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7L 8s

Revision as of 01:50, 16 December 2024 by BudjarnLambeth (talk | contribs) (Many minor)

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 ¢.

↖ 6L 7s ↑ 7L 7s 8L 7s ↗
← 6L 8s 7L 8s 8L 8s →
↙ 6L 9s ↓ 7L 9s 8L 9s ↘
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 ¢)
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It is notable for supporting porcupine, of the porcupine family.

Modes

Modes of 7L 8s
UDP Cyclic
order		 Step
pattern
14|0 1 LsLsLsLsLsLsLss
13|1 3 LsLsLsLsLsLssLs
12|2 5 LsLsLsLsLssLsLs
11|3 7 LsLsLsLssLsLsLs
10|4 9 LsLsLssLsLsLsLs
9|5 11 LsLssLsLsLsLsLs
8|6 13 LssLsLsLsLsLsLs
7|7 15 sLsLsLsLsLsLsLs
6|8 2 sLsLsLsLsLsLssL
5|9 4 sLsLsLsLsLssLsL
4|10 6 sLsLsLsLssLsLsL
3|11 8 sLsLsLssLsLsLsL
2|12 10 sLsLssLsLsLsLsL
1|13 12 sLssLsLsLsLsLsL
0|14 14 ssLsLsLsLsLsLsL

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 ¢

Scale tree

  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.
  Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
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 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
11\82 160.976 1039.024 6:5 1.200
9\67 161.194 1038.806 5:4 1.250
16\119 161.345 1038.655 9:7 1.286
7\52 161.538 1038.462 4:3 1.333 Supersoft 7L 8s
19\141 161.702 1038.298 11:8 1.375
12\89 161.798 1038.202 7:5 1.400
17\126 161.905 1038.095 10:7 1.429
5\37 162.162 1037.838 3:2 1.500 Soft 7L 8s
18\133 162.406 1037.594 11:7 1.571
13\96 162.500 1037.500 8:5 1.600
21\155 162.581 1037.419 13:8 1.625
8\59 162.712 1037.288 5:3 1.667 Semisoft 7L 8s
19\140 162.857 1037.143 12:7 1.714
11\81 162.963 1037.037 7:4 1.750
14\103 163.107 1036.893 9:5 1.800
3\22 163.636 1036.364 2:1 2.000 Basic 7L 8s
Scales with tunings softer than this are proper
13\95 164.211 1035.789 9:4 2.250
10\73 164.384 1035.616 7:3 2.333
17\124 164.516 1035.484 12:5 2.400
7\51 164.706 1035.294 5:2 2.500 Semihard 7L 8s
18\131 164.885 1035.115 13:5 2.600
11\80 165.000 1035.000 8:3 2.667
15\109 165.138 1034.862 11:4 2.750
4\29 165.517 1034.483 3:1 3.000 Hard 7L 8s
13\94 165.957 1034.043 10:3 3.333
9\65 166.154 1033.846 7:2 3.500
14\101 166.337 1033.663 11:3 3.667
5\36 166.667 1033.333 4:1 4.000 Superhard 7L 8s
11\79 167.089 1032.911 9:2 4.500
6\43 167.442 1032.558 5:1 5.000
7\50 168.000 1032.000 6:1 6.000
1\7 171.429 1028.571 1:0 → ∞ Collapsed 7L 8s


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