15L 5s

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← 14L 5s 15L 5s 16L 5s →
↙ 14L 6s ↓ 15L 6s 16L 6s ↘ 
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Scale structure
Step pattern LLLsLLLsLLLsLLLsLLLs
sLLLsLLLsLLLsLLLsLLL
Equave 2/1 (1200.0 ¢)
Period 1\5 (240.0 ¢)
Generator size
Bright 1\20 to 1\15 (60.0 ¢ to 80.0 ¢)
Dark 2\15 to 3\20 (160.0 ¢ to 180.0 ¢)
TAMNAMS information
Descends from 5L 5s (pentawood)
Ancestor's step ratio range 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 5L 10s
Sister 5L 15s
Daughters 20L 15s, 15L 20s
Neutralized 10L 10s
2-Flought 35L 5s, 15L 25s
Equal tunings
Equalized (L:s = 1:1) 1\20 (60.0 ¢)
Supersoft (L:s = 4:3) 4\75 (64.0 ¢)
Soft (L:s = 3:2) 3\55 (65.5 ¢)
Semisoft (L:s = 5:3) 5\90 (66.7 ¢)
Basic (L:s = 2:1) 2\35 (68.6 ¢)
Semihard (L:s = 5:2) 5\85 (70.6 ¢)
Hard (L:s = 3:1) 3\50 (72.0 ¢)
Superhard (L:s = 4:1) 4\65 (73.8 ¢)
Collapsed (L:s = 1:0) 1\15 (80.0 ¢)

15L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 5 small steps, with a period of 3 large steps and 1 small step that repeats every 240.0 ¢, or 5 times every octave. 15L 5s is a grandchild scale of 5L 5s, expanding it by 10 tones. Generators that produce this scale range from 60 ¢ to 80 ¢, or from 160 ¢ to 180 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

Modes

Modes of 15L 5s
UDP Cyclic
order		 Step
pattern
15|0(5) 1 LLLsLLLsLLLsLLLsLLLs
10|5(5) 2 LLsLLLsLLLsLLLsLLLsL
5|10(5) 3 LsLLLsLLLsLLLsLLLsLL
0|15(5) 4 sLLLsLLLsLLLsLLLsLLL

