Subgroup temperaments: Difference between revisions
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[[Comma list]]: 64/63, 91/90, 4394/4375 | [[Comma list]]: 64/63, 91/90, 4394/4375 | ||
[[Gencom]]: [2 4/3; | [[Gencom]]: [2 4/3; 64/63 91/90 4394/4375] | ||
[[Gencom|Gencom mapping]]: [{{val|1 2 8 2 0 11}}, {{val|0 -1 -14 2 0 -18}}] | [[Gencom|Gencom mapping]]: [{{val|1 2 8 2 0 11}}, {{val|0 -1 -14 2 0 -18}}] | ||
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[[Comma list]]: 91/90, 126/125, 169/168 | [[Comma list]]: 91/90, 126/125, 169/168 | ||
[[Gencom]]: [2 9/7; | [[Gencom]]: [2 9/7; 91/90 126/125 169/168] | ||
[[Gencom|Gencom mapping]]: [{{val|1 6 8 11 0 10}}, {{val|0 -7 -9 -13 0 -10}}] | [[Gencom|Gencom mapping]]: [{{val|1 6 8 11 0 10}}, {{val|0 -7 -9 -13 0 -10}}] | ||
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[[Comma list]]: 2205/2197, 2401/2400, 4096/4095 | [[Comma list]]: 2205/2197, 2401/2400, 4096/4095 | ||
[[Gencom]]: [2 15/14; | [[Gencom]]: [2 15/14; 2205/2197 2401/2400 4096/4095] | ||
[[Gencom|Gencom mapping]]: [{{val|1 -1 6 4 0 4}}, {{val|0 26 -37 -12 0 -3}}] | [[Gencom|Gencom mapping]]: [{{val|1 -1 6 4 0 4}}, {{val|0 26 -37 -12 0 -3}}] | ||
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[[Comma list]]: 833/832, 1275/1274, 2025/2023, 2205/2197 | [[Comma list]]: 833/832, 1275/1274, 2025/2023, 2205/2197 | ||
[[Gencom]]: [2 15/14; | [[Gencom]]: [2 15/14; 833/832 1275/1274 2025/2023 2205/2197] | ||
[[Gencom|Gencom mapping]]: [{{val|1 -1 6 4 0 4 2}}, {{val|0 26 -37 -12 0 -3 21}}] | [[Gencom|Gencom mapping]]: [{{val|1 -1 6 4 0 4 2}}, {{val|0 26 -37 -12 0 -3 21}}] | ||
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Subgroup: 2.3.5.7.13 | Subgroup: 2.3.5.7.13 | ||
[[Comma list]] | [[Comma list]]: 625/624 729/728 4096/4095 | ||
[[Gencom]]: [2 4/3; | [[Gencom]]: [2 4/3; 625/624 729/728 4096/4095] | ||
[[Gencom|Gencom mapping]]: [{{val|1 2 -1 19 0 -10}}, {{val|0 -1 8 -39 0 33}}] | [[Gencom|Gencom mapping]]: [{{val|1 2 -1 19 0 -10}}, {{val|0 -1 8 -39 0 33}}] | ||
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[[Comma list]]: 625/624, 729/728, 1225/1224, 2880/2873 | [[Comma list]]: 625/624, 729/728, 1225/1224, 2880/2873 | ||
[[Gencom]]: [2 4/3; | [[Gencom]]: [2 4/3; 625/624 729/728 1225/1224 2880/2873] | ||
[[Gencom|Gencom mapping]]: [{{val|1 2 -1 19 0 -10 29}}, {{val|0 -1 8 -39 0 33 -60}}] | [[Gencom|Gencom mapping]]: [{{val|1 2 -1 19 0 -10 29}}, {{val|0 -1 8 -39 0 33 -60}}] | ||
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[[Comma list]]: 4096/4095, 4375/4374, 13720/13689 | [[Comma list]]: 4096/4095, 4375/4374, 13720/13689 | ||
[[Gencom]]: [2 10/9; | [[Gencom]]: [2 10/9; 4096/4095 4375/4374 13720/13689] | ||
