16L 3s

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↖ 15L 2s ↑ 16L 2s 17L 2s ↗
← 15L 3s 16L 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 ¢)
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
Related to 3L 7s (sephiroid)
With tunings 3:1 to 4:1 (parahard)
Related MOS scales
Parent 3L 13s
Sister 3L 16s
Daughters 19L 16s, 16L 19s
Neutralized 13L 6s
2-Flought 35L 3s, 16L 22s
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 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 diatonic interval categories.

Intervals

Intervals of 16L 3s
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 63.2 ¢
Major 1-mosstep M1ms L 63.2 ¢ to 75.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 75.0 ¢ to 126.3 ¢
Major 2-mosstep M2ms 2L 126.3 ¢ to 150.0 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 150.0 ¢ to 189.5 ¢
Major 3-mosstep M3ms 3L 189.5 ¢ to 225.0 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 225.0 ¢ to 252.6 ¢
Major 4-mosstep M4ms 4L 252.6 ¢ to 300.0 ¢
5-mosstep Minor 5-mosstep m5ms 4L + s 300.0 ¢ to 315.8 ¢
Major 5-mosstep M5ms 5L 315.8 ¢ to 375.0 ¢
6-mosstep Perfect 6-mosstep P6ms 5L + s 375.0 ¢ to 378.9 ¢
Augmented 6-mosstep A6ms 6L 378.9 ¢ to 450.0 ¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 375.0 ¢ to 442.1 ¢
Major 7-mosstep M7ms 6L + s 442.1 ¢ to 450.0 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 450.0 ¢ to 505.3 ¢
Major 8-mosstep M8ms 7L + s 505.3 ¢ to 525.0 ¢
9-mosstep Minor 9-mosstep m9ms 7L + 2s 525.0 ¢ to 568.4 ¢
Major 9-mosstep M9ms 8L + s 568.4 ¢ to 600.0 ¢
10-mosstep Minor 10-mosstep m10ms 8L + 2s 600.0 ¢ to 631.6 ¢
Major 10-mosstep M10ms 9L + s 631.6 ¢ to 675.0 ¢
11-mosstep Minor 11-mosstep m11ms 9L + 2s 675.0 ¢ to 694.7 ¢
Major 11-mosstep M11ms 10L + s 694.7 ¢ to 750.0 ¢
12-mosstep Minor 12-mosstep m12ms 10L + 2s 750.0 ¢ to 757.9 ¢
Major 12-mosstep M12ms 11L + s 757.9 ¢ to 825.0 ¢
13-mosstep Diminished 13-mosstep d13ms 10L + 3s 750.0 ¢ to 821.1 ¢
Perfect 13-mosstep P13ms 11L + 2s 821.1 ¢ to 825.0 ¢
14-mosstep Minor 14-mosstep m14ms 11L + 3s 825.0 ¢ to 884.2 ¢
Major 14-mosstep M14ms 12L + 2s 884.2 ¢ to 900.0 ¢
15-mosstep Minor 15-mosstep m15ms 12L + 3s 900.0 ¢ to 947.4 ¢
Major 15-mosstep M15ms 13L + 2s 947.4 ¢ to 975.0 ¢
16-mosstep Minor 16-mosstep m16ms 13L + 3s 975.0 ¢ to 1010.5 ¢
Major 16-mosstep M16ms 14L + 2s 1010.5 ¢ to 1050.0 ¢
17-mosstep Minor 17-mosstep m17ms 14L + 3s 1050.0 ¢ to 1073.7 ¢
Major 17-mosstep M17ms 15L + 2s 1073.7 ¢ to 1125.0 ¢
18-mosstep Minor 18-mosstep m18ms 15L + 3s 1125.0 ¢ to 1136.8 ¢
Major 18-mosstep M18ms 16L + 2s 1136.8 ¢ to 1200.0 ¢
19-mosstep Perfect 19-mosstep P19ms 16L + 3s 1200.0 ¢

