12L 7s

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Scale structure
Step pattern LLsLLsLLsLsLLsLLsLs
sLsLLsLLsLsLLsLLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 11\19 to 7\12 (694.7 ¢ to 700.0 ¢)
Dark 5\12 to 8\19 (500.0 ¢ to 505.3 ¢)
TAMNAMS information
Related to 5L 2s (diatonic)
With tunings 3:2 to 2:1 (hyposoft)
Related MOS scales
Parent 7L 5s
Sister 7L 12s
Daughters 19L 12s, 12L 19s
Neutralized 5L 14s
2-Flought 31L 7s, 12L 26s
Equal tunings
Equalized (L:s = 1:1) 11\19 (694.7 ¢)
Supersoft (L:s = 4:3) 40\69 (695.7 ¢)
Soft (L:s = 3:2) 29\50 (696.0 ¢)
Semisoft (L:s = 5:3) 47\81 (696.3 ¢)
Basic (L:s = 2:1) 18\31 (696.8 ¢)
Semihard (L:s = 5:2) 43\74 (697.3 ¢)
Hard (L:s = 3:1) 25\43 (697.7 ¢)
Superhard (L:s = 4:1) 32\55 (698.2 ¢)
Collapsed (L:s = 1:0) 7\12 (700.0 ¢)

12L 7s, also called m-enharmonic, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 7 small steps, repeating every octave. 12L 7s is a grandchild scale of 5L 2s, expanding it by 12 tones. Generators that produce this scale range from 694.7 ¢ to 700 ¢, or from 500 ¢ to 505.3 ¢.

Essentially the entire range of this scale is spanned by various tunings of meantone, as the meantone 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 12L 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 63.2 ¢
Major 1-mosstep M1ms L 63.2 ¢ to 100.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 100.0 ¢ to 126.3 ¢
Major 2-mosstep M2ms 2L 126.3 ¢ to 200.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 100.0 ¢ to 189.5 ¢
Major 3-mosstep M3ms 2L + s 189.5 ¢ to 200.0 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 200.0 ¢ to 252.6 ¢
Major 4-mosstep M4ms 3L + s 252.6 ¢ to 300.0 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 300.0 ¢ to 315.8 ¢
Major 5-mosstep M5ms 4L + s 315.8 ¢ to 400.0 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 300.0 ¢ to 378.9 ¢
Major 6-mosstep M6ms 4L + 2s 378.9 ¢ to 400.0 ¢
7-mosstep Minor 7-mosstep m7ms 4L + 3s 400.0 ¢ to 442.1 ¢
Major 7-mosstep M7ms 5L + 2s 442.1 ¢ to 500.0 ¢
8-mosstep Perfect 8-mosstep P8ms 5L + 3s 500.0 ¢ to 505.3 ¢
Augmented 8-mosstep A8ms 6L + 2s 505.3 ¢ to 600.0 ¢
9-mosstep Minor 9-mosstep m9ms 5L + 4s 500.0 ¢ to 568.4 ¢
Major 9-mosstep M9ms 6L + 3s 568.4 ¢ to 600.0 ¢
10-mosstep Minor 10-mosstep m10ms 6L + 4s 600.0 ¢ to 631.6 ¢
Major 10-mosstep M10ms 7L + 3s 631.6 ¢ to 700.0 ¢
11-mosstep Diminished 11-mosstep d11ms 6L + 5s 600.0 ¢ to 694.7 ¢
Perfect 11-mosstep P11ms 7L + 4s 694.7 ¢ to 700.0 ¢
12-mosstep Minor 12-mosstep m12ms 7L + 5s 700.0 ¢ to 757.9 ¢
Major 12-mosstep M12ms 8L + 4s 757.9 ¢ to 800.0 ¢
13-mosstep Minor 13-mosstep m13ms 8L + 5s 800.0 ¢ to 821.1 ¢
Major 13-mosstep M13ms 9L + 4s 821.1 ¢ to 900.0 ¢
14-mosstep Minor 14-mosstep m14ms 8L + 6s 800.0 ¢ to 884.2 ¢
Major 14-mosstep M14ms 9L + 5s 884.2 ¢ to 900.0 ¢
15-mosstep Minor 15-mosstep m15ms 9L + 6s 900.0 ¢ to 947.4 ¢
Major 15-mosstep M15ms 10L + 5s 947.4 ¢ to 1000.0 ¢
16-mosstep Minor 16-mosstep m16ms 10L + 6s 1000.0 ¢ to 1010.5 ¢
Major 16-mosstep M16ms 11L + 5s 1010.5 ¢ to 1100.0 ¢
17-mosstep Minor 17-mosstep m17ms 10L + 7s 1000.0 ¢ to 1073.7 ¢
Major 17-mosstep M17ms 11L + 6s 1073.7 ¢ to 1100.0 ¢
18-mosstep Minor 18-mosstep m18ms 11L + 7s 1100.0 ¢ to 1136.8 ¢
Major 18-mosstep M18ms 12L + 6s 1136.8 ¢ to 1200.0 ¢
19-mosstep Perfect 19-mosstep P19ms 12L + 7s 1200.0 ¢

