13L 6s

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↖ 12L 5s ↑ 13L 5s 14L 5s ↗
← 12L 6s 13L 6s 14L 6s →
↙ 12L 7s ↓ 13L 7s 14L 7s ↘ 
┌╥╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬╥╥┬┐
│║║║│║║│║║│║║│║║│║║││
│││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLsLLsLLsLLsLLs
sLLsLLsLLsLLsLLsLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 16\19 to 11\13 (1010.5 ¢ to 1015.4 ¢)
Dark 2\13 to 3\19 (184.6 ¢ to 189.5 ¢)
TAMNAMS information
Descends from 6L 1s (archaeotonic)
Ancestor's step ratio range 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 6L 7s
Sister 6L 13s
Daughters 19L 13s, 13L 19s
Neutralized 7L 12s
2-Flought 32L 6s, 13L 25s
Equal tunings
Equalized (L:s = 1:1) 16\19 (1010.5 ¢)
Supersoft (L:s = 4:3) 59\70 (1011.4 ¢)
Soft (L:s = 3:2) 43\51 (1011.8 ¢)
Semisoft (L:s = 5:3) 70\83 (1012.0 ¢)
Basic (L:s = 2:1) 27\32 (1012.5 ¢)
Semihard (L:s = 5:2) 65\77 (1013.0 ¢)
Hard (L:s = 3:1) 38\45 (1013.3 ¢)
Superhard (L:s = 4:1) 49\58 (1013.8 ¢)
Collapsed (L:s = 1:0) 11\13 (1015.4 ¢)

13L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 6 small steps, repeating every octave. 13L 6s is a grandchild scale of 6L 1s, expanding it by 12 tones. Generators that produce this scale range from 1010.5 ¢ to 1015.4 ¢, or from 184.6 ¢ to 189.5 ¢.

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 diatonic interval categories.

Intervals

Intervals of 13L 6s
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 63.2 ¢
Major 1-mosstep M1ms L 63.2 ¢ to 92.3 ¢
2-mosstep Minor 2-mosstep m2ms L + s 92.3 ¢ to 126.3 ¢
Major 2-mosstep M2ms 2L 126.3 ¢ to 184.6 ¢
3-mosstep Perfect 3-mosstep P3ms 2L + s 184.6 ¢ to 189.5 ¢
Augmented 3-mosstep A3ms 3L 189.5 ¢ to 276.9 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 184.6 ¢ to 252.6 ¢
Major 4-mosstep M4ms 3L + s 252.6 ¢ to 276.9 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 276.9 ¢ to 315.8 ¢
Major 5-mosstep M5ms 4L + s 315.8 ¢ to 369.2 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 369.2 ¢ to 378.9 ¢
Major 6-mosstep M6ms 5L + s 378.9 ¢ to 461.5 ¢
7-mosstep Minor 7-mosstep m7ms 4L + 3s 369.2 ¢ to 442.1 ¢
Major 7-mosstep M7ms 5L + 2s 442.1 ¢ to 461.5 ¢
8-mosstep Minor 8-mosstep m8ms 5L + 3s 461.5 ¢ to 505.3 ¢
Major 8-mosstep M8ms 6L + 2s 505.3 ¢ to 553.8 ¢
9-mosstep Minor 9-mosstep m9ms 6L + 3s 553.8 ¢ to 568.4 ¢
Major 9-mosstep M9ms 7L + 2s 568.4 ¢ to 646.2 ¢
10-mosstep Minor 10-mosstep m10ms 6L + 4s 553.8 ¢ to 631.6 ¢
Major 10-mosstep M10ms 7L + 3s 631.6 ¢ to 646.2 ¢
11-mosstep Minor 11-mosstep m11ms 7L + 4s 646.2 ¢ to 694.7 ¢
Major 11-mosstep M11ms 8L + 3s 694.7 ¢ to 738.5 ¢
12-mosstep Minor 12-mosstep m12ms 8L + 4s 738.5 ¢ to 757.9 ¢
Major 12-mosstep M12ms 9L + 3s 757.9 ¢ to 830.8 ¢
13-mosstep Minor 13-mosstep m13ms 8L + 5s 738.5 ¢ to 821.1 ¢
Major 13-mosstep M13ms 9L + 4s 821.1 ¢ to 830.8 ¢
14-mosstep Minor 14-mosstep m14ms 9L + 5s 830.8 ¢ to 884.2 ¢
Major 14-mosstep M14ms 10L + 4s 884.2 ¢ to 923.1 ¢
15-mosstep Minor 15-mosstep m15ms 10L + 5s 923.1 ¢ to 947.4 ¢
Major 15-mosstep M15ms 11L + 4s 947.4 ¢ to 1015.4 ¢
16-mosstep Diminished 16-mosstep d16ms 10L + 6s 923.1 ¢ to 1010.5 ¢
Perfect 16-mosstep P16ms 11L + 5s 1010.5 ¢ to 1015.4 ¢
17-mosstep Minor 17-mosstep m17ms 11L + 6s 1015.4 ¢ to 1073.7 ¢
Major 17-mosstep M17ms 12L + 5s 1073.7 ¢ to 1107.7 ¢
18-mosstep Minor 18-mosstep m18ms 12L + 6s 1107.7 ¢ to 1136.8 ¢
Major 18-mosstep M18ms 13L + 5s 1136.8 ¢ to 1200.0 ¢
19-mosstep Perfect 19-mosstep P19ms 13L + 6s 1200.0 ¢

