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10L 13s

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10L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 13 small steps, repeating every octave. 10L 13s is a grandchild scale of 3L 7s, expanding it by 13 tones. Generators that produce this scale range from 834.8 ¢ to 840 ¢, or from 360 ¢ to 365.2 ¢.

↖ 9L 12s ↑ 10L 12s 11L 12s ↗
← 9L 13s 10L 13s 11L 13s →
↙ 9L 14s ↓ 10L 14s 11L 14s ↘
Scale structure
Step pattern LsLsLsLssLsLsLssLsLsLss
ssLsLsLssLsLsLssLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 16\23 to 7\10 (834.8 ¢ to 840.0 ¢)
Dark 3\10 to 7\23 (360.0 ¢ to 365.2 ¢)
TAMNAMS information
Related to 3L 7s (sephiroid)
With tunings 1:1 to 3:2 (soft)
Related MOS scales
Parent 10L 3s
Sister 13L 10s
Daughters 23L 10s, 10L 23s
Neutralized 20L 3s
2-Flought 33L 13s, 10L 36s
Equal tunings
Equalized (L:s = 1:1) 16\23 (834.8 ¢)
Supersoft (L:s = 4:3) 55\79 (835.4 ¢)
Soft (L:s = 3:2) 39\56 (835.7 ¢)
Semisoft (L:s = 5:3) 62\89 (836.0 ¢)
Basic (L:s = 2:1) 23\33 (836.4 ¢)
Semihard (L:s = 5:2) 53\76 (836.8 ¢)
Hard (L:s = 3:1) 30\43 (837.2 ¢)
Superhard (L:s = 4:1) 37\53 (837.7 ¢)
Collapsed (L:s = 1:0) 7\10 (840.0 ¢)
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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 10L 13s
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 120.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 104.3 ¢
Major 2-mosstep M2ms L + s 104.3 ¢ to 120.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 120.0 ¢ to 156.5 ¢
Major 3-mosstep M3ms 2L + s 156.5 ¢ to 240.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 120.0 ¢ to 208.7 ¢
Major 4-mosstep M4ms 2L + 2s 208.7 ¢ to 240.0 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 240.0 ¢ to 260.9 ¢
Major 5-mosstep M5ms 3L + 2s 260.9 ¢ to 360.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 240.0 ¢ to 313.0 ¢
Major 6-mosstep M6ms 3L + 3s 313.0 ¢ to 360.0 ¢
7-mosstep Perfect 7-mosstep P7ms 3L + 4s 360.0 ¢ to 365.2 ¢
Augmented 7-mosstep A7ms 4L + 3s 365.2 ¢ to 480.0 ¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 360.0 ¢ to 417.4 ¢
Major 8-mosstep M8ms 4L + 4s 417.4 ¢ to 480.0 ¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 360.0 ¢ to 469.6 ¢
Major 9-mosstep M9ms 4L + 5s 469.6 ¢ to 480.0 ¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 480.0 ¢ to 521.7 ¢
Major 10-mosstep M10ms 5L + 5s 521.7 ¢ to 600.0 ¢
11-mosstep Minor 11-mosstep m11ms 4L + 7s 480.0 ¢ to 573.9 ¢
Major 11-mosstep M11ms 5L + 6s 573.9 ¢ to 600.0 ¢
12-mosstep Minor 12-mosstep m12ms 5L + 7s 600.0 ¢ to 626.1 ¢
Major 12-mosstep M12ms 6L + 6s 626.1 ¢ to 720.0 ¢
13-mosstep Minor 13-mosstep m13ms 5L + 8s 600.0 ¢ to 678.3 ¢
Major 13-mosstep M13ms 6L + 7s 678.3 ¢ to 720.0 ¢
14-mosstep Minor 14-mosstep m14ms 6L + 8s 720.0 ¢ to 730.4 ¢
Major 14-mosstep M14ms 7L + 7s 730.4 ¢ to 840.0 ¢
15-mosstep Minor 15-mosstep m15ms 6L + 9s 720.0 ¢ to 782.6 ¢
Major 15-mosstep M15ms 7L + 8s 782.6 ¢ to 840.0 ¢
16-mosstep Diminished 16-mosstep d16ms 6L + 10s 720.0 ¢ to 834.8 ¢
Perfect 16-mosstep P16ms 7L + 9s 834.8 ¢ to 840.0 ¢
17-mosstep Minor 17-mosstep m17ms 7L + 10s 840.0 ¢ to 887.0 ¢
Major 17-mosstep M17ms 8L + 9s 887.0 ¢ to 960.0 ¢
18-mosstep Minor 18-mosstep m18ms 7L + 11s 840.0 ¢ to 939.1 ¢
Major 18-mosstep M18ms 8L + 10s 939.1 ¢ to 960.0 ¢
19-mosstep Minor 19-mosstep m19ms 8L + 11s 960.0 ¢ to 991.3 ¢
Major 19-mosstep M19ms 9L + 10s 991.3 ¢ to 1080.0 ¢
20-mosstep Minor 20-mosstep m20ms 8L + 12s 960.0 ¢ to 1043.5 ¢
Major 20-mosstep M20ms 9L + 11s 1043.5 ¢ to 1080.0 ¢
21-mosstep Minor 21-mosstep m21ms 9L + 12s 1080.0 ¢ to 1095.7 ¢
Major 21-mosstep M21ms 10L + 11s 1095.7 ¢ to 1200.0 ¢
22-mosstep Minor 22-mosstep m22ms 9L + 13s 1080.0 ¢ to 1147.8 ¢
Major 22-mosstep M22ms 10L + 12s 1147.8 ¢ to 1200.0 ¢
23-mosstep Perfect 23-mosstep P23ms 10L + 13s 1200.0 ¢

