13L 4s

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↖ 12L 3s ↑ 13L 3s 14L 3s ↗
← 12L 4s 13L 4s 14L 4s →
↙ 12L 5s ↓ 13L 5s 14L 5s ↘ 
┌╥╥╥╥┬╥╥╥┬╥╥╥┬╥╥╥┬┐
│║║║║│║║║│║║║│║║║││
│││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLsLLLsLLLs
sLLLsLLLsLLLsLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 13\17 to 10\13 (917.6 ¢ to 923.1 ¢)
Dark 3\13 to 4\17 (276.9 ¢ to 282.4 ¢)
TAMNAMS information
Descends from 4L 5s (gramitonic)
Ancestor's step ratio range 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 4L 9s
Sister 4L 13s
Daughters 17L 13s, 13L 17s
Neutralized 9L 8s
2-Flought 30L 4s, 13L 21s
Equal tunings
Equalized (L:s = 1:1) 13\17 (917.6 ¢)
Supersoft (L:s = 4:3) 49\64 (918.8 ¢)
Soft (L:s = 3:2) 36\47 (919.1 ¢)
Semisoft (L:s = 5:3) 59\77 (919.5 ¢)
Basic (L:s = 2:1) 23\30 (920.0 ¢)
Semihard (L:s = 5:2) 56\73 (920.5 ¢)
Hard (L:s = 3:1) 33\43 (920.9 ¢)
Superhard (L:s = 4:1) 43\56 (921.4 ¢)
Collapsed (L:s = 1:0) 10\13 (923.1 ¢)

13L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 4 small steps, repeating every octave. 13L 4s is a grandchild scale of 4L 5s, expanding it by 8 tones. Generators that produce this scale range from 917.6 ¢ to 923.1 ¢, or from 276.9 ¢ to 282.4 ¢.

Modes

Modes of 13L 4s
UDP Cyclic
order		 Step
pattern
16|0 1 LLLLsLLLsLLLsLLLs
15|1 14 LLLsLLLLsLLLsLLLs
14|2 10 LLLsLLLsLLLLsLLLs
13|3 6 LLLsLLLsLLLsLLLLs
12|4 2 LLLsLLLsLLLsLLLsL
11|5 15 LLsLLLLsLLLsLLLsL
10|6 11 LLsLLLsLLLLsLLLsL
9|7 7 LLsLLLsLLLsLLLLsL
8|8 3 LLsLLLsLLLsLLLsLL
7|9 16 LsLLLLsLLLsLLLsLL
6|10 12 LsLLLsLLLLsLLLsLL
5|11 8 LsLLLsLLLsLLLLsLL
4|12 4 LsLLLsLLLsLLLsLLL
3|13 17 sLLLLsLLLsLLLsLLL
2|14 13 sLLLsLLLLsLLLsLLL
1|15 9 sLLLsLLLsLLLLsLLL
0|16 5 sLLLsLLLsLLLsLLLL

