3L 15s

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↖ 2L 14s ↑ 3L 14s 4L 14s ↗
← 2L 15s 3L 15s 4L 15s →
↙ 2L 16s ↓ 3L 16s 4L 16s ↘ 
┌╥┬┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬┐
│║│││││║│││││║││││││
││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssssLsssssLsssss
sssssLsssssLsssssL
Equave 2/1 (1200.0 ¢)
Period 1\3 (400.0 ¢)
Generator size
Bright 5\18 to 1\3 (333.3 ¢ to 400.0 ¢)
Dark 0\3 to 1\18 (0.0 ¢ to 66.7 ¢)
TAMNAMS information
Related to 3L 6s (tcherepnin)
With tunings 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 3L 12s
Sister 15L 3s
Daughters 18L 3s, 3L 18s
Neutralized 6L 12s
2-Flought 21L 15s, 3L 33s
Equal tunings
Equalized (L:s = 1:1) 5\18 (333.3 ¢)
Supersoft (L:s = 4:3) 16\57 (336.8 ¢)
Soft (L:s = 3:2) 11\39 (338.5 ¢)
Semisoft (L:s = 5:3) 17\60 (340.0 ¢)
Basic (L:s = 2:1) 6\21 (342.9 ¢)
Semihard (L:s = 5:2) 13\45 (346.7 ¢)
Hard (L:s = 3:1) 7\24 (350.0 ¢)
Superhard (L:s = 4:1) 8\27 (355.6 ¢)
Collapsed (L:s = 1:0) 1\3 (400.0 ¢)

3L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 15 small steps, with a period of 1 large step and 5 small steps that repeats every 400.0 ¢, or 3 times every octave. 3L 15s is a great-grandchild scale of 3L 6s, expanding it by 9 tones. Generators that produce this scale range from 333.3 ¢ to 400 ¢, or from 0 ¢ to 66.7 ¢.

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 interval regions.

Intervals

Intervals of 3L 15s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Perfect 1-mosstep P1ms s 0.0 ¢ to 66.7 ¢
Augmented 1-mosstep A1ms L 66.7 ¢ to 400.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 133.3 ¢
Major 2-mosstep M2ms L + s 133.3 ¢ to 400.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 200.0 ¢
Major 3-mosstep M3ms L + 2s 200.0 ¢ to 400.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 266.7 ¢
Major 4-mosstep M4ms L + 3s 266.7 ¢ to 400.0 ¢
5-mosstep Diminished 5-mosstep d5ms 5s 0.0 ¢ to 333.3 ¢
Perfect 5-mosstep P5ms L + 4s 333.3 ¢ to 400.0 ¢
6-mosstep Perfect 6-mosstep P6ms L + 5s 400.0 ¢
7-mosstep Perfect 7-mosstep P7ms L + 6s 400.0 ¢ to 466.7 ¢
Augmented 7-mosstep A7ms 2L + 5s 466.7 ¢ to 800.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 400.0 ¢ to 533.3 ¢
Major 8-mosstep M8ms 2L + 6s 533.3 ¢ to 800.0 ¢
9-mosstep Minor 9-mosstep m9ms L + 8s 400.0 ¢ to 600.0 ¢
Major 9-mosstep M9ms 2L + 7s 600.0 ¢ to 800.0 ¢
10-mosstep Minor 10-mosstep m10ms L + 9s 400.0 ¢ to 666.7 ¢
Major 10-mosstep M10ms 2L + 8s 666.7 ¢ to 800.0 ¢
11-mosstep Diminished 11-mosstep d11ms L + 10s 400.0 ¢ to 733.3 ¢
Perfect 11-mosstep P11ms 2L + 9s 733.3 ¢ to 800.0 ¢
12-mosstep Perfect 12-mosstep P12ms 2L + 10s 800.0 ¢
13-mosstep Perfect 13-mosstep P13ms 2L + 11s 800.0 ¢ to 866.7 ¢
Augmented 13-mosstep A13ms 3L + 10s 866.7 ¢ to 1200.0 ¢
14-mosstep Minor 14-mosstep m14ms 2L + 12s 800.0 ¢ to 933.3 ¢
Major 14-mosstep M14ms 3L + 11s 933.3 ¢ to 1200.0 ¢
15-mosstep Minor 15-mosstep m15ms 2L + 13s 800.0 ¢ to 1000.0 ¢
Major 15-mosstep M15ms 3L + 12s 1000.0 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms 2L + 14s 800.0 ¢ to 1066.7 ¢
Major 16-mosstep M16ms 3L + 13s 1066.7 ¢ to 1200.0 ¢
17-mosstep Diminished 17-mosstep d17ms 2L + 15s 800.0 ¢ to 1133.3 ¢
Perfect 17-mosstep P17ms 3L + 14s 1133.3 ¢ to 1200.0 ¢
18-mosstep Perfect 18-mosstep P18ms 3L + 15s 1200.0 ¢

