2L 19s

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↖ 1L 18s ↑2L 18s 3L 18s ↗
← 1L 19s2L 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)
Required 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
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 cents), it achieves a harmonic entropy minimum at generator = 7/5 (almost exactly 17/35edo).

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