12L 7s: Difference between revisions

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This MOS divides its twelve large steps 2-2-2-1-2-2-1 like the familiar 12edo diatonic scale. The perfect fourth which generates it measures 5/12edo (500) to 8/19edo (505.263 cents).
{{Infobox MOS
| Periods = 1
| nLargeSteps = 12
| nSmallSteps = 7
| Equalized = 8
| Paucitonic = 5
| Pattern = sLsLLsLLsLsLLsLLsLL
| Name = Meantone mega-chromatic
}}


{| class="wikitable"
'''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).
 
The meantone mega-chromatic scale with generator between 13\31 (503.226 cents) and 8\19 (505.263 cents) is [[Rothenberg propriety|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 ==
{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
| 8\19 || || || || || || 505.263 || 1 || 1 || 1.000 ||
|-
| || || || || || 45\107 || 504.673 || 6 || 5 || 1.200 ||
|-
| || || || || 37\88 || || 504.545 || 5 || 4 || 1.250 ||
|-
| || || || || || 66\157 || 504.459 || 9 || 7 || 1.286 ||
|-
| || || || 29\69 || || || 504.348 || 4 || 3 || 1.333 ||
|-
| || || || || || 79\188 || 504.255 || 11 || 8 || 1.375 ||
|-
| || || || || 50\119 || || 504.202 || 7 || 5 || 1.400 ||
|-
|-
| | 5/12
| || || || || || 71\169 || 504.142 || 10 || 7 || 1.428 ||  
| |  
| |  
| |  
| |  
| | 500
|-
|-
| |  
| || || 21\50 || || || || 504.000 || 3 || 2 || 1.500 || [[Meantone]] / [[Meanpop]]
| |  
| |  
| |  
| | 28/67
| | 501.4925
|-
|-
| |  
| || || || || || 76\181 || 503.867 || 11 || 7 || 1.571 ||
| |  
| |  
| | 23/55
| |  
| | 501.818
|-
|-
| |  
| || || || || 55\131 || || 503.817 || 8 || 5 || 1.600 ||
| |  
| |  
| |  
| | 41/98
| | 502.041
|-
|-
| |  
| || || || || || 89\212 || 503.774 || 13 || 8 || 1.625 || [[Golden meantone]] (Generator = 503.7855 cents)
| |  
| |  
| |  
| |  
| | 502.237
|-
|-
| |  
| || || || 34\81 || || || 503.704 || 5 || 3 || 1.667 || Meantone / Meanpop
| |  
| | 18/43
| |  
| |  
| | 502.326
|-
|-
| |  
| || || || || || 81\193 || 503.627 || 12 || 7 || 1.714 ||
| |  
| |  
| |  
| |  
| | 502.524
|-
|-
| |  
| || || || || 47\112 || || 503.571 || 7 || 4 || 1.750 ||
| |  
| |  
| |  
| | 49/117
| | 502.564
|-
|-
| |  
| || || || || || 60\143 || 503.497 || 9 || 5 || 1.800 ||
| |  
| |  
| |  
| |  
| | 502.603
|-
|-
| |  
| || 13\31 || || || || || 503.226 || 2 || 1 || 2.000 || Basic meantone mega-chromatic <br>(Generators larger than this are proper)
| |  
| |  
| | 31/74
| |  
| | 502.703
|-
|-
| |  
| || || || || || 57\136 || 502.941 || 9 || 4 || 2.250 ||
| |  
| |  
| |  
| | 44/105
| | 502.857
|-
|-
| |  
| || || || || 44\105 || || 502.857 || 7 || 3 || 2.333 || Meantone / [[Huygens]]
| | 13/31
| |  
| |  
| |  
| | 503.226
|-
|-
| |  
| || || || || || 75\179 || 502.793 || 12 || 5 || 2.400 ||
| |  
| |  
| |  
| | 47/112
| | 503.429
|-
|-
| |  
| || || || 31\74 || || || 502.703 || 5 || 2 || 2.500 || Meantone / Huygens / [[Grosstone]]
| |  
| |  
| |  
| |  
| | 503.599
|-
|-
| |  
| || || || || || 80\191 || 502.618 || 13 || 5 || 2.600 || Golden grosstone (Generator = 502.6031 cents)
| |  
| |  
| | 34/81
| |  
| | 503.704
|-
|-
| |  
| || || || || 49\117 || || 502.564 || 8 || 3 || 2.667 ||
| |  
| |  
| |  
| |  
| | 503.7855
|-
|-
| |  
| || || || || || 67\160 || 502.500 || 11 || 4 || 2.750 ||
| |  
| |  
| |  
| | 55/131
| | 503.817
|-
|-
| |  
| || || 18\43 || || || || 502.326 || 3 || 1 || 3.000 || Meantone / [[Meridetone]]
| |  
| |  
| |  
| |  
| | 583.8685
|-
|-
| |  
| || || || || || 59\141 || 502.128 || 10 || 3 || 3.333 ||
| |  
| | 21/50
| |  
| |  
| | 504
|-
|-
| |  
| || || || || 41\98 || || 502.041 || 7 || 2 || 3.500 ||
| |  
| |  
| |  
| | 50/119
| | 504.202
|-
|-
| |  
| || || || || || 64\153 || 501.961 || 11 || 3 || 3.667 ||
| |  
| |  
| | 29/69
| |  
| | 504.348
|-
|-
| |  
| || || || 23\55 || || || 501.818 || 4 || 1 || 4.000 ||
| |  
| |  
| |  
| | 37/88
| | 504.5455
|-
|-
| | 8/19
| || || || || || 51\122 || 501.639 || 9 || 2 || 4.500 ||
| |  
|-
| |  
| || || || || 28\67 || || 501.493 || 5 || 1 || 5.000 ||
| |  
|-
| |  
| || || || || || 33\79 || 501.266 || 6 || 1 || 6.000 ||
| | 505.263
|-
| 5\12 || || || || || || 500.000 || 1 || 0 || → inf ||
|}
|}
[[Category:Scales]]
[[Category:Abstract MOS patterns]]
[[Category:19-tone scales]]
[[Category:Mega chromatic scales]]

