12L 7s: Difference between revisions

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Line 3: Line 3:
| nLargeSteps = 12
| nLargeSteps = 12
| nSmallSteps = 7
| nSmallSteps = 7
| Equalized = 8
| Equalized = 11
| Paucitonic = 5
| Paucitonic = 7
| Pattern = sLsLLsLLsLsLLsLLsLL
| Pattern = LLsLLsLLsLsLLsLLsLs
| Name = Meantone mega-chromatic
| Name = Meantone mega-chromatic
}}
}}


'''12L 7s''' is the MOS pattern of the [[meantone]] mega-chromatic scale. This MOS separates its small steps by intervals of 2L-2L-2L-1L-2L-2L-1L like the familiar [[12edo]] diatonic scale. The perfect fourth which generates it measures 5\12 (500 cents) to 8\19 (505.263 cents).
'''12L 7s''' is the MOS pattern of the [[meantone]] mega-chromatic scale. This MOS separates its small steps by intervals of 2L-2L-2L-1L-2L-2L-1L like the familiar [[12edo]] diatonic scale. The perfect fifth which generates it measures 11\19 (694.737 cents) to 7\12 (700 cents).


The meantone mega-chromatic scale with generator between 13\31 (503.226 cents) and 8\19 (505.263 cents) is [[Rothenberg propriety|proper]].
The meantone mega-chromatic scale with generator between 11\19 (694.737 cents) and 18\31 (696.774 cents) is [[Rothenberg propriety|proper]].


== Modes ==
== Modes ==
Line 35: Line 35:


