13L 7s

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↖ 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
Descends from 6L 1s
Ancestor's step ratio range 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¢)

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¢.

Modes

Modes of 13L 7s
UDP Cyclic
order		 Step
pattern
19|0 1 LLsLLsLLsLLsLLsLLsLs
18|1 4 LLsLLsLLsLLsLLsLsLLs
17|2 7 LLsLLsLLsLLsLsLLsLLs
16|3 10 LLsLLsLLsLsLLsLLsLLs
15|4 13 LLsLLsLsLLsLLsLLsLLs
14|5 16 LLsLsLLsLLsLLsLLsLLs
13|6 19 LsLLsLLsLLsLLsLLsLLs
12|7 2 LsLLsLLsLLsLLsLLsLsL
11|8 5 LsLLsLLsLLsLLsLsLLsL
10|9 8 LsLLsLLsLLsLsLLsLLsL
9|10 11 LsLLsLLsLsLLsLLsLLsL
8|11 14 LsLLsLsLLsLLsLLsLLsL
7|12 17 LsLsLLsLLsLLsLLsLLsL
6|13 20 sLLsLLsLLsLLsLLsLLsL
5|14 3 sLLsLLsLLsLLsLLsLsLL
4|15 6 sLLsLLsLLsLLsLsLLsLL
3|16 9 sLLsLLsLLsLsLLsLLsLL
2|17 12 sLLsLLsLsLLsLLsLLsLL
1|18 15 sLLsLsLLsLLsLLsLLsLL
0|19 18 sLsLLsLLsLLsLLsLLsLL

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¢

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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