[[Gencom|Gencom mapping]]: [{{val|1 -1 -3 6 0 11}}, {{val|0 17 35 -21 0 -48}}] | [[Gencom|Gencom mapping]]: [{{val|1 -1 -3 6 0 11}}, {{val|0 17 35 -21 0 -48}}] | ||
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[[Comma list]]: 833/832, 1225/1224, 1701/1700, 4096/4095 | [[Comma list]]: 833/832, 1225/1224, 1701/1700, 4096/4095 | ||
[[Gencom]]: [2 10/9; | [[Gencom]]: [2 10/9; 833/832 1225/1224 1701/1700 4096/4095] | ||
[[Gencom|Gencom mapping]]: [{{val|1 -1 -3 6 0 11 5}}, {{val|0 17 35 -21 0 -48 -6}}] | [[Gencom|Gencom mapping]]: [{{val|1 -1 -3 6 0 11 5}}, {{val|0 17 35 -21 0 -48 -6}}] | ||
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[[Comma list]]: 625/624, 2401/2400, 4096/4095 | [[Comma list]]: 625/624, 2401/2400, 4096/4095 | ||
[[Gencom]]: [2 117/112; | [[Gencom]]: [2 117/112; 625/624 2401/2400 4096/4095] | ||
[[Gencom|Gencom mapping]]: [{{val|1 3 2 3 0 1}}, {{val|0 -22 5 -3 0 42}}] | [[Gencom|Gencom mapping]]: [{{val|1 3 2 3 0 1}}, {{val|0 -22 5 -3 0 42}}] | ||
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[[Comma list]]: 625/624, 833/832, 1225/1224, 4096/4095 | [[Comma list]]: 625/624, 833/832, 1225/1224, 4096/4095 | ||
[[Gencom]]: [2 68/65; | [[Gencom]]: [2 68/65; 625/624 833/832 1225/1224 4096/4095] | ||
[[Gencom|Gencom mapping]]: [{{val|1 3 2 3 0 1 1}}, {{val|0 -22 5 -3 0 42 48}}] | [[Gencom|Gencom mapping]]: [{{val|1 3 2 3 0 1 1}}, {{val|0 -22 5 -3 0 42 48}}] | ||
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[[Comma list]]: 81/80, 121/120 | [[Comma list]]: 81/80, 121/120 | ||
[[Gencom]]: [2 11/9; | [[Gencom]]: [2 11/9; 81/80 121/120] | ||
[[Gencom|Gencom mapping]]: [{{val|1 1 0 0 2}}, {{val|0 2 8 0 5}}] | [[Gencom|Gencom mapping]]: [{{val|1 1 0 0 2}}, {{val|0 2 8 0 5}}] | ||
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[[Comma list]]: 100/99, 243/242 | [[Comma list]]: 100/99, 243/242 | ||
[[Gencom]]: [2 10/9; | [[Gencom]]: [2 10/9; 100/99 243/242] | ||
[[Gencom|Gencom mapping]]: [{{val|1 1 1 0 2}}, {{val|0 4 9 0 10}}] | [[Gencom|Gencom mapping]]: [{{val|1 1 1 0 2}}, {{val|0 4 9 0 10}}] | ||
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[[Comma list]]: 100/99, 144/143, 243/242 | [[Comma list]]: 100/99, 144/143, 243/242 | ||
[[Gencom]]: [2 10/9; | [[Gencom]]: [2 10/9; 100/99 243/242] | ||
[[Gencom|Gencom mapping]]: [{{val|1 1 1 0 2 4}}, {{val|0 4 9 0 10 -2}}] | [[Gencom|Gencom mapping]]: [{{val|1 1 1 0 2 4}}, {{val|0 4 9 0 10 -2}}] | ||
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Related temperaments: [[Gravity family|gravity]], [[Gravity family #Harry|harry]] | Related temperaments: [[Gravity family|gravity]], [[Gravity family #Harry|harry]] | ||
[[Gencom]]: [2 40/27; | [[Gencom]]: [2 40/27; 243/242 4000/3993] | ||
[[Gencom|Gencom mapping]]: [{{val|1 5 12 0 12}}, {{val|0 -6 -17 0 -15}}] | [[Gencom|Gencom mapping]]: [{{val|1 5 12 0 12}}, {{val|0 -6 -17 0 -15}}] | ||
