Trienstonic clan: Difference between revisions
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The '''trienstonic clan''' of temperaments tempers out [[28/27]], the septimal third-tone or trienstonic comma. | |||
Adding 16/15 to | |||
Adding 16/15 to 28/27 leads to father temperament, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are sharptone, sharp, and blacksmith. | |||
= Father = | |||
{{see also| Father family #Father }} | |||
Commas: 16/15, 28/27 | Commas: 16/15, 28/27 | ||
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[<1 0 0 0|, <3/2 0 -1/4 1/4|, <5/2 0 1/4 -1/4|, <5/2 0 -3/4 3/4|] | [<1 0 0 0|, <3/2 0 -1/4 1/4|, <5/2 0 1/4 -1/4|, <5/2 0 -3/4 3/4|] | ||
[[ | [[Eigenmonzo subgroup]]: 2.7/5 | ||
9-limit eigenmonzo subgroup: 2.9/5 | 9-limit eigenmonzo subgroup: 2.9/5 | ||
[[ | [[POTE generator]]: 742.002 | ||
Map: [<1 0 4 -2|, <0 1 -1 3|] | Map: [<1 0 4 -2|, <0 1 -1 3|] | ||
| Line 23: | Line 26: | ||
Badness: 0.0213 | Badness: 0.0213 | ||
=Uncle= | = Uncle = | ||
Commas: 28/27, 256/245 | Commas: 28/27, 256/245 | ||
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Badness: 0.0727 | Badness: 0.0727 | ||
=Octokaidecal= | = Octokaidecal = | ||
Commas: 28/27, 50/49 | Commas: 28/27, 50/49 | ||
| Line 45: | Line 48: | ||
9-limit eigenmonzo subgroup: 2.5 | 9-limit eigenmonzo subgroup: 2.5 | ||
[[ | [[POTE generator]]: 728.874 | ||
Map: [<2 0 -5 -4|, <0 1 3 3|] | Map: [<2 0 -5 -4|, <0 1 3 3|] | ||
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Badness: 0.0367 | Badness: 0.0367 | ||
==11-limit== | == 11-limit == | ||
Commas: 28/27, 50/49, 55/54 | Commas: 28/27, 50/49, 55/54 | ||
| Line 66: | Line 69: | ||
Badness: 0.0302 | Badness: 0.0302 | ||
=Opossum= | = Opossum = | ||
Commas: 28/27, 126/125 | Commas: 28/27, 126/125 | ||
| Line 73: | Line 76: | ||
9-limit eigenmonzo subgroup: 2.7 | 9-limit eigenmonzo subgroup: 2.7 | ||
[[ | [[POTE generator]]: ~10/9 = 159.691 | ||
Map: [<1 2 3 4|, <0 -3 -5 -9|] | Map: [<1 2 3 4|, <0 -3 -5 -9|] | ||
| Line 83: | Line 86: | ||
Badness: 0.0407 | Badness: 0.0407 | ||
==11-limit== | == 11-limit == | ||
Commas: 28/27, 55/54, 77/75 | Commas: 28/27, 55/54, 77/75 | ||
11-limit eigenmonzo subgroup: 2.7 | 11-limit eigenmonzo subgroup: 2.7 | ||
[[ | [[POTE generator]]: ~10/9 = 159.807 | ||
Map: [<1 2 3 4 4|, <0 -3 -5 -9 -4|] | Map: [<1 2 3 4 4|, <0 -3 -5 -9 -4|] | ||
| Line 96: | Line 99: | ||
Badness: 0.0223 | Badness: 0.0223 | ||
==13-limit== | == 13-limit == | ||
Commas: 28/27, 40/39, 55/54, 66/65 | Commas: 28/27, 40/39, 55/54, 66/65 | ||
| Line 103: | Line 106: | ||
15-limit eigenmonzo subgroup: 2.7 | 15-limit eigenmonzo subgroup: 2.7 | ||
[[ | [[POTE generator]]: ~10/9 = 158.805 | ||
Map: [<1 2 3 4 4 4|, <0 -3 -5 -9 -4 -2|] | Map: [<1 2 3 4 4 4|, <0 -3 -5 -9 -4 -2|] | ||
| Line 111: | Line 114: | ||
Badness: 0.0194 | Badness: 0.0194 | ||
=Wallaby= | = Wallaby = | ||
Commas: 28/27, 35/32 | Commas: 28/27, 35/32 | ||
| Line 124: | Line 127: | ||
Badness: 0.0585 | Badness: 0.0585 | ||
=Kangaroo= | = Kangaroo = | ||
== 5-limit == | |||
Comma: 64000/59049 | Comma: 64000/59049 | ||
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Badness: 0.2958 | Badness: 0.2958 | ||
==7-limit== | == 7-limit == | ||
Commas: 28/27, 1029/1000 | Commas: 28/27, 1029/1000 | ||
| Line 148: | Line 152: | ||
Badness: 0.0779 | Badness: 0.0779 | ||
==11-limit== | == 11-limit == | ||
Commas: 28/27, 77/75, 245/242 | Commas: 28/27, 77/75, 245/242 | ||
| Line 159: | Line 163: | ||
Badness: 0.0432 | Badness: 0.0432 | ||
==13-limit== | == 13-limit == | ||
Commas: 28/27, 40/39, 77/75, 147/143 | Commas: 28/27, 40/39, 77/75, 147/143 | ||
| Line 170: | Line 174: | ||
Badness: 0.0327 | Badness: 0.0327 | ||
=Quindecic= | = Quindecic = | ||
Commas: 28/27, 49/48, 55/54, 77/75 | Commas: 28/27, 49/48, 55/54, 77/75 | ||
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Badness: 0.0289 | Badness: 0.0289 | ||
[[Category:Theory]] | |||
[[Category:Temperament clan]] | |||
[[Category:Trienstonic]] | |||
[[Category:Rank 2]] | |||