8L 15s

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↖ 7L 14s ↑ 8L 14s 9L 14s ↗
← 7L 15s 8L 15s 9L 15s →
↙ 7L 16s ↓ 8L 16s 9L 16s ↘
┌╥┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬┐
│║│║││║││║││║││║││║││║│││
│││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLssLssLssLssLssLssLss
ssLssLssLssLssLssLssLsL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 20\23 to 7\8 (1043.5¢ to 1050.0¢)
Dark 1\8 to 3\23 (150.0¢ to 156.5¢)
TAMNAMS information
Descends from 7L 1s (pine)
Ancestor's step ratio range 1:1 to 3:2 (soft)
Related MOS scales
Parent 8L 7s
Sister 15L 8s
Daughters 23L 8s, 8L 23s
Neutralized 16L 7s
2-Flought 31L 15s, 8L 38s
Equal tunings
Equalized (L:s = 1:1) 20\23 (1043.5¢)
Supersoft (L:s = 4:3) 67\77 (1044.2¢)
Soft (L:s = 3:2) 47\54 (1044.4¢)
Semisoft (L:s = 5:3) 74\85 (1044.7¢)
Basic (L:s = 2:1) 27\31 (1045.2¢)
Semihard (L:s = 5:2) 61\70 (1045.7¢)
Hard (L:s = 3:1) 34\39 (1046.2¢)
Superhard (L:s = 4:1) 41\47 (1046.8¢)
Collapsed (L:s = 1:0) 7\8 (1050.0¢)

8L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 15 small steps, repeating every octave. 8L 15s is a grandchild scale of 7L 1s, expanding it by 15 tones. Generators that produce this scale range from 1043.5¢ to 1050¢, or from 150¢ to 156.5¢.

Modes

Modes of 8L 15s
UDP Cyclic
order
Step
pattern
22|0 1 LsLssLssLssLssLssLssLss
21|1 21 LssLsLssLssLssLssLssLss
20|2 18 LssLssLsLssLssLssLssLss
19|3 15 LssLssLssLsLssLssLssLss
18|4 12 LssLssLssLssLsLssLssLss
17|5 9 LssLssLssLssLssLsLssLss
16|6 6 LssLssLssLssLssLssLsLss
15|7 3 LssLssLssLssLssLssLssLs
14|8 23 sLsLssLssLssLssLssLssLs
13|9 20 sLssLsLssLssLssLssLssLs
12|10 17 sLssLssLsLssLssLssLssLs
11|11 14 sLssLssLssLsLssLssLssLs
10|12 11 sLssLssLssLssLsLssLssLs
9|13 8 sLssLssLssLssLssLsLssLs
8|14 5 sLssLssLssLssLssLssLsLs
7|15 2 sLssLssLssLssLssLssLssL
6|16 22 ssLsLssLssLssLssLssLssL
5|17 19 ssLssLsLssLssLssLssLssL
4|18 16 ssLssLssLsLssLssLssLssL
3|19 13 ssLssLssLssLsLssLssLssL
2|20 10 ssLssLssLssLssLsLssLssL
1|21 7 ssLssLssLssLssLssLsLssL
0|22 4 ssLssLssLssLssLssLssLsL