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Subgroup: 2.3.5.11 | Subgroup: 2.3.5.11 | ||
[[Comma list]]: 4000/3993, | [[Comma list]]: 4000/3993, 9453125/9437184 | ||
[[Gencom]]: [2 11/8; | [[Gencom]]: [2 11/8; 4000/3993 9453125/9437184] | ||
[[Gencom|Gencom mapping]]: [{{val|1 14 6 0 3}}, {{val|0 -27 -8 0 1}}] | [[Gencom|Gencom mapping]]: [{{val|1 14 6 0 3}}, {{val|0 -27 -8 0 1}}] | ||
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[[Mapping|Sval mapping]]: [{{val|1 14 6 3}}, {{val|0 -27 -8 1}}] | [[Mapping|Sval mapping]]: [{{val|1 14 6 3}}, {{val|0 -27 -8 1}}] | ||
[[Tp tuning|POL2 generator]]: ~11/8 = | [[Tp tuning|POL2 generator]]: ~11/8 = 551.7778 | ||
{{Val list|legend=1| 37, 50, 87, 137, 224 }} | {{Val list|legend=1| 37, 50, 87, 137, 224 }} | ||
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[[Mapping|Sval mapping]]: [{{val|1 14 6 3 6}}, {{val|0 -27 -8 1 -5}}] | [[Mapping|Sval mapping]]: [{{val|1 14 6 3 6}}, {{val|0 -27 -8 1 -5}}] | ||
[[Tp tuning|POL2 generator]]: ~11/8 = | [[Tp tuning|POL2 generator]]: ~11/8 = 551.7753 | ||
{{Val list|legend=1| 37, 50, 87, 137, 224 }} | {{Val list|legend=1| 37, 50, 87, 137, 224 }} | ||
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[[Comma list]]: 99/98, 864/847 | [[Comma list]]: 99/98, 864/847 | ||
[[Gencom]]: [2 12/11; | [[Gencom]]: [2 12/11; 99/98 864/847] | ||
[[Gencom|Gencom mapping]]: [{{val|1 1 0 2 3}}, {{val|0 5 0 7 4}}] | [[Gencom|Gencom mapping]]: [{{val|1 1 0 2 3}}, {{val|0 5 0 7 4}}] | ||
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[[Comma list]]: 78/77, 99/98, 144/143 | [[Comma list]]: 78/77, 99/98, 144/143 | ||
[[Gencom]]: [2 12/11; | [[Gencom]]: [2 12/11; 78/77 99/98 144/143] | ||
[[Gencom|Gencom mapping]]: [{{val|1 1 0 2 3 3}}, {{val|0 5 0 7 4 6}}] | [[Gencom|Gencom mapping]]: [{{val|1 1 0 2 3 3}}, {{val|0 5 0 7 4 6}}] | ||
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[[Comma list]]: 64/63, 78/77, 99/98 | [[Comma list]]: 64/63, 78/77, 99/98 | ||
[[Gencom]]: [2 3/2; | [[Gencom]]: [2 3/2; 64/63 78/77 99/98] | ||
[[Gencom|Gencom mapping]]: [{{val|1 1 0 4 7 9}}, {{val|0 1 0 -2 -6 -9}}] | [[Gencom|Gencom mapping]]: [{{val|1 1 0 4 7 9}}, {{val|0 1 0 -2 -6 -9}}] | ||
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[[Comma list]]: 64/63, 243/242 | [[Comma list]]: 64/63, 243/242 | ||
[[Gencom]]: [2 11/9; | [[Gencom]]: [2 11/9; 64/63 243/242] | ||
[[Gencom|Gencom mapping]]: [{{val|1 1 0 4 2}}, {{val|0 2 0 -4 5}}] | [[Gencom|Gencom mapping]]: [{{val|1 1 0 4 2}}, {{val|0 2 0 -4 5}}] | ||
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[[Comma list]]: 64/63, 78/77, 144/143 | [[Comma list]]: 64/63, 78/77, 144/143 | ||
[[Gencom]]: [2 11/9; | [[Gencom]]: [2 11/9; 64/63 78/77 144/143] | ||
