2L 19s
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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)
Related MOS scales
Parent
2L 17s
Sister
19L 2s
Daughters
21L 2s
2L 21s
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¢)
| ↖1L 18s | ↑2L 18s | 3L 18s↗ |
| ←1L 19s | 2L 19s | 3L 19s→ |
| ↙1L 20s | ↓2L 20s | 3L 20s↘ |
┌╥┬┬┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┬┬┬┐ │║│││││││││║│││││││││││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssssssssssLsssssssssL
2L 21s
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).
| Generator (in steps of 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 | |||||