Generator chain

Generator chain of 3L 15s
Bright gens Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev.
6 Augmented 0-mosdegree A0md Augmented 6-mosdegree A6md Augmented 12-mosdegree A12md
5 Augmented 1-mosdegree A1md Augmented 7-mosdegree A7md Augmented 13-mosdegree A13md
4 Major 2-mosdegree M2md Major 8-mosdegree M8md Major 14-mosdegree M14md
3 Major 3-mosdegree M3md Major 9-mosdegree M9md Major 15-mosdegree M15md
2 Major 4-mosdegree M4md Major 10-mosdegree M10md Major 16-mosdegree M16md
1 Perfect 5-mosdegree P5md Perfect 11-mosdegree P11md Perfect 17-mosdegree P17md
0 Perfect 0-mosdegree
Perfect 6-mosdegree		 P0md
P6md		 Perfect 6-mosdegree
Perfect 12-mosdegree		 P6md
P12md		 Perfect 12-mosdegree
Perfect 18-mosdegree		 P12md
P18md
−1 Perfect 1-mosdegree P1md Perfect 7-mosdegree P7md Perfect 13-mosdegree P13md
−2 Minor 2-mosdegree m2md Minor 8-mosdegree m8md Minor 14-mosdegree m14md
−3 Minor 3-mosdegree m3md Minor 9-mosdegree m9md Minor 15-mosdegree m15md
−4 Minor 4-mosdegree m4md Minor 10-mosdegree m10md Minor 16-mosdegree m16md
−5 Diminished 5-mosdegree d5md Diminished 11-mosdegree d11md Diminished 17-mosdegree d17md
−6 Diminished 6-mosdegree d6md Diminished 12-mosdegree d12md Diminished 18-mosdegree d18md

Modes

Scale degrees of the modes of 3L 15s
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
15|0(3) 1 LsssssLsssssLsssss Perf. Aug. Maj. Maj. Maj. Perf. Perf. Aug. Maj. Maj. Maj. Perf. Perf. Aug. Maj. Maj. Maj. Perf. Perf.
12|3(3) 6 sLsssssLsssssLssss Perf. Perf. Maj. Maj. Maj. Perf. Perf. Perf. Maj. Maj. Maj. Perf. Perf. Perf. Maj. Maj. Maj. Perf. Perf.
9|6(3) 5 ssLsssssLsssssLsss Perf. Perf. Min. Maj. Maj. Perf. Perf. Perf. Min. Maj. Maj. Perf. Perf. Perf. Min. Maj. Maj. Perf. Perf.
6|9(3) 4 sssLsssssLsssssLss Perf. Perf. Min. Min. Maj. Perf. Perf. Perf. Min. Min. Maj. Perf. Perf. Perf. Min. Min. Maj. Perf. Perf.
3|12(3) 3 ssssLsssssLsssssLs Perf. Perf. Min. Min. Min. Perf. Perf. Perf. Min. Min. Min. Perf. Perf. Perf. Min. Min. Min. Perf. Perf.
0|15(3) 2 sssssLsssssLsssssL Perf. Perf. Min. Min. Min. Dim. Perf. Perf. Min. Min. Min. Dim. Perf. Perf. Min. Min. Min. Dim. Perf.

Scale tree

Scale tree and tuning spectrum of 3L 15s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\18 333.333 66.667 1:1 1.000 Equalized 3L 15s
26\93 335.484 64.516 6:5 1.200
21\75 336.000 64.000 5:4 1.250
37\132 336.364 63.636 9:7 1.286
16\57 336.842 63.158 4:3 1.333 Supersoft 3L 15s
43\153 337.255 62.745 11:8 1.375
27\96 337.500 62.500 7:5 1.400
38\135 337.778 62.222 10:7 1.429
11\39 338.462 61.538 3:2 1.500 Soft 3L 15s
39\138 339.130 60.870 11:7 1.571
28\99 339.394 60.606 8:5 1.600
45\159 339.623 60.377 13:8 1.625
17\60 340.000 60.000 5:3 1.667 Semisoft 3L 15s
40\141 340.426 59.574 12:7 1.714
23\81 340.741 59.259 7:4 1.750
29\102 341.176 58.824 9:5 1.800
6\21 342.857 57.143 2:1 2.000 Basic 3L 15s
Scales with tunings softer than this are proper
25\87 344.828 55.172 9:4 2.250
19\66 345.455 54.545 7:3 2.333
32\111 345.946 54.054 12:5 2.400
13\45 346.667 53.333 5:2 2.500 Semihard 3L 15s
33\114 347.368 52.632 13:5 2.600
20\69 347.826 52.174 8:3 2.667
27\93 348.387 51.613 11:4 2.750
7\24 350.000 50.000 3:1 3.000 Hard 3L 15s
22\75 352.000 48.000 10:3 3.333
15\51 352.941 47.059 7:2 3.500
23\78 353.846 46.154 11:3 3.667
8\27 355.556 44.444 4:1 4.000 Superhard 3L 15s
17\57 357.895 42.105 9:2 4.500
9\30 360.000 40.000 5:1 5.000
10\33 363.636 36.364 6:1 6.000
1\3 400.000 0.000 1:0 → ∞ Collapsed 3L 15s
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