13L 10s

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Icon-Todo.png Todo: expand, confirm
Confirm temperaments that correspond with this mos
↖ 12L 9s ↑ 13L 9s 14L 9s ↗
← 12L 10s 13L 10s 14L 10s →
↙ 12L 11s ↓ 13L 11s 14L 11s ↘ 
┌╥╥┬╥┬╥┬╥╥┬╥┬╥┬╥╥┬╥┬╥┬╥┬┐
│║║│║│║│║║│║│║│║║│║│║│║││
│││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLsLLsLsLsLLsLsLsLs
sLsLsLsLLsLsLsLLsLsLsLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 7\23 to 4\13 (365.2¢ to 369.2¢)
Dark 9\13 to 16\23 (830.8¢ to 834.8¢)
TAMNAMS information
Descends from 3L 7s (sephiroid)
Ancestor's step ratio range 3:2 to 2:1 (hyposoft)
Related MOS scales
Parent 10L 3s
Sister 10L 13s
Daughters 23L 13s, 13L 23s
Neutralized 3L 20s
2-Flought 36L 10s, 13L 33s
Equal tunings
Equalized (L:s = 1:1) 7\23 (365.2¢)
Supersoft (L:s = 4:3) 25\82 (365.9¢)
Soft (L:s = 3:2) 18\59 (366.1¢)
Semisoft (L:s = 5:3) 29\95 (366.3¢)
Basic (L:s = 2:1) 11\36 (366.7¢)
Semihard (L:s = 5:2) 26\85 (367.1¢)
Hard (L:s = 3:1) 15\49 (367.3¢)
Superhard (L:s = 4:1) 19\62 (367.7¢)
Collapsed (L:s = 1:0) 4\13 (369.2¢)

13L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 10 small steps, repeating every octave. 13L 10s is a grandchild scale of 3L 7s, expanding it by 13 tones. Generators that produce this scale range from 365.2¢ to 369.2¢, or from 830.8¢ to 834.8¢.

This scale is the quartertone scale of unidec temperament.

Modes

Modes of 13L 10s
UDP Cyclic
order		 Step
pattern
22|0 1 LLsLsLsLLsLsLsLLsLsLsLs
21|1 8 LLsLsLsLLsLsLsLsLLsLsLs
20|2 15 LLsLsLsLsLLsLsLsLLsLsLs
19|3 22 LsLLsLsLsLLsLsLsLLsLsLs
18|4 6 LsLLsLsLsLLsLsLsLsLLsLs
17|5 13 LsLLsLsLsLsLLsLsLsLLsLs
16|6 20 LsLsLLsLsLsLLsLsLsLLsLs
15|7 4 LsLsLLsLsLsLLsLsLsLsLLs
14|8 11 LsLsLLsLsLsLsLLsLsLsLLs
13|9 18 LsLsLsLLsLsLsLLsLsLsLLs
12|10 2 LsLsLsLLsLsLsLLsLsLsLsL
11|11 9 LsLsLsLLsLsLsLsLLsLsLsL
10|12 16 LsLsLsLsLLsLsLsLLsLsLsL
9|13 23 sLLsLsLsLLsLsLsLLsLsLsL
8|14 7 sLLsLsLsLLsLsLsLsLLsLsL
7|15 14 sLLsLsLsLsLLsLsLsLLsLsL
6|16 21 sLsLLsLsLsLLsLsLsLLsLsL
5|17 5 sLsLLsLsLsLLsLsLsLsLLsL
4|18 12 sLsLLsLsLsLsLLsLsLsLLsL
3|19 19 sLsLsLLsLsLsLLsLsLsLLsL
2|20 3 sLsLsLLsLsLsLLsLsLsLsLL
1|21 10 sLsLsLLsLsLsLsLLsLsLsLL
0|22 17 sLsLsLsLLsLsLsLLsLsLsLL

