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13L 7s

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13L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 7 small steps, repeating every octave. 13L 7s is a grandchild scale of 6L 1s, expanding it by 13 tones. Generators that produce this scale range from 180 ¢ to 184.6 ¢, or from 1015.4 ¢ to 1020 ¢.

↖ 12L 6s ↑ 13L 6s 14L 6s ↗
← 12L 7s 13L 7s 14L 7s →
↙ 12L 8s ↓ 13L 8s 14L 8s ↘
Scale structure
Step pattern LLsLLsLLsLLsLLsLLsLs
sLsLLsLLsLLsLLsLLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 3\20 to 2\13 (180.0 ¢ to 184.6 ¢)
Dark 11\13 to 17\20 (1015.4 ¢ to 1020.0 ¢)
TAMNAMS information
Related to 6L 1s (archaeotonic)
With tunings 3:2 to 2:1 (hyposoft)
Related MOS scales
Parent 7L 6s
Sister 7L 13s
Daughters 20L 13s, 13L 20s
Neutralized 6L 14s
2-Flought 33L 7s, 13L 27s
Equal tunings
Equalized (L:s = 1:1) 3\20 (180.0 ¢)
Supersoft (L:s = 4:3) 11\73 (180.8 ¢)
Soft (L:s = 3:2) 8\53 (181.1 ¢)
Semisoft (L:s = 5:3) 13\86 (181.4 ¢)
Basic (L:s = 2:1) 5\33 (181.8 ¢)
Semihard (L:s = 5:2) 12\79 (182.3 ¢)
Hard (L:s = 3:1) 7\46 (182.6 ¢)
Superhard (L:s = 4:1) 9\59 (183.1 ¢)
Collapsed (L:s = 1:0) 2\13 (184.6 ¢)
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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 13L 7s
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 60.0 ¢
Major 1-mosstep M1ms L 60.0 ¢ to 92.3 ¢
2-mosstep Minor 2-mosstep m2ms L + s 92.3 ¢ to 120.0 ¢
Major 2-mosstep M2ms 2L 120.0 ¢ to 184.6 ¢
3-mosstep Diminished 3-mosstep d3ms L + 2s 92.3 ¢ to 180.0 ¢
Perfect 3-mosstep P3ms 2L + s 180.0 ¢ to 184.6 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 184.6 ¢ to 240.0 ¢
Major 4-mosstep M4ms 3L + s 240.0 ¢ to 276.9 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 276.9 ¢ to 300.0 ¢
Major 5-mosstep M5ms 4L + s 300.0 ¢ to 369.2 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 276.9 ¢ to 360.0 ¢
Major 6-mosstep M6ms 4L + 2s 360.0 ¢ to 369.2 ¢
7-mosstep Minor 7-mosstep m7ms 4L + 3s 369.2 ¢ to 420.0 ¢
Major 7-mosstep M7ms 5L + 2s 420.0 ¢ to 461.5 ¢
8-mosstep Minor 8-mosstep m8ms 5L + 3s 461.5 ¢ to 480.0 ¢
Major 8-mosstep M8ms 6L + 2s 480.0 ¢ to 553.8 ¢
9-mosstep Minor 9-mosstep m9ms 5L + 4s 461.5 ¢ to 540.0 ¢
Major 9-mosstep M9ms 6L + 3s 540.0 ¢ to 553.8 ¢
10-mosstep Minor 10-mosstep m10ms 6L + 4s 553.8 ¢ to 600.0 ¢
Major 10-mosstep M10ms 7L + 3s 600.0 ¢ to 646.2 ¢
11-mosstep Minor 11-mosstep m11ms 7L + 4s 646.2 ¢ to 660.0 ¢
Major 11-mosstep M11ms 8L + 3s 660.0 ¢ to 738.5 ¢
12-mosstep Minor 12-mosstep m12ms 7L + 5s 646.2 ¢ to 720.0 ¢
Major 12-mosstep M12ms 8L + 4s 720.0 ¢ to 738.5 ¢
13-mosstep Minor 13-mosstep m13ms 8L + 5s 738.5 ¢ to 780.0 ¢
Major 13-mosstep M13ms 9L + 4s 780.0 ¢ to 830.8 ¢
14-mosstep Minor 14-mosstep m14ms 9L + 5s 830.8 ¢ to 840.0 ¢
Major 14-mosstep M14ms 10L + 4s 840.0 ¢ to 923.1 ¢
15-mosstep Minor 15-mosstep m15ms 9L + 6s 830.8 ¢ to 900.0 ¢
Major 15-mosstep M15ms 10L + 5s 900.0 ¢ to 923.1 ¢
16-mosstep Minor 16-mosstep m16ms 10L + 6s 923.1 ¢ to 960.0 ¢
Major 16-mosstep M16ms 11L + 5s 960.0 ¢ to 1015.4 ¢
17-mosstep Perfect 17-mosstep P17ms 11L + 6s 1015.4 ¢ to 1020.0 ¢
Augmented 17-mosstep A17ms 12L + 5s 1020.0 ¢ to 1107.7 ¢
18-mosstep Minor 18-mosstep m18ms 11L + 7s 1015.4 ¢ to 1080.0 ¢
Major 18-mosstep M18ms 12L + 6s 1080.0 ¢ to 1107.7 ¢
19-mosstep Minor 19-mosstep m19ms 12L + 7s 1107.7 ¢ to 1140.0 ¢
Major 19-mosstep M19ms 13L + 6s 1140.0 ¢ to 1200.0 ¢
20-mosstep Perfect 20-mosstep P20ms 13L + 7s 1200.0 ¢

