7L 12s

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↖ 6L 11s ↑ 7L 11s 8L 11s ↗
← 6L 12s 7L 12s 8L 12s →
↙ 6L 13s ↓ 7L 13s 8L 13s ↘
Scale structure
Step pattern LsLssLssLsLssLssLss
ssLssLssLsLssLssLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 8\19 to 3\7 (505.3 ¢ to 514.3 ¢)
Dark 4\7 to 11\19 (685.7 ¢ to 694.7 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 1:1 to 3:2 (soft)
Related MOS scales
Parent 7L 5s
Sister 12L 7s
Daughters 19L 7s, 7L 19s
Neutralized 14L 5s
2-Flought 26L 12s, 7L 31s
Equal tunings
Equalized (L:s = 1:1) 8\19 (505.3 ¢)
Supersoft (L:s = 4:3) 27\64 (506.2 ¢)
Soft (L:s = 3:2) 19\45 (506.7 ¢)
Semisoft (L:s = 5:3) 30\71 (507.0 ¢)
Basic (L:s = 2:1) 11\26 (507.7 ¢)
Semihard (L:s = 5:2) 25\59 (508.5 ¢)
Hard (L:s = 3:1) 14\33 (509.1 ¢)
Superhard (L:s = 4:1) 17\40 (510.0 ¢)
Collapsed (L:s = 1:0) 3\7 (514.3 ¢)
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7L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 12 small steps, repeating every octave. 7L 12s is a grandchild scale of 5L 2s, expanding it by 12 tones. Generators that produce this scale range from 505.3 ¢ to 514.3 ¢, or from 685.7 ¢ to 694.7 ¢.

Temperaments associated with this scale include flattone, as the flattone enharmonic scale.

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 12s
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 171.4 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 126.3 ¢
Major 2-mosstep M2ms L + s 126.3 ¢ to 171.4 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 171.4 ¢ to 189.5 ¢
Major 3-mosstep M3ms 2L + s 189.5 ¢ to 342.9 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 171.4 ¢ to 252.6 ¢
Major 4-mosstep M4ms 2L + 2s 252.6 ¢ to 342.9 ¢
5-mosstep Minor 5-mosstep m5ms L + 4s 171.4 ¢ to 315.8 ¢
Major 5-mosstep M5ms 2L + 3s 315.8 ¢ to 342.9 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 342.9 ¢ to 378.9 ¢
Major 6-mosstep M6ms 3L + 3s 378.9 ¢ to 514.3 ¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 342.9 ¢ to 442.1 ¢
Major 7-mosstep M7ms 3L + 4s 442.1 ¢ to 514.3 ¢
8-mosstep Diminished 8-mosstep d8ms 2L + 6s 342.9 ¢ to 505.3 ¢
Perfect 8-mosstep P8ms 3L + 5s 505.3 ¢ to 514.3 ¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 514.3 ¢ to 568.4 ¢
Major 9-mosstep M9ms 4L + 5s 568.4 ¢ to 685.7 ¢
10-mosstep Minor 10-mosstep m10ms 3L + 7s 514.3 ¢ to 631.6 ¢
Major 10-mosstep M10ms 4L + 6s 631.6 ¢ to 685.7 ¢
11-mosstep Perfect 11-mosstep P11ms 4L + 7s 685.7 ¢ to 694.7 ¢
Augmented 11-mosstep A11ms 5L + 6s 694.7 ¢ to 857.1 ¢
12-mosstep Minor 12-mosstep m12ms 4L + 8s 685.7 ¢ to 757.9 ¢
Major 12-mosstep M12ms 5L + 7s 757.9 ¢ to 857.1 ¢
13-mosstep Minor 13-mosstep m13ms 4L + 9s 685.7 ¢ to 821.1 ¢
Major 13-mosstep M13ms 5L + 8s 821.1 ¢ to 857.1 ¢
14-mosstep Minor 14-mosstep m14ms 5L + 9s 857.1 ¢ to 884.2 ¢
Major 14-mosstep M14ms 6L + 8s 884.2 ¢ to 1028.6 ¢
15-mosstep Minor 15-mosstep m15ms 5L + 10s 857.1 ¢ to 947.4 ¢
Major 15-mosstep M15ms 6L + 9s 947.4 ¢ to 1028.6 ¢
16-mosstep Minor 16-mosstep m16ms 5L + 11s 857.1 ¢ to 1010.5 ¢
Major 16-mosstep M16ms 6L + 10s 1010.5 ¢ to 1028.6 ¢
17-mosstep Minor 17-mosstep m17ms 6L + 11s 1028.6 ¢ to 1073.7 ¢
Major 17-mosstep M17ms 7L + 10s 1073.7 ¢ to 1200.0 ¢
18-mosstep Minor 18-mosstep m18ms 6L + 12s 1028.6 ¢ to 1136.8 ¢
Major 18-mosstep M18ms 7L + 11s 1136.8 ¢ to 1200.0 ¢
19-mosstep Perfect 19-mosstep P19ms 7L + 12s 1200.0 ¢

