19L 3s
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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
Descends from
3L 7s (sephiroid)
Related MOS scales
Parent
3L 16s
Sister
3L 19s
Daughters
22L 19s
19L 22s
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¢)
| ↖18L 2s | ↑19L 2s | 20L 2s↗ |
| ←18L 3s | 19L 3s | 20L 3s→ |
| ↙18L 4s | ↓19L 4s | 20L 4s↘ |
┌╥╥╥╥╥╥╥┬╥╥╥╥╥╥┬╥╥╥╥╥╥┬┐ │║║║║║║║│║║║║║║│║║║║║║││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLLLsLLLLLLsLLLLLLL
19L 22s
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.
| Generator (in steps of 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 | |||||