3L 14s

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↖ 2L 13s ↑3L 13s 4L 13s ↗
← 2L 14s3L 14s 4L 14s →
↙ 2L 15s ↓3L 15s 4L 15s ↘
┌╥┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬┐
│║││││║│││││║││││││
│││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssssLsssssLsssss
sssssLsssssLssssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 11\17 to 2\3 (776.5¢ to 800.0¢)
Dark 1\3 to 6\17 (400.0¢ to 423.5¢)
TAMNAMS information
Descends from 3L 5s (checkertonic)
Required step ratio range 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 3L 11s
Sister 14L 3s
Daughters 17L 3s, 3L 17s
Neutralized 6L 11s
2-Flought 20L 14s, 3L 31s
Equal tunings
Equalized (L:s = 1:1) 11\17 (776.5¢)
Supersoft (L:s = 4:3) 35\54 (777.8¢)
Soft (L:s = 3:2) 24\37 (778.4¢)
Semisoft (L:s = 5:3) 37\57 (778.9¢)
Basic (L:s = 2:1) 13\20 (780.0¢)
Semihard (L:s = 5:2) 28\43 (781.4¢)
Hard (L:s = 3:1) 15\23 (782.6¢)
Superhard (L:s = 4:1) 17\26 (784.6¢)
Collapsed (L:s = 1:0) 2\3 (800.0¢)

3L 14s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 14 small steps, repeating every octave. 3L 14s is a great-grandchild scale of 3L 5s, expanding it by 9 tones. Generators that produce this scale range from 776.5¢ to 800¢, or from 400¢ to 423.5¢.

Modes

Modes of 3L 14s
UDP Rotational order Step pattern
16 | 0 1 LssssLsssssLsssss
15 | 1 12 LsssssLssssLsssss
14 | 2 6 LsssssLsssssLssss
13 | 3 17 sLssssLsssssLssss
12 | 4 11 sLsssssLssssLssss
11 | 5 5 sLsssssLsssssLsss
10 | 6 16 ssLssssLsssssLsss
9 | 7 10 ssLsssssLssssLsss
8 | 8 4 ssLsssssLsssssLss
7 | 9 15 sssLssssLsssssLss
6 | 10 9 sssLsssssLssssLss
5 | 11 3 sssLsssssLsssssLs
4 | 12 14 ssssLssssLsssssLs
3 | 13 8 ssssLsssssLssssLs
2 | 14 2 ssssLsssssLsssssL
1 | 15 13 sssssLssssLsssssL
0 | 16 7 sssssLsssssLssssL

Tuning spectrum

Symbolic / Sidi / Smate range

generator L s L/s gen (cents) comment
1\3 1 0 400.000
15\44 10 1 10.000 409.091
14\41 9 1 9.000 409.756 Hocus
27\79 17 2 8.500 410.127
13\38 8 1 8.000 410.526
12\35 7 1 7.000 411.429
23\67 13 2 6.500 411.940
11\32 6 1 6.000 412.500
32\93 17 3 5.667 412.903
21\61 11 2 5.500 413.115
31\90 16 3 5.333 413.333
10\29 5 1 5.000 413.793
39\113 19 4 4.750 414.159
29\84 14 3 4.667 414.286
19\55 9 2 4.500 414.545 Roman
28\81 13 3 4.333 414.815
37\107 17 4 4.250 414.953
9\26 4 1 4.000 415.385
35\101 15 4 3.750 415.842
26\75 11 3 3.667 416.000
17\49 7 2 3.500 416.327
25\72 10 3 3.333 416.667 Sqrtphi
33\95 13 4 3.250 416.842
41\118 16 5 3.200 416.949
8\23 3 1 3.000 417.391
39\112 14 5 2.800 417.857
31\89 11 4 2.750 417.978
23\66 8 3 2.667 418.182
38\109 13 5 2.600 418.349
15\43 5 2 2.500 418.605
37\106 12 5 2.400 418.868
22\63 7 3 2.333 419.048
29\83 9 4 2.250 419.277
36\103 11 5 2.200 419.417
7\20 2 1 2.000 420.000
41\117 11 6 1.833 420.513
34\97 9 5 1.800 420.619
27\77 7 4 1.750 420.779
20\57 5 3 1.667 421.053
33\94 8 5 1.600 421.277 Bossier
13\37 3 2 1.500 421.622
32\91 7 5 1.400 421.978
19\54 4 3 1.333 422.222
25\71 5 4 1.250 422.535
31\88 6 5 1.200 422.727
37\105 7 6 1.167 422.857
43\122 8 7 1.143 422.951
49\139 9 8 1.125 423.022
55\156 10 9 1.111 423.077
6\17 1 1 1.000 423.529