╥┬┐ │║║║║│║║║│║║║│║║║│║║║││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLsLLLsLLLsLLLsLLLL
16L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 16 large steps and 5 small steps, repeating every octave. 16L 5s is a great-grandchild scale of 5L 1s, expanding it by 15 tones. Generators that produce this scale range from 971.4¢ to 975¢, or from 225¢ to 228.6¢.
Modes
UDP | Cyclic Order |
Step Pattern |
---|---|---|
20|0 | 1 | LLLLsLLLsLLLsLLLsLLLs |
19|1 | 18 | LLLsLLLLsLLLsLLLsLLLs |
18|2 | 14 | LLLsLLLsLLLLsLLLsLLLs |
17|3 | 10 | LLLsLLLsLLLsLLLLsLLLs |
16|4 | 6 | LLLsLLLsLLLsLLLsLLLLs |
15|5 | 2 | LLLsLLLsLLLsLLLsLLLsL |
14|6 | 19 | LLsLLLLsLLLsLLLsLLLsL |
13|7 | 15 | LLsLLLsLLLLsLLLsLLLsL |
12|8 | 11 | LLsLLLsLLLsLLLLsLLLsL |
11|9 | 7 | LLsLLLsLLLsLLLsLLLLsL |
10|10 | 3 | LLsLLLsLLLsLLLsLLLsLL |
9|11 | 20 | LsLLLLsLLLsLLLsLLLsLL |
8|12 | 16 | LsLLLsLLLLsLLLsLLLsLL |
7|13 | 12 | LsLLLsLLLsLLLLsLLLsLL |
6|14 | 8 | LsLLLsLLLsLLLsLLLLsLL |
5|15 | 4 | LsLLLsLLLsLLLsLLLsLLL |
4|16 | 21 | sLLLLsLLLsLLLsLLLsLLL |
3|17 | 17 | sLLLsLLLLsLLLsLLLsLLL |
2|18 | 13 | sLLLsLLLsLLLLsLLLsLLL |
1|19 | 9 | sLLLsLLLsLLLsLLLLsLLL |
0|20 | 5 | sLLLsLLLsLLLsLLLsLLLL |
Scale tree
Generator(edo) | Cents | Step Ratio | Comments | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Bright | Dark | L:s | Hardness | |||||||
17\21 | 971.429 | 228.571 | 1:1 | 1.000 | Equalized 16L 5s | |||||
98\121 | 971.901 | 228.099 | 6:5 | 1.200 | ||||||
81\100 | 972.000 | 228.000 | 5:4 | 1.250 | ||||||
145\179 | 972.067 | 227.933 | 9:7 | 1.286 | ||||||
64\79 | 972.152 | 227.848 | 4:3 | 1.333 | Supersoft 16L 5s | |||||
175\216 | 972.222 | 227.778 | 11:8 | 1.375 | ||||||
111\137 | 972.263 | 227.737 | 7:5 | 1.400 | ||||||
158\195 | 972.308 | 227.692 | 10:7 | 1.429 | ||||||
47\58 | 972.414 | 227.586 | 3:2 | 1.500 | Soft 16L 5s | |||||
171\211 | 972.512 | 227.488 | 11:7 | 1.571 | ||||||
124\153 | 972.549 | 227.451 | 8:5 | 1.600 | ||||||
201\248 | 972.581 | 227.419 | 13:8 | 1.625 | ||||||
77\95 | 972.632 | 227.368 | 5:3 | 1.667 | Semisoft 16L 5s | |||||
184\227 | 972.687 | 227.313 | 12:7 | 1.714 | ||||||
107\132 | 972.727 | 227.273 | 7:4 | 1.750 | ||||||
137\169 | 972.781 | 227.219 | 9:5 | 1.800 | ||||||
30\37 | 972.973 | 227.027 | 2:1 | 2.000 | Basic 16L 5s Scales with tunings softer than this are proper | |||||
133\164 | 973.171 | 226.829 | 9:4 | 2.250 | ||||||
103\127 | 973.228 | 226.772 | 7:3 | 2.333 | ||||||
176\217 | 973.272 | 226.728 | 12:5 | 2.400 | ||||||
73\90 | 973.333 | 226.667 | 5:2 | 2.500 | Semihard 16L 5s | |||||
189\233 | 973.391 | 226.609 | 13:5 | 2.600 | ||||||
116\143 | 973.427 | 226.573 | 8:3 | 2.667 | ||||||
159\196 | 973.469 | 226.531 | 11:4 | 2.750 | ||||||
43\53 | 973.585 | 226.415 | 3:1 | 3.000 | Hard 16L 5s | |||||
142\175 | 973.714 | 226.286 | 10:3 | 3.333 | ||||||
99\122 | 973.770 | 226.230 | 7:2 | 3.500 | ||||||
155\191 | 973.822 | 226.178 | 11:3 | 3.667 | ||||||
56\69 | 973.913 | 226.087 | 4:1 | 4.000 | Superhard 16L 5s | |||||
125\154 | 974.026 | 225.974 | 9:2 | 4.500 | ||||||
69\85 | 974.118 | 225.882 | 5:1 | 5.000 | ||||||
82\101 | 974.257 | 225.743 | 6:1 | 6.000 | ||||||
13\16 | 975.000 | 225.000 | 1:0 | → ∞ | Collapsed 16L 5s |
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