Generator chain

Generator chain of 7L 12s
Bright gens Scale degree Abbrev.
25 Augmented 10-mosdegree A10md
24 Augmented 2-mosdegree A2md
23 Augmented 13-mosdegree A13md
22 Augmented 5-mosdegree A5md
21 Augmented 16-mosdegree A16md
20 Augmented 8-mosdegree A8md
19 Augmented 0-mosdegree A0md
18 Augmented 11-mosdegree A11md
17 Major 3-mosdegree M3md
16 Major 14-mosdegree M14md
15 Major 6-mosdegree M6md
14 Major 17-mosdegree M17md
13 Major 9-mosdegree M9md
12 Major 1-mosdegree M1md
11 Major 12-mosdegree M12md
10 Major 4-mosdegree M4md
9 Major 15-mosdegree M15md
8 Major 7-mosdegree M7md
7 Major 18-mosdegree M18md
6 Major 10-mosdegree M10md
5 Major 2-mosdegree M2md
4 Major 13-mosdegree M13md
3 Major 5-mosdegree M5md
2 Major 16-mosdegree M16md
1 Perfect 8-mosdegree P8md
0 Perfect 0-mosdegree
Perfect 19-mosdegree		 P0md
P19md
−1 Perfect 11-mosdegree P11md
−2 Minor 3-mosdegree m3md
−3 Minor 14-mosdegree m14md
−4 Minor 6-mosdegree m6md
−5 Minor 17-mosdegree m17md
−6 Minor 9-mosdegree m9md
−7 Minor 1-mosdegree m1md
−8 Minor 12-mosdegree m12md
−9 Minor 4-mosdegree m4md
−10 Minor 15-mosdegree m15md
−11 Minor 7-mosdegree m7md
−12 Minor 18-mosdegree m18md
−13 Minor 10-mosdegree m10md
−14 Minor 2-mosdegree m2md
−15 Minor 13-mosdegree m13md
−16 Minor 5-mosdegree m5md
−17 Minor 16-mosdegree m16md
−18 Diminished 8-mosdegree d8md
−19 Diminished 19-mosdegree d19md
−20 Diminished 11-mosdegree d11md
−21 Diminished 3-mosdegree d3md
−22 Diminished 14-mosdegree d14md
−23 Diminished 6-mosdegree d6md
−24 Diminished 17-mosdegree d17md
−25 Diminished 9-mosdegree d9md

