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.

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 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 ¢

Generator chain

Generator chain of 7L 15s
Bright gens Scale degree Abbrev.
28 Augmented 18-mosdegree A18md
27 Augmented 15-mosdegree A15md
26 Augmented 12-mosdegree A12md
25 Augmented 9-mosdegree A9md
24 Augmented 6-mosdegree A6md
23 Augmented 3-mosdegree A3md
22 Augmented 0-mosdegree A0md
21 Augmented 19-mosdegree A19md
20 Major 16-mosdegree M16md
19 Major 13-mosdegree M13md
18 Major 10-mosdegree M10md
17 Major 7-mosdegree M7md
16 Major 4-mosdegree M4md
15 Major 1-mosdegree M1md
14 Major 20-mosdegree M20md
13 Major 17-mosdegree M17md
12 Major 14-mosdegree M14md
11 Major 11-mosdegree M11md
10 Major 8-mosdegree M8md
9 Major 5-mosdegree M5md
8 Major 2-mosdegree M2md
7 Major 21-mosdegree M21md
6 Major 18-mosdegree M18md
5 Major 15-mosdegree M15md
4 Major 12-mosdegree M12md
3 Major 9-mosdegree M9md
2 Major 6-mosdegree M6md
1 Perfect 3-mosdegree P3md
0 Perfect 0-mosdegree
Perfect 22-mosdegree		 P0md
P22md
−1 Perfect 19-mosdegree P19md
−2 Minor 16-mosdegree m16md
−3 Minor 13-mosdegree m13md
−4 Minor 10-mosdegree m10md
−5 Minor 7-mosdegree m7md
−6 Minor 4-mosdegree m4md
−7 Minor 1-mosdegree m1md
−8 Minor 20-mosdegree m20md
−9 Minor 17-mosdegree m17md
−10 Minor 14-mosdegree m14md
−11 Minor 11-mosdegree m11md
−12 Minor 8-mosdegree m8md
−13 Minor 5-mosdegree m5md
−14 Minor 2-mosdegree m2md
−15 Minor 21-mosdegree m21md
−16 Minor 18-mosdegree m18md
−17 Minor 15-mosdegree m15md
−18 Minor 12-mosdegree m12md
−19 Minor 9-mosdegree m9md
−20 Minor 6-mosdegree m6md
−21 Diminished 3-mosdegree d3md
−22 Diminished 22-mosdegree d22md
−23 Diminished 19-mosdegree d19md
−24 Diminished 16-mosdegree d16md
−25 Diminished 13-mosdegree d13md
−26 Diminished 10-mosdegree d10md
−27 Diminished 7-mosdegree d7md
−28 Diminished 4-mosdegree d4md

Modes

Scale degrees of the modes of 7L 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 19 20 21 22
21|0 1 LssLssLssLssLssLssLsss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Perf.
20|1 4 LssLssLssLssLssLsssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
19|2 7 LssLssLssLssLsssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
18|3 10 LssLssLssLsssLssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
17|4 13 LssLssLsssLssLssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
16|5 16 LssLsssLssLssLssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
15|6 19 LsssLssLssLssLssLssLss Perf. Maj. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
14|7 22 sLssLssLssLssLssLssLss Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
13|8 3 sLssLssLssLssLssLsssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Min. Maj. Perf.
12|9 6 sLssLssLssLssLsssLssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
11|10 9 sLssLssLssLsssLssLssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
10|11 12 sLssLssLsssLssLssLssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
9|12 15 sLssLsssLssLssLssLssLs Perf. Min. Maj. Perf. Min. Maj. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
8|13 18 sLsssLssLssLssLssLssLs Perf. Min. Maj. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
7|14 21 ssLssLssLssLssLssLssLs Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Maj. Perf.
6|15 2 ssLssLssLssLssLssLsssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Perf. Min. Min. Perf.
5|16 5 ssLssLssLssLssLsssLssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Perf. Min. Min. Perf.
4|17 8 ssLssLssLssLsssLssLssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
3|18 11 ssLssLssLsssLssLssLssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
2|19 14 ssLssLsssLssLssLssLssL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
1|20 17 ssLsssLssLssLssLssLssL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
0|21 20 sssLssLssLssLssLssLssL Perf. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.

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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