Ragismic microtemperaments: Difference between revisions

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[[Mapping]]: [{{val|9 1 1 12}}, {{val|0 2 3 2}}]
[[Mapping]]: [{{val|9 1 1 12}}, {{val|0 2 3 2}}]


[[Wedgie]]: {{multival|18 27 18 1 -22 -34}}
{{Multival|legend=1|18 27 18 1 -22 -34}}


Mapping generators: ~27/25, ~5/3
Mapping generators: ~27/25, ~5/3


[[POTE generators]]: ~36/35 = 49.0205; ~10/9 = 182.354; ~6/5 = 315.687; ~49/40 = 350.980
[[POTE generator]]s: ~36/35 = 49.0205; ~10/9 = 182.354; ~6/5 = 315.687; ~49/40 = 350.980


[[Vals]]: {{Val list| 27, 45, 72, 99, 171, 441, 612 }}
{{Val list|legend=1| 27, 45, 72, 99, 171, 441, 612 }}


[[Badness]]: 0.003610
[[Badness]]: 0.003610
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[[Mapping]]: [{{val|1 6 10 3}}, {{val|0 -23 -40 -1}}]
[[Mapping]]: [{{val|1 6 10 3}}, {{val|0 -23 -40 -1}}]


[[Wedgie]]: {{multival|23 40 1 10 -63 -110}}
{{Multival|legend=1|23 40 1 10 -63 -110}}


[[POTE generator]] ~8/7 = 230.336
[[POTE generator]] ~8/7 = 230.336


[[Vals]]: {{Val list| 26, 73, 99, 224, 323, 422, 745d }}
{{Val list|legend=1| 26, 73, 99, 224, 323, 422, 745d }}


[[Badness]]: 0.037648
[[Badness]]: 0.037648
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= Supermajor =
= Supermajor =
The generator for supermajor temperament is a supermajor third, 9/7, tuned about 0.0002 cents flat. 37 of these give (2^15)/3, 46 give (2^19)/5, and 75 give (2^30)/7, leading to a wedgie of {{multival|37 46 75 -13 15 45}}. This is clearly quite a complex temperament; it makes up for it, to the extent it does, with extreme accuracy: 1106 or 1277 can be used as tunings, leading to accuracy even greater than that of ennealimmal. The 80 note MOS is presumably the place to start, and if that isn't enough notes for you, there's always the 171 note MOS.
The generator for supermajor temperament is a supermajor third, 9/7, tuned about 0.002 cents flat. 37 of these give (2^15)/3, 46 give (2^19)/5, and 75 give (2^30)/7, leading to a wedgie of {{multival|37 46 75 -13 15 45}}. This is clearly quite a complex temperament; it makes up for it, to the extent it does, with extreme accuracy: 1106 or 1277 can be used as tunings, leading to accuracy even greater than that of ennealimmal. The 80 note MOS is presumably the place to start, and if that isn't enough notes for you, there's always the 171 note MOS.


[[Comma list]]: 4375/4374, 52734375/52706752
[[Comma list]]: 4375/4374, 52734375/52706752
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[[Mapping]]: [{{val|1 15 19 30}}, {{val|0 -37 -46 -75}}]
[[Mapping]]: [{{val|1 15 19 30}}, {{val|0 -37 -46 -75}}]


[[Wedgie]]: {{multival|37 46 75 -13 15 45}}
{{Multival|legend=1|37 46 75 -13 15 45}}


[[POTE generator]]: ~9/7 = 435.082
[[POTE generator]]: ~9/7 = 435.082


[[Vals]]: {{Val list| 11, 80, 171, 764, 1106, 1277, 3660, 4937, 6214 }}
{{Val list|legend=1| 11, 80, 171, 764, 1106, 1277, 3660, 4937, 6214 }}


[[Badness]]: 0.010836
[[Badness]]: 0.010836
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[[Mapping]]: [{{val|19 0 14 -37}}, {{val|0 1 1 3}}]
[[Mapping]]: [{{val|19 0 14 -37}}, {{val|0 1 1 3}}]


[[Wedgie]]: {{multival|19 19 57 -14 37 79}}
{{Multival|legend=1|19 19 57 -14 37 79}}


Mapping generators: ~28/27, ~3
Mapping generators: ~28/27, ~3
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[[POTE generator]]: ~3/2 = 701.880
[[POTE generator]]: ~3/2 = 701.880


[[Vals]]: {{Val list| 19, 152, 171, 665, 836, 1007, 2185 }}
{{Val list|legend=1| 19, 152, 171, 665, 836, 1007, 2185 }}


