3L 14s

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↖ 2L 13s ↑ 3L 13s 4L 13s ↗
← 2L 14s 3L 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)
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 ¢.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.

Intervals

Intervals of 3L 14s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 70.6 ¢
Major 1-mosstep M1ms L 70.6 ¢ to 400.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 141.2 ¢
Major 2-mosstep M2ms L + s 141.2 ¢ to 400.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 211.8 ¢
Major 3-mosstep M3ms L + 2s 211.8 ¢ to 400.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 282.4 ¢
Major 4-mosstep M4ms L + 3s 282.4 ¢ to 400.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 352.9 ¢
Major 5-mosstep M5ms L + 4s 352.9 ¢ to 400.0 ¢
6-mosstep Perfect 6-mosstep P6ms L + 5s 400.0 ¢ to 423.5 ¢
Augmented 6-mosstep A6ms 2L + 4s 423.5 ¢ to 800.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 400.0 ¢ to 494.1 ¢
Major 7-mosstep M7ms 2L + 5s 494.1 ¢ to 800.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 400.0 ¢ to 564.7 ¢
Major 8-mosstep M8ms 2L + 6s 564.7 ¢ to 800.0 ¢
9-mosstep Minor 9-mosstep m9ms L + 8s 400.0 ¢ to 635.3 ¢
Major 9-mosstep M9ms 2L + 7s 635.3 ¢ to 800.0 ¢
10-mosstep Minor 10-mosstep m10ms L + 9s 400.0 ¢ to 705.9 ¢
Major 10-mosstep M10ms 2L + 8s 705.9 ¢ to 800.0 ¢
11-mosstep Diminished 11-mosstep d11ms L + 10s 400.0 ¢ to 776.5 ¢
Perfect 11-mosstep P11ms 2L + 9s 776.5 ¢ to 800.0 ¢
12-mosstep Minor 12-mosstep m12ms 2L + 10s 800.0 ¢ to 847.1 ¢
Major 12-mosstep M12ms 3L + 9s 847.1 ¢ to 1200.0 ¢
13-mosstep Minor 13-mosstep m13ms 2L + 11s 800.0 ¢ to 917.6 ¢
Major 13-mosstep M13ms 3L + 10s 917.6 ¢ to 1200.0 ¢
14-mosstep Minor 14-mosstep m14ms 2L + 12s 800.0 ¢ to 988.2 ¢
Major 14-mosstep M14ms 3L + 11s 988.2 ¢ to 1200.0 ¢
15-mosstep Minor 15-mosstep m15ms 2L + 13s 800.0 ¢ to 1058.8 ¢
Major 15-mosstep M15ms 3L + 12s 1058.8 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms 2L + 14s 800.0 ¢ to 1129.4 ¢
Major 16-mosstep M16ms 3L + 13s 1129.4 ¢ to 1200.0 ¢
17-mosstep Perfect 17-mosstep P17ms 3L + 14s 1200.0 ¢

Generator chain

Generator chain of 3L 14s
Bright gens Scale degree Abbrev.
19 Augmented 5-mosdegree A5md
18 Augmented 11-mosdegree A11md
17 Augmented 0-mosdegree A0md
16 Augmented 6-mosdegree A6md
15 Major 12-mosdegree M12md
14 Major 1-mosdegree M1md
13 Major 7-mosdegree M7md
12 Major 13-mosdegree M13md
11 Major 2-mosdegree M2md
10 Major 8-mosdegree M8md
9 Major 14-mosdegree M14md
8 Major 3-mosdegree M3md
7 Major 9-mosdegree M9md
6 Major 15-mosdegree M15md
5 Major 4-mosdegree M4md
4 Major 10-mosdegree M10md
3 Major 16-mosdegree M16md
2 Major 5-mosdegree M5md
1 Perfect 11-mosdegree P11md
0 Perfect 0-mosdegree
Perfect 17-mosdegree		 P0md
P17md
−1 Perfect 6-mosdegree P6md
−2 Minor 12-mosdegree m12md
−3 Minor 1-mosdegree m1md
−4 Minor 7-mosdegree m7md
−5 Minor 13-mosdegree m13md
−6 Minor 2-mosdegree m2md
−7 Minor 8-mosdegree m8md
−8 Minor 14-mosdegree m14md
−9 Minor 3-mosdegree m3md
−10 Minor 9-mosdegree m9md
−11 Minor 15-mosdegree m15md
−12 Minor 4-mosdegree m4md
−13 Minor 10-mosdegree m10md
−14 Minor 16-mosdegree m16md
−15 Minor 5-mosdegree m5md
−16 Diminished 11-mosdegree d11md
−17 Diminished 17-mosdegree d17md
−18 Diminished 6-mosdegree d6md
−19 Diminished 12-mosdegree d12md

Modes

Scale degrees of the modes of 3L 14s
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
16|0 1 LssssLsssssLsssss Perf. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Perf.
15|1 12 LsssssLssssLsssss Perf. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Perf.
14|2 6 LsssssLsssssLssss Perf. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Perf.
13|3 17 sLssssLsssssLssss Perf. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Perf.
12|4 11 sLsssssLssssLssss Perf. Min. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Maj. Perf.
11|5 5 sLsssssLsssssLsss Perf. Min. Maj. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Perf.
10|6 16 ssLssssLsssssLsss Perf. Min. Min. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Perf.
9|7 10 ssLsssssLssssLsss Perf. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Perf. Min. Min. Maj. Maj. Maj. Perf.
8|8 4 ssLsssssLsssssLss Perf. Min. Min. Maj. Maj. Maj. Perf. Min. Min. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Perf.
7|9 15 sssLssssLsssssLss Perf. Min. Min. Min. Maj. Maj. Perf. Min. Min. Maj. Maj. Perf. Min. Min. Min. Maj. Maj. Perf.
6|10 9 sssLsssssLssssLss Perf. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Maj. Perf. Min. Min. Min. Maj. Maj. Perf.
5|11 3 sssLsssssLsssssLs Perf. Min. Min. Min. Maj. Maj. Perf. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Maj. Perf.
4|12 14 ssssLssssLsssssLs Perf. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Maj. Perf.
3|13 8 ssssLsssssLssssLs Perf. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Maj. Perf.
2|14 2 ssssLsssssLsssssL Perf. Min. Min. Min. Min. Maj. Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Perf.
1|15 13 sssssLssssLsssssL Perf. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Perf.
0|16 7 sssssLsssssLssssL Perf. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Perf.

Scale tree

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 Bossier
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 Sqrtphi
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 Roman
19\29 786.207 413.793 5:1 5.000
21\32 787.500 412.500 6:1 6.000 Hocus ↓
2\3 800.000 400.000 1:0 → ∞ Collapsed 3L 14s
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