Generator chain

Generator chain of 13L 7s
Bright gens Scale degree Abbrev.
32 Augmented 16-mosdegree A16md
31 Augmented 13-mosdegree A13md
30 Augmented 10-mosdegree A10md
29 Augmented 7-mosdegree A7md
28 Augmented 4-mosdegree A4md
27 Augmented 1-mosdegree A1md
26 Augmented 18-mosdegree A18md
25 Augmented 15-mosdegree A15md
24 Augmented 12-mosdegree A12md
23 Augmented 9-mosdegree A9md
22 Augmented 6-mosdegree A6md
21 Augmented 3-mosdegree A3md
20 Augmented 0-mosdegree A0md
19 Augmented 17-mosdegree A17md
18 Major 14-mosdegree M14md
17 Major 11-mosdegree M11md
16 Major 8-mosdegree M8md
15 Major 5-mosdegree M5md
14 Major 2-mosdegree M2md
13 Major 19-mosdegree M19md
12 Major 16-mosdegree M16md
11 Major 13-mosdegree M13md
10 Major 10-mosdegree M10md
9 Major 7-mosdegree M7md
8 Major 4-mosdegree M4md
7 Major 1-mosdegree M1md
6 Major 18-mosdegree M18md
5 Major 15-mosdegree M15md
4 Major 12-mosdegree M12md
3 Major 9-mosdegree M9md
2 Major 6-mosdegree M6md
1 Perfect 3-mosdegree P3md
0 Perfect 0-mosdegree
Perfect 20-mosdegree		 P0md
P20md
−1 Perfect 17-mosdegree P17md
−2 Minor 14-mosdegree m14md
−3 Minor 11-mosdegree m11md
−4 Minor 8-mosdegree m8md
−5 Minor 5-mosdegree m5md
−6 Minor 2-mosdegree m2md
−7 Minor 19-mosdegree m19md
−8 Minor 16-mosdegree m16md
−9 Minor 13-mosdegree m13md
−10 Minor 10-mosdegree m10md
−11 Minor 7-mosdegree m7md
−12 Minor 4-mosdegree m4md
−13 Minor 1-mosdegree m1md
−14 Minor 18-mosdegree m18md
−15 Minor 15-mosdegree m15md
−16 Minor 12-mosdegree m12md
−17 Minor 9-mosdegree m9md
−18 Minor 6-mosdegree m6md
−19 Diminished 3-mosdegree d3md
−20 Diminished 20-mosdegree d20md
−21 Diminished 17-mosdegree d17md
−22 Diminished 14-mosdegree d14md
−23 Diminished 11-mosdegree d11md
−24 Diminished 8-mosdegree d8md
−25 Diminished 5-mosdegree d5md
−26 Diminished 2-mosdegree d2md
−27 Diminished 19-mosdegree d19md
−28 Diminished 16-mosdegree d16md
−29 Diminished 13-mosdegree d13md
−30 Diminished 10-mosdegree d10md
−31 Diminished 7-mosdegree d7md
−32 Diminished 4-mosdegree d4md