[[Gencom|Gencom mapping]]: [{{val|1 1 0 4 2 4}}, {{val|0 2 0 -4 5 -1}}] | [[Gencom|Gencom mapping]]: [{{val|1 1 0 4 2 4}}, {{val|0 2 0 -4 5 -1}}] | ||
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[[Comma list]]: 99/98, 243/242 | [[Comma list]]: 99/98, 243/242 | ||
[[Gencom]]: [2 9/7; | [[Gencom]]: [2 9/7; 99/98 243/242] | ||
[[Gencom|Gencom mapping]]: [{{val|1 3 0 6 7}}, {{val|0 -4 0 -9 -10}}] | [[Gencom|Gencom mapping]]: [{{val|1 3 0 6 7}}, {{val|0 -4 0 -9 -10}}] | ||
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Subgroup: 2.3.7 | Subgroup: 2.3.7 | ||
[[Comma list]] | [[Comma list]]: 14680064/14348907 | ||
[[Gencom]]: [2 3/2; 14680064/14348907] | [[Gencom]]: [2 3/2; 14680064/14348907] | ||
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[[Comma list]]: 896/891, 1331/1323 | [[Comma list]]: 896/891, 1331/1323 | ||
[[Gencom]]: [2 3/2; | [[Gencom]]: [2 3/2; 896/891 1331/1323] | ||
[[Gencom|Gencom mapping]]: [{{val|1 1 0 -6 -3}}, {{val|0 1 0 15 11}}] | [[Gencom|Gencom mapping]]: [{{val|1 1 0 -6 -3}}, {{val|0 1 0 15 11}}] | ||
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[[Comma list]]: 169/168, 352/351, 364/363 | [[Comma list]]: 169/168, 352/351, 364/363 | ||
[[Gencom]]: [2 3/2; | [[Gencom]]: [2 3/2; 169/169 352/351 364/363] | ||
[[Gencom|Gencom mapping]]: [{{val|1 1 0 -6 -3 -1}}, {{val|0 1 0 15 11 8}}] | [[Gencom|Gencom mapping]]: [{{val|1 1 0 -6 -3 -1}}, {{val|0 1 0 15 11 8}}] | ||
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Subgroup: 2.3.7 | Subgroup: 2.3.7 | ||
[[Comma]] | [[Comma]]: 177147/175616 | ||
[[Gencom]]: [2 81/56; 177147/175616] | [[Gencom]]: [2 81/56; 177147/175616] | ||
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[[Comma list]]: 169/168, 1029/1024 | [[Comma list]]: 169/168, 1029/1024 | ||
[[Gencom]]: [91/64 8/7; | [[Gencom]]: [91/64 8/7; 169/168 1029/1024] | ||
[[Mapping|Sval mapping]]: [{{val|2 2 6 7}}, {{val|0 3 -1 1}}] | [[Mapping|Sval mapping]]: [{{val|2 2 6 7}}, {{val|0 3 -1 1}}] | ||
[[Tp tuning|POL2 generator]]: ~8/7 = | [[Tp tuning|POL2 generator]]: ~8/7 = 233.6044 | ||
{{Val list|legend=1| 10, 26, 36, 154…, 190…, 226…, 262… }} | {{Val list|legend=1| 10, 26, 36, 154…, 190…, 226…, 262… }} | ||
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[[Comma list]]: 169/168, 273/272, 289/288 | [[Comma list]]: 169/168, 273/272, 289/288 | ||
[[Gencom]]: [17/12 8/7; | [[Gencom]]: [17/12 8/7; 169/168 273/272 289/288] | ||
[[Mapping|Sval mapping]]: [{{val|2 2 6 7 7}}, {{val|0 3 -1 1 3}}] | [[Mapping|Sval mapping]]: [{{val|2 2 6 7 7}}, {{val|0 3 -1 1 3}}] | ||
[[Tp tuning|POL2 generator]]: ~8/7 = | [[Tp tuning|POL2 generator]]: ~8/7 = 233.6155 | ||
{{Val list|legend=1| 10, 26, 36, 154…, 190…, 226… }} | {{Val list|legend=1| 10, 26, 36, 154…, 190…, 226… }} | ||
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Subgroup: 2.3.7 | Subgroup: 2.3.7 | ||
