19L 5s

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↖ 18L 4s ↑ 19L 4s 20L 4s ↗
← 18L 5s 19L 5s 20L 5s →
↙ 18L 6s ↓ 19L 6s 20L 6s ↘ 
┌╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬╥╥╥┬┐
│║║║║│║║║║│║║║║│║║║║│║║║││
││││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLLsLLLLsLLLLsLLLs
sLLLsLLLLsLLLLsLLLLsLLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 5\24 to 4\19 (250.0¢ to 252.6¢)
Dark 15\19 to 19\24 (947.4¢ to 950.0¢)
TAMNAMS information
Descends from 5L 4s (semiquartal)
Ancestor's step ratio range 3:1 to 4:1 (parahard)
Related MOS scales
Parent 5L 14s
Sister 5L 19s
Daughters 24L 19s, 19L 24s
Neutralized 14L 10s
2-Flought 43L 5s, 19L 29s
Equal tunings
Equalized (L:s = 1:1) 5\24 (250.0¢)
Supersoft (L:s = 4:3) 19\91 (250.5¢)
Soft (L:s = 3:2) 14\67 (250.7¢)
Semisoft (L:s = 5:3) 23\110 (250.9¢)
Basic (L:s = 2:1) 9\43 (251.2¢)
Semihard (L:s = 5:2) 22\105 (251.4¢)
Hard (L:s = 3:1) 13\62 (251.6¢)
Superhard (L:s = 4:1) 17\81 (251.9¢)
Collapsed (L:s = 1:0) 4\19 (252.6¢)

19L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 19 large steps and 5 small steps, repeating every octave. 19L 5s is a great-grandchild scale of 5L 4s, expanding it by 15 tones. Generators that produce this scale range from 250¢ to 252.6¢, or from 947.4¢ to 950¢.

Modes

Modes of 19L 5s
UDP Cyclic
order		 Step
pattern
23|0 1 LLLLsLLLLsLLLLsLLLLsLLLs
22|1 6 LLLLsLLLLsLLLLsLLLsLLLLs
21|2 11 LLLLsLLLLsLLLsLLLLsLLLLs
20|3 16 LLLLsLLLsLLLLsLLLLsLLLLs
19|4 21 LLLsLLLLsLLLLsLLLLsLLLLs
18|5 2 LLLsLLLLsLLLLsLLLLsLLLsL
17|6 7 LLLsLLLLsLLLLsLLLsLLLLsL
16|7 12 LLLsLLLLsLLLsLLLLsLLLLsL
15|8 17 LLLsLLLsLLLLsLLLLsLLLLsL
14|9 22 LLsLLLLsLLLLsLLLLsLLLLsL
13|10 3 LLsLLLLsLLLLsLLLLsLLLsLL
12|11 8 LLsLLLLsLLLLsLLLsLLLLsLL
11|12 13 LLsLLLLsLLLsLLLLsLLLLsLL
10|13 18 LLsLLLsLLLLsLLLLsLLLLsLL
9|14 23 LsLLLLsLLLLsLLLLsLLLLsLL
8|15 4 LsLLLLsLLLLsLLLLsLLLsLLL
7|16 9 LsLLLLsLLLLsLLLsLLLLsLLL
6|17 14 LsLLLLsLLLsLLLLsLLLLsLLL
5|18 19 LsLLLsLLLLsLLLLsLLLLsLLL
4|19 24 sLLLLsLLLLsLLLLsLLLLsLLL
3|20 5 sLLLLsLLLLsLLLLsLLLsLLLL
2|21 10 sLLLLsLLLLsLLLsLLLLsLLLL
1|22 15 sLLLLsLLLsLLLLsLLLLsLLLL
0|23 20 sLLLsLLLLsLLLLsLLLLsLLLL

Scale tree

Scale Tree and Tuning Spectrum of 19L 5s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\24 250.000 950.000 1:1 1.000 Equalized 19L 5s
29\139 250.360 949.640 6:5 1.200
24\115 250.435 949.565 5:4 1.250
43\206 250.485 949.515 9:7 1.286
19\91 250.549 949.451 4:3 1.333 Supersoft 19L 5s
52\249 250.602 949.398 11:8 1.375
33\158 250.633 949.367 7:5 1.400
47\225 250.667 949.333 10:7 1.429
14\67 250.746 949.254 3:2 1.500 Soft 19L 5s
51\244 250.820 949.180 11:7 1.571
37\177 250.847 949.153 8:5 1.600
60\287 250.871 949.129 13:8 1.625
23\110 250.909 949.091 5:3 1.667 Semisoft 19L 5s
55\263 250.951 949.049 12:7 1.714
32\153 250.980 949.020 7:4 1.750
41\196 251.020 948.980 9:5 1.800
9\43 251.163 948.837 2:1 2.000 Basic 19L 5s
Scales with tunings softer than this are proper
40\191 251.309 948.691 9:4 2.250
31\148 251.351 948.649 7:3 2.333
53\253 251.383 948.617 12:5 2.400
22\105 251.429 948.571 5:2 2.500 Semihard 19L 5s
57\272 251.471 948.529 13:5 2.600
35\167 251.497 948.503 8:3 2.667
48\229 251.528 948.472 11:4 2.750
13\62 251.613 948.387 3:1 3.000 Hard 19L 5s
43\205 251.707 948.293 10:3 3.333
30\143 251.748 948.252 7:2 3.500
47\224 251.786 948.214 11:3 3.667
17\81 251.852 948.148 4:1 4.000 Superhard 19L 5s
38\181 251.934 948.066 9:2 4.500
21\100 252.000 948.000 5:1 5.000
25\119 252.101 947.899 6:1 6.000
4\19 252.632 947.368 1:0 → ∞ Collapsed 19L 5s
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