Intervals

Intervals of 13L 4s
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 92.3 ¢
2-mosstep Minor 2-mosstep m2ms L + s 92.3 ¢ to 141.2 ¢
Major 2-mosstep M2ms 2L 141.2 ¢ to 184.6 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 184.6 ¢ to 211.8 ¢
Major 3-mosstep M3ms 3L 211.8 ¢ to 276.9 ¢
4-mosstep Perfect 4-mosstep P4ms 3L + s 276.9 ¢ to 282.4 ¢
Augmented 4-mosstep A4ms 4L 282.4 ¢ to 369.2 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 276.9 ¢ to 352.9 ¢
Major 5-mosstep M5ms 4L + s 352.9 ¢ to 369.2 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 369.2 ¢ to 423.5 ¢
Major 6-mosstep M6ms 5L + s 423.5 ¢ to 461.5 ¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 461.5 ¢ to 494.1 ¢
Major 7-mosstep M7ms 6L + s 494.1 ¢ to 553.8 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 553.8 ¢ to 564.7 ¢
Major 8-mosstep M8ms 7L + s 564.7 ¢ to 646.2 ¢
9-mosstep Minor 9-mosstep m9ms 6L + 3s 553.8 ¢ to 635.3 ¢
Major 9-mosstep M9ms 7L + 2s 635.3 ¢ to 646.2 ¢
10-mosstep Minor 10-mosstep m10ms 7L + 3s 646.2 ¢ to 705.9 ¢
Major 10-mosstep M10ms 8L + 2s 705.9 ¢ to 738.5 ¢
11-mosstep Minor 11-mosstep m11ms 8L + 3s 738.5 ¢ to 776.5 ¢
Major 11-mosstep M11ms 9L + 2s 776.5 ¢ to 830.8 ¢
12-mosstep Minor 12-mosstep m12ms 9L + 3s 830.8 ¢ to 847.1 ¢
Major 12-mosstep M12ms 10L + 2s 847.1 ¢ to 923.1 ¢
13-mosstep Diminished 13-mosstep d13ms 9L + 4s 830.8 ¢ to 917.6 ¢
Perfect 13-mosstep P13ms 10L + 3s 917.6 ¢ to 923.1 ¢
14-mosstep Minor 14-mosstep m14ms 10L + 4s 923.1 ¢ to 988.2 ¢
Major 14-mosstep M14ms 11L + 3s 988.2 ¢ to 1015.4 ¢
15-mosstep Minor 15-mosstep m15ms 11L + 4s 1015.4 ¢ to 1058.8 ¢
Major 15-mosstep M15ms 12L + 3s 1058.8 ¢ to 1107.7 ¢
16-mosstep Minor 16-mosstep m16ms 12L + 4s 1107.7 ¢ to 1129.4 ¢
Major 16-mosstep M16ms 13L + 3s 1129.4 ¢ to 1200.0 ¢
17-mosstep Perfect 17-mosstep P17ms 13L + 4s 1200.0 ¢

Scale tree

Icon-Deprecated.png Scale tree is deprecated. Please use Template: MOS tuning spectrum instead.
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 4s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
13\17 917.647 282.353 1:1 1.000 Equalized 13L 4s
75\98 918.367 281.633 6:5 1.200
62\81 918.519 281.481 5:4 1.250
111\145 918.621 281.379 9:7 1.286
49\64 918.750 281.250 4:3 1.333 Supersoft 13L 4s
134\175 918.857 281.143 11:8 1.375
85\111 918.919 281.081 7:5 1.400
121\158 918.987 281.013 10:7 1.429
36\47 919.149 280.851 3:2 1.500 Soft 13L 4s
131\171 919.298 280.702 11:7 1.571
95\124 919.355 280.645 8:5 1.600
154\201 919.403 280.597 13:8 1.625
59\77 919.481 280.519 5:3 1.667 Semisoft 13L 4s
141\184 919.565 280.435 12:7 1.714
82\107 919.626 280.374 7:4 1.750
105\137 919.708 280.292 9:5 1.800
23\30 920.000 280.000 2:1 2.000 Basic 13L 4s
Scales with tunings softer than this are proper
102\133 920.301 279.699 9:4 2.250
79\103 920.388 279.612 7:3 2.333
135\176 920.455 279.545 12:5 2.400
56\73 920.548 279.452 5:2 2.500 Semihard 13L 4s
145\189 920.635 279.365 13:5 2.600
89\116 920.690 279.310 8:3 2.667
122\159 920.755 279.245 11:4 2.750
33\43 920.930 279.070 3:1 3.000 Hard 13L 4s
109\142 921.127 278.873 10:3 3.333
76\99 921.212 278.788 7:2 3.500
119\155 921.290 278.710 11:3 3.667
43\56 921.429 278.571 4:1 4.000 Superhard 13L 4s
96\125 921.600 278.400 9:2 4.500
53\69 921.739 278.261 5:1 5.000
63\82 921.951 278.049 6:1 6.000
10\13 923.077 276.923 1:0 → ∞ Collapsed 13L 4s


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