19L 3s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖18L 2s ↑19L 2s 20L 2s↗
←18L 3s19L 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¢)
Step size ranges
Large 1\22 to 1\19 (54.5¢ to 63.2¢)
Small 0\19 to 1\22 (0.0¢ to 54.5¢)
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¢)

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 tree and tuning spectrum of 19L 3s
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