Revision as of 23:02, 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 fourth which generates it measures 5\12 (500 cents) to 8\19 (505.263 cents).

The meantone mega-chromatic scale with generator between 13\31 (503.226 cents) and 8\19 (505.263 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

Generator Cents L s L/s Comments
8\19 505.263 1 1 1.000
45\107 504.673 6 5 1.200
37\88 504.545 5 4 1.250
66\157 504.459 9 7 1.286
29\69 504.348 4 3 1.333
79\188 504.255 11 8 1.375
50\119 504.202 7 5 1.400
71\169 504.142 10 7 1.428
21\50 504.000 3 2 1.500 Meantone / Meanpop
76\181 503.867 11 7 1.571
55\131 503.817 8 5 1.600
89\212 503.774 13 8 1.625 Golden meantone (Generator = 503.7855 cents)
34\81 503.704 5 3 1.667 Meantone / Meanpop
81\193 503.627 12 7 1.714
47\112 503.571 7 4 1.750
60\143 503.497 9 5 1.800
13\31 503.226 2 1 2.000 Basic meantone mega-chromatic
(Generators larger than this are proper)
57\136 502.941 9 4 2.250
44\105 502.857 7 3 2.333 Meantone / Huygens
75\179 502.793 12 5 2.400
31\74 502.703 5 2 2.500 Meantone / Huygens / Grosstone
80\191 502.618 13 5 2.600 Golden grosstone (Generator = 502.6031 cents)
49\117 502.564 8 3 2.667
67\160 502.500 11 4 2.750
18\43 502.326 3 1 3.000 Meantone / Meridetone
59\141 502.128 10 3 3.333
41\98 502.041 7 2 3.500
64\153 501.961 11 3 3.667
23\55 501.818 4 1 4.000
51\122 501.639 9 2 4.500
28\67 501.493 5 1 5.000
33\79 501.266 6 1 6.000
5\12 500.000 1 0 → inf
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