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
Related to 6L 1s (archaeotonic)
With tunings 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 ¢.

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 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 ¢

Generator chain

Generator chain of 7L 13s
Bright gens Scale degree Abbrev.
26 Augmented 2-mosdegree A2md
25 Augmented 5-mosdegree A5md
24 Augmented 8-mosdegree A8md
23 Augmented 11-mosdegree A11md
22 Augmented 14-mosdegree A14md
21 Augmented 17-mosdegree A17md
20 Augmented 0-mosdegree A0md
19 Augmented 3-mosdegree A3md
18 Major 6-mosdegree M6md
17 Major 9-mosdegree M9md
16 Major 12-mosdegree M12md
15 Major 15-mosdegree M15md
14 Major 18-mosdegree M18md
13 Major 1-mosdegree M1md
12 Major 4-mosdegree M4md
11 Major 7-mosdegree M7md
10 Major 10-mosdegree M10md
9 Major 13-mosdegree M13md
8 Major 16-mosdegree M16md
7 Major 19-mosdegree M19md
6 Major 2-mosdegree M2md
5 Major 5-mosdegree M5md
4 Major 8-mosdegree M8md
3 Major 11-mosdegree M11md
2 Major 14-mosdegree M14md
1 Perfect 17-mosdegree P17md
0 Perfect 0-mosdegree
Perfect 20-mosdegree		 P0md
P20md
−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 1-mosdegree m1md
−8 Minor 4-mosdegree m4md
−9 Minor 7-mosdegree m7md
−10 Minor 10-mosdegree m10md
−11 Minor 13-mosdegree m13md
−12 Minor 16-mosdegree m16md
−13 Minor 19-mosdegree m19md
−14 Minor 2-mosdegree m2md
−15 Minor 5-mosdegree m5md
−16 Minor 8-mosdegree m8md
−17 Minor 11-mosdegree m11md
−18 Minor 14-mosdegree m14md
−19 Diminished 17-mosdegree d17md
−20 Diminished 20-mosdegree d20md
−21 Diminished 3-mosdegree d3md
−22 Diminished 6-mosdegree d6md
−23 Diminished 9-mosdegree d9md
−24 Diminished 12-mosdegree d12md
−25 Diminished 15-mosdegree d15md
−26 Diminished 18-mosdegree d18md

Modes

Scale degrees of the modes of 7L 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
19|0 1 LsLssLssLssLssLssLss Perf. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
18|1 18 LssLsLssLssLssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
17|2 15 LssLssLsLssLssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
16|3 12 LssLssLssLsLssLssLss Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
15|4 9 LssLssLssLssLsLssLss Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
14|5 6 LssLssLssLssLssLsLss Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf. Maj. Maj. Perf.
13|6 3 LssLssLssLssLssLssLs Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf. Min. Maj. Perf.
12|7 20 sLsLssLssLssLssLssLs Perf. Min. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf. Min. Maj. Perf.
11|8 17 sLssLsLssLssLssLssLs Perf. Min. Maj. Perf. Min. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf. Min. Maj. Perf.
10|9 14 sLssLssLsLssLssLssLs Perf. Min. Maj. Perf. Min. Maj. Min. Min. Maj. Min. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf. Min. Maj. Perf.
9|10 11 sLssLssLssLsLssLssLs Perf. Min. Maj. Perf. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Maj. Maj. Min. Maj. Perf. Min. Maj. Perf.
8|11 8 sLssLssLssLssLsLssLs Perf. Min. Maj. Perf. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Maj. Perf. Min. Maj. Perf.
7|12 5 sLssLssLssLssLssLsLs Perf. Min. Maj. Perf. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Maj. Perf.
6|13 2 sLssLssLssLssLssLssL Perf. Min. Maj. Perf. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
5|14 19 ssLsLssLssLssLssLssL Perf. Min. Min. Perf. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
4|15 16 ssLssLsLssLssLssLssL Perf. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
3|16 13 ssLssLssLsLssLssLssL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
2|17 10 ssLssLssLssLsLssLssL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf.
1|18 7 ssLssLssLssLssLsLssL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
0|19 4 ssLssLssLssLssLssLsL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Perf.