Intervals

Intervals of 8L 15s
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 52.2¢
Major 1-mosstep M1ms L 52.2¢ to 150.0¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 104.3¢
Major 2-mosstep M2ms L + s 104.3¢ to 150.0¢
3-mosstep Perfect 3-mosstep P3ms L + 2s 150.0¢ to 156.5¢
Augmented 3-mosstep A3ms 2L + s 156.5¢ to 300.0¢
4-mosstep Minor 4-mosstep m4ms L + 3s 150.0¢ to 208.7¢
Major 4-mosstep M4ms 2L + 2s 208.7¢ to 300.0¢
5-mosstep Minor 5-mosstep m5ms L + 4s 150.0¢ to 260.9¢
Major 5-mosstep M5ms 2L + 3s 260.9¢ to 300.0¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 300.0¢ to 313.0¢
Major 6-mosstep M6ms 3L + 3s 313.0¢ to 450.0¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 300.0¢ to 365.2¢
Major 7-mosstep M7ms 3L + 4s 365.2¢ to 450.0¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 300.0¢ to 417.4¢
Major 8-mosstep M8ms 3L + 5s 417.4¢ to 450.0¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 450.0¢ to 469.6¢
Major 9-mosstep M9ms 4L + 5s 469.6¢ to 600.0¢
10-mosstep Minor 10-mosstep m10ms 3L + 7s 450.0¢ to 521.7¢
Major 10-mosstep M10ms 4L + 6s 521.7¢ to 600.0¢
11-mosstep Minor 11-mosstep m11ms 3L + 8s 450.0¢ to 573.9¢
Major 11-mosstep M11ms 4L + 7s 573.9¢ to 600.0¢
12-mosstep Minor 12-mosstep m12ms 4L + 8s 600.0¢ to 626.1¢
Major 12-mosstep M12ms 5L + 7s 626.1¢ to 750.0¢
13-mosstep Minor 13-mosstep m13ms 4L + 9s 600.0¢ to 678.3¢
Major 13-mosstep M13ms 5L + 8s 678.3¢ to 750.0¢
14-mosstep Minor 14-mosstep m14ms 4L + 10s 600.0¢ to 730.4¢
Major 14-mosstep M14ms 5L + 9s 730.4¢ to 750.0¢
15-mosstep Minor 15-mosstep m15ms 5L + 10s 750.0¢ to 782.6¢
Major 15-mosstep M15ms 6L + 9s 782.6¢ to 900.0¢
16-mosstep Minor 16-mosstep m16ms 5L + 11s 750.0¢ to 834.8¢
Major 16-mosstep M16ms 6L + 10s 834.8¢ to 900.0¢
17-mosstep Minor 17-mosstep m17ms 5L + 12s 750.0¢ to 887.0¢
Major 17-mosstep M17ms 6L + 11s 887.0¢ to 900.0¢
18-mosstep Minor 18-mosstep m18ms 6L + 12s 900.0¢ to 939.1¢
Major 18-mosstep M18ms 7L + 11s 939.1¢ to 1050.0¢
19-mosstep Minor 19-mosstep m19ms 6L + 13s 900.0¢ to 991.3¢
Major 19-mosstep M19ms 7L + 12s 991.3¢ to 1050.0¢
20-mosstep Diminished 20-mosstep d20ms 6L + 14s 900.0¢ to 1043.5¢
Perfect 20-mosstep P20ms 7L + 13s 1043.5¢ to 1050.0¢
21-mosstep Minor 21-mosstep m21ms 7L + 14s 1050.0¢ to 1095.7¢
Major 21-mosstep M21ms 8L + 13s 1095.7¢ to 1200.0¢
22-mosstep Minor 22-mosstep m22ms 7L + 15s 1050.0¢ to 1147.8¢
Major 22-mosstep M22ms 8L + 14s 1147.8¢ to 1200.0¢
23-mosstep Perfect 23-mosstep P23ms 8L + 15s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 8L 15s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
20\23 1043.478 156.522 1:1 1.000 Equalized 8L 15s
107\123 1043.902 156.098 6:5 1.200
87\100 1044.000 156.000 5:4 1.250
154\177 1044.068 155.932 9:7 1.286
67\77 1044.156 155.844 4:3 1.333 Supersoft 8L 15s
181\208 1044.231 155.769 11:8 1.375
114\131 1044.275 155.725 7:5 1.400
161\185 1044.324 155.676 10:7 1.429
47\54 1044.444 155.556 3:2 1.500 Soft 8L 15s
168\193 1044.560 155.440 11:7 1.571
121\139 1044.604 155.396 8:5 1.600
195\224 1044.643 155.357 13:8 1.625
74\85 1044.706 155.294 5:3 1.667 Semisoft 8L 15s
175\201 1044.776 155.224 12:7 1.714
101\116 1044.828 155.172 7:4 1.750
128\147 1044.898 155.102 9:5 1.800
27\31 1045.161 154.839 2:1 2.000 Basic 8L 15s
Scales with tunings softer than this are proper
115\132 1045.455 154.545 9:4 2.250
88\101 1045.545 154.455 7:3 2.333
149\171 1045.614 154.386 12:5 2.400
61\70 1045.714 154.286 5:2 2.500 Semihard 8L 15s
156\179 1045.810 154.190 13:5 2.600
95\109 1045.872 154.128 8:3 2.667
129\148 1045.946 154.054 11:4 2.750
34\39 1046.154 153.846 3:1 3.000 Hard 8L 15s
109\125 1046.400 153.600 10:3 3.333
75\86 1046.512 153.488 7:2 3.500
116\133 1046.617 153.383 11:3 3.667
41\47 1046.809 153.191 4:1 4.000 Superhard 8L 15s
89\102 1047.059 152.941 9:2 4.500
48\55 1047.273 152.727 5:1 5.000
55\63 1047.619 152.381 6:1 6.000
7\8 1050.000 150.000 1:0 → ∞ Collapsed 8L 15s


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