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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 ||
|}
|}


Retrieved from "https://en.xen.wiki/w/12L_7s"