7L 15s

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↖ 6L 14s ↑ 7L 14s 8L 14s ↗
← 6L 15s 7L 15s 8L 15s →
↙ 6L 16s ↓ 7L 16s 8L 16s ↘ 
┌╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬┬┐
│║││║││║││║││║││║││║││││
││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssLssLssLssLssLssLsss
sssLssLssLssLssLssLssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 3\22 to 1\7 (163.6¢ to 171.4¢)
Dark 6\7 to 19\22 (1028.6¢ to 1036.4¢)
TAMNAMS information
Descends from 7L 1s (pine)
Ancestor's step ratio range 3:1 to 1:0 (hard)
Related MOS scales
Parent 7L 8s
Sister 15L 7s
Daughters 22L 7s, 7L 22s
Neutralized 14L 8s
2-Flought 29L 15s, 7L 37s
Equal tunings
Equalized (L:s = 1:1) 3\22 (163.6¢)
Supersoft (L:s = 4:3) 10\73 (164.4¢)
Soft (L:s = 3:2) 7\51 (164.7¢)
Semisoft (L:s = 5:3) 11\80 (165.0¢)
Basic (L:s = 2:1) 4\29 (165.5¢)
Semihard (L:s = 5:2) 9\65 (166.2¢)
Hard (L:s = 3:1) 5\36 (166.7¢)
Superhard (L:s = 4:1) 6\43 (167.4¢)
Collapsed (L:s = 1:0) 1\7 (171.4¢)

7L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 15 small steps, repeating every octave. 7L 15s is a grandchild scale of 7L 1s, expanding it by 14 tones. Generators that produce this scale range from 163.6¢ to 171.4¢, or from 1028.6¢ to 1036.4¢. It is the enharmonic scale of Coendou temperament.

Modes

Modes of 7L 15s
UDP Cyclic
order		 Step
pattern
21|0 1 LssLssLssLssLssLssLsss
20|1 4 LssLssLssLssLssLsssLss
19|2 7 LssLssLssLssLsssLssLss
18|3 10 LssLssLssLsssLssLssLss
17|4 13 LssLssLsssLssLssLssLss
16|5 16 LssLsssLssLssLssLssLss
15|6 19 LsssLssLssLssLssLssLss
14|7 22 sLssLssLssLssLssLssLss
13|8 3 sLssLssLssLssLssLsssLs
12|9 6 sLssLssLssLssLsssLssLs
11|10 9 sLssLssLssLsssLssLssLs
10|11 12 sLssLssLsssLssLssLssLs
9|12 15 sLssLsssLssLssLssLssLs
8|13 18 sLsssLssLssLssLssLssLs
7|14 21 ssLssLssLssLssLssLssLs
6|15 2 ssLssLssLssLssLssLsssL
5|16 5 ssLssLssLssLssLsssLssL
4|17 8 ssLssLssLssLsssLssLssL
3|18 11 ssLssLssLsssLssLssLssL
2|19 14 ssLssLsssLssLssLssLssL
1|20 17 ssLsssLssLssLssLssLssL
0|21 20 sssLssLssLssLssLssLssL

