3L 19s

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↖ 2L 18s ↑ 3L 18s 4L 18s ↗
← 2L 19s 3L 19s 4L 19s →
↙ 2L 20s ↓ 3L 20s 4L 20s ↘ 
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssssssLssssssLsssssss
sssssssLssssssLssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 7\22 to 1\3 (381.8 ¢ to 400.0 ¢)
Dark 2\3 to 15\22 (800.0 ¢ to 818.2 ¢)
TAMNAMS information
Related to 3L 7s (sephiroid)
With tunings 5:1 to 1:0
Related MOS scales
Parent 3L 16s
Sister 19L 3s
Daughters 22L 3s, 3L 22s
Neutralized 6L 16s
2-Flought 25L 19s, 3L 41s
Equal tunings
Equalized (L:s = 1:1) 7\22 (381.8 ¢)
Supersoft (L:s = 4:3) 22\69 (382.6 ¢)
Soft (L:s = 3:2) 15\47 (383.0 ¢)
Semisoft (L:s = 5:3) 23\72 (383.3 ¢)
Basic (L:s = 2:1) 8\25 (384.0 ¢)
Semihard (L:s = 5:2) 17\53 (384.9 ¢)
Hard (L:s = 3:1) 9\28 (385.7 ¢)
Superhard (L:s = 4:1) 10\31 (387.1 ¢)
Collapsed (L:s = 1:0) 1\3 (400.0 ¢)

3L 19s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 19 small steps, repeating every octave. 3L 19s is related to 3L 7s, expanding it by 12 tones. Generators that produce this scale range from 381.8 ¢ to 400 ¢, or from 800 ¢ to 818.2 ¢.

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 3L 19s
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 54.5 ¢
Major 1-mosstep M1ms L 54.5 ¢ to 400.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 109.1 ¢
Major 2-mosstep M2ms L + s 109.1 ¢ to 400.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 163.6 ¢
Major 3-mosstep M3ms L + 2s 163.6 ¢ to 400.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 218.2 ¢
Major 4-mosstep M4ms L + 3s 218.2 ¢ to 400.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 272.7 ¢
Major 5-mosstep M5ms L + 4s 272.7 ¢ to 400.0 ¢
6-mosstep Minor 6-mosstep m6ms 6s 0.0 ¢ to 327.3 ¢
Major 6-mosstep M6ms L + 5s 327.3 ¢ to 400.0 ¢
7-mosstep Diminished 7-mosstep d7ms 7s 0.0 ¢ to 381.8 ¢
Perfect 7-mosstep P7ms L + 6s 381.8 ¢ to 400.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 400.0 ¢ to 436.4 ¢
Major 8-mosstep M8ms 2L + 6s 436.4 ¢ to 800.0 ¢
9-mosstep Minor 9-mosstep m9ms L + 8s 400.0 ¢ to 490.9 ¢
Major 9-mosstep M9ms 2L + 7s 490.9 ¢ to 800.0 ¢
10-mosstep Minor 10-mosstep m10ms L + 9s 400.0 ¢ to 545.5 ¢
Major 10-mosstep M10ms 2L + 8s 545.5 ¢ to 800.0 ¢
11-mosstep Minor 11-mosstep m11ms L + 10s 400.0 ¢ to 600.0 ¢
Major 11-mosstep M11ms 2L + 9s 600.0 ¢ to 800.0 ¢
12-mosstep Minor 12-mosstep m12ms L + 11s 400.0 ¢ to 654.5 ¢
Major 12-mosstep M12ms 2L + 10s 654.5 ¢ to 800.0 ¢
13-mosstep Minor 13-mosstep m13ms L + 12s 400.0 ¢ to 709.1 ¢
Major 13-mosstep M13ms 2L + 11s 709.1 ¢ to 800.0 ¢
14-mosstep Minor 14-mosstep m14ms L + 13s 400.0 ¢ to 763.6 ¢
Major 14-mosstep M14ms 2L + 12s 763.6 ¢ to 800.0 ¢
15-mosstep Perfect 15-mosstep P15ms 2L + 13s 800.0 ¢ to 818.2 ¢
Augmented 15-mosstep A15ms 3L + 12s 818.2 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms 2L + 14s 800.0 ¢ to 872.7 ¢
Major 16-mosstep M16ms 3L + 13s 872.7 ¢ to 1200.0 ¢
17-mosstep Minor 17-mosstep m17ms 2L + 15s 800.0 ¢ to 927.3 ¢
Major 17-mosstep M17ms 3L + 14s 927.3 ¢ to 1200.0 ¢
18-mosstep Minor 18-mosstep m18ms 2L + 16s 800.0 ¢ to 981.8 ¢
Major 18-mosstep M18ms 3L + 15s 981.8 ¢ to 1200.0 ¢
19-mosstep Minor 19-mosstep m19ms 2L + 17s 800.0 ¢ to 1036.4 ¢
Major 19-mosstep M19ms 3L + 16s 1036.4 ¢ to 1200.0 ¢
20-mosstep Minor 20-mosstep m20ms 2L + 18s 800.0 ¢ to 1090.9 ¢
Major 20-mosstep M20ms 3L + 17s 1090.9 ¢ to 1200.0 ¢
21-mosstep Minor 21-mosstep m21ms 2L + 19s 800.0 ¢ to 1145.5 ¢
Major 21-mosstep M21ms 3L + 18s 1145.5 ¢ to 1200.0 ¢
22-mosstep Perfect 22-mosstep P22ms 3L + 19s 1200.0 ¢

