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| The '''porwell family''' of rank-3 temperaments tempers out the porwell comma, {{monzo| 11 1 -3 -2 }} = [[6144/6125]]. | | The '''porwell family''' of rank-3 temperaments tempers out the porwell comma, {{monzo| 11 1 -3 -2 }} = [[6144/6125]]. |
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| == Porwell aka hewuermity == | | == Porwell a.k.a. hewuermity == |
| [[Subgroup]]: 2.3.5.7 | | [[Subgroup]]: 2.3.5.7 |
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| == Zeus == | | == Zeus == |
| {{Main| Zeus }} | | {{Main| Zeus }} |
| {{See also| Biyatismic clan #Zeus }}
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| [[Subgroup]]: 2.3.5.7.11 | | Zeus tempers out [[121/120]], [[176/175]], and [[385/384]]. See [[Biyatismic clan #Zeus]]. |
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| [[Comma list]]: 121/120, 176/175
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| {{Mapping|legend=1| 1 0 1 4 2 | 0 1 1 -1 1 | 0 0 -2 3 1 }}
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| [[Mapping to lattice]]: [{{val| 0 1 -1 2 0 }}, {{val| 0 1 1 -1 1 }}]
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| Lattice basis:
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| : 11/10, 11/8
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| : Angle (11/10, 11/8) = 87.464 degrees
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| [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.1530, ~11/10 = 157.0881 | |
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| [[Minimax tuning]]:
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| * [[11-odd-limit]]
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| : [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/9 10/9 -1/3 -2/9 0 }}, {{monzo| 22/9 2/9 1/3 -4/9 0 }}, {{monzo| 22/9 2/9 -2/3 5/9 0 }}, {{monzo| 10/3 2/3 0 -1/3 0 }}]
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| : [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5.9/7
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| {{Optimal ET sequence|legend=1| 15, 22, 31, 46, 53, 68, 77, 99, 130e }}
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| [[Badness]]: 0.400 × 10<sup>-3</sup>
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| [[Projection pair]]s: 5 600/121 7 2662/375 11 120/11 to 2.3.11/5 | |
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| Zeus11[22] [[hobbit]] [[transversal]]
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| : 33/32, 16/15, 11/10, 8/7, 64/55, 77/64, 5/4, 14/11, 4/3,
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| : 11/8, 45/32, 16/11, 3/2, 11/7, 8/5, 5/3, 55/32, 7/4,
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| : 11/6, 15/8, 64/33, 2
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| Zeus11[24] hobbit transversal
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| : 33/32, 16/15, 11/10, 9/8, 8/7, 77/64, 11/9, 5/4, 21/16, 4/3,
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| : 11/8, 45/32, 16/11, 3/2, 32/21, 8/5, 18/11, 5/3, 7/4, 16/9,
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| : 11/6, 15/8, 64/33, 2
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 121/120, 176/175, 351/350
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| Mapping: {{mapping| 1 0 1 4 2 7 | 0 1 1 -1 1 -2 | 0 0 -2 3 -1 -1 }}
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| Mapping to lattice: [{{val| 0 1 -1 2 0 -3 }}, {{val| 0 1 1 -1 1 -2 }}]
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| Lattice basis:
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| : 11/10 length = 0.7898, 11/8 length = 1.002
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| : Angle (11/10, 11/8) = 106.7439 degrees
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| Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.8679, ~11/10 = 156.9582
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| Minimax tuning:
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| * 13-odd-limit
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| : [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 11/9 10/9 -1/3 -2/9 0 0 }}, {{monzo| 22/9 2/9 1/3 -4/9 0 0 }}, {{monzo| 22/9 2/9 -2/3 5/9 0 0 }}, {{monzo| 10/3 2/3 0 -1/3 0 0 }}, {{monzo| 14/3 -8/3 1 1/3 0 0 }}]
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| : eigenmonzo (unchanged-interval) basis: 2.9/5.9/7
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| * 15-odd-limit
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| : [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 0 1 0 0 0 0 }}, {{monzo| 11/5 1/5 2/5 -2/5 0 0 }}, {{monzo| 11/5 1/5 -3/5 3/5 0 0 }}, {{monzo| 13/5 3/5 1/5 -1/5 0 0 }}, {{monzo| 38/5 -12/5 1/5 -1/5 0 0 }}]
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| : eigenmonzo (unchanged-interval) basis: 2.3.7/5
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| {{Optimal ET sequence|legend=1| 15, 22, 31, 46, 53, 77, 99, 130e }}
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| Badness: 0.934 × 10<sup>-3</sup>
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| Projection pairs: 5 600/121 7 2662/375 11 120/11 13 1280/99 to 2.3.11/5
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| Zeus13[22] hobbit transversal
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| : 260/243, 88/81, 11/10, 44/39, 162/143, 11/9, 16/13, 320/243, 4/3, 1040/729, 13/9, 729/520, 3/2, 99/65, 44/27, 18/11, 1280/729, 16/9, 11/6, 24/13, 243/130, 2
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| === Tinia ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 66/65, 121/120, 176/175
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| Mapping: {{mapping| 1 0 1 4 2 2 | 0 1 1 -1 1 1 | 0 0 -2 3 -1 -1 }}
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| Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 699.3420, ~11/10 = 155.3666
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| {{Optimal ET sequence|legend=1| 7, 9, 15, 22f, 24, 31 }}
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| Badness: 0.808 × 10<sup>-3</sup>
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| == Jupiter == | | == Jupiter == |