12L 7s

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↖ 11L 6s ↑ 12L 6s 13L 6s ↗
← 11L 7s 12L 7s 13L 7s →
↙ 11L 8s ↓ 12L 8s 13L 8s ↘ 
┌╥╥┬╥╥┬╥╥┬╥┬╥╥┬╥╥┬╥┬┐
│║║│║║│║║│║│║║│║║│║││
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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
Descends from 5L 2s
Ancestor's step ratio range 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¢.

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

Modes

Modes of 12L 7s
UDP Cyclic
order		 Step
pattern
18|0 1 LLsLLsLLsLsLLsLLsLs
17|1 12 LLsLLsLsLLsLLsLLsLs
16|2 4 LLsLLsLsLLsLLsLsLLs
15|3 15 LLsLsLLsLLsLLsLsLLs
14|4 7 LLsLsLLsLLsLsLLsLLs
13|5 18 LsLLsLLsLLsLsLLsLLs
12|6 10 LsLLsLLsLsLLsLLsLLs
11|7 2 LsLLsLLsLsLLsLLsLsL
10|8 13 LsLLsLsLLsLLsLLsLsL
9|9 5 LsLLsLsLLsLLsLsLLsL
8|10 16 LsLsLLsLLsLLsLsLLsL
7|11 8 LsLsLLsLLsLsLLsLLsL
6|12 19 sLLsLLsLLsLsLLsLLsL
5|13 11 sLLsLLsLsLLsLLsLLsL
4|14 3 sLLsLLsLsLLsLLsLsLL
3|15 14 sLLsLsLLsLLsLLsLsLL
2|16 6 sLLsLsLLsLLsLsLLsLL
1|17 17 sLsLLsLLsLLsLsLLsLL
0|18 9 sLsLLsLLsLsLLsLLsLL

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¢

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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