7L 8s

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↖ 6L 7s ↑ 7L 7s 8L 7s ↗
← 6L 8s 7L 8s 8L 8s →
↙ 6L 9s ↓ 7L 9s 8L 9s ↘ 
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Scale structure
Step pattern LsLsLsLsLsLsLss
ssLsLsLsLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 2\15 to 1\7 (160.0 ¢ to 171.4 ¢)
Dark 6\7 to 13\15 (1028.6 ¢ to 1040.0 ¢)
TAMNAMS information
Related to 7L 1s (pine)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 7L 1s
Sister 8L 7s
Daughters 15L 7s, 7L 15s
Neutralized 14L 1s
2-Flought 22L 8s, 7L 23s
Equal tunings
Equalized (L:s = 1:1) 2\15 (160.0 ¢)
Supersoft (L:s = 4:3) 7\52 (161.5 ¢)
Soft (L:s = 3:2) 5\37 (162.2 ¢)
Semisoft (L:s = 5:3) 8\59 (162.7 ¢)
Basic (L:s = 2:1) 3\22 (163.6 ¢)
Semihard (L:s = 5:2) 7\51 (164.7 ¢)
Hard (L:s = 3:1) 4\29 (165.5 ¢)
Superhard (L:s = 4:1) 5\36 (166.7 ¢)
Collapsed (L:s = 1:0) 1\7 (171.4 ¢)

7L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 8 small steps, repeating every octave. 7L 8s is a child scale of 7L 1s, expanding it by 7 tones. Generators that produce this scale range from 160 ¢ to 171.4 ¢, or from 1028.6 ¢ to 1040 ¢.

It is notable for supporting Porcupine, of the porcupine family.

Name

Leriendil uses the name "roklotic" for 7L 8s, due to its similarity to the Roklotian scale used in Famanan music theory.

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 8s
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 80.0 ¢
Major 1-mosstep M1ms L 80.0 ¢ to 171.4 ¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0 ¢ to 160.0 ¢
Perfect 2-mosstep P2ms L + s 160.0 ¢ to 171.4 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 171.4 ¢ to 240.0 ¢
Major 3-mosstep M3ms 2L + s 240.0 ¢ to 342.9 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 171.4 ¢ to 320.0 ¢
Major 4-mosstep M4ms 2L + 2s 320.0 ¢ to 342.9 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 342.9 ¢ to 400.0 ¢
Major 5-mosstep M5ms 3L + 2s 400.0 ¢ to 514.3 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 342.9 ¢ to 480.0 ¢
Major 6-mosstep M6ms 3L + 3s 480.0 ¢ to 514.3 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 514.3 ¢ to 560.0 ¢
Major 7-mosstep M7ms 4L + 3s 560.0 ¢ to 685.7 ¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 514.3 ¢ to 640.0 ¢
Major 8-mosstep M8ms 4L + 4s 640.0 ¢ to 685.7 ¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 685.7 ¢ to 720.0 ¢
Major 9-mosstep M9ms 5L + 4s 720.0 ¢ to 857.1 ¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 685.7 ¢ to 800.0 ¢
Major 10-mosstep M10ms 5L + 5s 800.0 ¢ to 857.1 ¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 857.1 ¢ to 880.0 ¢
Major 11-mosstep M11ms 6L + 5s 880.0 ¢ to 1028.6 ¢
12-mosstep Minor 12-mosstep m12ms 5L + 7s 857.1 ¢ to 960.0 ¢
Major 12-mosstep M12ms 6L + 6s 960.0 ¢ to 1028.6 ¢
13-mosstep Perfect 13-mosstep P13ms 6L + 7s 1028.6 ¢ to 1040.0 ¢
Augmented 13-mosstep A13ms 7L + 6s 1040.0 ¢ to 1200.0 ¢
14-mosstep Minor 14-mosstep m14ms 6L + 8s 1028.6 ¢ to 1120.0 ¢
Major 14-mosstep M14ms 7L + 7s 1120.0 ¢ to 1200.0 ¢
15-mosstep Perfect 15-mosstep P15ms 7L + 8s 1200.0 ¢

Generator chain

Generator chain of 7L 8s
Bright gens Scale degree Abbrev.
21 Augmented 12-mosdegree A12md
20 Augmented 10-mosdegree A10md
19 Augmented 8-mosdegree A8md
18 Augmented 6-mosdegree A6md
17 Augmented 4-mosdegree A4md
16 Augmented 2-mosdegree A2md
15 Augmented 0-mosdegree A0md
14 Augmented 13-mosdegree A13md
13 Major 11-mosdegree M11md
12 Major 9-mosdegree M9md
11 Major 7-mosdegree M7md
10 Major 5-mosdegree M5md
9 Major 3-mosdegree M3md
8 Major 1-mosdegree M1md
7 Major 14-mosdegree M14md
6 Major 12-mosdegree M12md
5 Major 10-mosdegree M10md
4 Major 8-mosdegree M8md
3 Major 6-mosdegree M6md
2 Major 4-mosdegree M4md
1 Perfect 2-mosdegree P2md
0 Perfect 0-mosdegree
Perfect 15-mosdegree		 P0md
P15md
−1 Perfect 13-mosdegree P13md
−2 Minor 11-mosdegree m11md
−3 Minor 9-mosdegree m9md
−4 Minor 7-mosdegree m7md
−5 Minor 5-mosdegree m5md
−6 Minor 3-mosdegree m3md
−7 Minor 1-mosdegree m1md
−8 Minor 14-mosdegree m14md
−9 Minor 12-mosdegree m12md
−10 Minor 10-mosdegree m10md
−11 Minor 8-mosdegree m8md
−12 Minor 6-mosdegree m6md
−13 Minor 4-mosdegree m4md
−14 Diminished 2-mosdegree d2md
−15 Diminished 15-mosdegree d15md
−16 Diminished 13-mosdegree d13md
−17 Diminished 11-mosdegree d11md
−18 Diminished 9-mosdegree d9md
−19 Diminished 7-mosdegree d7md
−20 Diminished 5-mosdegree d5md
−21 Diminished 3-mosdegree d3md