Modes

Scale degrees of the modes of 13L 7s
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
19|0 1 LLsLLsLLsLLsLLsLLsLs Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Perf.
18|1 4 LLsLLsLLsLLsLLsLsLLs Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
17|2 7 LLsLLsLLsLLsLsLLsLLs Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
16|3 10 LLsLLsLLsLsLLsLLsLLs Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
15|4 13 LLsLLsLsLLsLLsLLsLLs Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
14|5 16 LLsLsLLsLLsLLsLLsLLs Perf. Maj. Maj. Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
13|6 19 LsLLsLLsLLsLLsLLsLLs Perf. Maj. Min. Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
12|7 2 LsLLsLLsLLsLLsLLsLsL Perf. Maj. Min. Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Min. Perf.
11|8 5 LsLLsLLsLLsLLsLsLLsL Perf. Maj. Min. Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Min. Perf. Maj. Min. Perf.
10|9 8 LsLLsLLsLLsLsLLsLLsL Perf. Maj. Min. Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Min. Min. Maj. Min. Perf. Maj. Min. Perf.
9|10 11 LsLLsLLsLsLLsLLsLLsL Perf. Maj. Min. Perf. Maj. Min. Maj. Maj. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Perf. Maj. Min. Perf.
8|11 14 LsLLsLsLLsLLsLLsLLsL Perf. Maj. Min. Perf. Maj. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Perf. Maj. Min. Perf.
7|12 17 LsLsLLsLLsLLsLLsLLsL Perf. Maj. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Perf. Maj. Min. Perf.
6|13 20 sLLsLLsLLsLLsLLsLLsL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Perf. Maj. Min. Perf.
5|14 3 sLLsLLsLLsLLsLLsLsLL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Perf. Min. Min. Perf.
4|15 6 sLLsLLsLLsLLsLsLLsLL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Min. Perf. Min. Min. Perf.
3|16 9 sLLsLLsLLsLsLLsLLsLL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
2|17 12 sLLsLLsLsLLsLLsLLsLL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
1|18 15 sLLsLsLLsLLsLLsLLsLL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
0|19 18 sLsLLsLLsLLsLLsLLsLL Perf. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 13L 7s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
3\20 180.000 1020.000 1:1 1.000 Equalized 13L 7s
17\113 180.531 1019.469 6:5 1.200
14\93 180.645 1019.355 5:4 1.250
25\166 180.723 1019.277 9:7 1.286
11\73 180.822 1019.178 4:3 1.333 Supersoft 13L 7s
30\199 180.905 1019.095 11:8 1.375
19\126 180.952 1019.048 7:5 1.400
27\179 181.006 1018.994 10:7 1.429
8\53 181.132 1018.868 3:2 1.500 Soft 13L 7s
29\192 181.250 1018.750 11:7 1.571
21\139 181.295 1018.705 8:5 1.600
34\225 181.333 1018.667 13:8 1.625
13\86 181.395 1018.605 5:3 1.667 Semisoft 13L 7s
31\205 181.463 1018.537 12:7 1.714
18\119 181.513 1018.487 7:4 1.750
23\152 181.579 1018.421 9:5 1.800
5\33 181.818 1018.182 2:1 2.000 Basic 13L 7s
Scales with tunings softer than this are proper
22\145 182.069 1017.931 9:4 2.250
17\112 182.143 1017.857 7:3 2.333
29\191 182.199 1017.801 12:5 2.400
12\79 182.278 1017.722 5:2 2.500 Semihard 13L 7s
31\204 182.353 1017.647 13:5 2.600
19\125 182.400 1017.600 8:3 2.667
26\171 182.456 1017.544 11:4 2.750
7\46 182.609 1017.391 3:1 3.000 Hard 13L 7s
Mitonic / Minortone
23\151 182.781 1017.219 10:3 3.333
16\105 182.857 1017.143 7:2 3.500
25\164 182.927 1017.073 11:3 3.667
9\59 183.051 1016.949 4:1 4.000 Superhard 13L 7s
20\131 183.206 1016.794 9:2 4.500
11\72 183.333 1016.667 5:1 5.000
13\85 183.529 1016.471 6:1 6.000
2\13 184.615 1015.385 1:0 → ∞ Collapsed 13L 7s

See also

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