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8L 9s

Revision as of 00:42, 15 December 2024 by BudjarnLambeth (talk | contribs) (-todo:expand, already stub which is more accurate; add intervals)

8L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 9 small steps, repeating every octave. 8L 9s is a child scale of 8L 1s, expanding it by 8 tones. Generators that produce this scale range from 141.2 ¢ to 150 ¢, or from 1050 ¢ to 1058.8 ¢.

↖ 7L 8s ↑ 8L 8s 9L 8s ↗
← 7L 9s 8L 9s 9L 9s →
↙ 7L 10s ↓ 8L 10s 9L 10s ↘
Scale structure
Step pattern LsLsLsLsLsLsLsLss
ssLsLsLsLsLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 2\17 to 1\8 (141.2 ¢ to 150.0 ¢)
Dark 7\8 to 15\17 (1050.0 ¢ to 1058.8 ¢)
TAMNAMS information
Related to 8L 1s (subneutralic)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 8L 1s
Sister 9L 8s
Daughters 17L 8s, 8L 17s
Neutralized 16L 1s
2-Flought 25L 9s, 8L 26s
Equal tunings
Equalized (L:s = 1:1) 2\17 (141.2 ¢)
Supersoft (L:s = 4:3) 7\59 (142.4 ¢)
Soft (L:s = 3:2) 5\42 (142.9 ¢)
Semisoft (L:s = 5:3) 8\67 (143.3 ¢)
Basic (L:s = 2:1) 3\25 (144.0 ¢)
Semihard (L:s = 5:2) 7\58 (144.8 ¢)
Hard (L:s = 3:1) 4\33 (145.5 ¢)
Superhard (L:s = 4:1) 5\41 (146.3 ¢)
Collapsed (L:s = 1:0) 1\8 (150.0 ¢)
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Modes

Modes of 8L 9s
UDP Cyclic
order		 Step
pattern
16|0 1 LsLsLsLsLsLsLsLss
15|1 3 LsLsLsLsLsLsLssLs
14|2 5 LsLsLsLsLsLssLsLs
13|3 7 LsLsLsLsLssLsLsLs
12|4 9 LsLsLsLssLsLsLsLs
11|5 11 LsLsLssLsLsLsLsLs
10|6 13 LsLssLsLsLsLsLsLs
9|7 15 LssLsLsLsLsLsLsLs
8|8 17 sLsLsLsLsLsLsLsLs
7|9 2 sLsLsLsLsLsLsLssL
6|10 4 sLsLsLsLsLsLssLsL
5|11 6 sLsLsLsLsLssLsLsL
4|12 8 sLsLsLsLssLsLsLsL
3|13 10 sLsLsLssLsLsLsLsL
2|14 12 sLsLssLsLsLsLsLsL
1|15 14 sLssLsLsLsLsLsLsL
0|16 16 ssLsLsLsLsLsLsLsL

Intervals

Intervals of 8L 9s
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 70.6 ¢
Major 1-mosstep M1ms L 70.6 ¢ to 150.0 ¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0 ¢ to 141.2 ¢
Perfect 2-mosstep P2ms L + s 141.2 ¢ to 150.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 150.0 ¢ to 211.8 ¢
Major 3-mosstep M3ms 2L + s 211.8 ¢ to 300.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 150.0 ¢ to 282.4 ¢
Major 4-mosstep M4ms 2L + 2s 282.4 ¢ to 300.0 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 300.0 ¢ to 352.9 ¢
Major 5-mosstep M5ms 3L + 2s 352.9 ¢ to 450.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 300.0 ¢ to 423.5 ¢
Major 6-mosstep M6ms 3L + 3s 423.5 ¢ to 450.0 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 450.0 ¢ to 494.1 ¢
Major 7-mosstep M7ms 4L + 3s 494.1 ¢ to 600.0 ¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 450.0 ¢ to 564.7 ¢
Major 8-mosstep M8ms 4L + 4s 564.7 ¢ to 600.0 ¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 600.0 ¢ to 635.3 ¢
Major 9-mosstep M9ms 5L + 4s 635.3 ¢ to 750.0 ¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 600.0 ¢ to 705.9 ¢
Major 10-mosstep M10ms 5L + 5s 705.9 ¢ to 750.0 ¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 750.0 ¢ to 776.5 ¢
Major 11-mosstep M11ms 6L + 5s 776.5 ¢ to 900.0 ¢
12-mosstep Minor 12-mosstep m12ms 5L + 7s 750.0 ¢ to 847.1 ¢
Major 12-mosstep M12ms 6L + 6s 847.1 ¢ to 900.0 ¢
13-mosstep Minor 13-mosstep m13ms 6L + 7s 900.0 ¢ to 917.6 ¢
Major 13-mosstep M13ms 7L + 6s 917.6 ¢ to 1050.0 ¢
14-mosstep Minor 14-mosstep m14ms 6L + 8s 900.0 ¢ to 988.2 ¢
Major 14-mosstep M14ms 7L + 7s 988.2 ¢ to 1050.0 ¢
15-mosstep Perfect 15-mosstep P15ms 7L + 8s 1050.0 ¢ to 1058.8 ¢
Augmented 15-mosstep A15ms 8L + 7s 1058.8 ¢ to 1200.0 ¢
16-mosstep Minor 16-mosstep m16ms 7L + 9s 1050.0 ¢ to 1129.4 ¢
Major 16-mosstep M16ms 8L + 8s 1129.4 ¢ to 1200.0 ¢
17-mosstep Perfect 17-mosstep P17ms 8L + 9s 1200.0 ¢

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 8L 9s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\17 141.176 1058.824 1:1 1.000 Equalized 8L 9s
11\93 141.935 1058.065 6:5 1.200
9\76 142.105 1057.895 5:4 1.250
16\135 142.222 1057.778 9:7 1.286
7\59 142.373 1057.627 4:3 1.333 Supersoft 8L 9s
19\160 142.500 1057.500 11:8 1.375
12\101 142.574 1057.426 7:5 1.400
17\143 142.657 1057.343 10:7 1.429
5\42 142.857 1057.143 3:2 1.500 Soft 8L 9s
18\151 143.046 1056.954 11:7 1.571
13\109 143.119 1056.881 8:5 1.600
21\176 143.182 1056.818 13:8 1.625
8\67 143.284 1056.716 5:3 1.667 Semisoft 8L 9s
19\159 143.396 1056.604 12:7 1.714
11\92 143.478 1056.522 7:4 1.750
14\117 143.590 1056.410 9:5 1.800
3\25 144.000 1056.000 2:1 2.000 Basic 8L 9s
Scales with tunings softer than this are proper
13\108 144.444 1055.556 9:4 2.250
10\83 144.578 1055.422 7:3 2.333
17\141 144.681 1055.319 12:5 2.400
7\58 144.828 1055.172 5:2 2.500 Semihard 8L 9s
18\149 144.966 1055.034 13:5 2.600
11\91 145.055 1054.945 8:3 2.667
15\124 145.161 1054.839 11:4 2.750
4\33 145.455 1054.545 3:1 3.000 Hard 8L 9s
13\107 145.794 1054.206 10:3 3.333
9\74 145.946 1054.054 7:2 3.500
14\115 146.087 1053.913 11:3 3.667
5\41 146.341 1053.659 4:1 4.000 Superhard 8L 9s
11\90 146.667 1053.333 9:2 4.500
6\49 146.939 1053.061 5:1 5.000
7\57 147.368 1052.632 6:1 6.000
1\8 150.000 1050.000 1:0 → ∞ Collapsed 8L 9s


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