3L 14s

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↖ 2L 13s↑ 3L 13s 4L 13s ↗
← 2L 14s3L 14s4L 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)
Ancestor's 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 Cyclic
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

Icon-Todo.png Todo: review
Review entries from past page revision and enter them into the scale tree.

Symbolic / Sidi / Smate range

Scale Tree and Tuning Spectrum of 3L 14s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
11\17 776.471 423.529 1:1 1.000 Equalized 3L 14s
57\88 777.273 422.727 6:5 1.200
46\71 777.465 422.535 5:4 1.250
81\125 777.600 422.400 9:7 1.286
35\54 777.778 422.222 4:3 1.333 Supersoft 3L 14s
94\145 777.931 422.069 11:8 1.375
59\91 778.022 421.978 7:5 1.400
83\128 778.125 421.875 10:7 1.429
24\37 778.378 421.622 3:2 1.500 Soft 3L 14s
85\131 778.626 421.374 11:7 1.571
61\94 778.723 421.277 8:5 1.600
98\151 778.808 421.192 13:8 1.625
37\57 778.947 421.053 5:3 1.667 Semisoft 3L 14s
87\134 779.104 420.896 12:7 1.714
50\77 779.221 420.779 7:4 1.750
63\97 779.381 420.619 9:5 1.800
13\20 780.000 420.000 2:1 2.000 Basic 3L 14s
Scales with tunings softer than this are proper
54\83 780.723 419.277 9:4 2.250
41\63 780.952 419.048 7:3 2.333
69\106 781.132 418.868 12:5 2.400
28\43 781.395 418.605 5:2 2.500 Semihard 3L 14s
71\109 781.651 418.349 13:5 2.600
43\66 781.818 418.182 8:3 2.667
58\89 782.022 417.978 11:4 2.750
15\23 782.609 417.391 3:1 3.000 Hard 3L 14s
47\72 783.333 416.667 10:3 3.333
32\49 783.673 416.327 7:2 3.500
49\75 784.000 416.000 11:3 3.667
17\26 784.615 415.385 4:1 4.000 Superhard 3L 14s
36\55 785.455 414.545 9:2 4.500
19\29 786.207 413.793 5:1 5.000
21\32 787.500 412.500 6:1 6.000
2\3 800.000 400.000 1:0 → ∞ Collapsed 3L 14s