Generator chain

Generator chain of 12L 7s
Bright gens Scale degree Abbrev.
30 Augmented 7-mosdegree A7md
29 Augmented 15-mosdegree A15md
28 Augmented 4-mosdegree A4md
27 Augmented 12-mosdegree A12md
26 Augmented 1-mosdegree A1md
25 Augmented 9-mosdegree A9md
24 Augmented 17-mosdegree A17md
23 Augmented 6-mosdegree A6md
22 Augmented 14-mosdegree A14md
21 Augmented 3-mosdegree A3md
20 Augmented 11-mosdegree A11md
19 Augmented 0-mosdegree A0md
18 Augmented 8-mosdegree A8md
17 Major 16-mosdegree M16md
16 Major 5-mosdegree M5md
15 Major 13-mosdegree M13md
14 Major 2-mosdegree M2md
13 Major 10-mosdegree M10md
12 Major 18-mosdegree M18md
11 Major 7-mosdegree M7md
10 Major 15-mosdegree M15md
9 Major 4-mosdegree M4md
8 Major 12-mosdegree M12md
7 Major 1-mosdegree M1md
6 Major 9-mosdegree M9md
5 Major 17-mosdegree M17md
4 Major 6-mosdegree M6md
3 Major 14-mosdegree M14md
2 Major 3-mosdegree M3md
1 Perfect 11-mosdegree P11md
0 Perfect 0-mosdegree
Perfect 19-mosdegree		 P0md
P19md
−1 Perfect 8-mosdegree P8md
−2 Minor 16-mosdegree m16md
−3 Minor 5-mosdegree m5md
−4 Minor 13-mosdegree m13md
−5 Minor 2-mosdegree m2md
−6 Minor 10-mosdegree m10md
−7 Minor 18-mosdegree m18md
−8 Minor 7-mosdegree m7md
−9 Minor 15-mosdegree m15md
−10 Minor 4-mosdegree m4md
−11 Minor 12-mosdegree m12md
−12 Minor 1-mosdegree m1md
−13 Minor 9-mosdegree m9md
−14 Minor 17-mosdegree m17md
−15 Minor 6-mosdegree m6md
−16 Minor 14-mosdegree m14md
−17 Minor 3-mosdegree m3md
−18 Diminished 11-mosdegree d11md
−19 Diminished 19-mosdegree d19md
−20 Diminished 8-mosdegree d8md
−21 Diminished 16-mosdegree d16md
−22 Diminished 5-mosdegree d5md
−23 Diminished 13-mosdegree d13md
−24 Diminished 2-mosdegree d2md
−25 Diminished 10-mosdegree d10md
−26 Diminished 18-mosdegree d18md
−27 Diminished 7-mosdegree d7md
−28 Diminished 15-mosdegree d15md
−29 Diminished 4-mosdegree d4md
−30 Diminished 12-mosdegree d12md