Generator chain

Generator chain of 13L 6s
Bright gens Scale degree Abbrev.
31 Augmented 2-mosdegree A2md
30 Augmented 5-mosdegree A5md
29 Augmented 8-mosdegree A8md
28 Augmented 11-mosdegree A11md
27 Augmented 14-mosdegree A14md
26 Augmented 17-mosdegree A17md
25 Augmented 1-mosdegree A1md
24 Augmented 4-mosdegree A4md
23 Augmented 7-mosdegree A7md
22 Augmented 10-mosdegree A10md
21 Augmented 13-mosdegree A13md
20 Augmented 16-mosdegree A16md
19 Augmented 0-mosdegree A0md
18 Augmented 3-mosdegree A3md
17 Major 6-mosdegree M6md
16 Major 9-mosdegree M9md
15 Major 12-mosdegree M12md
14 Major 15-mosdegree M15md
13 Major 18-mosdegree M18md
12 Major 2-mosdegree M2md
11 Major 5-mosdegree M5md
10 Major 8-mosdegree M8md
9 Major 11-mosdegree M11md
8 Major 14-mosdegree M14md
7 Major 17-mosdegree M17md
6 Major 1-mosdegree M1md
5 Major 4-mosdegree M4md
4 Major 7-mosdegree M7md
3 Major 10-mosdegree M10md
2 Major 13-mosdegree M13md
1 Perfect 16-mosdegree P16md
0 Perfect 0-mosdegree
Perfect 19-mosdegree		 P0md
P19md
−1 Perfect 3-mosdegree P3md
−2 Minor 6-mosdegree m6md
−3 Minor 9-mosdegree m9md
−4 Minor 12-mosdegree m12md
−5 Minor 15-mosdegree m15md
−6 Minor 18-mosdegree m18md
−7 Minor 2-mosdegree m2md
−8 Minor 5-mosdegree m5md
−9 Minor 8-mosdegree m8md
−10 Minor 11-mosdegree m11md
−11 Minor 14-mosdegree m14md
−12 Minor 17-mosdegree m17md
−13 Minor 1-mosdegree m1md
−14 Minor 4-mosdegree m4md
−15 Minor 7-mosdegree m7md
−16 Minor 10-mosdegree m10md
−17 Minor 13-mosdegree m13md
−18 Diminished 16-mosdegree d16md
−19 Diminished 19-mosdegree d19md
−20 Diminished 3-mosdegree d3md
−21 Diminished 6-mosdegree d6md
−22 Diminished 9-mosdegree d9md
−23 Diminished 12-mosdegree d12md
−24 Diminished 15-mosdegree d15md
−25 Diminished 18-mosdegree d18md
−26 Diminished 2-mosdegree d2md
−27 Diminished 5-mosdegree d5md
−28 Diminished 8-mosdegree d8md
−29 Diminished 11-mosdegree d11md
−30 Diminished 14-mosdegree d14md
−31 Diminished 17-mosdegree d17md

