16L 5s

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↖ 15L 4s ↑ 16L 4s 17L 4s ↗
← 15L 5s 16L 5s 17L 5s →
↙ 15L 6s ↓ 16L 6s 17L 6s ↘ 
┌╥╥╥╥┬╥╥╥┬╥╥╥┬╥╥╥┬╥╥╥┬┐
│║║║║│║║║│║║║│║║║│║║║││
│││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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
Related to 5L 1s (machinoid)
With tunings 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 ¢.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 16L 5s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 57.1 ¢
Major 1-mosstep M1ms L 57.1 ¢ to 75.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 75.0 ¢ to 114.3 ¢
Major 2-mosstep M2ms 2L 114.3 ¢ to 150.0 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 150.0 ¢ to 171.4 ¢
Major 3-mosstep M3ms 3L 171.4 ¢ to 225.0 ¢
4-mosstep Perfect 4-mosstep P4ms 3L + s 225.0 ¢ to 228.6 ¢
Augmented 4-mosstep A4ms 4L 228.6 ¢ to 300.0 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 225.0 ¢ to 285.7 ¢
Major 5-mosstep M5ms 4L + s 285.7 ¢ to 300.0 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 300.0 ¢ to 342.9 ¢
Major 6-mosstep M6ms 5L + s 342.9 ¢ to 375.0 ¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 375.0 ¢ to 400.0 ¢
Major 7-mosstep M7ms 6L + s 400.0 ¢ to 450.0 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 450.0 ¢ to 457.1 ¢
Major 8-mosstep M8ms 7L + s 457.1 ¢ to 525.0 ¢
9-mosstep Minor 9-mosstep m9ms 6L + 3s 450.0 ¢ to 514.3 ¢
Major 9-mosstep M9ms 7L + 2s 514.3 ¢ to 525.0 ¢
10-mosstep Minor 10-mosstep m10ms 7L + 3s 525.0 ¢ to 571.4 ¢
Major 10-mosstep M10ms 8L + 2s 571.4 ¢ to 600.0 ¢
11-mosstep Minor 11-mosstep m11ms 8L + 3s 600.0 ¢ to 628.6 ¢
Major 11-mosstep M11ms 9L + 2s 628.6 ¢ to 675.0 ¢
12-mosstep Minor 12-mosstep m12ms 9L + 3s 675.0 ¢ to 685.7 ¢
Major 12-mosstep M12ms 10L + 2s 685.7 ¢ to 750.0 ¢
13-mosstep Minor 13-mosstep m13ms 9L + 4s 675.0 ¢ to 742.9 ¢
Major 13-mosstep M13ms 10L + 3s 742.9 ¢ to 750.0 ¢
14-mosstep Minor 14-mosstep m14ms 10L + 4s 750.0 ¢ to 800.0 ¢
Major 14-mosstep M14ms 11L + 3s 800.0 ¢ to 825.0 ¢
15-mosstep Minor 15-mosstep m15ms 11L + 4s 825.0 ¢ to 857.1 ¢
Major 15-mosstep M15ms 12L + 3s 857.1 ¢ to 900.0 ¢
16-mosstep Minor 16-mosstep m16ms 12L + 4s 900.0 ¢ to 914.3 ¢
Major 16-mosstep M16ms 13L + 3s 914.3 ¢ to 975.0 ¢
17-mosstep Diminished 17-mosstep d17ms 12L + 5s 900.0 ¢ to 971.4 ¢
Perfect 17-mosstep P17ms 13L + 4s 971.4 ¢ to 975.0 ¢
18-mosstep Minor 18-mosstep m18ms 13L + 5s 975.0 ¢ to 1028.6 ¢
Major 18-mosstep M18ms 14L + 4s 1028.6 ¢ to 1050.0 ¢
19-mosstep Minor 19-mosstep m19ms 14L + 5s 1050.0 ¢ to 1085.7 ¢
Major 19-mosstep M19ms 15L + 4s 1085.7 ¢ to 1125.0 ¢
20-mosstep Minor 20-mosstep m20ms 15L + 5s 1125.0 ¢ to 1142.9 ¢
Major 20-mosstep M20ms 16L + 4s 1142.9 ¢ to 1200.0 ¢
21-mosstep Perfect 21-mosstep P21ms 16L + 5s 1200.0 ¢