Modes

Scale degrees of the modes of 7L 8s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
14|0 1 LsLsLsLsLsLsLss Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Perf.
13|1 3 LsLsLsLsLsLssLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
12|2 5 LsLsLsLsLssLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Perf.
11|3 7 LsLsLsLssLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
10|4 9 LsLsLssLsLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
9|5 11 LsLssLsLsLsLsLs Perf. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
8|6 13 LssLsLsLsLsLsLs Perf. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
7|7 15 sLsLsLsLsLsLsLs Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
6|8 2 sLsLsLsLsLsLssL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Perf.
5|9 4 sLsLsLsLsLssLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Min. Perf. Min. Perf.
4|10 6 sLsLsLsLssLsLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Min. Min. Min. Perf. Min. Perf.
3|11 8 sLsLsLssLsLsLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
2|12 10 sLsLssLsLsLsLsL Perf. Min. Perf. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
1|13 12 sLssLsLsLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
0|14 14 ssLsLsLsLsLsLsL Perf. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.

Scale tree

Icon-Todo.png Todo: complete table

There was previously octachord info in the old scale tree, in the form of the step pattern LsLsLsL. Please add it to the new scale tree.

Scale tree and tuning spectrum of 7L 8s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\15 160.000 1040.000 1:1 1.000 Equalized 7L 8s
13\97 160.825 1039.175 7:6 1.167
11\82 160.976 1039.024 6:5 1.200
20\149 161.074 1038.926 11:9 1.222
9\67 161.194 1038.806 5:4 1.250
25\186 161.290 1038.710 14:11 1.273
16\119 161.345 1038.655 9:7 1.286
23\171 161.404 1038.596 13:10 1.300
7\52 161.538 1038.462 4:3 1.333 Supersoft 7L 8s
26\193 161.658 1038.342 15:11 1.364
19\141 161.702 1038.298 11:8 1.375
31\230 161.739 1038.261 18:13 1.385
12\89 161.798 1038.202 7:5 1.400
29\215 161.860 1038.140 17:12 1.417
17\126 161.905 1038.095 10:7 1.429
22\163 161.963 1038.037 13:9 1.444
5\37 162.162 1037.838 3:2 1.500 Soft 7L 8s
Optimal rank range (L/s = 3/2) porcupine
23\170 162.353 1037.647 14:9 1.556
18\133 162.406 1037.594 11:7 1.571
31\229 162.445 1037.555 19:12 1.583
13\96 162.500 1037.500 8:5 1.600
34\251 162.550 1037.450 21:13 1.615
21\155 162.581 1037.419 13:8 1.625 Golden porcupine L/s = φ
29\214 162.617 1037.383 18:11 1.636
8\59 162.712 1037.288 5:3 1.667 Semisoft 7L 8s
27\199 162.814 1037.186 17:10 1.700
19\140 162.857 1037.143 12:7 1.714
30\221 162.896 1037.104 19:11 1.727
11\81 162.963 1037.037 7:4 1.750
25\184 163.043 1036.957 16:9 1.778
14\103 163.107 1036.893 9:5 1.800
17\125 163.200 1036.800 11:6 1.833
3\22 163.636 1036.364 2:1 2.000 Basic 7L 8s
Scales with tunings softer than this are proper
16\117 164.103 1035.897 11:5 2.200
13\95 164.211 1035.789 9:4 2.250
23\168 164.286 1035.714 16:7 2.286
10\73 164.384 1035.616 7:3 2.333
27\197 164.467 1035.533 19:8 2.375
17\124 164.516 1035.484 12:5 2.400
24\175 164.571 1035.429 17:7 2.429
7\51 164.706 1035.294 5:2 2.500 Semihard 7L 8s
25\182 164.835 1035.165 18:7 2.571
18\131 164.885 1035.115 13:5 2.600
29\211 164.929 1035.071 21:8 2.625
11\80 165.000 1035.000 8:3 2.667
26\189 165.079 1034.921 19:7 2.714
15\109 165.138 1034.862 11:4 2.750
19\138 165.217 1034.783 14:5 2.800
4\29 165.517 1034.483 3:1 3.000 Hard 7L 8s
17\123 165.854 1034.146 13:4 3.250
13\94 165.957 1034.043 10:3 3.333
22\159 166.038 1033.962 17:5 3.400
9\65 166.154 1033.846 7:2 3.500
23\166 166.265 1033.735 18:5 3.600
14\101 166.337 1033.663 11:3 3.667
19\137 166.423 1033.577 15:4 3.750
5\36 166.667 1033.333 4:1 4.000 Superhard 7L 8s
16\115 166.957 1033.043 13:3 4.333
11\79 167.089 1032.911 9:2 4.500
17\122 167.213 1032.787 14:3 4.667
6\43 167.442 1032.558 5:1 5.000
13\93 167.742 1032.258 11:2 5.500
7\50 168.000 1032.000 6:1 6.000
8\57 168.421 1031.579 7:1 7.000
1\7 171.429 1028.571 1:0 → ∞ Collapsed 7L 8s
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