2L 16s

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↖ 1L 15s ↑ 2L 15s 3L 15s ↗
← 1L 16s 2L 16s 3L 16s →
↙ 1L 17s ↓ 2L 17s 3L 17s ↘ 
┌╥┬┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┬┐
│║││││││││║│││││││││
││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssssssssLssssssss
ssssssssLssssssssL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 8\18 to 1\2 (533.3 ¢ to 600.0 ¢)
Dark 0\2 to 1\18 (0.0 ¢ to 66.7 ¢)
TAMNAMS information
Related to 2L 8s (jaric)
With tunings 5:1 to 1:0
Related MOS scales
Parent 2L 14s
Sister 16L 2s
Daughters 18L 2s, 2L 18s
Neutralized 4L 14s
2-Flought 20L 16s, 2L 34s
Equal tunings
Equalized (L:s = 1:1) 8\18 (533.3 ¢)
Supersoft (L:s = 4:3) 25\56 (535.7 ¢)
Soft (L:s = 3:2) 17\38 (536.8 ¢)
Semisoft (L:s = 5:3) 26\58 (537.9 ¢)
Basic (L:s = 2:1) 9\20 (540.0 ¢)
Semihard (L:s = 5:2) 19\42 (542.9 ¢)
Hard (L:s = 3:1) 10\22 (545.5 ¢)
Superhard (L:s = 4:1) 11\24 (550.0 ¢)
Collapsed (L:s = 1:0) 1\2 (600.0 ¢)

2L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 16 small steps, with a period of 1 large step and 8 small steps that repeats every 600.0 ¢, or twice every octave. 2L 16s is related to 2L 8s, expanding it by 8 tones. Generators that produce this scale range from 533.3 ¢ to 600 ¢, or from 0 ¢ to 66.7 ¢.

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 2L 16s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Perfect 1-mosstep P1ms s 0.0 ¢ to 66.7 ¢
Augmented 1-mosstep A1ms L 66.7 ¢ to 600.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 133.3 ¢
Major 2-mosstep M2ms L + s 133.3 ¢ to 600.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 200.0 ¢
Major 3-mosstep M3ms L + 2s 200.0 ¢ to 600.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 266.7 ¢
Major 4-mosstep M4ms L + 3s 266.7 ¢ to 600.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 333.3 ¢
Major 5-mosstep M5ms L + 4s 333.3 ¢ to 600.0 ¢
6-mosstep Minor 6-mosstep m6ms 6s 0.0 ¢ to 400.0 ¢
Major 6-mosstep M6ms L + 5s 400.0 ¢ to 600.0 ¢
7-mosstep Minor 7-mosstep m7ms 7s 0.0 ¢ to 466.7 ¢
Major 7-mosstep M7ms L + 6s 466.7 ¢ to 600.0 ¢
8-mosstep Diminished 8-mosstep d8ms 8s 0.0 ¢ to 533.3 ¢
Perfect 8-mosstep P8ms L + 7s 533.3 ¢ to 600.0 ¢
9-mosstep Perfect 9-mosstep P9ms L + 8s 600.0 ¢
10-mosstep Perfect 10-mosstep P10ms L + 9s 600.0 ¢ to 666.7 ¢
Augmented 10-mosstep A10ms 2L + 8s 666.7 ¢ to 1200.0 ¢
11-mosstep Minor 11-mosstep m11ms L + 10s 600.0 ¢ to 733.3 ¢
Major 11-mosstep M11ms 2L + 9s 733.3 ¢ to 1200.0 ¢
12-mosstep Minor 12-mosstep m12ms L + 11s 600.0 ¢ to 800.0 ¢
Major 12-mosstep M12ms 2L + 10s 800.0 ¢ to 1200.0 ¢
13-mosstep Minor 13-mosstep m13ms L + 12s 600.0 ¢ to 866.7 ¢
Major 13-mosstep M13ms 2L + 11s 866.7 ¢ to 1200.0 ¢
14-mosstep Minor 14-mosstep m14ms L + 13s 600.0 ¢ to 933.3 ¢
Major 14-mosstep M14ms 2L + 12s 933.3 ¢ to 1200.0 ¢
15-mosstep Minor 15-mosstep m15ms L + 14s 600.0 ¢ to 1000.0 ¢
Major 15-mosstep M15ms 2L + 13s 1000.0 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms L + 15s 600.0 ¢ to 1066.7 ¢
Major 16-mosstep M16ms 2L + 14s 1066.7 ¢ to 1200.0 ¢
17-mosstep Diminished 17-mosstep d17ms L + 16s 600.0 ¢ to 1133.3 ¢
Perfect 17-mosstep P17ms 2L + 15s 1133.3 ¢ to 1200.0 ¢
18-mosstep Perfect 18-mosstep P18ms 2L + 16s 1200.0 ¢

