19L 3s

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↖ 18L 2s ↑ 19L 2s 20L 2s ↗
← 18L 3s 19L 3s 20L 3s →
↙ 18L 4s ↓ 19L 4s 20L 4s ↘ 
┌╥╥╥╥╥╥╥┬╥╥╥╥╥╥┬╥╥╥╥╥╥┬┐
│║║║║║║║│║║║║║║│║║║║║║││
││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLLsLLLLLLsLLLLLLs
sLLLLLLsLLLLLLsLLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 15\22 to 13\19 (818.2 ¢ to 821.1 ¢)
Dark 6\19 to 7\22 (378.9 ¢ to 381.8 ¢)
TAMNAMS information
Related to 3L 7s (sephiroid)
With tunings 4:1 to 5:1
Related MOS scales
Parent 3L 16s
Sister 3L 19s
Daughters 22L 19s, 19L 22s
Neutralized 16L 6s
2-Flought 41L 3s, 19L 25s
Equal tunings
Equalized (L:s = 1:1) 15\22 (818.2 ¢)
Supersoft (L:s = 4:3) 58\85 (818.8 ¢)
Soft (L:s = 3:2) 43\63 (819.0 ¢)
Semisoft (L:s = 5:3) 71\104 (819.2 ¢)
Basic (L:s = 2:1) 28\41 (819.5 ¢)
Semihard (L:s = 5:2) 69\101 (819.8 ¢)
Hard (L:s = 3:1) 41\60 (820.0 ¢)
Superhard (L:s = 4:1) 54\79 (820.3 ¢)
Collapsed (L:s = 1:0) 13\19 (821.1 ¢)

19L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 19 large steps and 3 small steps, repeating every octave. 19L 3s is related to 3L 7s, expanding it by 12 tones. Generators that produce this scale range from 818.2 ¢ to 821.1 ¢, or from 378.9 ¢ to 381.8 ¢.

It is notable for supporting Magic temperament.

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 interval regions.

Intervals

Intervals of 19L 3s
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 63.2 ¢
2-mosstep Minor 2-mosstep m2ms L + s 63.2 ¢ to 109.1 ¢
Major 2-mosstep M2ms 2L 109.1 ¢ to 126.3 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 126.3 ¢ to 163.6 ¢
Major 3-mosstep M3ms 3L 163.6 ¢ to 189.5 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 189.5 ¢ to 218.2 ¢
Major 4-mosstep M4ms 4L 218.2 ¢ to 252.6 ¢
5-mosstep Minor 5-mosstep m5ms 4L + s 252.6 ¢ to 272.7 ¢
Major 5-mosstep M5ms 5L 272.7 ¢ to 315.8 ¢
6-mosstep Minor 6-mosstep m6ms 5L + s 315.8 ¢ to 327.3 ¢
Major 6-mosstep M6ms 6L 327.3 ¢ to 378.9 ¢
7-mosstep Perfect 7-mosstep P7ms 6L + s 378.9 ¢ to 381.8 ¢
Augmented 7-mosstep A7ms 7L 381.8 ¢ to 442.1 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 378.9 ¢ to 436.4 ¢
Major 8-mosstep M8ms 7L + s 436.4 ¢ to 442.1 ¢
9-mosstep Minor 9-mosstep m9ms 7L + 2s 442.1 ¢ to 490.9 ¢
Major 9-mosstep M9ms 8L + s 490.9 ¢ to 505.3 ¢
10-mosstep Minor 10-mosstep m10ms 8L + 2s 505.3 ¢ to 545.5 ¢
Major 10-mosstep M10ms 9L + s 545.5 ¢ to 568.4 ¢
11-mosstep Minor 11-mosstep m11ms 9L + 2s 568.4 ¢ to 600.0 ¢
Major 11-mosstep M11ms 10L + s 600.0 ¢ to 631.6 ¢
12-mosstep Minor 12-mosstep m12ms 10L + 2s 631.6 ¢ to 654.5 ¢
Major 12-mosstep M12ms 11L + s 654.5 ¢ to 694.7 ¢
13-mosstep Minor 13-mosstep m13ms 11L + 2s 694.7 ¢ to 709.1 ¢
Major 13-mosstep M13ms 12L + s 709.1 ¢ to 757.9 ¢
14-mosstep Minor 14-mosstep m14ms 12L + 2s 757.9 ¢ to 763.6 ¢
Major 14-mosstep M14ms 13L + s 763.6 ¢ to 821.1 ¢
15-mosstep Diminished 15-mosstep d15ms 12L + 3s 757.9 ¢ to 818.2 ¢
Perfect 15-mosstep P15ms 13L + 2s 818.2 ¢ to 821.1 ¢
16-mosstep Minor 16-mosstep m16ms 13L + 3s 821.1 ¢ to 872.7 ¢
Major 16-mosstep M16ms 14L + 2s 872.7 ¢ to 884.2 ¢
17-mosstep Minor 17-mosstep m17ms 14L + 3s 884.2 ¢ to 927.3 ¢
Major 17-mosstep M17ms 15L + 2s 927.3 ¢ to 947.4 ¢
18-mosstep Minor 18-mosstep m18ms 15L + 3s 947.4 ¢ to 981.8 ¢
Major 18-mosstep M18ms 16L + 2s 981.8 ¢ to 1010.5 ¢
19-mosstep Minor 19-mosstep m19ms 16L + 3s 1010.5 ¢ to 1036.4 ¢
Major 19-mosstep M19ms 17L + 2s 1036.4 ¢ to 1073.7 ¢
20-mosstep Minor 20-mosstep m20ms 17L + 3s 1073.7 ¢ to 1090.9 ¢
Major 20-mosstep M20ms 18L + 2s 1090.9 ¢ to 1136.8 ¢
21-mosstep Minor 21-mosstep m21ms 18L + 3s 1136.8 ¢ to 1145.5 ¢
Major 21-mosstep M21ms 19L + 2s 1145.5 ¢ to 1200.0 ¢
22-mosstep Perfect 22-mosstep P22ms 19L + 3s 1200.0 ¢

