9L 9s

Revision as of 01:55, 21 September 2024 by BudjarnLambeth (talk | contribs) (Add scale tree)

9L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 9 small steps, with a period of 1 large step and 1 small step that repeats every 133.3 ¢, or 9 times every octave. Generators that produce this scale range from 66.7 ¢ to 133.3 ¢, or from 0 ¢ to 66.7 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

↖ 8L 8s ↑ 9L 8s 10L 8s ↗
← 8L 9s 9L 9s 10L 9s →
↙ 8L 10s ↓ 9L 10s 10L 10s ↘
Scale structure
Step pattern LsLsLsLsLsLsLsLsLs
sLsLsLsLsLsLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 1\9 (133.3 ¢)
Generator size
Bright 1\18 to 1\9 (66.7 ¢ to 133.3 ¢)
Dark 0\9 to 1\18 (0.0 ¢ to 66.7 ¢)
Related MOS scales
Parent none
Sister 9L 9s (self)
Daughters 18L 9s, 9L 18s
Neutralized 18edo
2-Flought 27L 9s, 9L 27s
Equal tunings
Equalized (L:s = 1:1) 1\18 (66.7 ¢)
Supersoft (L:s = 4:3) 4\63 (76.2 ¢)
Soft (L:s = 3:2) 3\45 (80.0 ¢)
Semisoft (L:s = 5:3) 5\72 (83.3 ¢)
Basic (L:s = 2:1) 2\27 (88.9 ¢)
Semihard (L:s = 5:2) 5\63 (95.2 ¢)
Hard (L:s = 3:1) 3\36 (100.0 ¢)
Superhard (L:s = 4:1) 4\45 (106.7 ¢)
Collapsed (L:s = 1:0) 1\9 (133.3 ¢)
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Modes

Modes of 9L 9s
UDP Cyclic
order
Step
pattern
9|0(9) 1 LsLsLsLsLsLsLsLsLs
0|9(9) 2 sLsLsLsLsLsLsLsLsL

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 9L 9s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\18 66.667 66.667 1:1 1.000 Equalized 9L 9s
6\99 72.727 60.606 6:5 1.200
5\81 74.074 59.259 5:4 1.250
9\144 75.000 58.333 9:7 1.286
4\63 76.190 57.143 4:3 1.333 Supersoft 9L 9s
11\171 77.193 56.140 11:8 1.375
7\108 77.778 55.556 7:5 1.400
10\153 78.431 54.902 10:7 1.429
3\45 80.000 53.333 3:2 1.500 Soft 9L 9s
11\162 81.481 51.852 11:7 1.571
8\117 82.051 51.282 8:5 1.600
13\189 82.540 50.794 13:8 1.625
5\72 83.333 50.000 5:3 1.667 Semisoft 9L 9s
12\171 84.211 49.123 12:7 1.714
7\99 84.848 48.485 7:4 1.750
9\126 85.714 47.619 9:5 1.800
2\27 88.889 44.444 2:1 2.000 Basic 9L 9s
9\117 92.308 41.026 9:4 2.250
7\90 93.333 40.000 7:3 2.333
12\153 94.118 39.216 12:5 2.400
5\63 95.238 38.095 5:2 2.500 Semihard 9L 9s
13\162 96.296 37.037 13:5 2.600
8\99 96.970 36.364 8:3 2.667
11\135 97.778 35.556 11:4 2.750
3\36 100.000 33.333 3:1 3.000 Hard 9L 9s
10\117 102.564 30.769 10:3 3.333
7\81 103.704 29.630 7:2 3.500
11\126 104.762 28.571 11:3 3.667
4\45 106.667 26.667 4:1 4.000 Superhard 9L 9s
9\99 109.091 24.242 9:2 4.500
5\54 111.111 22.222 5:1 5.000
6\63 114.286 19.048 6:1 6.000
1\9 133.333 0.000 1:0 → ∞ Collapsed 9L 9s
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