Generator chain

Generator chain of 10L 13s
Bright gens Scale degree Abbrev.
32 Augmented 6-mosdegree A6md
31 Augmented 13-mosdegree A13md
30 Augmented 20-mosdegree A20md
29 Augmented 4-mosdegree A4md
28 Augmented 11-mosdegree A11md
27 Augmented 18-mosdegree A18md
26 Augmented 2-mosdegree A2md
25 Augmented 9-mosdegree A9md
24 Augmented 16-mosdegree A16md
23 Augmented 0-mosdegree A0md
22 Augmented 7-mosdegree A7md
21 Major 14-mosdegree M14md
20 Major 21-mosdegree M21md
19 Major 5-mosdegree M5md
18 Major 12-mosdegree M12md
17 Major 19-mosdegree M19md
16 Major 3-mosdegree M3md
15 Major 10-mosdegree M10md
14 Major 17-mosdegree M17md
13 Major 1-mosdegree M1md
12 Major 8-mosdegree M8md
11 Major 15-mosdegree M15md
10 Major 22-mosdegree M22md
9 Major 6-mosdegree M6md
8 Major 13-mosdegree M13md
7 Major 20-mosdegree M20md
6 Major 4-mosdegree M4md
5 Major 11-mosdegree M11md
4 Major 18-mosdegree M18md
3 Major 2-mosdegree M2md
2 Major 9-mosdegree M9md
1 Perfect 16-mosdegree P16md
0 Perfect 0-mosdegree
Perfect 23-mosdegree		 P0md
P23md
−1 Perfect 7-mosdegree P7md
−2 Minor 14-mosdegree m14md
−3 Minor 21-mosdegree m21md
−4 Minor 5-mosdegree m5md
−5 Minor 12-mosdegree m12md
−6 Minor 19-mosdegree m19md
−7 Minor 3-mosdegree m3md
−8 Minor 10-mosdegree m10md
−9 Minor 17-mosdegree m17md
−10 Minor 1-mosdegree m1md
−11 Minor 8-mosdegree m8md
−12 Minor 15-mosdegree m15md
−13 Minor 22-mosdegree m22md
−14 Minor 6-mosdegree m6md
−15 Minor 13-mosdegree m13md
−16 Minor 20-mosdegree m20md
−17 Minor 4-mosdegree m4md
−18 Minor 11-mosdegree m11md
−19 Minor 18-mosdegree m18md
−20 Minor 2-mosdegree m2md
−21 Minor 9-mosdegree m9md
−22 Diminished 16-mosdegree d16md
−23 Diminished 23-mosdegree d23md
−24 Diminished 7-mosdegree d7md
−25 Diminished 14-mosdegree d14md
−26 Diminished 21-mosdegree d21md
−27 Diminished 5-mosdegree d5md
−28 Diminished 12-mosdegree d12md
−29 Diminished 19-mosdegree d19md
−30 Diminished 3-mosdegree d3md
−31 Diminished 10-mosdegree d10md
−32 Diminished 17-mosdegree d17md

