3L 11s

From Xenharmonic Wiki
Jump to navigation Jump to search
Todo: review
Adopt scale tree template, review entries
↖ 2L 10s ↑3L 10s 4L 10s ↗
← 2L 11s3L 11s 4L 11s →
↙ 2L 12s ↓3L 12s 4L 12s ↘
┌╥┬┬┬╥┬┬┬┬╥┬┬┬┬┐
│║│││║││││║│││││
││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssLssssLssss
ssssLssssLsssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 9\14 to 2\3 (771.4¢ to 800.0¢)
Dark 1\3 to 5\14 (400.0¢ to 428.6¢)
TAMNAMS information
Descends from 3L 5s (checkertonic)
Required step ratio range 3:1 to 1:0 (hard)
Related MOS scales
Parent 3L 8s
Sister 11L 3s
Daughters 14L 3s, 3L 14s
Neutralized 6L 8s
2-Flought 17L 11s, 3L 25s
Equal tunings
Equalized (L:s = 1:1) 9\14 (771.4¢)
Supersoft (L:s = 4:3) 29\45 (773.3¢)
Soft (L:s = 3:2) 20\31 (774.2¢)
Semisoft (L:s = 5:3) 31\48 (775.0¢)
Basic (L:s = 2:1) 11\17 (776.5¢)
Semihard (L:s = 5:2) 24\37 (778.4¢)
Hard (L:s = 3:1) 13\20 (780.0¢)
Superhard (L:s = 4:1) 15\23 (782.6¢)
Collapsed (L:s = 1:0) 2\3 (800.0¢)

3L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 11 small steps, repeating every octave. 3L 11s is a grandchild scale of 3L 5s, expanding it by 6 tones. Generators that produce this scale range from 771.4¢ to 800¢, or from 400¢ to 428.6¢.

Modes

Modes of 3L 11s
UDP Rotational order Step pattern
13|0 1 LsssLssssLssss
12|1 10 LssssLsssLssss
11|2 5 LssssLssssLsss
10|3 14 sLsssLssssLsss
9|4 9 sLssssLsssLsss
8|5 4 sLssssLssssLss
7|6 13 ssLsssLssssLss
6|7 8 ssLssssLsssLss
5|8 3 ssLssssLssssLs
4|9 12 sssLsssLssssLs
3|10 7 sssLssssLsssLs
2|11 2 sssLssssLssssL
1|12 11 ssssLsssLssssL
0|13 6 ssssLssssLsssL

Tuning spectrum

generator L s L/s gen (cents) comment
1\3 1 0 400.000
12\35 8 1 8.000 411.429
11\32 7 1 7.000 412.500
10\29 6 1 6.000 413.793
19\55 11 2 5.500 414.545
9\26 5 1 5.000 415.385
26\75 14 3 4.667 416.000
17\49 9 2 4.500 416.327
25\72 13 3 4.333 416.667 Sqrtphi is around here
8\23 4 1 4.000 417.391
31\89 15 4 3.750 417.978
23\66 11 3 3.667 418.182
15\43 7 2 3.500 418.605
22\63 10 3 3.333 419.048
29\83 13 4 3.250 419.277
7\20 3 1 3.000 420.000
34\97 14 5 2.800 420.619
27\77 11 4 2.750 420.779 Symbolic is around here
20\57 8 3 2.667 421.053
33\94 13 5 2.600 421.277
13\37 5 2 2.500 421.622
32\91 12 5 2.400 421.978
19\54 7 3 2.333 422.222
25\71 9 4 2.250 422.535
31\88 11 5 2.200 422.727
6\17 2 1 2.000 423.529
35\99 11 6 1.833 424.242
29\82 9 5 1.800 424.390
23\65 7 4 1.750 424.615
17\48 5 3 1.667 425.000
28\79 8 5 1.600 425.316
11\31 3 2 1.500 425.806 Squares and Sentinel are around here
27\76 7 5 1.400 426.316
16\45 4 3 1.333 426.667
21\59 5 4 1.250 427.119
26\73 6 5 1.200 427.397
31\87 7 6 1.167 427.586
36\101 8 7 1.143 427.723
5\14 1 1 1.000 428.571