19L 7s

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↖18L 6s ↑19L 6s 20L 6s↗
←18L 7s19L 7s 20L 7s→
↙18L 8s ↓19L 8s 20L 8s↘
 
┌╥╥╥┬╥╥╥┬╥╥╥┬╥╥┬╥╥╥┬╥╥╥┬╥╥┬┐
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLLsLLLsLLsLLLsLLLsLLs
sLLsLLLsLLLsLLsLLLsLLLsLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 15\26 to 11\19 (692.3¢ to 694.7¢)
Dark 8\19 to 11\26 (505.3¢ to 507.7¢)
TAMNAMS information
Descends from 5L 2s (diatonic)
Required step ratio range 4:3 to 3:2 (parasoft)
Related MOS scales
Parent 7L 12s
Sister 7L 19s
Daughters 26L 19s
19L 26s
Equal tunings
Equalized (L:s = 1:1) 15\26 (692.3¢)
Supersoft (L:s = 4:3) 56\97 (692.8¢)
Soft (L:s = 3:2) 41\71 (693.0¢)
Semisoft (L:s = 5:3) 67\116 (693.1¢)
Basic (L:s = 2:1) 26\45 (693.3¢)
Semihard (L:s = 5:2) 63\109 (693.6¢)
Hard (L:s = 3:1) 37\64 (693.8¢)
Superhard (L:s = 4:1) 48\83 (694.0¢)
Collapsed (L:s = 1:0) 11\19 (694.7¢)

19L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 19 large steps and 7 small steps, repeating every octave. 19L 7s is a great-grandchild scale of 5L 2s, expanding it by 19 tones. Generators that produce this scale range from 692.3¢ to 694.7¢, or from 505.3¢ to 507.7¢.

Temperaments associated with this scale include flattone, whose generator is treated as 3/2, and marfifths, whose generator is treated as 75/56 (marvelous 4th).

Modes

Modes of 19L 7s
UDP Rotational order Step pattern
25|0 1 LLLsLLLsLLLsLLsLLLsLLLsLLs
24|1 16 LLLsLLLsLLsLLLsLLLsLLLsLLs
23|2 5 LLLsLLLsLLsLLLsLLLsLLsLLLs
22|3 20 LLLsLLsLLLsLLLsLLLsLLsLLLs
21|4 9 LLLsLLsLLLsLLLsLLsLLLsLLLs
20|5 24 LLsLLLsLLLsLLLsLLsLLLsLLLs
19|6 13 LLsLLLsLLLsLLsLLLsLLLsLLLs
18|7 2 LLsLLLsLLLsLLsLLLsLLLsLLsL
17|8 17 LLsLLLsLLsLLLsLLLsLLLsLLsL
16|9 6 LLsLLLsLLsLLLsLLLsLLsLLLsL
15|10 21 LLsLLsLLLsLLLsLLLsLLsLLLsL
14|11 10 LLsLLsLLLsLLLsLLsLLLsLLLsL
13|12 25 LsLLLsLLLsLLLsLLsLLLsLLLsL
12|13 14 LsLLLsLLLsLLsLLLsLLLsLLLsL
11|14 3 LsLLLsLLLsLLsLLLsLLLsLLsLL
10|15 18 LsLLLsLLsLLLsLLLsLLLsLLsLL
9|16 7 LsLLLsLLsLLLsLLLsLLsLLLsLL
8|17 22 LsLLsLLLsLLLsLLLsLLsLLLsLL
7|18 11 LsLLsLLLsLLLsLLsLLLsLLLsLL
6|19 26 sLLLsLLLsLLLsLLsLLLsLLLsLL
5|20 15 sLLLsLLLsLLsLLLsLLLsLLLsLL
4|21 4 sLLLsLLLsLLsLLLsLLLsLLsLLL
3|22 19 sLLLsLLsLLLsLLLsLLLsLLsLLL
2|23 8 sLLLsLLsLLLsLLLsLLsLLLsLLL
1|24 23 sLLsLLLsLLLsLLLsLLsLLLsLLL
0|25 12 sLLsLLLsLLLsLLsLLLsLLLsLLL