Generator chain

Generator chain of 16L 5s
Bright gens Scale degree Abbrev.
36 Augmented 3-mosdegree A3md
35 Augmented 7-mosdegree A7md
34 Augmented 11-mosdegree A11md
33 Augmented 15-mosdegree A15md
32 Augmented 19-mosdegree A19md
31 Augmented 2-mosdegree A2md
30 Augmented 6-mosdegree A6md
29 Augmented 10-mosdegree A10md
28 Augmented 14-mosdegree A14md
27 Augmented 18-mosdegree A18md
26 Augmented 1-mosdegree A1md
25 Augmented 5-mosdegree A5md
24 Augmented 9-mosdegree A9md
23 Augmented 13-mosdegree A13md
22 Augmented 17-mosdegree A17md
21 Augmented 0-mosdegree A0md
20 Augmented 4-mosdegree A4md
19 Major 8-mosdegree M8md
18 Major 12-mosdegree M12md
17 Major 16-mosdegree M16md
16 Major 20-mosdegree M20md
15 Major 3-mosdegree M3md
14 Major 7-mosdegree M7md
13 Major 11-mosdegree M11md
12 Major 15-mosdegree M15md
11 Major 19-mosdegree M19md
10 Major 2-mosdegree M2md
9 Major 6-mosdegree M6md
8 Major 10-mosdegree M10md
7 Major 14-mosdegree M14md
6 Major 18-mosdegree M18md
5 Major 1-mosdegree M1md
4 Major 5-mosdegree M5md
3 Major 9-mosdegree M9md
2 Major 13-mosdegree M13md
1 Perfect 17-mosdegree P17md
0 Perfect 0-mosdegree
Perfect 21-mosdegree		 P0md
P21md
−1 Perfect 4-mosdegree P4md
−2 Minor 8-mosdegree m8md
−3 Minor 12-mosdegree m12md
−4 Minor 16-mosdegree m16md
−5 Minor 20-mosdegree m20md
−6 Minor 3-mosdegree m3md
−7 Minor 7-mosdegree m7md
−8 Minor 11-mosdegree m11md
−9 Minor 15-mosdegree m15md
−10 Minor 19-mosdegree m19md
−11 Minor 2-mosdegree m2md
−12 Minor 6-mosdegree m6md
−13 Minor 10-mosdegree m10md
−14 Minor 14-mosdegree m14md
−15 Minor 18-mosdegree m18md
−16 Minor 1-mosdegree m1md
−17 Minor 5-mosdegree m5md
−18 Minor 9-mosdegree m9md
−19 Minor 13-mosdegree m13md
−20 Diminished 17-mosdegree d17md
−21 Diminished 21-mosdegree d21md
−22 Diminished 4-mosdegree d4md
−23 Diminished 8-mosdegree d8md
−24 Diminished 12-mosdegree d12md
−25 Diminished 16-mosdegree d16md
−26 Diminished 20-mosdegree d20md
−27 Diminished 3-mosdegree d3md
−28 Diminished 7-mosdegree d7md
−29 Diminished 11-mosdegree d11md
−30 Diminished 15-mosdegree d15md
−31 Diminished 19-mosdegree d19md
−32 Diminished 2-mosdegree d2md
−33 Diminished 6-mosdegree d6md
−34 Diminished 10-mosdegree d10md
−35 Diminished 14-mosdegree d14md
−36 Diminished 18-mosdegree d18md

Modes

Scale degrees of the modes of 16L 5s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
20|0 1 LLLLsLLLsLLLsLLLsLLLs Perf. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
19|1 18 LLLsLLLLsLLLsLLLsLLLs Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
18|2 14 LLLsLLLsLLLLsLLLsLLLs Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
17|3 10 LLLsLLLsLLLsLLLLsLLLs Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
16|4 6 LLLsLLLsLLLsLLLsLLLLs Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Perf.
15|5 2 LLLsLLLsLLLsLLLsLLLsL Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Perf. Maj. Maj. Min. Perf.
14|6 19 LLsLLLLsLLLsLLLsLLLsL Perf. Maj. Maj. Min. Perf. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Perf. Maj. Maj. Min. Perf.
13|7 15 LLsLLLsLLLLsLLLsLLLsL Perf. Maj. Maj. Min. Perf. Maj. Maj. Min. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Min. Perf. Maj. Maj. Min. Perf.
12|8 11 LLsLLLsLLLsLLLLsLLLsL Perf. Maj. Maj. Min. Perf. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Maj. Min. Perf. Maj. Maj. Min. Perf.
11|9 7 LLsLLLsLLLsLLLsLLLLsL Perf. Maj. Maj. Min. Perf. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Perf. Maj. Maj. Min. Perf.
10|10 3 LLsLLLsLLLsLLLsLLLsLL Perf. Maj. Maj. Min. Perf. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Perf. Maj. Min. Min. Perf.
9|11 20 LsLLLLsLLLsLLLsLLLsLL Perf. Maj. Min. Min. Perf. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Perf. Maj. Min. Min. Perf.
8|12 16 LsLLLsLLLLsLLLsLLLsLL Perf. Maj. Min. Min. Perf. Maj. Min. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Min. Min. Perf. Maj. Min. Min. Perf.
7|13 12 LsLLLsLLLsLLLLsLLLsLL Perf. Maj. Min. Min. Perf. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Maj. Min. Min. Perf. Maj. Min. Min. Perf.
6|14 8 LsLLLsLLLsLLLsLLLLsLL Perf. Maj. Min. Min. Perf. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Maj. Min. Min. Perf.
5|15 4 LsLLLsLLLsLLLsLLLsLLL Perf. Maj. Min. Min. Perf. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf.
4|16 21 sLLLLsLLLsLLLsLLLsLLL Perf. Min. Min. Min. Perf. Maj. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf.
3|17 17 sLLLsLLLLsLLLsLLLsLLL Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf.
2|18 13 sLLLsLLLsLLLLsLLLsLLL Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf.
1|19 9 sLLLsLLLsLLLsLLLLsLLL Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Perf.
0|20 5 sLLLsLLLsLLLsLLLsLLLL Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Perf.

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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