[[Badness]]: 0.010954
[[Badness]]: 0.010954
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[[Mapping]]: [{{val|10 4 9 2}}, {{val|0 5 6 11}}]
[[Mapping]]: [{{val|10 4 9 2}}, {{val|0 5 6 11}}]


[[Wedgie]]: {{multival|50 60 110 -21 34 87}}
{{Multival|legend=1|50 60 110 -21 34 87}}


[[POTE generator]]: ~6/5 = 315.577
[[POTE generator]]: ~6/5 = 315.577


[[Vals]]: {{Val list| 80, 190, 270, 1270, 1540, 1810, 2080 }}
{{Val list|legend=1| 80, 190, 270, 1270, 1540, 1810, 2080 }}


[[Badness]]: 0.080637
[[Badness]]: 0.080637
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[[Mapping]]: [{{val|1 -1 -3 6}}, {{val|0 17 35 -21}}]
[[Mapping]]: [{{val|1 -1 -3 6}}, {{val|0 17 35 -21}}]


[[Wedgie]]: {{val|17 35 -21 16 -81 -147}}
{{Multival|legend=1|17 35 -21 16 -81 -147}}


[[POTE generator]]: ~10/9 = 182.458
[[POTE generator]]: ~10/9 = 182.458


[[Vals]]: {{Val list| 46, 125, 171 }}
{{Val list|legend=1| 46, 125, 171 }}


[[Badness]]: 0.025184
[[Badness]]: 0.025184
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[[Mapping]]: [{{val|1 2 3 3}}, {{val|0 -19 -31 -9}}]
[[Mapping]]: [{{val|1 2 3 3}}, {{val|0 -19 -31 -9}}]


[[Wedgie]]: {{multival|19 31 9 5 -39 -66}}
{{Multival|legend=1|19 31 9 5 -39 -66}}


[[POTE generator]]: ~49/48 = 26.287
[[POTE generator]]: ~49/48 = 26.287


[[Vals]]: {{Val list| 45, 46, 91, 137d }}
{{Val list|legend=1| 45, 46, 91, 137d }}


[[Badness]]: 0.123291
[[Badness]]: 0.123291
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[[Mapping]]: [{{val|2 7 13 -1}}, {{val|0 -11 -24 19}}]
[[Mapping]]: [{{val|2 7 13 -1}}, {{val|0 -11 -24 19}}]


[[Wedgie]]: {{multival|22 48 -38 25 -122 -223}}
{{Multival|legend=1|22 48 -38 25 -122 -223}}


[[POTE generator]]: ~6912/6125 = 208.899
[[POTE generator]]: ~6912/6125 = 208.899


[[Vals]]: {{Val list| 46, 132, 178, 224, 270, 494, 764, 1034, 1798 }}
{{Val list|legend=1| 46, 132, 178, 224, 270, 494, 764, 1034, 1798 }}


[[Badness]]: 0.037000
[[Badness]]: 0.037000
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[[POTE generator]]: ~162/125 = 449.1269
[[POTE generator]]: ~162/125 = 449.1269


[[Vals]]: {{Val list| 8, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}
{{Val list|legend=1| 8, 163, 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}


[[Badness]]: 0.754866
[[Badness]]: 0.754866
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[[Mapping]]: [{{val|1 36 48 61}}, {{val|0 -55 -73 -93}}]
[[Mapping]]: [{{val|1 36 48 61}}, {{val|0 -55 -73 -93}}]


[[Wedgie]]: {{multival|55 73 93 -12 -7 11}}
{{Multival|legend=1|55 73 93 -12 -7 11}}


[[POTE generator]]: ~35/27 = 449.1270
[[POTE generator]]: ~35/27 = 449.1270


[[Vals]]: {{Val list| 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}
{{Val list|legend=1| 171, 863, 1034, 1205, 1376, 1547, 1718, 4983, 6701, 8419 }}


[[Badness]]: 0.015075
[[Badness]]: 0.015075
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[[Mapping]]: [{{val|7 2 -8 53}}, {{val|0 3 8 -11}}]
[[Mapping]]: [{{val|7 2 -8 53}}, {{val|0 3 8 -11}}]


[[Wedgie]]: {{multival|21 56 -77 40 -181 -336}}
{{Multival|legend=1|21 56 -77 40 -181 -336}}


[[POTE generator]]: ~27/20 = 519.716
[[POTE generator]]: ~27/20 = 519.716


[[Vals]]: {{Val list| 7, 217, 224, 441, 1106, 1547 }}
{{Val list|legend=1| 7, 217, 224, 441, 1106, 1547 }}


[[Badness]]: 0.029122
[[Badness]]: 0.029122