2L 19s
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Step pattern
LsssssssssLssssssssss
ssssssssssLsssssssssL
Equave
2/1 (1200.0 ¢)
Period
2/1 (1200.0 ¢)
Bright
10\21 to 1\2 (571.4 ¢ to 600.0 ¢)
Dark
1\2 to 11\21 (600.0 ¢ to 628.6 ¢)
Descends from
2L 7s (balzano)
Ancestor's step ratio range
7:1 to 1:0
Parent
2L 17s
Sister
19L 2s
Daughters
21L 2s, 2L 21s
Neutralized
4L 17s
2-Flought
23L 19s, 2L 40s
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 ↘ |
┌╥┬┬┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┬┬┬┐ │║│││││││││║│││││││││││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
ssssssssssLsssssssssL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
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 | 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
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
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
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 |