13L 10s

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↖ 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
Related to 3L 7s (sephiroid)
With tunings 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.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

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 ¢

Generator chain

Generator chain of 13L 10s
Bright gens Scale degree Abbrev.
35 Augmented 15-mosdegree A15md
34 Augmented 8-mosdegree A8md
33 Augmented 1-mosdegree A1md
32 Augmented 17-mosdegree A17md
31 Augmented 10-mosdegree A10md
30 Augmented 3-mosdegree A3md
29 Augmented 19-mosdegree A19md
28 Augmented 12-mosdegree A12md
27 Augmented 5-mosdegree A5md
26 Augmented 21-mosdegree A21md
25 Augmented 14-mosdegree A14md
24 Augmented 7-mosdegree A7md
23 Augmented 0-mosdegree A0md
22 Augmented 16-mosdegree A16md
21 Major 9-mosdegree M9md
20 Major 2-mosdegree M2md
19 Major 18-mosdegree M18md
18 Major 11-mosdegree M11md
17 Major 4-mosdegree M4md
16 Major 20-mosdegree M20md
15 Major 13-mosdegree M13md
14 Major 6-mosdegree M6md
13 Major 22-mosdegree M22md
12 Major 15-mosdegree M15md
11 Major 8-mosdegree M8md
10 Major 1-mosdegree M1md
9 Major 17-mosdegree M17md
8 Major 10-mosdegree M10md
7 Major 3-mosdegree M3md
6 Major 19-mosdegree M19md
5 Major 12-mosdegree M12md
4 Major 5-mosdegree M5md
3 Major 21-mosdegree M21md
2 Major 14-mosdegree M14md
1 Perfect 7-mosdegree P7md
0 Perfect 0-mosdegree
Perfect 23-mosdegree		 P0md
P23md
−1 Perfect 16-mosdegree P16md
−2 Minor 9-mosdegree m9md
−3 Minor 2-mosdegree m2md
−4 Minor 18-mosdegree m18md
−5 Minor 11-mosdegree m11md
−6 Minor 4-mosdegree m4md
−7 Minor 20-mosdegree m20md
−8 Minor 13-mosdegree m13md
−9 Minor 6-mosdegree m6md
−10 Minor 22-mosdegree m22md
−11 Minor 15-mosdegree m15md
−12 Minor 8-mosdegree m8md
−13 Minor 1-mosdegree m1md
−14 Minor 17-mosdegree m17md
−15 Minor 10-mosdegree m10md
−16 Minor 3-mosdegree m3md
−17 Minor 19-mosdegree m19md
−18 Minor 12-mosdegree m12md
−19 Minor 5-mosdegree m5md
−20 Minor 21-mosdegree m21md
−21 Minor 14-mosdegree m14md
−22 Diminished 7-mosdegree d7md
−23 Diminished 23-mosdegree d23md
−24 Diminished 16-mosdegree d16md
−25 Diminished 9-mosdegree d9md
−26 Diminished 2-mosdegree d2md
−27 Diminished 18-mosdegree d18md
−28 Diminished 11-mosdegree d11md
−29 Diminished 4-mosdegree d4md
−30 Diminished 20-mosdegree d20md
−31 Diminished 13-mosdegree d13md
−32 Diminished 6-mosdegree d6md
−33 Diminished 22-mosdegree d22md
−34 Diminished 15-mosdegree d15md
−35 Diminished 8-mosdegree d8md

Modes

Scale degrees of the modes of 13L 10s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
22|0 1 LLsLsLsLLsLsLsLLsLsLsLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
21|1 8 LLsLsLsLLsLsLsLsLLsLsLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
20|2 15 LLsLsLsLsLLsLsLsLLsLsLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
19|3 22 LsLLsLsLsLLsLsLsLLsLsLs Perf. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
18|4 6 LsLLsLsLsLLsLsLsLsLLsLs Perf. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Min. Maj. Maj. Maj. Maj. Perf.
17|5 13 LsLLsLsLsLsLLsLsLsLLsLs Perf. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Min. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Min. Maj. Maj. Maj. Maj. Perf.
16|6 20 LsLsLLsLsLsLLsLsLsLLsLs Perf. Maj. Min. Maj. Min. Maj. Maj. Perf. Maj. Min. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Min. Maj. Maj. Maj. Maj. Perf.
15|7 4 LsLsLLsLsLsLLsLsLsLsLLs Perf. Maj. Min. Maj. Min. Maj. Maj. Perf. Maj. Min. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Min. Maj. Min. Maj. Maj. Perf.
14|8 11 LsLsLLsLsLsLsLLsLsLsLLs Perf. Maj. Min. Maj. Min. Maj. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Maj. Perf. Maj. Min. Maj. Min. Maj. Maj. Perf.
13|9 18 LsLsLsLLsLsLsLLsLsLsLLs Perf. Maj. Min. Maj. Min. Maj. Min. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Maj. Perf. Maj. Min. Maj. Min. Maj. Maj. Perf.
12|10 2 LsLsLsLLsLsLsLLsLsLsLsL Perf. Maj. Min. Maj. Min. Maj. Min. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Perf.
11|11 9 LsLsLsLLsLsLsLsLLsLsLsL Perf. Maj. Min. Maj. Min. Maj. Min. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Maj. Min. Maj. Min. Maj. Min. Perf.
10|12 16 LsLsLsLsLLsLsLsLLsLsLsL Perf. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Maj. Min. Maj. Min. Maj. Min. Perf.
9|13 23 sLLsLsLsLLsLsLsLLsLsLsL Perf. Min. Min. Maj. Min. Maj. Min. Perf. Min. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Maj. Min. Maj. Min. Maj. Min. Perf.
8|14 7 sLLsLsLsLLsLsLsLsLLsLsL Perf. Min. Min. Maj. Min. Maj. Min. Perf. Min. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Min. Maj. Min. Maj. Min. Perf.
7|15 14 sLLsLsLsLsLLsLsLsLLsLsL Perf. Min. Min. Maj. Min. Maj. Min. Perf. Min. Min. Min. Min. Maj. Min. Maj. Min. Perf. Min. Min. Maj. Min. Maj. Min. Perf.
6|16 21 sLsLLsLsLsLLsLsLsLLsLsL Perf. Min. Min. Min. Min. Maj. Min. Perf. Min. Min. Min. Min. Maj. Min. Maj. Min. Perf. Min. Min. Maj. Min. Maj. Min. Perf.
5|17 5 sLsLLsLsLsLLsLsLsLsLLsL Perf. Min. Min. Min. Min. Maj. Min. Perf. Min. Min. Min. Min. Maj. Min. Maj. Min. Perf. Min. Min. Min. Min. Maj. Min. Perf.
4|18 12 sLsLLsLsLsLsLLsLsLsLLsL Perf. Min. Min. Min. Min. Maj. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Perf. Min. Min. Min. Min. Maj. Min. Perf.
3|19 19 sLsLsLLsLsLsLLsLsLsLLsL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Perf. Min. Min. Min. Min. Maj. Min. Perf.
2|20 3 sLsLsLLsLsLsLLsLsLsLsLL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
1|21 10 sLsLsLLsLsLsLsLLsLsLsLL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
0|22 17 sLsLsLsLLsLsLsLLsLsLsLL Perf. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.

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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