Generator chain

Generator chain of 2L 16s
Bright gens Scale degree Abbrev. Scale degree Abbrev.
9 Augmented 0-mosdegree A0md Augmented 9-mosdegree A9md
8 Augmented 1-mosdegree A1md Augmented 10-mosdegree A10md
7 Major 2-mosdegree M2md Major 11-mosdegree M11md
6 Major 3-mosdegree M3md Major 12-mosdegree M12md
5 Major 4-mosdegree M4md Major 13-mosdegree M13md
4 Major 5-mosdegree M5md Major 14-mosdegree M14md
3 Major 6-mosdegree M6md Major 15-mosdegree M15md
2 Major 7-mosdegree M7md Major 16-mosdegree M16md
1 Perfect 8-mosdegree P8md Perfect 17-mosdegree P17md
0 Perfect 0-mosdegree
Perfect 9-mosdegree		 P0md
P9md		 Perfect 9-mosdegree
Perfect 18-mosdegree		 P9md
P18md
−1 Perfect 1-mosdegree P1md Perfect 10-mosdegree P10md
−2 Minor 2-mosdegree m2md Minor 11-mosdegree m11md
−3 Minor 3-mosdegree m3md Minor 12-mosdegree m12md
−4 Minor 4-mosdegree m4md Minor 13-mosdegree m13md
−5 Minor 5-mosdegree m5md Minor 14-mosdegree m14md
−6 Minor 6-mosdegree m6md Minor 15-mosdegree m15md
−7 Minor 7-mosdegree m7md Minor 16-mosdegree m16md
−8 Diminished 8-mosdegree d8md Diminished 17-mosdegree d17md
−9 Diminished 9-mosdegree d9md Diminished 18-mosdegree d18md

Modes

Scale degrees of the modes of 2L 16s
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
16|0(2) 1 LssssssssLssssssss Perf. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
14|2(2) 9 sLssssssssLsssssss Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
12|4(2) 8 ssLssssssssLssssss Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
10|6(2) 7 sssLssssssssLsssss Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf.
8|8(2) 6 ssssLssssssssLssss Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Perf. Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Perf. Perf.
6|10(2) 5 sssssLssssssssLsss Perf. Perf. Min. Min. Min. Min. Maj. Maj. Perf. Perf. Perf. Min. Min. Min. Min. Maj. Maj. Perf. Perf.
4|12(2) 4 ssssssLssssssssLss Perf. Perf. Min. Min. Min. Min. Min. Maj. Perf. Perf. Perf. Min. Min. Min. Min. Min. Maj. Perf. Perf.
2|14(2) 3 sssssssLssssssssLs Perf. Perf. Min. Min. Min. Min. Min. Min. Perf. Perf. Perf. Min. Min. Min. Min. Min. Min. Perf. Perf.
0|16(2) 2 ssssssssLssssssssL Perf. Perf. Min. Min. Min. Min. Min. Min. Dim. Perf. Perf. Min. Min. Min. Min. Min. Min. Dim. Perf.

Scale tree

Scale tree and tuning spectrum of 2L 16s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
8\18 533.333 66.667 1:1 1.000 Equalized 2L 16s
41\92 534.783 65.217 6:5 1.200
33\74 535.135 64.865 5:4 1.250
58\130 535.385 64.615 9:7 1.286
25\56 535.714 64.286 4:3 1.333 Supersoft 2L 16s
67\150 536.000 64.000 11:8 1.375
42\94 536.170 63.830 7:5 1.400
59\132 536.364 63.636 10:7 1.429
17\38 536.842 63.158 3:2 1.500 Soft 2L 16s
60\134 537.313 62.687 11:7 1.571
43\96 537.500 62.500 8:5 1.600
69\154 537.662 62.338 13:8 1.625
26\58 537.931 62.069 5:3 1.667 Semisoft 2L 16s
61\136 538.235 61.765 12:7 1.714
35\78 538.462 61.538 7:4 1.750
44\98 538.776 61.224 9:5 1.800
9\20 540.000 60.000 2:1 2.000 Basic 2L 16s
Scales with tunings softer than this are proper
37\82 541.463 58.537 9:4 2.250
28\62 541.935 58.065 7:3 2.333
47\104 542.308 57.692 12:5 2.400
19\42 542.857 57.143 5:2 2.500 Semihard 2L 16s
48\106 543.396 56.604 13:5 2.600
29\64 543.750 56.250 8:3 2.667
39\86 544.186 55.814 11:4 2.750
10\22 545.455 54.545 3:1 3.000 Hard 2L 16s
31\68 547.059 52.941 10:3 3.333
21\46 547.826 52.174 7:2 3.500
32\70 548.571 51.429 11:3 3.667
11\24 550.000 50.000 4:1 4.000 Superhard 2L 16s
23\50 552.000 48.000 9:2 4.500
12\26 553.846 46.154 5:1 5.000
13\28 557.143 42.857 6:1 6.000
1\2 600.000 0.000 1:0 → ∞ Collapsed 2L 16s
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