3L 16s

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↖ 2L 15s ↑3L 15s 4L 15s ↗
← 2L 16s3L 16s 4L 16s →
↙ 2L 17s ↓3L 17s 4L 17s ↘
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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)
Required 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
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¢)

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

  • 18|0 LsssssLsssssLssssss
  • 17|1 LsssssLssssssLsssss
  • 16|2 LssssssLsssssLsssss
  • 15|3 sLsssssLsssssLsssss
  • 14|4 sLsssssLssssssLssss
  • 13|5 sLssssssLsssssLssss
  • 12|6 ssLsssssLsssssLssss
  • 11|7 ssLsssssLssssssLsss
  • 10|8 ssLssssssLsssssLsss
  • 9|9 sssLsssssLsssssLsss
  • 8|10 sssLsssssLssssssLss
  • 7|11 sssLssssssLsssssLss
  • 6|12 ssssLsssssLsssssLss
  • 5|13 ssssLsssssLssssssLs
  • 4|14 ssssLssssssLsssssLs
  • 3|15 sssssLsssssLsssssLs
  • 2|16 sssssLsssssLssssssL
  • 1|17 sssssLssssssLsssssL
  • 0|18 ssssssLsssssLsssssL

Scales tree

Generator ranges:

  • Bright generator: 378.9474 cents (6\19) to 400 cents (1\3)
  • Dark generator: 800 cents (2\3) to 821.0526 cents (13\19)
Bright generator Cents L s L/s Comments
6\19 378.947 1 1 1.000
31\98 379.592 6 5 1.200
25\79 379.747 5 4 1.250
44\139 379.856 9 7 1.286
19\60 380.000 4 3 1.333
51\161 380.124 11 8 1.375 Witchcraft
32\101 380.198 7 5 1.400
45\142 380.282 10 7 1.429
13\41 380.488 3 2 1.500 Magic is around here
46\145 380.690 11 7 1.571
33\104 380.769 8 5 1.600
53\167 380.838 13 8 1.625 Necromancy
Golden magic (380.8191¢)
20\63 380.952 5 3 1.667
47\148 381.081 12 7 1.714
27\85 381.176 7 4 1.750
34\107 381.308 9 5 1.800
7\22 381.818 2 1 2.000 Basic 3L 16s
(Generators smaller than this are proper)
29\91 382.418 9 4 2.250
22\69 382.609 7 3 2.333 Marveltri
37\116 382.759 12 5 2.400 Marveltri
15\47 382.979 5 2 2.500 Marveltri
38\119 383.193 13 5 2.600 Unnamed golden tuning (383.2314¢)
23\72 383.333 8 3 2.667
31\97 383.505 11 4 2.750
8\25 384.000 3 1 3.000
25\78 384.615 10 3 3.333
17\53 384.906 7 2 3.500
26\81 385.185 11 3 3.667
9\28 385.714 4 1 4.000
19\59 386.441 9 2 4.500 Sulis
10\31 387.097 5 1 5.000 Grendel/Würschmidt
11\34 388.235 6 1 6.000
1\3 400.000 1 0 → inf