Modes

Scale degrees of the modes of 10L 13s
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 LsLsLsLssLsLsLssLsLsLss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
21|1 17 LsLsLssLsLsLsLssLsLsLss 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 10 LsLsLssLsLsLssLsLsLsLss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
19|3 3 LsLsLssLsLsLssLsLsLssLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf.
18|4 19 LsLssLsLsLsLssLsLsLssLs Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf.
17|5 12 LsLssLsLsLssLsLsLsLssLs Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf.
16|6 5 LsLssLsLsLssLsLsLssLsLs Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Perf.
15|7 21 LssLsLsLsLssLsLsLssLsLs Perf. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Perf.
14|8 14 LssLsLsLssLsLsLsLssLsLs Perf. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Perf.
13|9 7 LssLsLsLssLsLsLssLsLsLs Perf. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Perf.
12|10 23 sLsLsLsLssLsLsLssLsLsLs Perf. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Perf.
11|11 16 sLsLsLssLsLsLsLssLsLsLs Perf. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Perf.
10|12 9 sLsLsLssLsLsLssLsLsLsLs Perf. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Perf.
9|13 2 sLsLsLssLsLsLssLsLsLssL Perf. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Min. Perf. Min. Maj. Min. Maj. Min. Min. Perf.
8|14 18 sLsLssLsLsLsLssLsLsLssL Perf. Min. Maj. Min. Maj. Min. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Min. Perf. Min. Maj. Min. Maj. Min. Min. Perf.
7|15 11 sLsLssLsLsLssLsLsLsLssL Perf. Min. Maj. Min. Maj. Min. Min. Perf. Min. Maj. Min. Maj. Min. Min. Min. Min. Perf. Min. Maj. Min. Maj. Min. Min. Perf.
6|16 4 sLsLssLsLsLssLsLsLssLsL Perf. Min. Maj. Min. Maj. Min. Min. Perf. Min. Maj. Min. Maj. Min. Min. Min. Min. Perf. Min. Maj. Min. Min. Min. Min. Perf.
5|17 20 sLssLsLsLsLssLsLsLssLsL Perf. Min. Maj. Min. Min. Min. Min. Perf. Min. Maj. Min. Maj. Min. Min. Min. Min. Perf. Min. Maj. Min. Min. Min. Min. Perf.
4|18 13 sLssLsLsLssLsLsLsLssLsL Perf. Min. Maj. Min. Min. Min. Min. Perf. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Maj. Min. Min. Min. Min. Perf.
3|19 6 sLssLsLsLssLsLsLssLsLsL Perf. Min. Maj. Min. Min. Min. Min. Perf. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
2|20 22 ssLsLsLsLssLsLsLssLsLsL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Perf.
1|21 15 ssLsLsLssLsLsLsLssLsLsL 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 8 ssLsLsLssLsLsLssLsLsLsL Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 10L 13s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
16\23 834.783 365.217 1:1 1.000 Equalized 10L 13s
87\125 835.200 364.800 6:5 1.200
71\102 835.294 364.706 5:4 1.250
126\181 835.359 364.641 9:7 1.286
55\79 835.443 364.557 4:3 1.333 Supersoft 10L 13s
149\214 835.514 364.486 11:8 1.375
94\135 835.556 364.444 7:5 1.400
133\191 835.602 364.398 10:7 1.429
39\56 835.714 364.286 3:2 1.500 Soft 10L 13s
140\201 835.821 364.179 11:7 1.571
101\145 835.862 364.138 8:5 1.600
163\234 835.897 364.103 13:8 1.625
62\89 835.955 364.045 5:3 1.667 Semisoft 10L 13s
147\211 836.019 363.981 12:7 1.714
85\122 836.066 363.934 7:4 1.750
108\155 836.129 363.871 9:5 1.800
23\33 836.364 363.636 2:1 2.000 Basic 10L 13s
Scales with tunings softer than this are proper
99\142 836.620 363.380 9:4 2.250
76\109 836.697 363.303 7:3 2.333
129\185 836.757 363.243 12:5 2.400
53\76 836.842 363.158 5:2 2.500 Semihard 10L 13s
136\195 836.923 363.077 13:5 2.600
83\119 836.975 363.025 8:3 2.667
113\162 837.037 362.963 11:4 2.750
30\43 837.209 362.791 3:1 3.000 Hard 10L 13s
97\139 837.410 362.590 10:3 3.333
67\96 837.500 362.500 7:2 3.500
104\149 837.584 362.416 11:3 3.667
37\53 837.736 362.264 4:1 4.000 Superhard 10L 13s
81\116 837.931 362.069 9:2 4.500
44\63 838.095 361.905 5:1 5.000
51\73 838.356 361.644 6:1 6.000
7\10 840.000 360.000 1:0 → ∞ Collapsed 10L 13s
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