== Scale tree ==
== Scale tree ==
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)
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="6" | Generator
! colspan="6" | Generator
Line 43: Line 47:
! Comments
! Comments
|-
|-
| 8\19 || || || || || || 505.263 || 1 || 1 || 1.000 ||  
| 11\19 || || || || || || 694.737 || 1 || 1 || 1.000 ||  
|-
|-
| || || || || || 45\107 || 504.673 || 6 || 5 || 1.200 ||  
| || || || || || 62\107 || 695.327 || 6 || 5 || 1.200 ||  
|-
|-
| || || || || 37\88 || || 504.545 || 5 || 4 || 1.250 ||  
| || || || || 51\88 || || 695.455 || 5 || 4 || 1.250 ||  
|-
|-
| || || || || || 66\157 || 504.459 || 9 || 7 || 1.286 ||  
| || || || || || 91\157 || 695.541 || 9 || 7 || 1.286 ||  
|-
|-
| || || || 29\69 || || || 504.348 || 4 || 3 || 1.333 ||  
| || || || 40\69 || || || 695.652 || 4 || 3 || 1.333 ||  
|-
|-
| || || || || || 79\188 || 504.255 || 11 || 8 || 1.375 ||
| || || || || || 109\188 || 695.745 || 11 || 8 || 1.375 ||
|-
|-
| || || || || 50\119 || || 504.202 || 7 || 5 || 1.400 ||  
| || || || || 69\119 || || 695.798 || 7 || 5 || 1.400 ||  
|-
|-
| || || || || || 71\169 || 504.142 || 10 || 7 || 1.428 ||  
| || || || || || 98\169 || 695.858 || 10 || 7 || 1.428 ||  
|-
|-
| || || 21\50 || || || || 504.000 || 3 || 2 || 1.500 || [[Meantone]] / [[Meanpop]]
| || || 29\50 || || || || 696.000 || 3 || 2 || 1.500 || [[Meantone]] / [[Meanpop]]
|-
|-
| || || || || || 76\181 || 503.867 || 11 || 7 || 1.571 ||
| || || || || || 105\181 || 696.133 || 11 || 7 || 1.571 ||
|-
|-
| || || || || 55\131 || || 503.817 || 8 || 5 || 1.600 ||  
| || || || || 76\131 || || 696.183 || 8 || 5 || 1.600 ||  
|-
|-
| || || || || || 89\212 || 503.774 || 13 || 8 || 1.625 || [[Golden meantone]] (Generator = 503.7855 cents)
| || || || || || 123\212 || 696.226 || 13 || 8 || 1.625 || [[Golden meantone]] (696.2145¢)
|-
|-
| || || || 34\81 || || || 503.704 || 5 || 3 || 1.667 || Meantone / Meanpop
| || || || 47\81 || || || 696.296 || 5 || 3 || 1.667 || Meantone / Meanpop
|-
|-
| || || || || || 81\193 || 503.627 || 12 || 7 || 1.714 ||
| || || || || || 112\193 || 696.373 || 12 || 7 || 1.714 ||
|-
|-
| || || || || 47\112 || || 503.571 || 7 || 4 || 1.750 ||
| || || || || 65\112 || || 696.429 || 7 || 4 || 1.750 ||
|-
|-
| || || || || || 60\143 || 503.497 || 9 || 5 || 1.800 ||
| || || || || || 83\143 || 696.503 || 9 || 5 || 1.800 ||
|-
|-
| || 13\31 || || || || || 503.226 || 2 || 1 || 2.000 || Basic meantone mega-chromatic <br>(Generators larger than this are proper)
| || 18\31 || || || || || 696.774 || 2 || 1 || 2.000 || Basic meantone mega-chromatic <br>(Generators smaller than this are proper)
|-
|-
| || || || || || 57\136 || 502.941 || 9 || 4 || 2.250 ||
| || || || || || 79\136 || 697.059 || 9 || 4 || 2.250 ||
|-
|-
| || || || || 44\105 || || 502.857 || 7 || 3 || 2.333 || Meantone / [[Huygens]]
| || || || || 61\105 || || 697.143 || 7 || 3 || 2.333 || Meantone / [[Huygens]]
|-
|-
| || || || || || 75\179 || 502.793 || 12 || 5 || 2.400 ||
| || || || || || 104\179 || 697.207 || 12 || 5 || 2.400 ||
|-
|-
| || || || 31\74 || || || 502.703 || 5 || 2 || 2.500 || Meantone / Huygens / [[Grosstone]]
| || || || 43\74 || || || 697.297 || 5 || 2 || 2.500 || Meantone / Huygens / [[Grosstone]]
|-
|-
| || || || || || 80\191 || 502.618 || 13 || 5 || 2.600 || Golden grosstone (Generator = 502.6031 cents)
| || || || || || 111\191 || 697.382 || 13 || 5 || 2.600 || Golden grosstone (697.3969¢)
|-
|-
| || || || || 49\117 || || 502.564 || 8 || 3 || 2.667 ||
| || || || || 68\117 || || 697.436 || 8 || 3 || 2.667 ||
|-
|-
| || || || || || 67\160 || 502.500 || 11 || 4 || 2.750 ||
| || || || || || 93\160 || 697.500 || 11 || 4 || 2.750 ||
|-
|-
| || || 18\43 || || || || 502.326 || 3 || 1 || 3.000 || Meantone / [[Meridetone]]
| || || 25\43 || || || || 697.674 || 3 || 1 || 3.000 || Meantone / [[Meridetone]]
|-
|-
| || || || || || 59\141 || 502.128 || 10 || 3 || 3.333 ||
| || || || || || 82\141 || 697.872 || 10 || 3 || 3.333 ||
|-
|-
| || || || || 41\98 || || 502.041 || 7 || 2 || 3.500 ||
| || || || || 57\98 || || 697.959 || 7 || 2 || 3.500 ||
|-
|-
| || || || || || 64\153 || 501.961 || 11 || 3 || 3.667 ||
| || || || || || 89\153 || 698.039 || 11 || 3 || 3.667 ||
|-
|-
| || || || 23\55 || || || 501.818 || 4 || 1 || 4.000 ||
| || || || 32\55 || || || 698.182 || 4 || 1 || 4.000 ||
|-
|-
| || || || || || 51\122 || 501.639 || 9 || 2 || 4.500 ||
| || || || || || 71\122 || 698.361 || 9 || 2 || 4.500 ||
|-
|-
| || || || || 28\67 || || 501.493 || 5 || 1 || 5.000 ||
| || || || || 39\67 || || 698.507 || 5 || 1 || 5.000 ||
|-
|-
| || || || || || 33\79 || 501.266 || 6 || 1 || 6.000 ||
| || || || || || 46\79 || 698.734 || 6 || 1 || 6.000 ||
|-
|-
| 5\12 || || || || || || 500.000 || 1 || 0 || → inf ||
| 7\12 || || || || || || 700.000 || 1 || 0 || → inf ||
|}
|}


Revision as of 23:54, 12 February 2022

↖ 11L 6s ↑ 12L 6s 13L 6s ↗
← 11L 7s 12L 7s 13L 7s →
↙ 11L 8s ↓ 12L 8s 13L 8s ↘ 
┌╥╥┬╥╥┬╥╥┬╥┬╥╥┬╥╥┬╥┬┐
│║║│║║│║║│║│║║│║║│║││
│││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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 is the MOS pattern of the meantone mega-chromatic scale. This MOS separates its small steps by intervals of 2L-2L-2L-1L-2L-2L-1L like the familiar 12edo diatonic scale. The perfect fifth which generates it measures 11\19 (694.737 cents) to 7\12 (700 cents).

The meantone mega-chromatic scale with generator between 11\19 (694.737 cents) and 18\31 (696.774 cents) is proper.

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

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 meantone mega-chromatic
(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
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