2L 19s

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↖ 1L 18s ↑ 2L 18s 3L 18s ↗
← 1L 19s 2L 19s 3L 19s →
↙ 1L 20s ↓ 2L 20s 3L 20s ↘ 
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Scale structure
Step pattern LsssssssssLssssssssss
ssssssssssLsssssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 10\21 to 1\2 (571.4 ¢ to 600.0 ¢)
Dark 1\2 to 11\21 (600.0 ¢ to 628.6 ¢)
TAMNAMS information
Descends from 2L 7s (balzano)
Ancestor's step ratio range 7:1 to 1:0
Related MOS scales
Parent 2L 17s
Sister 19L 2s
Daughters 21L 2s, 2L 21s
Neutralized 4L 17s
2-Flought 23L 19s, 2L 40s
Equal tunings
Equalized (L:s = 1:1) 10\21 (571.4 ¢)
Supersoft (L:s = 4:3) 31\65 (572.3 ¢)
Soft (L:s = 3:2) 21\44 (572.7 ¢)
Semisoft (L:s = 5:3) 32\67 (573.1 ¢)
Basic (L:s = 2:1) 11\23 (573.9 ¢)
Semihard (L:s = 5:2) 23\48 (575.0 ¢)
Hard (L:s = 3:1) 12\25 (576.0 ¢)
Superhard (L:s = 4:1) 13\27 (577.8 ¢)
Collapsed (L:s = 1:0) 1\2 (600.0 ¢)

2L 19s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 19 small steps, repeating every octave. 2L 19s is related to 2L 7s, expanding it by 12 tones. Generators that produce this scale range from 571.4 ¢ to 600 ¢, or from 600 ¢ to 628.6 ¢.

This is the MOS where the small steps split 10-9 between the large steps. With a generator no smaller than 10/21edo (571.429 ¢), it achieves a harmonic entropy minimum at generator = 7/5 (almost exactly 17/35edo).

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 2L 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 57.1 ¢
Major 1-mosstep M1ms L 57.1 ¢ to 600.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 114.3 ¢
Major 2-mosstep M2ms L + s 114.3 ¢ to 600.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 171.4 ¢
Major 3-mosstep M3ms L + 2s 171.4 ¢ to 600.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 228.6 ¢
Major 4-mosstep M4ms L + 3s 228.6 ¢ to 600.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 285.7 ¢
Major 5-mosstep M5ms L + 4s 285.7 ¢ to 600.0 ¢
6-mosstep Minor 6-mosstep m6ms 6s 0.0 ¢ to 342.9 ¢
Major 6-mosstep M6ms L + 5s 342.9 ¢ to 600.0 ¢
7-mosstep Minor 7-mosstep m7ms 7s 0.0 ¢ to 400.0 ¢
Major 7-mosstep M7ms L + 6s 400.0 ¢ to 600.0 ¢
8-mosstep Minor 8-mosstep m8ms 8s 0.0 ¢ to 457.1 ¢
Major 8-mosstep M8ms L + 7s 457.1 ¢ to 600.0 ¢
9-mosstep Minor 9-mosstep m9ms 9s 0.0 ¢ to 514.3 ¢
Major 9-mosstep M9ms L + 8s 514.3 ¢ to 600.0 ¢
10-mosstep Diminished 10-mosstep d10ms 10s 0.0 ¢ to 571.4 ¢
Perfect 10-mosstep P10ms L + 9s 571.4 ¢ to 600.0 ¢
11-mosstep Perfect 11-mosstep P11ms L + 10s 600.0 ¢ to 628.6 ¢
Augmented 11-mosstep A11ms 2L + 9s 628.6 ¢ to 1200.0 ¢
12-mosstep Minor 12-mosstep m12ms L + 11s 600.0 ¢ to 685.7 ¢
Major 12-mosstep M12ms 2L + 10s 685.7 ¢ to 1200.0 ¢
13-mosstep Minor 13-mosstep m13ms L + 12s 600.0 ¢ to 742.9 ¢
Major 13-mosstep M13ms 2L + 11s 742.9 ¢ to 1200.0 ¢
14-mosstep Minor 14-mosstep m14ms L + 13s 600.0 ¢ to 800.0 ¢
Major 14-mosstep M14ms 2L + 12s 800.0 ¢ to 1200.0 ¢
15-mosstep Minor 15-mosstep m15ms L + 14s 600.0 ¢ to 857.1 ¢
Major 15-mosstep M15ms 2L + 13s 857.1 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms L + 15s 600.0 ¢ to 914.3 ¢
Major 16-mosstep M16ms 2L + 14s 914.3 ¢ to 1200.0 ¢
17-mosstep Minor 17-mosstep m17ms L + 16s 600.0 ¢ to 971.4 ¢
Major 17-mosstep M17ms 2L + 15s 971.4 ¢ to 1200.0 ¢
18-mosstep Minor 18-mosstep m18ms L + 17s 600.0 ¢ to 1028.6 ¢
Major 18-mosstep M18ms 2L + 16s 1028.6 ¢ to 1200.0 ¢
19-mosstep Minor 19-mosstep m19ms L + 18s 600.0 ¢ to 1085.7 ¢
Major 19-mosstep M19ms 2L + 17s 1085.7 ¢ to 1200.0 ¢
20-mosstep Minor 20-mosstep m20ms L + 19s 600.0 ¢ to 1142.9 ¢
Major 20-mosstep M20ms 2L + 18s 1142.9 ¢ to 1200.0 ¢
21-mosstep Perfect 21-mosstep P21ms 2L + 19s 1200.0 ¢

