4L 14s

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↖ 3L 13s ↑ 4L 13s 5L 13s ↗
← 3L 14s 4L 14s 5L 14s →
↙ 3L 15s ↓ 4L 15s 5L 15s ↘ 
┌╥┬┬┬╥┬┬┬┬╥┬┬┬╥┬┬┬┬┐
│║│││║││││║│││║│││││
││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssLssssLsssLssss
ssssLsssLssssLsssL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 4\18 to 1\4 (266.7 ¢ to 300.0 ¢)
Dark 1\4 to 5\18 (300.0 ¢ to 333.3 ¢)
TAMNAMS information
Descends from 4L 6s (lime)
Ancestor's step ratio range 3:1 to 1:0 (hard)
Related MOS scales
Parent 4L 10s
Sister 14L 4s
Daughters 18L 4s, 4L 18s
Neutralized 8L 10s
2-Flought 22L 14s, 4L 32s
Equal tunings
Equalized (L:s = 1:1) 4\18 (266.7 ¢)
Supersoft (L:s = 4:3) 13\58 (269.0 ¢)
Soft (L:s = 3:2) 9\40 (270.0 ¢)
Semisoft (L:s = 5:3) 14\62 (271.0 ¢)
Basic (L:s = 2:1) 5\22 (272.7 ¢)
Semihard (L:s = 5:2) 11\48 (275.0 ¢)
Hard (L:s = 3:1) 6\26 (276.9 ¢)
Superhard (L:s = 4:1) 7\30 (280.0 ¢)
Collapsed (L:s = 1:0) 1\4 (300.0 ¢)

4L 14s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 14 small steps, with a period of 2 large steps and 7 small steps that repeats every 600.0 ¢, or twice every octave. 4L 14s is a grandchild scale of 4L 6s, expanding it by 8 tones. Generators that produce this scale range from 266.7 ¢ to 300 ¢, or from 300 ¢ to 333.3 ¢.

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 4L 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 66.7 ¢
Major 1-mosstep M1ms L 66.7 ¢ to 300.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 133.3 ¢
Major 2-mosstep M2ms L + s 133.3 ¢ to 300.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 200.0 ¢
Major 3-mosstep M3ms L + 2s 200.0 ¢ to 300.0 ¢
4-mosstep Diminished 4-mosstep d4ms 4s 0.0 ¢ to 266.7 ¢
Perfect 4-mosstep P4ms L + 3s 266.7 ¢ to 300.0 ¢
5-mosstep Perfect 5-mosstep P5ms L + 4s 300.0 ¢ to 333.3 ¢
Augmented 5-mosstep A5ms 2L + 3s 333.3 ¢ to 600.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 300.0 ¢ to 400.0 ¢
Major 6-mosstep M6ms 2L + 4s 400.0 ¢ to 600.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 300.0 ¢ to 466.7 ¢
Major 7-mosstep M7ms 2L + 5s 466.7 ¢ to 600.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 300.0 ¢ to 533.3 ¢
Major 8-mosstep M8ms 2L + 6s 533.3 ¢ to 600.0 ¢
9-mosstep Perfect 9-mosstep P9ms 2L + 7s 600.0 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 600.0 ¢ to 666.7 ¢
Major 10-mosstep M10ms 3L + 7s 666.7 ¢ to 900.0 ¢
11-mosstep Minor 11-mosstep m11ms 2L + 9s 600.0 ¢ to 733.3 ¢
Major 11-mosstep M11ms 3L + 8s 733.3 ¢ to 900.0 ¢
12-mosstep Minor 12-mosstep m12ms 2L + 10s 600.0 ¢ to 800.0 ¢
Major 12-mosstep M12ms 3L + 9s 800.0 ¢ to 900.0 ¢
13-mosstep Diminished 13-mosstep d13ms 2L + 11s 600.0 ¢ to 866.7 ¢
Perfect 13-mosstep P13ms 3L + 10s 866.7 ¢ to 900.0 ¢
14-mosstep Perfect 14-mosstep P14ms 3L + 11s 900.0 ¢ to 933.3 ¢
Augmented 14-mosstep A14ms 4L + 10s 933.3 ¢ to 1200.0 ¢
15-mosstep Minor 15-mosstep m15ms 3L + 12s 900.0 ¢ to 1000.0 ¢
Major 15-mosstep M15ms 4L + 11s 1000.0 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms 3L + 13s 900.0 ¢ to 1066.7 ¢
Major 16-mosstep M16ms 4L + 12s 1066.7 ¢ to 1200.0 ¢
17-mosstep Minor 17-mosstep m17ms 3L + 14s 900.0 ¢ to 1133.3 ¢
Major 17-mosstep M17ms 4L + 13s 1133.3 ¢ to 1200.0 ¢
18-mosstep Perfect 18-mosstep P18ms 4L + 14s 1200.0 ¢