Intervals

Intervals of 15L 5s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Diminished 1-mosstep d1ms s 0.0 ¢ to 60.0 ¢
Perfect 1-mosstep P1ms L 60.0 ¢ to 80.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 80.0 ¢ to 120.0 ¢
Major 2-mosstep M2ms 2L 120.0 ¢ to 160.0 ¢
3-mosstep Perfect 3-mosstep P3ms 2L + s 160.0 ¢ to 180.0 ¢
Augmented 3-mosstep A3ms 3L 180.0 ¢ to 240.0 ¢
4-mosstep Perfect 4-mosstep P4ms 3L + s 240.0 ¢
5-mosstep Diminished 5-mosstep d5ms 3L + 2s 240.0 ¢ to 300.0 ¢
Perfect 5-mosstep P5ms 4L + s 300.0 ¢ to 320.0 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 320.0 ¢ to 360.0 ¢
Major 6-mosstep M6ms 5L + s 360.0 ¢ to 400.0 ¢
7-mosstep Perfect 7-mosstep P7ms 5L + 2s 400.0 ¢ to 420.0 ¢
Augmented 7-mosstep A7ms 6L + s 420.0 ¢ to 480.0 ¢
8-mosstep Perfect 8-mosstep P8ms 6L + 2s 480.0 ¢
9-mosstep Diminished 9-mosstep d9ms 6L + 3s 480.0 ¢ to 540.0 ¢
Perfect 9-mosstep P9ms 7L + 2s 540.0 ¢ to 560.0 ¢
10-mosstep Minor 10-mosstep m10ms 7L + 3s 560.0 ¢ to 600.0 ¢
Major 10-mosstep M10ms 8L + 2s 600.0 ¢ to 640.0 ¢
11-mosstep Perfect 11-mosstep P11ms 8L + 3s 640.0 ¢ to 660.0 ¢
Augmented 11-mosstep A11ms 9L + 2s 660.0 ¢ to 720.0 ¢
12-mosstep Perfect 12-mosstep P12ms 9L + 3s 720.0 ¢
13-mosstep Diminished 13-mosstep d13ms 9L + 4s 720.0 ¢ to 780.0 ¢
Perfect 13-mosstep P13ms 10L + 3s 780.0 ¢ to 800.0 ¢
14-mosstep Minor 14-mosstep m14ms 10L + 4s 800.0 ¢ to 840.0 ¢
Major 14-mosstep M14ms 11L + 3s 840.0 ¢ to 880.0 ¢
15-mosstep Perfect 15-mosstep P15ms 11L + 4s 880.0 ¢ to 900.0 ¢
Augmented 15-mosstep A15ms 12L + 3s 900.0 ¢ to 960.0 ¢
16-mosstep Perfect 16-mosstep P16ms 12L + 4s 960.0 ¢
17-mosstep Diminished 17-mosstep d17ms 12L + 5s 960.0 ¢ to 1020.0 ¢
Perfect 17-mosstep P17ms 13L + 4s 1020.0 ¢ to 1040.0 ¢
18-mosstep Minor 18-mosstep m18ms 13L + 5s 1040.0 ¢ to 1080.0 ¢
Major 18-mosstep M18ms 14L + 4s 1080.0 ¢ to 1120.0 ¢
19-mosstep Perfect 19-mosstep P19ms 14L + 5s 1120.0 ¢ to 1140.0 ¢
Augmented 19-mosstep A19ms 15L + 4s 1140.0 ¢ to 1200.0 ¢
20-mosstep Perfect 20-mosstep P20ms 15L + 5s 1200.0 ¢

Scale tree

Icon-Deprecated.png Scale tree is deprecated. Please use Template: MOS tuning spectrum instead.
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 15L 5s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\20 60.000 180.000 1:1 1.000 Equalized 15L 5s
6\115 62.609 177.391 6:5 1.200
5\95 63.158 176.842 5:4 1.250
9\170 63.529 176.471 9:7 1.286
4\75 64.000 176.000 4:3 1.333 Supersoft 15L 5s
11\205 64.390 175.610 11:8 1.375
7\130 64.615 175.385 7:5 1.400
10\185 64.865 175.135 10:7 1.429
3\55 65.455 174.545 3:2 1.500 Soft 15L 5s
11\200 66.000 174.000 11:7 1.571
8\145 66.207 173.793 8:5 1.600
13\235 66.383 173.617 13:8 1.625
5\90 66.667 173.333 5:3 1.667 Semisoft 15L 5s
12\215 66.977 173.023 12:7 1.714
7\125 67.200 172.800 7:4 1.750
9\160 67.500 172.500 9:5 1.800
2\35 68.571 171.429 2:1 2.000 Basic 15L 5s
9\155 69.677 170.323 9:4 2.250
7\120 70.000 170.000 7:3 2.333
12\205 70.244 169.756 12:5 2.400
5\85 70.588 169.412 5:2 2.500 Semihard 15L 5s
13\220 70.909 169.091 13:5 2.600
8\135 71.111 168.889 8:3 2.667
11\185 71.351 168.649 11:4 2.750
3\50 72.000 168.000 3:1 3.000 Hard 15L 5s
10\165 72.727 167.273 10:3 3.333
7\115 73.043 166.957 7:2 3.500
11\180 73.333 166.667 11:3 3.667
4\65 73.846 166.154 4:1 4.000 Superhard 15L 5s
9\145 74.483 165.517 9:2 4.500
5\80 75.000 165.000 5:1 5.000
6\95 75.789 164.211 6:1 6.000
1\15 80.000 160.000 1:0 → ∞ Collapsed 15L 5s


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