Modes

Scale degrees of the modes of 12L 7s
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 LLsLLsLLsLsLLsLLsLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
17|1 12 LLsLLsLsLLsLLsLLsLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
16|2 4 LLsLLsLsLLsLLsLsLLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf.
15|3 15 LLsLsLLsLLsLLsLsLLs Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf.
14|4 7 LLsLsLLsLLsLsLLsLLs Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf.
13|5 18 LsLLsLLsLLsLsLLsLLs Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf.
12|6 10 LsLLsLLsLsLLsLLsLLs Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Min. Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf.
11|7 2 LsLLsLLsLsLLsLLsLsL Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Min. Perf. Maj. Min. Maj. Maj. Min. Maj. Min. Perf.
10|8 13 LsLLsLsLLsLLsLLsLsL Perf. Maj. Min. Maj. Maj. Min. Maj. Min. Perf. Maj. Min. Perf. Maj. Min. Maj. Maj. Min. Maj. Min. Perf.
9|9 5 LsLLsLsLLsLLsLsLLsL Perf. Maj. Min. Maj. Maj. Min. Maj. Min. Perf. Maj. Min. Perf. Maj. Min. Maj. Min. Min. Maj. Min. Perf.
8|10 16 LsLsLLsLLsLLsLsLLsL Perf. Maj. Min. Maj. Min. Min. Maj. Min. Perf. Maj. Min. Perf. Maj. Min. Maj. Min. Min. Maj. Min. Perf.
7|11 8 LsLsLLsLLsLsLLsLLsL Perf. Maj. Min. Maj. Min. Min. Maj. Min. Perf. Maj. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Perf.
6|12 19 sLLsLLsLLsLsLLsLLsL Perf. Min. Min. Maj. Min. Min. Maj. Min. Perf. Maj. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Perf.
5|13 11 sLLsLLsLsLLsLLsLLsL Perf. Min. Min. Maj. Min. Min. Maj. Min. Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Perf.
4|14 3 sLLsLLsLsLLsLLsLsLL Perf. Min. Min. Maj. Min. Min. Maj. Min. Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Min. Perf.
3|15 14 sLLsLsLLsLLsLLsLsLL Perf. Min. Min. Maj. Min. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Min. Perf.
2|16 6 sLLsLsLLsLLsLsLLsLL Perf. Min. Min. Maj. Min. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Perf.
1|17 17 sLsLLsLLsLLsLsLLsLL Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Perf.
0|18 9 sLsLLsLLsLsLLsLLsLL Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 12L 7s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
11\19 694.737 505.263 1:1 1.000 Equalized 12L 7s
62\107 695.327 504.673 6:5 1.200
51\88 695.455 504.545 5:4 1.250
91\157 695.541 504.459 9:7 1.286
40\69 695.652 504.348 4:3 1.333 Supersoft 12L 7s
109\188 695.745 504.255 11:8 1.375
69\119 695.798 504.202 7:5 1.400
98\169 695.858 504.142 10:7 1.429
29\50 696.000 504.000 3:2 1.500 Soft 12L 7s
105\181 696.133 503.867 11:7 1.571
76\131 696.183 503.817 8:5 1.600
123\212 696.226 503.774 13:8 1.625 Golden meantone (696.2145¢);
47\81 696.296 503.704 5:3 1.667 Semisoft 12L 7s
Meantone / meanpop;
112\193 696.373 503.627 12:7 1.714
65\112 696.429 503.571 7:4 1.750
83\143 696.503 503.497 9:5 1.800
18\31 696.774 503.226 2:1 2.000 Basic 12L 7s
Scales with tunings softer than this are proper
79\136 697.059 502.941 9:4 2.250
61\105 697.143 502.857 7:3 2.333 Meantone / huygens;
104\179 697.207 502.793 12:5 2.400
43\74 697.297 502.703 5:2 2.500 Semihard 12L 7s
Meantone / huygens / grosstone;
111\191 697.382 502.618 13:5 2.600 Golden grosstone (697.3969¢);
68\117 697.436 502.564 8:3 2.667
93\160 697.500 502.500 11:4 2.750
25\43 697.674 502.326 3:1 3.000 Hard 12L 7s
Meantone / meridetone
82\141 697.872 502.128 10:3 3.333
57\98 697.959 502.041 7:2 3.500
89\153 698.039 501.961 11:3 3.667
32\55 698.182 501.818 4:1 4.000 Superhard 12L 7s
71\122 698.361 501.639 9:2 4.500
39\67 698.507 501.493 5:1 5.000
46\79 698.734 501.266 6:1 6.000
7\12 700.000 500.000 1:0 → ∞ Collapsed 12L 7s
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