Generator chain

Generator chain of 2L 19s
Bright gens Scale degree Abbrev.
22 Augmented 10-mosdegree A10md
21 Augmented 0-mosdegree A0md
20 Augmented 11-mosdegree A11md
19 Major 1-mosdegree M1md
18 Major 12-mosdegree M12md
17 Major 2-mosdegree M2md
16 Major 13-mosdegree M13md
15 Major 3-mosdegree M3md
14 Major 14-mosdegree M14md
13 Major 4-mosdegree M4md
12 Major 15-mosdegree M15md
11 Major 5-mosdegree M5md
10 Major 16-mosdegree M16md
9 Major 6-mosdegree M6md
8 Major 17-mosdegree M17md
7 Major 7-mosdegree M7md
6 Major 18-mosdegree M18md
5 Major 8-mosdegree M8md
4 Major 19-mosdegree M19md
3 Major 9-mosdegree M9md
2 Major 20-mosdegree M20md
1 Perfect 10-mosdegree P10md
0 Perfect 0-mosdegree
Perfect 21-mosdegree		 P0md
P21md
−1 Perfect 11-mosdegree P11md
−2 Minor 1-mosdegree m1md
−3 Minor 12-mosdegree m12md
−4 Minor 2-mosdegree m2md
−5 Minor 13-mosdegree m13md
−6 Minor 3-mosdegree m3md
−7 Minor 14-mosdegree m14md
−8 Minor 4-mosdegree m4md
−9 Minor 15-mosdegree m15md
−10 Minor 5-mosdegree m5md
−11 Minor 16-mosdegree m16md
−12 Minor 6-mosdegree m6md
−13 Minor 17-mosdegree m17md
−14 Minor 7-mosdegree m7md
−15 Minor 18-mosdegree m18md
−16 Minor 8-mosdegree m8md
−17 Minor 19-mosdegree m19md
−18 Minor 9-mosdegree m9md
−19 Minor 20-mosdegree m20md
−20 Diminished 10-mosdegree d10md
−21 Diminished 21-mosdegree d21md
−22 Diminished 11-mosdegree d11md

Modes

Scale degrees of the modes of 2L 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
20|0 1 LsssssssssLssssssssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
19|1 11 LssssssssssLsssssssss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
18|2 21 sLsssssssssLsssssssss Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
17|3 10 sLssssssssssLssssssss Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
16|4 20 ssLsssssssssLssssssss Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
15|5 9 ssLssssssssssLsssssss Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
14|6 19 sssLsssssssssLsssssss Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
13|7 8 sssLssssssssssLssssss Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
12|8 18 ssssLsssssssssLssssss Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
11|9 7 ssssLssssssssssLsssss Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf.
10|10 17 sssssLsssssssssLsssss Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Maj. Perf.
9|11 6 sssssLssssssssssLssss Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf.
8|12 16 ssssssLsssssssssLssss Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Min. Maj. Maj. Maj. Maj. Perf.
7|13 5 ssssssLssssssssssLsss Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf.
6|14 15 sssssssLsssssssssLsss Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Min. Min. Maj. Maj. Maj. Perf.
5|15 4 sssssssLssssssssssLss Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf.
4|16 14 ssssssssLsssssssssLss Perf. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Maj. Perf.
3|17 3 ssssssssLssssssssssLs Perf. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Perf.
2|18 13 sssssssssLsssssssssLs Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Perf.
1|19 2 sssssssssLssssssssssL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf.
0|20 12 ssssssssssLsssssssssL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 2L 19s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
10\21 571.429 628.571 1:1 1.000 Equalized 2L 19s
51\107 571.963 628.037 6:5 1.200
41\86 572.093 627.907 5:4 1.250
72\151 572.185 627.815 9:7 1.286
31\65 572.308 627.692 4:3 1.333 Supersoft 2L 19s
83\174 572.414 627.586 11:8 1.375
52\109 572.477 627.523 7:5 1.400
73\153 572.549 627.451 10:7 1.429
21\44 572.727 627.273 3:2 1.500 Soft 2L 19s
74\155 572.903 627.097 11:7 1.571
53\111 572.973 627.027 8:5 1.600
85\178 573.034 626.966 13:8 1.625
32\67 573.134 626.866 5:3 1.667 Semisoft 2L 19s
75\157 573.248 626.752 12:7 1.714
43\90 573.333 626.667 7:4 1.750
54\113 573.451 626.549 9:5 1.800
11\23 573.913 626.087 2:1 2.000 Basic 2L 19s
Scales with tunings softer than this are proper
45\94 574.468 625.532 9:4 2.250
34\71 574.648 625.352 7:3 2.333
57\119 574.790 625.210 12:5 2.400
23\48 575.000 625.000 5:2 2.500 Semihard 2L 19s
58\121 575.207 624.793 13:5 2.600
35\73 575.342 624.658 8:3 2.667
47\98 575.510 624.490 11:4 2.750
12\25 576.000 624.000 3:1 3.000 Hard 2L 19s
37\77 576.623 623.377 10:3 3.333
25\52 576.923 623.077 7:2 3.500
38\79 577.215 622.785 11:3 3.667
13\27 577.778 622.222 4:1 4.000 Superhard 2L 19s
27\56 578.571 621.429 9:2 4.500
14\29 579.310 620.690 5:1 5.000
15\31 580.645 619.355 6:1 6.000
1\2 600.000 600.000 1:0 → ∞ Collapsed 2L 19s
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