Intervals

Intervals of 7L 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 54.5¢
Major 1-mosstep M1ms L 54.5¢ to 171.4¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 109.1¢
Major 2-mosstep M2ms L + s 109.1¢ to 171.4¢
3-mosstep Diminished 3-mosstep d3ms 3s 0.0¢ to 163.6¢
Perfect 3-mosstep P3ms L + 2s 163.6¢ to 171.4¢
4-mosstep Minor 4-mosstep m4ms L + 3s 171.4¢ to 218.2¢
Major 4-mosstep M4ms 2L + 2s 218.2¢ to 342.9¢
5-mosstep Minor 5-mosstep m5ms L + 4s 171.4¢ to 272.7¢
Major 5-mosstep M5ms 2L + 3s 272.7¢ to 342.9¢
6-mosstep Minor 6-mosstep m6ms L + 5s 171.4¢ to 327.3¢
Major 6-mosstep M6ms 2L + 4s 327.3¢ to 342.9¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 342.9¢ to 381.8¢
Major 7-mosstep M7ms 3L + 4s 381.8¢ to 514.3¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 342.9¢ to 436.4¢
Major 8-mosstep M8ms 3L + 5s 436.4¢ to 514.3¢
9-mosstep Minor 9-mosstep m9ms 2L + 7s 342.9¢ to 490.9¢
Major 9-mosstep M9ms 3L + 6s 490.9¢ to 514.3¢
10-mosstep Minor 10-mosstep m10ms 3L + 7s 514.3¢ to 545.5¢
Major 10-mosstep M10ms 4L + 6s 545.5¢ to 685.7¢
11-mosstep Minor 11-mosstep m11ms 3L + 8s 514.3¢ to 600.0¢
Major 11-mosstep M11ms 4L + 7s 600.0¢ to 685.7¢
12-mosstep Minor 12-mosstep m12ms 3L + 9s 514.3¢ to 654.5¢
Major 12-mosstep M12ms 4L + 8s 654.5¢ to 685.7¢
13-mosstep Minor 13-mosstep m13ms 4L + 9s 685.7¢ to 709.1¢
Major 13-mosstep M13ms 5L + 8s 709.1¢ to 857.1¢
14-mosstep Minor 14-mosstep m14ms 4L + 10s 685.7¢ to 763.6¢
Major 14-mosstep M14ms 5L + 9s 763.6¢ to 857.1¢
15-mosstep Minor 15-mosstep m15ms 4L + 11s 685.7¢ to 818.2¢
Major 15-mosstep M15ms 5L + 10s 818.2¢ to 857.1¢
16-mosstep Minor 16-mosstep m16ms 5L + 11s 857.1¢ to 872.7¢
Major 16-mosstep M16ms 6L + 10s 872.7¢ to 1028.6¢
17-mosstep Minor 17-mosstep m17ms 5L + 12s 857.1¢ to 927.3¢
Major 17-mosstep M17ms 6L + 11s 927.3¢ to 1028.6¢
18-mosstep Minor 18-mosstep m18ms 5L + 13s 857.1¢ to 981.8¢
Major 18-mosstep M18ms 6L + 12s 981.8¢ to 1028.6¢
19-mosstep Perfect 19-mosstep P19ms 6L + 13s 1028.6¢ to 1036.4¢
Augmented 19-mosstep A19ms 7L + 12s 1036.4¢ to 1200.0¢
20-mosstep Minor 20-mosstep m20ms 6L + 14s 1028.6¢ to 1090.9¢
Major 20-mosstep M20ms 7L + 13s 1090.9¢ to 1200.0¢
21-mosstep Minor 21-mosstep m21ms 6L + 15s 1028.6¢ to 1145.5¢
Major 21-mosstep M21ms 7L + 14s 1145.5¢ to 1200.0¢
22-mosstep Perfect 22-mosstep P22ms 7L + 15s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 7L 15s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
3\22 163.636 1036.364 1:1 1.000 Equalized 7L 15s
16\117 164.103 1035.897 6:5 1.200
13\95 164.211 1035.789 5:4 1.250
23\168 164.286 1035.714 9:7 1.286
10\73 164.384 1035.616 4:3 1.333 Supersoft 7L 15s
27\197 164.467 1035.533 11:8 1.375
17\124 164.516 1035.484 7:5 1.400
24\175 164.571 1035.429 10:7 1.429
7\51 164.706 1035.294 3:2 1.500 Soft 7L 15s
25\182 164.835 1035.165 11:7 1.571
18\131 164.885 1035.115 8:5 1.600
29\211 164.929 1035.071 13:8 1.625
11\80 165.000 1035.000 5:3 1.667 Semisoft 7L 15s
26\189 165.079 1034.921 12:7 1.714
15\109 165.138 1034.862 7:4 1.750
19\138 165.217 1034.783 9:5 1.800
4\29 165.517 1034.483 2:1 2.000 Basic 7L 15s
Scales with tunings softer than this are proper
17\123 165.854 1034.146 9:4 2.250
13\94 165.957 1034.043 7:3 2.333 Coendou
22\159 166.038 1033.962 12:5 2.400
9\65 166.154 1033.846 5:2 2.500 Semihard 7L 15s
23\166 166.265 1033.735 13:5 2.600
14\101 166.337 1033.663 8:3 2.667
19\137 166.423 1033.577 11:4 2.750
5\36 166.667 1033.333 3:1 3.000 Hard 7L 15s
16\115 166.957 1033.043 10:3 3.333
11\79 167.089 1032.911 7:2 3.500
17\122 167.213 1032.787 11:3 3.667
6\43 167.442 1032.558 4:1 4.000 Superhard 7L 15s
13\93 167.742 1032.258 9:2 4.500
7\50 168.000 1032.000 5:1 5.000
8\57 168.421 1031.579 6:1 6.000
1\7 171.429 1028.571 1:0 → ∞ Collapsed 7L 15s


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