[[Comma]] | [[Comma]]: 1605632/1594323 | ||
[[Gencom]]: [2 2187/1792; | [[Gencom]]: [2 2187/1792; 1605632/1594323] | ||
[[Gencom|Gencom mapping]]: [{{val|1 1 0 -1}}, {{val|0 2 0 13}}] | [[Gencom|Gencom mapping]]: [{{val|1 1 0 -1}}, {{val|0 2 0 13}}] | ||
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[[Comma list]]: 243/242, 896/891 | [[Comma list]]: 243/242, 896/891 | ||
[[Gencom]]: [2 11/9; | [[Gencom]]: [2 11/9; 243/242 896/891] | ||
[[Gencom|Gencom mapping]]: [{{val|1 1 0 -1 2}}, {{val|0 2 0 13 5}}] | [[Gencom|Gencom mapping]]: [{{val|1 1 0 -1 2}}, {{val|0 2 0 13 5}}] | ||
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[[Comma list]]: 144/143, 243/242, 364/363 | [[Comma list]]: 144/143, 243/242, 364/363 | ||
[[Gencom]]: [2 11/9; | [[Gencom]]: [2 11/9; 144/143 243/242 364/363] | ||
[[Gencom|Gencom mapping]]: [{{val|1 1 0 -1 2 4}}, {{val|0 2 0 13 5 -1}}] | [[Gencom|Gencom mapping]]: [{{val|1 1 0 -1 2 4}}, {{val|0 2 0 13 5 -1}}] | ||
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The gencom below gives [[Margo Schulter]]'s favored basis | The gencom below gives [[Margo Schulter]]'s favored basis | ||
[[Gencom]]: [2 3/2 28/27; | [[Gencom]]: [2 3/2 28/27; 352/351 364/363] | ||
[[Gencom]] [[mapping]]: [{{val| 1 1 0 1 4 6 }}, {{val| 0 1 0 3 -1 -4 }}, {{val| 0 0 0 1 1 1 }}] | [[Gencom]] [[mapping]]: [{{val| 1 1 0 1 4 6 }}, {{val| 0 1 0 3 -1 -4 }}, {{val| 0 0 0 1 1 1 }}] | ||
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[[Comma list]]: 144/143, 243/242 | [[Comma list]]: 144/143, 243/242 | ||
[[Gencom]]: [2 11/9; | [[Gencom]]: [2 11/9; 144/143 243/242] | ||
[[Gencom|Gencom mapping]]: [{{val|1 1 0 0 2 4}}, {{val|0 2 0 0 5 -1}}] | [[Gencom|Gencom mapping]]: [{{val|1 1 0 0 2 4}}, {{val|0 2 0 0 5 -1}}] | ||
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Subgroup: 2.5.7 | Subgroup: 2.5.7 | ||
[[Comma]] | [[Comma]]: 4194304/4117715 | ||
[[Gencom]]: [2 8/7; 4194304/4117715] | [[Gencom]]: [2 8/7; 4194304/4117715] | ||
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=== Mercy === | === Mercy === | ||
Two generators make an [[8/7]]; seven generators make | Two generators make an [[8/7]]; seven generators make a [[8/5]]. Mercy can be thought of as a way to conceptualize the 2.5.7.13.17.19 subgroup of [[31edo]], and is the no-threes or elevens version of [[miracle]]. | ||
Subgroup: 2.5.7 | Subgroup: 2.5.7 | ||
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[[Comma list]]: 343/338, 640/637 | [[Comma list]]: 343/338, 640/637 | ||
[[Gencom]]: [2 14/13; | [[Gencom]]: [2 14/13; 343/338 640/637] | ||
[[Gencom|Gencom mapping]]: [{{val|1 0 3 3 4}}, {{val|0 0 -7 -2 -3}}] | [[Gencom|Gencom mapping]]: [{{val|1 0 3 3 4}}, {{val|0 0 -7 -2 -3}}] | ||