Intervals

Intervals of 13L 10s
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 52.2¢
Major 1-mosstep M1ms L 52.2¢ to 92.3¢
2-mosstep Minor 2-mosstep m2ms L + s 92.3¢ to 104.3¢
Major 2-mosstep M2ms 2L 104.3¢ to 184.6¢
3-mosstep Minor 3-mosstep m3ms L + 2s 92.3¢ to 156.5¢
Major 3-mosstep M3ms 2L + s 156.5¢ to 184.6¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 184.6¢ to 208.7¢
Major 4-mosstep M4ms 3L + s 208.7¢ to 276.9¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 184.6¢ to 260.9¢
Major 5-mosstep M5ms 3L + 2s 260.9¢ to 276.9¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 276.9¢ to 313.0¢
Major 6-mosstep M6ms 4L + 2s 313.0¢ to 369.2¢
7-mosstep Diminished 7-mosstep d7ms 3L + 4s 276.9¢ to 365.2¢
Perfect 7-mosstep P7ms 4L + 3s 365.2¢ to 369.2¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 369.2¢ to 417.4¢
Major 8-mosstep M8ms 5L + 3s 417.4¢ to 461.5¢
9-mosstep Minor 9-mosstep m9ms 5L + 4s 461.5¢ to 469.6¢
Major 9-mosstep M9ms 6L + 3s 469.6¢ to 553.8¢
10-mosstep Minor 10-mosstep m10ms 5L + 5s 461.5¢ to 521.7¢
Major 10-mosstep M10ms 6L + 4s 521.7¢ to 553.8¢
11-mosstep Minor 11-mosstep m11ms 6L + 5s 553.8¢ to 573.9¢
Major 11-mosstep M11ms 7L + 4s 573.9¢ to 646.2¢
12-mosstep Minor 12-mosstep m12ms 6L + 6s 553.8¢ to 626.1¢
Major 12-mosstep M12ms 7L + 5s 626.1¢ to 646.2¢
13-mosstep Minor 13-mosstep m13ms 7L + 6s 646.2¢ to 678.3¢
Major 13-mosstep M13ms 8L + 5s 678.3¢ to 738.5¢
14-mosstep Minor 14-mosstep m14ms 7L + 7s 646.2¢ to 730.4¢
Major 14-mosstep M14ms 8L + 6s 730.4¢ to 738.5¢
15-mosstep Minor 15-mosstep m15ms 8L + 7s 738.5¢ to 782.6¢
Major 15-mosstep M15ms 9L + 6s 782.6¢ to 830.8¢
16-mosstep Perfect 16-mosstep P16ms 9L + 7s 830.8¢ to 834.8¢
Augmented 16-mosstep A16ms 10L + 6s 834.8¢ to 923.1¢
17-mosstep Minor 17-mosstep m17ms 9L + 8s 830.8¢ to 887.0¢
Major 17-mosstep M17ms 10L + 7s 887.0¢ to 923.1¢
18-mosstep Minor 18-mosstep m18ms 10L + 8s 923.1¢ to 939.1¢
Major 18-mosstep M18ms 11L + 7s 939.1¢ to 1015.4¢
19-mosstep Minor 19-mosstep m19ms 10L + 9s 923.1¢ to 991.3¢
Major 19-mosstep M19ms 11L + 8s 991.3¢ to 1015.4¢
20-mosstep Minor 20-mosstep m20ms 11L + 9s 1015.4¢ to 1043.5¢
Major 20-mosstep M20ms 12L + 8s 1043.5¢ to 1107.7¢
21-mosstep Minor 21-mosstep m21ms 11L + 10s 1015.4¢ to 1095.7¢
Major 21-mosstep M21ms 12L + 9s 1095.7¢ to 1107.7¢
22-mosstep Minor 22-mosstep m22ms 12L + 10s 1107.7¢ to 1147.8¢
Major 22-mosstep M22ms 13L + 9s 1147.8¢ to 1200.0¢
23-mosstep Perfect 23-mosstep P23ms 13L + 10s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 13L 10s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
7\23 365.217 834.783 1:1 1.000 Equalized 13L 10s
39\128 365.625 834.375 6:5 1.200
32\105 365.714 834.286 5:4 1.250
57\187 365.775 834.225 9:7 1.286
25\82 365.854 834.146 4:3 1.333 Supersoft 13L 10s
68\223 365.919 834.081 11:8 1.375
43\141 365.957 834.043 7:5 1.400
61\200 366.000 834.000 10:7 1.429
18\59 366.102 833.898 3:2 1.500 Soft 13L 10s
65\213 366.197 833.803 11:7 1.571
47\154 366.234 833.766 8:5 1.600
76\249 366.265 833.735 13:8 1.625
29\95 366.316 833.684 5:3 1.667 Semisoft 13L 10s
69\226 366.372 833.628 12:7 1.714
40\131 366.412 833.588 7:4 1.750
51\167 366.467 833.533 9:5 1.800
11\36 366.667 833.333 2:1 2.000 Basic 13L 10s
Scales with tunings softer than this are proper
48\157 366.879 833.121 9:4 2.250
37\121 366.942 833.058 7:3 2.333
63\206 366.990 833.010 12:5 2.400
26\85 367.059 832.941 5:2 2.500 Semihard 13L 10s
67\219 367.123 832.877 13:5 2.600
41\134 367.164 832.836 8:3 2.667
56\183 367.213 832.787 11:4 2.750
15\49 367.347 832.653 3:1 3.000 Hard 13L 10s
49\160 367.500 832.500 10:3 3.333
34\111 367.568 832.432 7:2 3.500
53\173 367.630 832.370 11:3 3.667
19\62 367.742 832.258 4:1 4.000 Superhard 13L 10s
42\137 367.883 832.117 9:2 4.500
23\75 368.000 832.000 5:1 5.000
27\88 368.182 831.818 6:1 6.000
4\13 369.231 830.769 1:0 → ∞ Collapsed 13L 10s
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