16L 5s

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↖ 15L 4s↑ 16L 4s 17L 4s ↗
← 15L 5s16L 5s17L 5s →
↙ 15L 6s↓ 16L 6s 17L 6s ↘
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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¢)

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

Modes of 16L 5s
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

Scale Tree and Tuning Spectrum of 16L 5s
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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