Generator chain

Generator chain of 19L 3s
Bright gens Scale degree Abbrev.
40 Augmented 6-mosdegree A6md
39 Augmented 13-mosdegree A13md
38 Augmented 20-mosdegree A20md
37 Augmented 5-mosdegree A5md
36 Augmented 12-mosdegree A12md
35 Augmented 19-mosdegree A19md
34 Augmented 4-mosdegree A4md
33 Augmented 11-mosdegree A11md
32 Augmented 18-mosdegree A18md
31 Augmented 3-mosdegree A3md
30 Augmented 10-mosdegree A10md
29 Augmented 17-mosdegree A17md
28 Augmented 2-mosdegree A2md
27 Augmented 9-mosdegree A9md
26 Augmented 16-mosdegree A16md
25 Augmented 1-mosdegree A1md
24 Augmented 8-mosdegree A8md
23 Augmented 15-mosdegree A15md
22 Augmented 0-mosdegree A0md
21 Augmented 7-mosdegree A7md
20 Major 14-mosdegree M14md
19 Major 21-mosdegree M21md
18 Major 6-mosdegree M6md
17 Major 13-mosdegree M13md
16 Major 20-mosdegree M20md
15 Major 5-mosdegree M5md
14 Major 12-mosdegree M12md
13 Major 19-mosdegree M19md
12 Major 4-mosdegree M4md
11 Major 11-mosdegree M11md
10 Major 18-mosdegree M18md
9 Major 3-mosdegree M3md
8 Major 10-mosdegree M10md
7 Major 17-mosdegree M17md
6 Major 2-mosdegree M2md
5 Major 9-mosdegree M9md
4 Major 16-mosdegree M16md
3 Major 1-mosdegree M1md
2 Major 8-mosdegree M8md
1 Perfect 15-mosdegree P15md
0 Perfect 0-mosdegree
Perfect 22-mosdegree		 P0md
P22md
−1 Perfect 7-mosdegree P7md
−2 Minor 14-mosdegree m14md
−3 Minor 21-mosdegree m21md
−4 Minor 6-mosdegree m6md
−5 Minor 13-mosdegree m13md
−6 Minor 20-mosdegree m20md
−7 Minor 5-mosdegree m5md
−8 Minor 12-mosdegree m12md
−9 Minor 19-mosdegree m19md
−10 Minor 4-mosdegree m4md
−11 Minor 11-mosdegree m11md
−12 Minor 18-mosdegree m18md
−13 Minor 3-mosdegree m3md
−14 Minor 10-mosdegree m10md
−15 Minor 17-mosdegree m17md
−16 Minor 2-mosdegree m2md
−17 Minor 9-mosdegree m9md
−18 Minor 16-mosdegree m16md
−19 Minor 1-mosdegree m1md
−20 Minor 8-mosdegree m8md
−21 Diminished 15-mosdegree d15md
−22 Diminished 22-mosdegree d22md
−23 Diminished 7-mosdegree d7md
−24 Diminished 14-mosdegree d14md
−25 Diminished 21-mosdegree d21md
−26 Diminished 6-mosdegree d6md
−27 Diminished 13-mosdegree d13md
−28 Diminished 20-mosdegree d20md
−29 Diminished 5-mosdegree d5md
−30 Diminished 12-mosdegree d12md
−31 Diminished 19-mosdegree d19md
−32 Diminished 4-mosdegree d4md
−33 Diminished 11-mosdegree d11md
−34 Diminished 18-mosdegree d18md
−35 Diminished 3-mosdegree d3md
−36 Diminished 10-mosdegree d10md
−37 Diminished 17-mosdegree d17md
−38 Diminished 2-mosdegree d2md
−39 Diminished 9-mosdegree d9md
−40 Diminished 16-mosdegree d16md

