4L 13s

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↖ 3L 12s ↑ 4L 12s 5L 12s ↗
← 3L 13s 4L 13s 5L 13s →
↙ 3L 14s ↓ 4L 14s 5L 14s ↘ 
┌╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬┬┐
│║│││║│││║│││║│││││
│││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssLsssLsssLssss
ssssLsssLsssLsssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 4\17 to 1\4 (282.4 ¢ to 300.0 ¢)
Dark 3\4 to 13\17 (900.0 ¢ to 917.6 ¢)
TAMNAMS information
Descends from 4L 5s (gramitonic)
Ancestor's step ratio range 3:1 to 1:0 (hard)
Related MOS scales
Parent 4L 9s
Sister 13L 4s
Daughters 17L 4s, 4L 17s
Neutralized 8L 9s
2-Flought 21L 13s, 4L 30s
Equal tunings
Equalized (L:s = 1:1) 4\17 (282.4 ¢)
Supersoft (L:s = 4:3) 13\55 (283.6 ¢)
Soft (L:s = 3:2) 9\38 (284.2 ¢)
Semisoft (L:s = 5:3) 14\59 (284.7 ¢)
Basic (L:s = 2:1) 5\21 (285.7 ¢)
Semihard (L:s = 5:2) 11\46 (287.0 ¢)
Hard (L:s = 3:1) 6\25 (288.0 ¢)
Superhard (L:s = 4:1) 7\29 (289.7 ¢)
Collapsed (L:s = 1:0) 1\4 (300.0 ¢)

4L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 13 small steps, repeating every octave. 4L 13s is a grandchild scale of 4L 5s, expanding it by 8 tones. Generators that produce this scale range from 282.4 ¢ to 300 ¢, or from 900 ¢ to 917.6 ¢.

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 13s
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 300.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 141.2 ¢
Major 2-mosstep M2ms L + s 141.2 ¢ to 300.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 211.8 ¢
Major 3-mosstep M3ms L + 2s 211.8 ¢ to 300.0 ¢
4-mosstep Diminished 4-mosstep d4ms 4s 0.0 ¢ to 282.4 ¢
Perfect 4-mosstep P4ms L + 3s 282.4 ¢ to 300.0 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 300.0 ¢ to 352.9 ¢
Major 5-mosstep M5ms 2L + 3s 352.9 ¢ to 600.0 ¢
6-mosstep Minor 6-mosstep m6ms L + 5s 300.0 ¢ to 423.5 ¢
Major 6-mosstep M6ms 2L + 4s 423.5 ¢ to 600.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 300.0 ¢ to 494.1 ¢
Major 7-mosstep M7ms 2L + 5s 494.1 ¢ to 600.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 300.0 ¢ to 564.7 ¢
Major 8-mosstep M8ms 2L + 6s 564.7 ¢ to 600.0 ¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 600.0 ¢ to 635.3 ¢
Major 9-mosstep M9ms 3L + 6s 635.3 ¢ to 900.0 ¢
10-mosstep Minor 10-mosstep m10ms 2L + 8s 600.0 ¢ to 705.9 ¢
Major 10-mosstep M10ms 3L + 7s 705.9 ¢ to 900.0 ¢
11-mosstep Minor 11-mosstep m11ms 2L + 9s 600.0 ¢ to 776.5 ¢
Major 11-mosstep M11ms 3L + 8s 776.5 ¢ to 900.0 ¢
12-mosstep Minor 12-mosstep m12ms 2L + 10s 600.0 ¢ to 847.1 ¢
Major 12-mosstep M12ms 3L + 9s 847.1 ¢ to 900.0 ¢
13-mosstep Perfect 13-mosstep P13ms 3L + 10s 900.0 ¢ to 917.6 ¢
Augmented 13-mosstep A13ms 4L + 9s 917.6 ¢ to 1200.0 ¢
14-mosstep Minor 14-mosstep m14ms 3L + 11s 900.0 ¢ to 988.2 ¢
Major 14-mosstep M14ms 4L + 10s 988.2 ¢ to 1200.0 ¢
15-mosstep Minor 15-mosstep m15ms 3L + 12s 900.0 ¢ to 1058.8 ¢
Major 15-mosstep M15ms 4L + 11s 1058.8 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms 3L + 13s 900.0 ¢ to 1129.4 ¢
Major 16-mosstep M16ms 4L + 12s 1129.4 ¢ to 1200.0 ¢
17-mosstep Perfect 17-mosstep P17ms 4L + 13s 1200.0 ¢