Tuning spectrum

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
108\127 1020.472 179.528 7:6 1.167
91\107 1020.561 179.439 6:5 1.200
165\194 1020.619 179.381 11:9 1.222
74\87 1020.690 179.310 5:4 1.250
205\241 1020.747 179.253 14:11 1.273
131\154 1020.779 179.221 9:7 1.286
188\221 1020.814 179.186 13:10 1.300
57\67 1020.896 179.104 4:3 1.333 Supersoft 7L 13s
211\248 1020.968 179.032 15:11 1.364
154\181 1020.994 179.006 11:8 1.375
251\295 1021.017 178.983 18:13 1.385
97\114 1021.053 178.947 7:5 1.400
234\275 1021.091 178.909 17:12 1.417
137\161 1021.118 178.882 10:7 1.429
177\208 1021.154 178.846 13:9 1.444
40\47 1021.277 178.723 3:2 1.500 Soft 7L 13s
183\215 1021.395 178.605 14:9 1.556
143\168 1021.429 178.571 11:7 1.571
246\289 1021.453 178.547 19:12 1.583
103\121 1021.488 178.512 8:5 1.600
269\316 1021.519 178.481 21:13 1.615
166\195 1021.538 178.462 13:8 1.625
229\269 1021.561 178.439 18:11 1.636
63\74 1021.622 178.378 5:3 1.667 Semisoft 7L 13s
212\249 1021.687 178.313 17:10 1.700
149\175 1021.714 178.286 12:7 1.714
235\276 1021.739 178.261 19:11 1.727
86\101 1021.782 178.218 7:4 1.750
195\229 1021.834 178.166 16:9 1.778
109\128 1021.875 178.125 9:5 1.800
132\155 1021.935 178.065 11:6 1.833
23\27 1022.222 177.778 2:1 2.000 Basic 7L 13s
Scales with tunings softer than this are proper
121\142 1022.535 177.465 11:5 2.200
98\115 1022.609 177.391 9:4 2.250 Wollemia
173\203 1022.660 177.340 16:7 2.286
75\88 1022.727 177.273 7:3 2.333 Ponens
202\237 1022.785 177.215 19:8 2.375
127\149 1022.819 177.181 12:5 2.400
179\210 1022.857 177.143 17:7 2.429
52\61 1022.951 177.049 5:2 2.500 Semihard 7L 13s
185\217 1023.041 176.959 18:7 2.571
133\156 1023.077 176.923 13:5 2.600
214\251 1023.108 176.892 21:8 2.625
81\95 1023.158 176.842 8:3 2.667 Modus
191\224 1023.214 176.786 19:7 2.714
110\129 1023.256 176.744 11:4 2.750
139\163 1023.313 176.687 14:5 2.800
29\34 1023.529 176.471 3:1 3.000 Hard 7L 13s
122\143 1023.776 176.224 13:4 3.250
93\109 1023.853 176.147 10:3 3.333 Tetracot
157\184 1023.913 176.087 17:5 3.400
64\75 1024.000 176.000 7:2 3.500
163\191 1024.084 175.916 18:5 3.600
99\116 1024.138 175.862 11:3 3.667 Bunya
134\157 1024.204 175.796 15:4 3.750
35\41 1024.390 175.610 4:1 4.000 Superhard 7L 13s
Monkey
111\130 1024.615 175.385 13:3 4.333
76\89 1024.719 175.281 9:2 4.500 Sesquiquartififths
117\137 1024.818 175.182 14:3 4.667
41\48 1025.000 175.000 5:1 5.000
88\103 1025.243 174.757 11:2 5.500
47\55 1025.455 174.545 6:1 6.000
53\62 1025.806 174.194 7:1 7.000 Enipucrop ↓
6\7 1028.571 171.429 1:0 → ∞ Collapsed 7L 13s
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