Modes

Scale degrees of the modes of 19L 3s
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 LLLLLLLsLLLLLLsLLLLLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
20|1 16 LLLLLLsLLLLLLLsLLLLLLs 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 9 LLLLLLsLLLLLLsLLLLLLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
18|3 2 LLLLLLsLLLLLLsLLLLLLsL Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf.
17|4 17 LLLLLsLLLLLLLsLLLLLLsL Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf.
16|5 10 LLLLLsLLLLLLsLLLLLLLsL Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf.
15|6 3 LLLLLsLLLLLLsLLLLLLsLL Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Maj. Min. Min. Perf.
14|7 18 LLLLsLLLLLLLsLLLLLLsLL Perf. Maj. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Maj. Min. Min. Perf.
13|8 11 LLLLsLLLLLLsLLLLLLLsLL Perf. Maj. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Maj. Maj. Min. Min. Perf.
12|9 4 LLLLsLLLLLLsLLLLLLsLLL Perf. Maj. Maj. Maj. Maj. Min. Min. Perf. Maj. Maj. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Min. Perf.
11|10 19 LLLsLLLLLLLsLLLLLLsLLL Perf. Maj. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Min. Perf.
10|11 12 LLLsLLLLLLsLLLLLLLsLLL Perf. Maj. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Min. Perf.
9|12 5 LLLsLLLLLLsLLLLLLsLLLL Perf. Maj. Maj. Maj. Min. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Min. Perf.
8|13 20 LLsLLLLLLLsLLLLLLsLLLL Perf. Maj. Maj. Min. Min. Min. Min. Perf. Maj. Maj. Maj. Min. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Min. Perf.
7|14 13 LLsLLLLLLsLLLLLLLsLLLL Perf. Maj. Maj. Min. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Min. Perf.
6|15 6 LLsLLLLLLsLLLLLLsLLLLL Perf. Maj. Maj. Min. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Min. Perf.
5|16 21 LsLLLLLLLsLLLLLLsLLLLL Perf. Maj. Min. Min. Min. Min. Min. Perf. Maj. Maj. Min. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Min. Perf.
4|17 14 LsLLLLLLsLLLLLLLsLLLLL Perf. Maj. Min. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Min. Perf.
3|18 7 LsLLLLLLsLLLLLLsLLLLLL Perf. Maj. Min. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
2|19 22 sLLLLLLLsLLLLLLsLLLLLL Perf. Min. Min. Min. Min. Min. Min. Perf. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
1|20 15 sLLLLLLsLLLLLLLsLLLLLL 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 8 sLLLLLLsLLLLLLsLLLLLLL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 19L 3s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
15\22 818.182 381.818 1:1 1.000 Equalized 19L 3s
88\129 818.605 381.395 6:5 1.200
73\107 818.692 381.308 5:4 1.250
131\192 818.750 381.250 9:7 1.286
58\85 818.824 381.176 4:3 1.333 Supersoft 19L 3s
159\233 818.884 381.116 11:8 1.375
101\148 818.919 381.081 7:5 1.400
144\211 818.957 381.043 10:7 1.429
43\63 819.048 380.952 3:2 1.500 Soft 19L 3s
157\230 819.130 380.870 11:7 1.571
114\167 819.162 380.838 8:5 1.600
185\271 819.188 380.812 13:8 1.625
71\104 819.231 380.769 5:3 1.667 Semisoft 19L 3s
170\249 819.277 380.723 12:7 1.714
99\145 819.310 380.690 7:4 1.750
127\186 819.355 380.645 9:5 1.800
28\41 819.512 380.488 2:1 2.000 Basic 19L 3s
Scales with tunings softer than this are proper
Simplest tuning for Magic[22]
125\183 819.672 380.328 9:4 2.250
97\142 819.718 380.282 7:3 2.333
166\243 819.753 380.247 12:5 2.400
69\101 819.802 380.198 5:2 2.500 Semihard 19L 3s
179\262 819.847 380.153 13:5 2.600
110\161 819.876 380.124 8:3 2.667
151\221 819.910 380.090 11:4 2.750
41\60 820.000 380.000 3:1 3.000 Hard 19L 3s
136\199 820.101 379.899 10:3 3.333
95\139 820.144 379.856 7:2 3.500
149\218 820.183 379.817 11:3 3.667
54\79 820.253 379.747 4:1 4.000 Superhard 19L 3s
121\177 820.339 379.661 9:2 4.500
67\98 820.408 379.592 5:1 5.000
80\117 820.513 379.487 6:1 6.000
13\19 821.053 378.947 1:0 → ∞ Collapsed 19L 3s
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