3L 16s
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Scale structure
Step pattern
LsssssLsssssLssssss
ssssssLsssssLsssssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
6\19 to 1\3 (378.9¢ to 400.0¢)
Dark
2\3 to 13\19 (800.0¢ to 821.1¢)
TAMNAMS information
Descends from
3L 7s (sephiroid)
Ancestor's step ratio range
4:1 to 1:0 (ultrahard)
Related MOS scales
Parent
3L 13s
Sister
16L 3s
Daughters
19L 3s, 3L 19s
Neutralized
6L 13s
2-Flought
22L 16s, 3L 35s
Equal tunings
Equalized (L:s = 1:1)
6\19 (378.9¢)
Supersoft (L:s = 4:3)
19\60 (380.0¢)
Soft (L:s = 3:2)
13\41 (380.5¢)
Semisoft (L:s = 5:3)
20\63 (381.0¢)
Basic (L:s = 2:1)
7\22 (381.8¢)
Semihard (L:s = 5:2)
15\47 (383.0¢)
Hard (L:s = 3:1)
8\25 (384.0¢)
Superhard (L:s = 4:1)
9\28 (385.7¢)
Collapsed (L:s = 1:0)
1\3 (400.0¢)
| ↖ 2L 15s | ↑ 3L 15s | 4L 15s ↗ |
| ← 2L 16s | 3L 16s | 4L 16s → |
| ↙ 2L 17s | ↓ 3L 17s | 4L 17s ↘ |
┌╥┬┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬┬┐ │║│││││║│││││║│││││││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssssssLsssssLsssssL
3L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 16 small steps, repeating every octave. 3L 16s is a great-grandchild scale of 3L 7s, expanding it by 9 tones. Generators that produce this scale range from 378.9¢ to 400¢, or from 800¢ to 821.1¢. This scale is associated with magic temperament, where 5 bright generators maps to 3/1, and würschmidt temperament, where the generator is 5/4.
Modes
| UDP | Cyclic Order |
Step Pattern |
|---|---|---|
| 18|0 | 1 | LsssssLsssssLssssss |
| 17|1 | 7 | LsssssLssssssLsssss |
| 16|2 | 13 | LssssssLsssssLsssss |
| 15|3 | 19 | sLsssssLsssssLsssss |
| 14|4 | 6 | sLsssssLssssssLssss |
| 13|5 | 12 | sLssssssLsssssLssss |
| 12|6 | 18 | ssLsssssLsssssLssss |
| 11|7 | 5 | ssLsssssLssssssLsss |
| 10|8 | 11 | ssLssssssLsssssLsss |
| 9|9 | 17 | sssLsssssLsssssLsss |
| 8|10 | 4 | sssLsssssLssssssLss |
| 7|11 | 10 | sssLssssssLsssssLss |
| 6|12 | 16 | ssssLsssssLsssssLss |
| 5|13 | 3 | ssssLsssssLssssssLs |
| 4|14 | 9 | ssssLssssssLsssssLs |
| 3|15 | 15 | sssssLsssssLsssssLs |
| 2|16 | 2 | sssssLsssssLssssssL |
| 1|17 | 8 | sssssLssssssLsssssL |
| 0|18 | 14 | ssssssLsssssLsssssL |
Scale tree
 |
Todo: review Review entries from past page revision and enter them into the scale tree. |
| Generator(edo) | Cents | Step Ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 6\19 | 378.947 | 821.053 | 1:1 | 1.000 | Equalized 3L 16s | |||||
| 31\98 | 379.592 | 820.408 | 6:5 | 1.200 | ||||||
| 25\79 | 379.747 | 820.253 | 5:4 | 1.250 | ||||||
| 44\139 | 379.856 | 820.144 | 9:7 | 1.286 | ||||||
| 19\60 | 380.000 | 820.000 | 4:3 | 1.333 | Supersoft 3L 16s | |||||
| 51\161 | 380.124 | 819.876 | 11:8 | 1.375 | Witchcraft | |||||
| 32\101 | 380.198 | 819.802 | 7:5 | 1.400 | ||||||
| 45\142 | 380.282 | 819.718 | 10:7 | 1.429 | ||||||
| 13\41 | 380.488 | 819.512 | 3:2 | 1.500 | Soft 3L 16s Magic is around here | |||||
| 46\145 | 380.690 | 819.310 | 11:7 | 1.571 | ||||||
| 33\104 | 380.769 | 819.231 | 8:5 | 1.600 | ||||||
| 53\167 | 380.838 | 819.162 | 13:8 | 1.625 | Necromancy Golden magic (380.8191¢) | |||||
| 20\63 | 380.952 | 819.048 | 5:3 | 1.667 | Semisoft 3L 16s | |||||
| 47\148 | 381.081 | 818.919 | 12:7 | 1.714 | ||||||
| 27\85 | 381.176 | 818.824 | 7:4 | 1.750 | ||||||
| 34\107 | 381.308 | 818.692 | 9:5 | 1.800 | ||||||
| 7\22 | 381.818 | 818.182 | 2:1 | 2.000 | Basic 3L 16s Scales with tunings softer than this are proper | |||||
| 29\91 | 382.418 | 817.582 | 9:4 | 2.250 | ||||||
| 22\69 | 382.609 | 817.391 | 7:3 | 2.333 | ||||||
| 37\116 | 382.759 | 817.241 | 12:5 | 2.400 | Marveltri is around here | |||||
| 15\47 | 382.979 | 817.021 | 5:2 | 2.500 | Semihard 3L 16s | |||||
| 38\119 | 383.193 | 816.807 | 13:5 | 2.600 | Unnamed golden tuning (383.2314¢) | |||||
| 23\72 | 383.333 | 816.667 | 8:3 | 2.667 | ||||||
| 31\97 | 383.505 | 816.495 | 11:4 | 2.750 | ||||||
| 8\25 | 384.000 | 816.000 | 3:1 | 3.000 | Hard 3L 16s | |||||
| 25\78 | 384.615 | 815.385 | 10:3 | 3.333 | ||||||
| 17\53 | 384.906 | 815.094 | 7:2 | 3.500 | ||||||
| 26\81 | 385.185 | 814.815 | 11:3 | 3.667 | ||||||
| 9\28 | 385.714 | 814.286 | 4:1 | 4.000 | Superhard 3L 16s | |||||
| 19\59 | 386.441 | 813.559 | 9:2 | 4.500 | Sulis | |||||
| 10\31 | 387.097 | 812.903 | 5:1 | 5.000 | Grendel/Würschmidt | |||||
| 11\34 | 388.235 | 811.765 | 6:1 | 6.000 | ||||||
| 1\3 | 400.000 | 800.000 | 1:0 | → ∞ | Collapsed 3L 16s | |||||