Generator chain

Generator chain of 4L 13s
Bright gens Scale degree Abbrev.
20 Augmented 12-mosdegree A12md
19 Augmented 8-mosdegree A8md
18 Augmented 4-mosdegree A4md
17 Augmented 0-mosdegree A0md
16 Augmented 13-mosdegree A13md
15 Major 9-mosdegree M9md
14 Major 5-mosdegree M5md
13 Major 1-mosdegree M1md
12 Major 14-mosdegree M14md
11 Major 10-mosdegree M10md
10 Major 6-mosdegree M6md
9 Major 2-mosdegree M2md
8 Major 15-mosdegree M15md
7 Major 11-mosdegree M11md
6 Major 7-mosdegree M7md
5 Major 3-mosdegree M3md
4 Major 16-mosdegree M16md
3 Major 12-mosdegree M12md
2 Major 8-mosdegree M8md
1 Perfect 4-mosdegree P4md
0 Perfect 0-mosdegree
Perfect 17-mosdegree		 P0md
P17md
−1 Perfect 13-mosdegree P13md
−2 Minor 9-mosdegree m9md
−3 Minor 5-mosdegree m5md
−4 Minor 1-mosdegree m1md
−5 Minor 14-mosdegree m14md
−6 Minor 10-mosdegree m10md
−7 Minor 6-mosdegree m6md
−8 Minor 2-mosdegree m2md
−9 Minor 15-mosdegree m15md
−10 Minor 11-mosdegree m11md
−11 Minor 7-mosdegree m7md
−12 Minor 3-mosdegree m3md
−13 Minor 16-mosdegree m16md
−14 Minor 12-mosdegree m12md
−15 Minor 8-mosdegree m8md
−16 Diminished 4-mosdegree d4md
−17 Diminished 17-mosdegree d17md
−18 Diminished 13-mosdegree d13md
−19 Diminished 9-mosdegree d9md
−20 Diminished 5-mosdegree d5md

Modes

Scale degrees of the modes of 4L 13s
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 LsssLsssLsssLssss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Perf.
15|1 5 LsssLsssLssssLsss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
14|2 9 LsssLssssLsssLsss Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
13|3 13 LssssLsssLsssLsss Perf. Maj. Maj. Maj. Perf. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
12|4 17 sLsssLsssLsssLsss Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
11|5 4 sLsssLsssLssssLss Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Maj. Min. Maj. Maj. Maj. Perf. Min. Maj. Maj. Perf.
10|6 8 sLsssLssssLsssLss Perf. Min. Maj. Maj. Perf. Min. Maj. Maj. Maj. Min. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
9|7 12 sLssssLsssLsssLss Perf. Min. Maj. Maj. Perf. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
8|8 16 ssLsssLsssLsssLss Perf. Min. Min. Maj. Perf. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Perf. Min. Maj. Maj. Perf.
7|9 3 ssLsssLsssLssssLs Perf. Min. Min. Maj. Perf. Min. Min. Maj. Maj. Min. Min. Maj. Maj. Perf. Min. Min. Maj. Perf.
6|10 7 ssLsssLssssLsssLs Perf. Min. Min. Maj. Perf. Min. Min. Maj. Maj. Min. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
5|11 11 ssLssssLsssLsssLs Perf. Min. Min. Maj. Perf. Min. Min. Min. Maj. Min. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
4|12 15 sssLsssLsssLsssLs Perf. Min. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Min. Maj. Perf. Min. Min. Maj. Perf.
3|13 2 sssLsssLsssLssssL Perf. Min. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Min. Maj. Perf. Min. Min. Min. Perf.
2|14 6 sssLsssLssssLsssL Perf. Min. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Min. Min. Perf. Min. Min. Min. Perf.
1|15 10 sssLssssLsssLsssL Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Perf.
0|16 14 ssssLsssLsssLsssL Perf. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 4L 13s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\17 282.353 917.647 1:1 1.000 Equalized 4L 13s
21\89 283.146 916.854 6:5 1.200
17\72 283.333 916.667 5:4 1.250
30\127 283.465 916.535 9:7 1.286
13\55 283.636 916.364 4:3 1.333 Supersoft 4L 13s
35\148 283.784 916.216 11:8 1.375
22\93 283.871 916.129 7:5 1.400
31\131 283.969 916.031 10:7 1.429
9\38 284.211 915.789 3:2 1.500 Soft 4L 13s
32\135 284.444 915.556 11:7 1.571
23\97 284.536 915.464 8:5 1.600
37\156 284.615 915.385 13:8 1.625
14\59 284.746 915.254 5:3 1.667 Semisoft 4L 13s
33\139 284.892 915.108 12:7 1.714
19\80 285.000 915.000 7:4 1.750
24\101 285.149 914.851 9:5 1.800
5\21 285.714 914.286 2:1 2.000 Basic 4L 13s
Scales with tunings softer than this are proper
21\88 286.364 913.636 9:4 2.250
16\67 286.567 913.433 7:3 2.333
27\113 286.726 913.274 12:5 2.400
11\46 286.957 913.043 5:2 2.500 Semihard 4L 13s
28\117 287.179 912.821 13:5 2.600
17\71 287.324 912.676 8:3 2.667
23\96 287.500 912.500 11:4 2.750
6\25 288.000 912.000 3:1 3.000 Hard 4L 13s
19\79 288.608 911.392 10:3 3.333
13\54 288.889 911.111 7:2 3.500
20\83 289.157 910.843 11:3 3.667
7\29 289.655 910.345 4:1 4.000 Superhard 4L 13s
15\62 290.323 909.677 9:2 4.500
8\33 290.909 909.091 5:1 5.000
9\37 291.892 908.108 6:1 6.000
1\4 300.000 900.000 1:0 → ∞ Collapsed 4L 13s
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