Generator chain

Generator chain of 3L 19s
Bright gens Scale degree Abbrev.
24 Augmented 14-mosdegree A14md
23 Augmented 7-mosdegree A7md
22 Augmented 0-mosdegree A0md
21 Augmented 15-mosdegree A15md
20 Major 8-mosdegree M8md
19 Major 1-mosdegree M1md
18 Major 16-mosdegree M16md
17 Major 9-mosdegree M9md
16 Major 2-mosdegree M2md
15 Major 17-mosdegree M17md
14 Major 10-mosdegree M10md
13 Major 3-mosdegree M3md
12 Major 18-mosdegree M18md
11 Major 11-mosdegree M11md
10 Major 4-mosdegree M4md
9 Major 19-mosdegree M19md
8 Major 12-mosdegree M12md
7 Major 5-mosdegree M5md
6 Major 20-mosdegree M20md
5 Major 13-mosdegree M13md
4 Major 6-mosdegree M6md
3 Major 21-mosdegree M21md
2 Major 14-mosdegree M14md
1 Perfect 7-mosdegree P7md
0 Perfect 0-mosdegree
Perfect 22-mosdegree		 P0md
P22md
−1 Perfect 15-mosdegree P15md
−2 Minor 8-mosdegree m8md
−3 Minor 1-mosdegree m1md
−4 Minor 16-mosdegree m16md
−5 Minor 9-mosdegree m9md
−6 Minor 2-mosdegree m2md
−7 Minor 17-mosdegree m17md
−8 Minor 10-mosdegree m10md
−9 Minor 3-mosdegree m3md
−10 Minor 18-mosdegree m18md
−11 Minor 11-mosdegree m11md
−12 Minor 4-mosdegree m4md
−13 Minor 19-mosdegree m19md
−14 Minor 12-mosdegree m12md
−15 Minor 5-mosdegree m5md
−16 Minor 20-mosdegree m20md
−17 Minor 13-mosdegree m13md
−18 Minor 6-mosdegree m6md
−19 Minor 21-mosdegree m21md
−20 Minor 14-mosdegree m14md
−21 Diminished 7-mosdegree d7md
−22 Diminished 22-mosdegree d22md
−23 Diminished 15-mosdegree d15md
−24 Diminished 8-mosdegree d8md

