7L 13s

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↖ 6L 12s ↑ 7L 12s 8L 12s ↗
← 6L 13s 7L 13s 8L 13s →
↙ 6L 14s ↓ 7L 14s 8L 14s ↘
┌╥┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬┐
│║│║││║││║││║││║││║│││
││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLssLssLssLssLssLss
ssLssLssLssLssLssLsL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 17\20 to 6\7 (1020.0¢ to 1028.6¢)
Dark 1\7 to 3\20 (171.4¢ to 180.0¢)
TAMNAMS information
Descends from 6L 1s
Ancestor's step ratio range 1:1 to 3:2 (soft)
Related MOS scales
Parent 7L 6s
Sister 13L 7s
Daughters 20L 7s, 7L 20s
Neutralized 14L 6s
2-Flought 27L 13s, 7L 33s
Equal tunings
Equalized (L:s = 1:1) 17\20 (1020.0¢)
Supersoft (L:s = 4:3) 57\67 (1020.9¢)
Soft (L:s = 3:2) 40\47 (1021.3¢)
Semisoft (L:s = 5:3) 63\74 (1021.6¢)
Basic (L:s = 2:1) 23\27 (1022.2¢)
Semihard (L:s = 5:2) 52\61 (1023.0¢)
Hard (L:s = 3:1) 29\34 (1023.5¢)
Superhard (L:s = 4:1) 35\41 (1024.4¢)
Collapsed (L:s = 1:0) 6\7 (1028.6¢)

7L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 13 small steps, repeating every octave. 7L 13s is a grandchild scale of 6L 1s, expanding it by 13 tones. Generators that produce this scale range from 1020¢ to 1028.6¢, or from 171.4¢ to 180¢.

Modes

Modes of 7L 13s
UDP Cyclic
order
Step
pattern
19|0 1 LsLssLssLssLssLssLss
18|1 18 LssLsLssLssLssLssLss
17|2 15 LssLssLsLssLssLssLss
16|3 12 LssLssLssLsLssLssLss
15|4 9 LssLssLssLssLsLssLss
14|5 6 LssLssLssLssLssLsLss
13|6 3 LssLssLssLssLssLssLs
12|7 20 sLsLssLssLssLssLssLs
11|8 17 sLssLsLssLssLssLssLs
10|9 14 sLssLssLsLssLssLssLs
9|10 11 sLssLssLssLsLssLssLs
8|11 8 sLssLssLssLssLsLssLs
7|12 5 sLssLssLssLssLssLsLs
6|13 2 sLssLssLssLssLssLssL
5|14 19 ssLsLssLssLssLssLssL
4|15 16 ssLssLsLssLssLssLssL
3|16 13 ssLssLssLsLssLssLssL
2|17 10 ssLssLssLssLsLssLssL
1|18 7 ssLssLssLssLssLsLssL
0|19 4 ssLssLssLssLssLssLsL