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[[Comma list]]: 170/169, 224/221, 640/637 | [[Comma list]]: 170/169, 224/221, 640/637 | ||
[[Gencom]]: [2 14/13; | [[Gencom]]: [2 14/13; 170/169 224/221 640/637] | ||
[[Gencom|Gencom mapping]]: [{{val|1 0 3 3 4 4}}, {{val|0 0 -7 -2 -3 1}}] | [[Gencom|Gencom mapping]]: [{{val|1 0 3 3 4 4}}, {{val|0 0 -7 -2 -3 1}}] | ||
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[[Comma list]]: 170/169, 343/338, 640/637, 16384/16055 | [[Comma list]]: 170/169, 343/338, 640/637, 16384/16055 | ||
[[Gencom]]: [2 14/13; | [[Gencom]]: [2 14/13; 170/169 343/338 640/637 16384/16055] | ||
[[Gencom|Gencom mapping]]: [{{val|1 0 3 3 4 4 3}}, {{val|0 0 -7 -2 -3 1 13}}] | [[Gencom|Gencom mapping]]: [{{val|1 0 3 3 4 4 3}}, {{val|0 0 -7 -2 -3 1 13}}] | ||
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[[Comma list]]: 896/891, 26411/26244 | [[Comma list]]: 896/891, 26411/26244 | ||
[[Gencom]]: [2 9/7; | [[Gencom]]: [2 9/7; 896/891 26411/26244] | ||
[[Gencom|Gencom mapping]]: [{{val|1 5/2 0 5 2}}, {{val|0 -5/2 0 -6 4}}] | [[Gencom|Gencom mapping]]: [{{val|1 5/2 0 5 2}}, {{val|0 -5/2 0 -6 4}}] | ||
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Subgroup: 2.9.7.11 | Subgroup: 2.9.7.11 | ||
[[Comma list]]: 41503/41472, | [[Comma list]]: 41503/41472, 322102/321489 | ||
[[Gencom]]: [2 77/72; 41503/41472 322102/321489] | [[Gencom]]: [2 77/72; 41503/41472 322102/321489] | ||
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[[Comma list]]: 225/224, 245/243 | [[Comma list]]: 225/224, 245/243 | ||
[[Gencom]]: [2 9/7; | [[Gencom]]: [2 9/7; 225/224 245/243] | ||
[[Gencom|Gencom mapping]]: [{{val|1 5/2 5/2 5}}, {{val|0 -5/2 -1/2 -6}}] | [[Gencom|Gencom mapping]]: [{{val|1 5/2 5/2 5}}, {{val|0 -5/2 -1/2 -6}}] | ||
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Comma list: 100/99, 225/224, 245/243 | Comma list: 100/99, 225/224, 245/243 | ||
Gencom: [2 9/7; | Gencom: [2 9/7; 100/99 225/224 245/243] | ||
Gencom mapping: [{{val|1 5/2 5/2 5 2}}, {{val|0 -5/2 -1/2 -6 4}}] | Gencom mapping: [{{val|1 5/2 5/2 5 2}}, {{val|0 -5/2 -1/2 -6 4}}] | ||
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Comma list: 100/99, 105/104, 144/143, 196/195 | Comma list: 100/99, 105/104, 144/143, 196/195 | ||
Gencom: [2 9/7; | Gencom: [2 9/7; 100/99 105/104 144/143 196/195] | ||
Gencom mapping: [{{val|1 5/2 5/2 5 2 7}}, {{val|0 -5/2 -1/2 -6 4 -9}}] | Gencom mapping: [{{val|1 5/2 5/2 5 2 7}}, {{val|0 -5/2 -1/2 -6 4 -9}}] | ||
| Line 1,135: | Line 1,135: | ||
[[Mapping|Sval mapping]]: [{{val|1 5 1 1 0}}, {{val|0 -4 7 8 11}}] | [[Mapping|Sval mapping]]: [{{val|1 5 1 1 0}}, {{val|0 -4 7 8 11}}] | ||
[[Tp tuning|POL2 generator]]: ~17/13 = | [[Tp tuning|POL2 generator]]: ~17/13 = 462.9606 | ||
{{Val list|legend=1| 13, 44, 57, 70}} | {{Val list|legend=1| 13, 44, 57, 70}} | ||