Modes

Scale degrees of the modes of 13L 6s
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
18|0 1 LLLsLLsLLsLLsLLsLLs Perf. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
17|1 17 LLsLLLsLLsLLsLLsLLs Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
16|2 14 LLsLLsLLLsLLsLLsLLs Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
15|3 11 LLsLLsLLsLLLsLLsLLs Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
14|4 8 LLsLLsLLsLLsLLLsLLs Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
13|5 5 LLsLLsLLsLLsLLsLLLs Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Maj. Perf.
12|6 2 LLsLLsLLsLLsLLsLLsL Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Min. Perf.
11|7 18 LsLLLsLLsLLsLLsLLsL Perf. Maj. Min. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Min. Perf.
10|8 15 LsLLsLLLsLLsLLsLLsL Perf. Maj. Min. Perf. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Min. Perf.
9|9 12 LsLLsLLsLLLsLLsLLsL Perf. Maj. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Maj. Maj. Min. Perf. Maj. Min. Perf.
8|10 9 LsLLsLLsLLsLLLsLLsL Perf. Maj. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Maj. Min. Perf. Maj. Min. Perf.
7|11 6 LsLLsLLsLLsLLsLLLsL Perf. Maj. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Maj. Min. Perf.
6|12 3 LsLLsLLsLLsLLsLLsLL Perf. Maj. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
5|13 19 sLLLsLLsLLsLLsLLsLL Perf. Min. Min. Perf. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
4|14 16 sLLsLLLsLLsLLsLLsLL Perf. Min. Min. Perf. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
3|15 13 sLLsLLsLLLsLLsLLsLL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
2|16 10 sLLsLLsLLsLLLsLLsLL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
1|17 7 sLLsLLsLLsLLsLLLsLL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
0|18 4 sLLsLLsLLsLLsLLsLLL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 13L 6s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
16\19 1010.526 189.474 1:1 1.000 Equalized 13L 6s
91\108 1011.111 188.889 6:5 1.200
75\89 1011.236 188.764 5:4 1.250
134\159 1011.321 188.679 9:7 1.286
59\70 1011.429 188.571 4:3 1.333 Supersoft 13L 6s
161\191 1011.518 188.482 11:8 1.375
102\121 1011.570 188.430 7:5 1.400
145\172 1011.628 188.372 10:7 1.429
43\51 1011.765 188.235 3:2 1.500 Soft 13L 6s
156\185 1011.892 188.108 11:7 1.571
113\134 1011.940 188.060 8:5 1.600
183\217 1011.982 188.018 13:8 1.625
70\83 1012.048 187.952 5:3 1.667 Semisoft 13L 6s
167\198 1012.121 187.879 12:7 1.714
97\115 1012.174 187.826 7:4 1.750
124\147 1012.245 187.755 9:5 1.800
27\32 1012.500 187.500 2:1 2.000 Basic 13L 6s
Scales with tunings softer than this are proper
119\141 1012.766 187.234 9:4 2.250
92\109 1012.844 187.156 7:3 2.333
157\186 1012.903 187.097 12:5 2.400
65\77 1012.987 187.013 5:2 2.500 Semihard 13L 6s
168\199 1013.065 186.935 13:5 2.600
103\122 1013.115 186.885 8:3 2.667
141\167 1013.174 186.826 11:4 2.750
38\45 1013.333 186.667 3:1 3.000 Hard 13L 6s
125\148 1013.514 186.486 10:3 3.333
87\103 1013.592 186.408 7:2 3.500
136\161 1013.665 186.335 11:3 3.667
49\58 1013.793 186.207 4:1 4.000 Superhard 13L 6s
109\129 1013.953 186.047 9:2 4.500
60\71 1014.085 185.915 5:1 5.000
71\84 1014.286 185.714 6:1 6.000
11\13 1015.385 184.615 1:0 → ∞ Collapsed 13L 6s
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