Intervals

Intervals of 7L 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 60.0¢
Major 1-mosstep M1ms L 60.0¢ to 171.4¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 120.0¢
Major 2-mosstep M2ms L + s 120.0¢ to 171.4¢
3-mosstep Perfect 3-mosstep P3ms L + 2s 171.4¢ to 180.0¢
Augmented 3-mosstep A3ms 2L + s 180.0¢ to 342.9¢
4-mosstep Minor 4-mosstep m4ms L + 3s 171.4¢ to 240.0¢
Major 4-mosstep M4ms 2L + 2s 240.0¢ to 342.9¢
5-mosstep Minor 5-mosstep m5ms L + 4s 171.4¢ to 300.0¢
Major 5-mosstep M5ms 2L + 3s 300.0¢ to 342.9¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 342.9¢ to 360.0¢
Major 6-mosstep M6ms 3L + 3s 360.0¢ to 514.3¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 342.9¢ to 420.0¢
Major 7-mosstep M7ms 3L + 4s 420.0¢ to 514.3¢
8-mosstep Minor 8-mosstep m8ms 2L + 6s 342.9¢ to 480.0¢
Major 8-mosstep M8ms 3L + 5s 480.0¢ to 514.3¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 514.3¢ to 540.0¢
Major 9-mosstep M9ms 4L + 5s 540.0¢ to 685.7¢
10-mosstep Minor 10-mosstep m10ms 3L + 7s 514.3¢ to 600.0¢
Major 10-mosstep M10ms 4L + 6s 600.0¢ to 685.7¢
11-mosstep Minor 11-mosstep m11ms 3L + 8s 514.3¢ to 660.0¢
Major 11-mosstep M11ms 4L + 7s 660.0¢ to 685.7¢
12-mosstep Minor 12-mosstep m12ms 4L + 8s 685.7¢ to 720.0¢
Major 12-mosstep M12ms 5L + 7s 720.0¢ to 857.1¢
13-mosstep Minor 13-mosstep m13ms 4L + 9s 685.7¢ to 780.0¢
Major 13-mosstep M13ms 5L + 8s 780.0¢ to 857.1¢
14-mosstep Minor 14-mosstep m14ms 4L + 10s 685.7¢ to 840.0¢
Major 14-mosstep M14ms 5L + 9s 840.0¢ to 857.1¢
15-mosstep Minor 15-mosstep m15ms 5L + 10s 857.1¢ to 900.0¢
Major 15-mosstep M15ms 6L + 9s 900.0¢ to 1028.6¢
16-mosstep Minor 16-mosstep m16ms 5L + 11s 857.1¢ to 960.0¢
Major 16-mosstep M16ms 6L + 10s 960.0¢ to 1028.6¢
17-mosstep Diminished 17-mosstep d17ms 5L + 12s 857.1¢ to 1020.0¢
Perfect 17-mosstep P17ms 6L + 11s 1020.0¢ to 1028.6¢
18-mosstep Minor 18-mosstep m18ms 6L + 12s 1028.6¢ to 1080.0¢
Major 18-mosstep M18ms 7L + 11s 1080.0¢ to 1200.0¢
19-mosstep Minor 19-mosstep m19ms 6L + 13s 1028.6¢ to 1140.0¢
Major 19-mosstep M19ms 7L + 12s 1140.0¢ to 1200.0¢
20-mosstep Perfect 20-mosstep P20ms 7L + 13s 1200.0¢

Tuning spectrum

Icon-Todo.png Todo: review

Review entries from past page revision and enter them into the scale tree.

Tetracot / enipucrop range. See also 7L 6s 7L 13s and 13L 7s.

Scale tree and tuning spectrum of 7L 13s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
17\20 1020.000 180.000 1:1 1.000 Equalized 7L 13s
91\107 1020.561 179.439 6:5 1.200
74\87 1020.690 179.310 5:4 1.250
131\154 1020.779 179.221 9:7 1.286
57\67 1020.896 179.104 4:3 1.333 Supersoft 7L 13s
154\181 1020.994 179.006 11:8 1.375
97\114 1021.053 178.947 7:5 1.400
137\161 1021.118 178.882 10:7 1.429
40\47 1021.277 178.723 3:2 1.500 Soft 7L 13s
143\168 1021.429 178.571 11:7 1.571
103\121 1021.488 178.512 8:5 1.600
166\195 1021.538 178.462 13:8 1.625
63\74 1021.622 178.378 5:3 1.667 Semisoft 7L 13s
149\175 1021.714 178.286 12:7 1.714
86\101 1021.782 178.218 7:4 1.750
109\128 1021.875 178.125 9:5 1.800
23\27 1022.222 177.778 2:1 2.000 Basic 7L 13s
Scales with tunings softer than this are proper
98\115 1022.609 177.391 9:4 2.250
75\88 1022.727 177.273 7:3 2.333
127\149 1022.819 177.181 12:5 2.400
52\61 1022.951 177.049 5:2 2.500 Semihard 7L 13s
133\156 1023.077 176.923 13:5 2.600
81\95 1023.158 176.842 8:3 2.667
110\129 1023.256 176.744 11:4 2.750
29\34 1023.529 176.471 3:1 3.000 Hard 7L 13s
93\109 1023.853 176.147 10:3 3.333
64\75 1024.000 176.000 7:2 3.500
99\116 1024.138 175.862 11:3 3.667
35\41 1024.390 175.610 4:1 4.000 Superhard 7L 13s
76\89 1024.719 175.281 9:2 4.500
41\48 1025.000 175.000 5:1 5.000
47\55 1025.455 174.545 6:1 6.000
6\7 1028.571 171.429 1:0 → ∞ Collapsed 7L 13s


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