Modes

Scale degrees of the modes of 7L 12s
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 LsLssLssLsLssLssLss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
17|1 9 LsLssLssLssLsLssLss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
16|2 17 LssLsLssLssLsLssLss Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
15|3 6 LssLsLssLssLssLsLss Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf.
14|4 14 LssLssLsLssLssLsLss Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Maj. Maj. Perf.
13|5 3 LssLssLsLssLssLssLs Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf.
12|6 11 LssLssLssLsLssLssLs Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf. Min. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf.
11|7 19 sLsLssLssLsLssLssLs Perf. Min. Maj. Min. Maj. Maj. Min. Maj. Perf. Min. Maj. Perf. Maj. Maj. Min. Maj. Maj. Min. Maj. Perf.
10|8 8 sLsLssLssLssLsLssLs Perf. Min. Maj. Min. Maj. Maj. Min. Maj. Perf. Min. Maj. Perf. Min. Maj. Min. Maj. Maj. Min. Maj. Perf.
9|9 16 sLssLsLssLssLsLssLs Perf. Min. Maj. Min. Min. Maj. Min. Maj. Perf. Min. Maj. Perf. Min. Maj. Min. Maj. Maj. Min. Maj. Perf.
8|10 5 sLssLsLssLssLssLsLs Perf. Min. Maj. Min. Min. Maj. Min. Maj. Perf. Min. Maj. Perf. Min. Maj. Min. Min. Maj. Min. Maj. Perf.
7|11 13 sLssLssLsLssLssLsLs Perf. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Maj. Perf. Min. Maj. Min. Min. Maj. Min. Maj. Perf.
6|12 2 sLssLssLsLssLssLssL Perf. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Maj. Perf. Min. Maj. Min. Min. Maj. Min. Min. Perf.
5|13 10 sLssLssLssLsLssLssL Perf. Min. Maj. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf. Min. Maj. Min. Min. Maj. Min. Min. Perf.
4|14 18 ssLsLssLssLsLssLssL Perf. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf. Min. Maj. Min. Min. Maj. Min. Min. Perf.
3|15 7 ssLsLssLssLssLsLssL Perf. Min. Min. Min. Min. Maj. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Perf.
2|16 15 ssLssLsLssLssLsLssL Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Min. Maj. Min. Min. Perf.
1|17 4 ssLssLsLssLssLssLsL Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Perf.
0|18 12 ssLssLssLsLssLssLsL Perf. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 7L 12s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
8\19 505.263 694.737 1:1 1.000 Equalized 7L 12s
43\102 505.882 694.118 6:5 1.200
35\83 506.024 693.976 5:4 1.250
62\147 506.122 693.878 9:7 1.286
27\64 506.250 693.750 4:3 1.333 Supersoft 7L 12s
73\173 506.358 693.642 11:8 1.375
46\109 506.422 693.578 7:5 1.400
65\154 506.494 693.506 10:7 1.429
19\45 506.667 693.333 3:2 1.500 Soft 7L 12s
Flattone
68\161 506.832 693.168 11:7 1.571
49\116 506.897 693.103 8:5 1.600
79\187 506.952 693.048 13:8 1.625 Golden flattone (506.9365 ¢)
30\71 507.042 692.958 5:3 1.667 Semisoft 7L 12s
71\168 507.143 692.857 12:7 1.714
41\97 507.216 692.784 7:4 1.750
52\123 507.317 692.683 9:5 1.800
11\26 507.692 692.308 2:1 2.000 Basic 7L 12s
Scales with tunings softer than this are proper
47\111 508.108 691.892 9:4 2.250
36\85 508.235 691.765 7:3 2.333
61\144 508.333 691.667 12:5 2.400
25\59 508.475 691.525 5:2 2.500 Semihard 7L 12s
Flattertone
64\151 508.609 691.391 13:5 2.600 Unnamed golden tuning (508.6329 ¢)
39\92 508.696 691.304 8:3 2.667
53\125 508.800 691.200 11:4 2.750
14\33 509.091 690.909 3:1 3.000 Hard 7L 12s
45\106 509.434 690.566 10:3 3.333
31\73 509.589 690.411 7:2 3.500
48\113 509.735 690.265 11:3 3.667
17\40 510.000 690.000 4:1 4.000 Superhard 7L 12s
37\87 510.345 689.655 9:2 4.500
20\47 510.638 689.362 5:1 5.000
23\54 511.111 688.889 6:1 6.000 Deeptone
3\7 514.286 685.714 1:0 → ∞ Collapsed 7L 12s
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