12L 7s

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Todo: review
Adopt scale tree, review entries
↖ 11L 6s ↑12L 6s 13L 6s ↗
← 11L 7s12L 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 (diatonic)
Required 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
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 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

  • 18|0 LLsLLsLLsLsLLsLLsLs
  • 17|1 LLsLLsLsLLsLLsLLsLs
  • 16|2 LLsLLsLsLLsLLsLsLLs
  • 15|3 LLsLsLLsLLsLLsLsLLs
  • 14|4 LLsLsLLsLLsLsLLsLLs
  • 13|5 LsLLsLLsLLsLsLLsLLs
  • 12|6 LsLLsLLsLsLLsLLsLLs
  • 11|7 LsLLsLLsLsLLsLLsLsL
  • 10|8 LsLLsLsLLsLLsLLsLsL
  • 9|9 LsLLsLsLLsLLsLsLLsL
  • 8|10 LsLsLLsLLsLLsLsLLsL
  • 7|11 LsLsLLsLLsLsLLsLLsL
  • 6|12 sLLsLLsLLsLsLLsLLsL
  • 5|13 sLLsLLsLsLLsLLsLLsL
  • 4|14 sLLsLLsLsLLsLLsLsLL
  • 3|15 sLLsLsLLsLLsLLsLsLL
  • 2|16 sLLsLsLLsLLsLsLLsLL
  • 1|17 sLsLLsLLsLLsLsLLsLL
  • 0|18 sLsLLsLLsLsLLsLLsLL

Scale tree

Generator ranges:

  • Chroma-positive generator: 694.7368 cents (11\19) to 700 cents (7\12)
  • Chroma-negative generator: 500 cents (5\12) to 505.2632 cents (8\19)
Generator Cents L s L/s Comments
11\19 694.737 1 1 1.000
62\107 695.327 6 5 1.200
51\88 695.455 5 4 1.250
91\157 695.541 9 7 1.286
40\69 695.652 4 3 1.333
109\188 695.745 11 8 1.375
69\119 695.798 7 5 1.400
98\169 695.858 10 7 1.428
29\50 696.000 3 2 1.500 Meantone / Meanpop
105\181 696.133 11 7 1.571
76\131 696.183 8 5 1.600
123\212 696.226 13 8 1.625 Golden meantone (696.2145¢)
47\81 696.296 5 3 1.667 Meantone / Meanpop
112\193 696.373 12 7 1.714
65\112 696.429 7 4 1.750
83\143 696.503 9 5 1.800
18\31 696.774 2 1 2.000 Basic 12L 7s
(Generators smaller than this are proper)
79\136 697.059 9 4 2.250
61\105 697.143 7 3 2.333 Meantone / Huygens
104\179 697.207 12 5 2.400
43\74 697.297 5 2 2.500 Meantone / Huygens / Grosstone
111\191 697.382 13 5 2.600 Golden grosstone (697.3969¢)
68\117 697.436 8 3 2.667
93\160 697.500 11 4 2.750
25\43 697.674 3 1 3.000 Meantone / Meridetone
82\141 697.872 10 3 3.333
57\98 697.959 7 2 3.500
89\153 698.039 11 3 3.667
32\55 698.182 4 1 4.000
71\122 698.361 9 2 4.500
39\67 698.507 5 1 5.000
46\79 698.734 6 1 6.000
7\12 700.000 1 0 → inf