7L 13s

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↖ 6L 12s ↑ 7L 12s 8L 12s ↗
← 6L 13s 7L 13s 8L 13s →
↙ 6L 14s ↓ 7L 14s 8L 14s ↘ 
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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 (archaeotonic)
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 ¢.

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

The intervals of 7L 13s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the root and octave (perfect 0-mosstep and perfect 20-mosstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.

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

A chain of bright generators, each a perfect 17-mosstep, produces the following scale degrees. A chain of 20 bright generators contains the scale degrees of one of the modes of 7L 13s. Expanding the chain to 27 scale degrees produces the modes of either 20L 7s (for soft-of-basic tunings) or 7L 20s (for hard-of-basic tunings).

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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