Modes

Scale degrees of the modes of 3L 19s
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 22
21|0 1 LssssssLssssssLsssssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
20|1 8 LssssssLsssssssLssssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
19|2 15 LsssssssLssssssLssssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
18|3 22 sLssssssLssssssLssssss Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
17|4 7 sLssssssLsssssssLsssss Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf.
16|5 14 sLsssssssLssssssLsssss Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf.
15|6 21 ssLssssssLssssssLsssss Perf. Min. Min. Maj. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Maj. Perf.
14|7 6 ssLssssssLsssssssLssss Perf. Min. Min. Maj. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Maj. Perf.
13|8 13 ssLsssssssLssssssLssss Perf. Min. Min. Maj. Maj. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Maj. Perf.
12|9 20 sssLssssssLssssssLssss Perf. Min. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Maj. Perf.
11|10 5 sssLssssssLsssssssLsss Perf. Min. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Maj. Perf.
10|11 12 sssLsssssssLssssssLsss Perf. Min. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Maj. Perf.
9|12 19 ssssLssssssLssssssLsss Perf. Min. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Maj. Perf.
8|13 4 ssssLssssssLsssssssLss Perf. Min. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Min. Min. Maj. Maj. Perf.
7|14 11 ssssLsssssssLssssssLss Perf. Min. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Min. Maj. Maj. Perf.
6|15 18 sssssLssssssLssssssLss Perf. Min. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Min. Maj. Maj. Perf.
5|16 3 sssssLssssssLsssssssLs Perf. Min. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Min. Min. Maj. Perf.
4|17 10 sssssLsssssssLssssssLs Perf. Min. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Min. Maj. Perf.
3|18 17 ssssssLssssssLssssssLs Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Min. Maj. Perf.
2|19 2 ssssssLssssssLsssssssL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Min. Min. Perf.
1|20 9 ssssssLsssssssLssssssL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
0|21 16 sssssssLssssssLssssssL Perf. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 3L 19s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\22 381.818 818.182 1:1 1.000 Equalized 3L 19s
36\113 382.301 817.699 6:5 1.200
29\91 382.418 817.582 5:4 1.250
51\160 382.500 817.500 9:7 1.286
22\69 382.609 817.391 4:3 1.333 Supersoft 3L 19s
59\185 382.703 817.297 11:8 1.375
37\116 382.759 817.241 7:5 1.400
52\163 382.822 817.178 10:7 1.429
15\47 382.979 817.021 3:2 1.500 Soft 3L 19s
53\166 383.133 816.867 11:7 1.571
38\119 383.193 816.807 8:5 1.600
61\191 383.246 816.754 13:8 1.625
23\72 383.333 816.667 5:3 1.667 Semisoft 3L 19s
54\169 383.432 816.568 12:7 1.714
31\97 383.505 816.495 7:4 1.750
39\122 383.607 816.393 9:5 1.800
8\25 384.000 816.000 2:1 2.000 Basic 3L 19s
Scales with tunings softer than this are proper
33\103 384.466 815.534 9:4 2.250
25\78 384.615 815.385 7:3 2.333
42\131 384.733 815.267 12:5 2.400
17\53 384.906 815.094 5:2 2.500 Semihard 3L 19s
43\134 385.075 814.925 13:5 2.600
26\81 385.185 814.815 8:3 2.667
35\109 385.321 814.679 11:4 2.750
9\28 385.714 814.286 3:1 3.000 Hard 3L 19s
28\87 386.207 813.793 10:3 3.333
19\59 386.441 813.559 7:2 3.500
29\90 386.667 813.333 11:3 3.667
10\31 387.097 812.903 4:1 4.000 Superhard 3L 19s
21\65 387.692 812.308 9:2 4.500
11\34 388.235 811.765 5:1 5.000
12\37 389.189 810.811 6:1 6.000
1\3 400.000 800.000 1:0 → ∞ Collapsed 3L 19s
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