Generator chain

Generator chain of 16L 3s
Bright gens Scale degree Abbrev.
34 Augmented 5-mosdegree A5md
33 Augmented 11-mosdegree A11md
32 Augmented 17-mosdegree A17md
31 Augmented 4-mosdegree A4md
30 Augmented 10-mosdegree A10md
29 Augmented 16-mosdegree A16md
28 Augmented 3-mosdegree A3md
27 Augmented 9-mosdegree A9md
26 Augmented 15-mosdegree A15md
25 Augmented 2-mosdegree A2md
24 Augmented 8-mosdegree A8md
23 Augmented 14-mosdegree A14md
22 Augmented 1-mosdegree A1md
21 Augmented 7-mosdegree A7md
20 Augmented 13-mosdegree A13md
19 Augmented 0-mosdegree A0md
18 Augmented 6-mosdegree A6md
17 Major 12-mosdegree M12md
16 Major 18-mosdegree M18md
15 Major 5-mosdegree M5md
14 Major 11-mosdegree M11md
13 Major 17-mosdegree M17md
12 Major 4-mosdegree M4md
11 Major 10-mosdegree M10md
10 Major 16-mosdegree M16md
9 Major 3-mosdegree M3md
8 Major 9-mosdegree M9md
7 Major 15-mosdegree M15md
6 Major 2-mosdegree M2md
5 Major 8-mosdegree M8md
4 Major 14-mosdegree M14md
3 Major 1-mosdegree M1md
2 Major 7-mosdegree M7md
1 Perfect 13-mosdegree P13md
0 Perfect 0-mosdegree
Perfect 19-mosdegree		 P0md
P19md
−1 Perfect 6-mosdegree P6md
−2 Minor 12-mosdegree m12md
−3 Minor 18-mosdegree m18md
−4 Minor 5-mosdegree m5md
−5 Minor 11-mosdegree m11md
−6 Minor 17-mosdegree m17md
−7 Minor 4-mosdegree m4md
−8 Minor 10-mosdegree m10md
−9 Minor 16-mosdegree m16md
−10 Minor 3-mosdegree m3md
−11 Minor 9-mosdegree m9md
−12 Minor 15-mosdegree m15md
−13 Minor 2-mosdegree m2md
−14 Minor 8-mosdegree m8md
−15 Minor 14-mosdegree m14md
−16 Minor 1-mosdegree m1md
−17 Minor 7-mosdegree m7md
−18 Diminished 13-mosdegree d13md
−19 Diminished 19-mosdegree d19md
−20 Diminished 6-mosdegree d6md
−21 Diminished 12-mosdegree d12md
−22 Diminished 18-mosdegree d18md
−23 Diminished 5-mosdegree d5md
−24 Diminished 11-mosdegree d11md
−25 Diminished 17-mosdegree d17md
−26 Diminished 4-mosdegree d4md
−27 Diminished 10-mosdegree d10md
−28 Diminished 16-mosdegree d16md
−29 Diminished 3-mosdegree d3md
−30 Diminished 9-mosdegree d9md
−31 Diminished 15-mosdegree d15md
−32 Diminished 2-mosdegree d2md
−33 Diminished 8-mosdegree d8md
−34 Diminished 14-mosdegree d14md

Modes

Scale degrees of the modes of 16L 3s
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
18|0 1 LLLLLLsLLLLLsLLLLLs Perf. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Perf.
17|1 14 LLLLLsLLLLLLsLLLLLs Perf. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Perf.
16|2 8 LLLLLsLLLLLsLLLLLLs Perf. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Maj. Perf.
15|3 2 LLLLLsLLLLLsLLLLLsL Perf. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Min. Perf.
14|4 15 LLLLsLLLLLLsLLLLLsL Perf. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Min. Perf.
13|5 9 LLLLsLLLLLsLLLLLLsL Perf. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Maj. Min. Perf.
12|6 3 LLLLsLLLLLsLLLLLsLL Perf. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Perf.
11|7 16 LLLsLLLLLLsLLLLLsLL Perf. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Perf.
10|8 10 LLLsLLLLLsLLLLLLsLL Perf. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Perf.
9|9 4 LLLsLLLLLsLLLLLsLLL Perf. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Perf.
8|10 17 LLsLLLLLLsLLLLLsLLL Perf. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Perf.
7|11 11 LLsLLLLLsLLLLLLsLLL Perf. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Perf.
6|12 5 LLsLLLLLsLLLLLsLLLL Perf. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Perf.
5|13 18 LsLLLLLLsLLLLLsLLLL Perf. Maj. Min. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Perf.
4|14 12 LsLLLLLsLLLLLLsLLLL Perf. Maj. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Perf.
3|15 6 LsLLLLLsLLLLLsLLLLL Perf. Maj. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Perf.
2|16 19 sLLLLLLsLLLLLsLLLLL Perf. Min. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Perf.
1|17 13 sLLLLLsLLLLLLsLLLLL Perf. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Perf.
0|18 7 sLLLLLsLLLLLsLLLLLL Perf. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 16L 3s
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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