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13L 3s

Revision as of 07:24, 15 December 2024 by BudjarnLambeth (talk | contribs) (== Intervals == {{MOS intervals}})

13L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 3 small steps, repeating every octave. 13L 3s is a grandchild scale of 3L 7s, expanding it by 6 tones. Generators that produce this scale range from 825 ¢ to 830.8 ¢, or from 369.2 ¢ to 375 ¢.

↖ 12L 2s ↑ 13L 2s 14L 2s ↗
← 12L 3s 13L 3s 14L 3s →
↙ 12L 4s ↓ 13L 4s 14L 4s ↘
Scale structure
Step pattern LLLLLsLLLLsLLLLs
sLLLLsLLLLsLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 11\16 to 9\13 (825.0 ¢ to 830.8 ¢)
Dark 4\13 to 5\16 (369.2 ¢ to 375.0 ¢)
TAMNAMS information
Related to 3L 7s (sephiroid)
With tunings 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 3L 10s
Sister 3L 13s
Daughters 16L 13s, 13L 16s
Neutralized 10L 6s
2-Flought 29L 3s, 13L 19s
Equal tunings
Equalized (L:s = 1:1) 11\16 (825.0 ¢)
Supersoft (L:s = 4:3) 42\61 (826.2 ¢)
Soft (L:s = 3:2) 31\45 (826.7 ¢)
Semisoft (L:s = 5:3) 51\74 (827.0 ¢)
Basic (L:s = 2:1) 20\29 (827.6 ¢)
Semihard (L:s = 5:2) 49\71 (828.2 ¢)
Hard (L:s = 3:1) 29\42 (828.6 ¢)
Superhard (L:s = 4:1) 38\55 (829.1 ¢)
Collapsed (L:s = 1:0) 9\13 (830.8 ¢)
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Modes

Modes of 13L 3s
UDP Cyclic
order		 Step
pattern
15|0 1 LLLLLsLLLLsLLLLs
14|1 12 LLLLsLLLLLsLLLLs
13|2 7 LLLLsLLLLsLLLLLs
12|3 2 LLLLsLLLLsLLLLsL
11|4 13 LLLsLLLLLsLLLLsL
10|5 8 LLLsLLLLsLLLLLsL
9|6 3 LLLsLLLLsLLLLsLL
8|7 14 LLsLLLLLsLLLLsLL
7|8 9 LLsLLLLsLLLLLsLL
6|9 4 LLsLLLLsLLLLsLLL
5|10 15 LsLLLLLsLLLLsLLL
4|11 10 LsLLLLsLLLLLsLLL
3|12 5 LsLLLLsLLLLsLLLL
2|13 16 sLLLLLsLLLLsLLLL
1|14 11 sLLLLsLLLLLsLLLL
0|15 6 sLLLLsLLLLsLLLLL

Intervals

Intervals of 13L 3s
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 75.0 ¢
Major 1-mosstep M1ms L 75.0 ¢ to 92.3 ¢
2-mosstep Minor 2-mosstep m2ms L + s 92.3 ¢ to 150.0 ¢
Major 2-mosstep M2ms 2L 150.0 ¢ to 184.6 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 184.6 ¢ to 225.0 ¢
Major 3-mosstep M3ms 3L 225.0 ¢ to 276.9 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 276.9 ¢ to 300.0 ¢
Major 4-mosstep M4ms 4L 300.0 ¢ to 369.2 ¢
5-mosstep Perfect 5-mosstep P5ms 4L + s 369.2 ¢ to 375.0 ¢
Augmented 5-mosstep A5ms 5L 375.0 ¢ to 461.5 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 369.2 ¢ to 450.0 ¢
Major 6-mosstep M6ms 5L + s 450.0 ¢ to 461.5 ¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 461.5 ¢ to 525.0 ¢
Major 7-mosstep M7ms 6L + s 525.0 ¢ to 553.8 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 553.8 ¢ to 600.0 ¢
Major 8-mosstep M8ms 7L + s 600.0 ¢ to 646.2 ¢
9-mosstep Minor 9-mosstep m9ms 7L + 2s 646.2 ¢ to 675.0 ¢
Major 9-mosstep M9ms 8L + s 675.0 ¢ to 738.5 ¢
10-mosstep Minor 10-mosstep m10ms 8L + 2s 738.5 ¢ to 750.0 ¢
Major 10-mosstep M10ms 9L + s 750.0 ¢ to 830.8 ¢
11-mosstep Diminished 11-mosstep d11ms 8L + 3s 738.5 ¢ to 825.0 ¢
Perfect 11-mosstep P11ms 9L + 2s 825.0 ¢ to 830.8 ¢
12-mosstep Minor 12-mosstep m12ms 9L + 3s 830.8 ¢ to 900.0 ¢
Major 12-mosstep M12ms 10L + 2s 900.0 ¢ to 923.1 ¢
13-mosstep Minor 13-mosstep m13ms 10L + 3s 923.1 ¢ to 975.0 ¢
Major 13-mosstep M13ms 11L + 2s 975.0 ¢ to 1015.4 ¢
14-mosstep Minor 14-mosstep m14ms 11L + 3s 1015.4 ¢ to 1050.0 ¢
Major 14-mosstep M14ms 12L + 2s 1050.0 ¢ to 1107.7 ¢
15-mosstep Minor 15-mosstep m15ms 12L + 3s 1107.7 ¢ to 1125.0 ¢
Major 15-mosstep M15ms 13L + 2s 1125.0 ¢ to 1200.0 ¢
16-mosstep Perfect 16-mosstep P16ms 13L + 3s 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 13L 3s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
11\16 825.000 375.000 1:1 1.000 Equalized 13L 3s
64\93 825.806 374.194 6:5 1.200
53\77 825.974 374.026 5:4 1.250
95\138 826.087 373.913 9:7 1.286
42\61 826.230 373.770 4:3 1.333 Supersoft 13L 3s
115\167 826.347 373.653 11:8 1.375
73\106 826.415 373.585 7:5 1.400
104\151 826.490 373.510 10:7 1.429
31\45 826.667 373.333 3:2 1.500 Soft 13L 3s
113\164 826.829 373.171 11:7 1.571
82\119 826.891 373.109 8:5 1.600
133\193 826.943 373.057 13:8 1.625
51\74 827.027 372.973 5:3 1.667 Semisoft 13L 3s
122\177 827.119 372.881 12:7 1.714
71\103 827.184 372.816 7:4 1.750
91\132 827.273 372.727 9:5 1.800
20\29 827.586 372.414 2:1 2.000 Basic 13L 3s
Scales with tunings softer than this are proper
89\129 827.907 372.093 9:4 2.250
69\100 828.000 372.000 7:3 2.333
118\171 828.070 371.930 12:5 2.400
49\71 828.169 371.831 5:2 2.500 Semihard 13L 3s
127\184 828.261 371.739 13:5 2.600
78\113 828.319 371.681 8:3 2.667
107\155 828.387 371.613 11:4 2.750
29\42 828.571 371.429 3:1 3.000 Hard 13L 3s
96\139 828.777 371.223 10:3 3.333
67\97 828.866 371.134 7:2 3.500
105\152 828.947 371.053 11:3 3.667
38\55 829.091 370.909 4:1 4.000 Superhard 13L 3s
85\123 829.268 370.732 9:2 4.500
47\68 829.412 370.588 5:1 5.000
56\81 829.630 370.370 6:1 6.000
9\13 830.769 369.231 1:0 → ∞ Collapsed 13L 3s


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