Scale tree

Scale Tree and Tuning Spectrum of 19L 7s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
15\26 692.308 507.692 1:1 1.000 Equalized 19L 7s
101\175 692.571 507.429 7:6 1.167
86\149 692.617 507.383 6:5 1.200
157\272 692.647 507.353 11:9 1.222
71\123 692.683 507.317 5:4 1.250
198\343 692.711 507.289 14:11 1.273
127\220 692.727 507.273 9:7 1.286
183\317 692.744 507.256 13:10 1.300
56\97 692.784 507.216 4:3 1.333 Supersoft 19L 7s
209\362 692.818 507.182 15:11 1.364
153\265 692.830 507.170 11:8 1.375
250\433 692.841 507.159 18:13 1.385
97\168 692.857 507.143 7:5 1.400
235\407 692.875 507.125 17:12 1.417
138\239 692.887 507.113 10:7 1.429
179\310 692.903 507.097 13:9 1.444
41\71 692.958 507.042 3:2 1.500 Soft 19L 7s
190\329 693.009 506.991 14:9 1.556
149\258 693.023 506.977 11:7 1.571
257\445 693.034 506.966 19:12 1.583
108\187 693.048 506.952 8:5 1.600
283\490 693.061 506.939 21:13 1.615
175\303 693.069 506.931 13:8 1.625
242\419 693.079 506.921 18:11 1.636
67\116 693.103 506.897 5:3 1.667 Semisoft 19L 7s
227\393 693.130 506.870 17:10 1.700
160\277 693.141 506.859 12:7 1.714
253\438 693.151 506.849 19:11 1.727
93\161 693.168 506.832 7:4 1.750
212\367 693.188 506.812 16:9 1.778
119\206 693.204 506.796 9:5 1.800
145\251 693.227 506.773 11:6 1.833
26\45 693.333 506.667 2:1 2.000 Basic 19L 7s
Scales with tunings softer than this are proper
141\244 693.443 506.557 11:5 2.200
115\199 693.467 506.533 9:4 2.250
204\353 693.484 506.516 16:7 2.286
89\154 693.506 506.494 7:3 2.333
241\417 693.525 506.475 19:8 2.375
152\263 693.536 506.464 12:5 2.400
215\372 693.548 506.452 17:7 2.429
63\109 693.578 506.422 5:2 2.500 Semihard 19L 7s
226\391 693.606 506.394 18:7 2.571
163\282 693.617 506.383 13:5 2.600
263\455 693.626 506.374 21:8 2.625
100\173 693.642 506.358 8:3 2.667
237\410 693.659 506.341 19:7 2.714
137\237 693.671 506.329 11:4 2.750
174\301 693.688 506.312 14:5 2.800
37\64 693.750 506.250 3:1 3.000 Hard 19L 7s
159\275 693.818 506.182 13:4 3.250
122\211 693.839 506.161 10:3 3.333
207\358 693.855 506.145 17:5 3.400
85\147 693.878 506.122 7:2 3.500
218\377 693.899 506.101 18:5 3.600
133\230 693.913 506.087 11:3 3.667
181\313 693.930 506.070 15:4 3.750
48\83 693.976 506.024 4:1 4.000 Superhard 19L 7s
155\268 694.030 505.970 13:3 4.333
107\185 694.054 505.946 9:2 4.500
166\287 694.077 505.923 14:3 4.667
59\102 694.118 505.882 5:1 5.000
129\223 694.170 505.830 11:2 5.500
70\121 694.215 505.785 6:1 6.000
81\140 694.286 505.714 7:1 7.000
11\19 694.737 505.263 1:0 → ∞ Collapsed 19L 7s
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