Generator chain

Generator chain of 4L 14s
Bright gens Scale degree Abbrev. Scale degree Abbrev.
10 Augmented 4-mosdegree A4md Augmented 13-mosdegree A13md
9 Augmented 0-mosdegree A0md Augmented 9-mosdegree A9md
8 Augmented 5-mosdegree A5md Augmented 14-mosdegree A14md
7 Major 1-mosdegree M1md Major 10-mosdegree M10md
6 Major 6-mosdegree M6md Major 15-mosdegree M15md
5 Major 2-mosdegree M2md Major 11-mosdegree M11md
4 Major 7-mosdegree M7md Major 16-mosdegree M16md
3 Major 3-mosdegree M3md Major 12-mosdegree M12md
2 Major 8-mosdegree M8md Major 17-mosdegree M17md
1 Perfect 4-mosdegree P4md Perfect 13-mosdegree P13md
0 Perfect 0-mosdegree
Perfect 9-mosdegree		 P0md
P9md		 Perfect 9-mosdegree
Perfect 18-mosdegree		 P9md
P18md
−1 Perfect 5-mosdegree P5md Perfect 14-mosdegree P14md
−2 Minor 1-mosdegree m1md Minor 10-mosdegree m10md
−3 Minor 6-mosdegree m6md Minor 15-mosdegree m15md
−4 Minor 2-mosdegree m2md Minor 11-mosdegree m11md
−5 Minor 7-mosdegree m7md Minor 16-mosdegree m16md
−6 Minor 3-mosdegree m3md Minor 12-mosdegree m12md
−7 Minor 8-mosdegree m8md Minor 17-mosdegree m17md
−8 Diminished 4-mosdegree d4md Diminished 13-mosdegree d13md
−9 Diminished 9-mosdegree d9md Diminished 18-mosdegree d18md
−10 Diminished 5-mosdegree d5md Diminished 14-mosdegree d14md

Modes

Scale degrees of the modes of 4L 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 18
16|0(2) 1 LsssLssssLsssLssss Perf. Maj. Maj. Maj. Perf. Aug. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Aug. Maj. Maj. Maj. Perf.
14|2(2) 5 LssssLsssLssssLsss Perf. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Perf.
12|4(2) 9 sLsssLssssLsssLsss Perf. Min. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Perf. Min. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Perf.
10|6(2) 4 sLssssLsssLssssLss Perf. Min. Maj. Maj. Perf. Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf. Perf. Min. Maj. Maj. Perf.
8|8(2) 8 ssLsssLssssLsssLss Perf. Min. Min. Maj. Perf. Perf. Min. Maj. Maj. Perf. Min. Min. Maj. Perf. Perf. Min. Maj. Maj. Perf.
6|10(2) 3 ssLssssLsssLssssLs Perf. Min. Min. Maj. Perf. Perf. Min. Min. Maj. Perf. Min. Min. Maj. Perf. Perf. Min. Min. Maj. Perf.
4|12(2) 7 sssLsssLssssLsssLs Perf. Min. Min. Min. Perf. Perf. Min. Min. Maj. Perf. Min. Min. Min. Perf. Perf. Min. Min. Maj. Perf.
2|14(2) 2 sssLssssLsssLssssL Perf. Min. Min. Min. Perf. Perf. Min. Min. Min. Perf. Min. Min. Min. Perf. Perf. Min. Min. Min. Perf.
0|16(2) 6 ssssLsssLssssLsssL Perf. Min. Min. Min. Dim. Perf. Min. Min. Min. Perf. Min. Min. Min. Dim. Perf. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 4L 14s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\18 266.667 333.333 1:1 1.000 Equalized 4L 14s
21\94 268.085 331.915 6:5 1.200
17\76 268.421 331.579 5:4 1.250
30\134 268.657 331.343 9:7 1.286
13\58 268.966 331.034 4:3 1.333 Supersoft 4L 14s
35\156 269.231 330.769 11:8 1.375
22\98 269.388 330.612 7:5 1.400
31\138 269.565 330.435 10:7 1.429
9\40 270.000 330.000 3:2 1.500 Soft 4L 14s
32\142 270.423 329.577 11:7 1.571
23\102 270.588 329.412 8:5 1.600
37\164 270.732 329.268 13:8 1.625
14\62 270.968 329.032 5:3 1.667 Semisoft 4L 14s
33\146 271.233 328.767 12:7 1.714
19\84 271.429 328.571 7:4 1.750
24\106 271.698 328.302 9:5 1.800
5\22 272.727 327.273 2:1 2.000 Basic 4L 14s
Scales with tunings softer than this are proper
21\92 273.913 326.087 9:4 2.250
16\70 274.286 325.714 7:3 2.333
27\118 274.576 325.424 12:5 2.400
11\48 275.000 325.000 5:2 2.500 Semihard 4L 14s
28\122 275.410 324.590 13:5 2.600
17\74 275.676 324.324 8:3 2.667
23\100 276.000 324.000 11:4 2.750
6\26 276.923 323.077 3:1 3.000 Hard 4L 14s
19\82 278.049 321.951 10:3 3.333
13\56 278.571 321.429 7:2 3.500
20\86 279.070 320.930 11:3 3.667
7\30 280.000 320.000 4:1 4.000 Superhard 4L 14s
15\64 281.250 318.750 9:2 4.500
8\34 282.353 317.647 5:1 5.000
9\38 284.211 315.789 6:1 6.000
1\4 300.000 300.000 1:0 → ∞ Collapsed 4L 14s
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