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| The '''porwell family''' of rank-3 temperaments tempers out the porwell comma, {{monzo| 11 1 -3 -2 }} = [[6144/6125]]. | | {{Technical data page}} |
| | The '''porwell family''' of [[rank-3 temperament]]s tempers out the porwell comma, {{monzo| 11 1 -3 -2 }} = [[6144/6125]]. |
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| == Hewuermity == | | == Porwell a.k.a. hewuermity == |
| Subgroup: 2.3.5.7 | | [[Subgroup]]: 2.3.5.7 |
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| [[Comma list]]: [[6144/6125]] | | [[Comma list]]: [[6144/6125]] |
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| [[Mapping]]: [{{val| 1 0 1 4 }}, {{val| 0 1 1 -1 }}, {{val| 0 0 -2 3 }}]
| | {{Mapping|legend=1| 1 0 1 4 | 0 1 1 -1 | 0 0 -2 3 }} |
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| Mapping generators: ~2, ~3, ~35/32
| | : mapping generators: ~2, ~3, ~35/32 |
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| [[POTE generator]]s: ~3/2 = 702.3482, ~35/32 = 157.4677 | | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.3482, ~35/32 = 157.4677 |
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| [[Minimax tuning]]: | | [[Minimax tuning]]: |
| * 7- and [[9-odd-limit]] | | * 7- and [[9-odd-limit]] |
| : [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 11/5 1/5 2/5 -2/5 }}, {{monzo| 11/5 1/5 -3/5 3/5 }}] | | : {{monzo list| 1 0 0 0 | 0 1 0 0 | 11/5 1/5 2/5 -2/5 | 11/5 1/5 -3/5 3/5 }} |
| : [[Eigenmonzo]]s (unchanged-intervals): 4/3, 7/5 | | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5 |
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| {{Val list|legend=1| 15, 22, 31, 46, 53, 84, 99, 229, 251, 282, 381 }} | | {{Optimal ET sequence|legend=1| 15, 22, 31, 46, 53, 84, 99, 229, 251, 282, 381 }} |
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| [[Badness]]: 0.142 × 10<sup>-3</sup> | | [[Badness]]: 0.142 × 10<sup>-3</sup> |
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| == Zeus == | | == Zeus == |
| Subgroup: 2.3.5.7.11
| | {{Main| Zeus }} |
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| [[Comma list]]: 121/120, 176/175 | | Zeus tempers out [[121/120]], [[176/175]], and [[385/384]]. See [[Biyatismic clan #Zeus]]. |
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| [[Mapping]]: [{{val| 1 0 1 4 2 }}, {{val| 0 1 1 -1 1 }}, {{val| 0 0 -2 3 1 }}]
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| Mapping generators: ~2, ~3, ~11/10
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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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| [[POTE generator]]s: ~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]]s (unchanged-intervals): 2, 9/7, 7/5
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| {{Val list|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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| Scales:
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| * [[genus1155zeus|Euler(1155) genus in zeus temperament]]
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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: [{{val| 1 0 1 4 2 7 }}, {{val| 0 1 1 -1 1 -2 }}, {{val| 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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| POTE generators: ~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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| : Eigenmonzos (unchanged-intervals): 2, 9/7, 7/5
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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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| : Eigenmonzos (unchanged-intervals): 2, 4/3, 7/5
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| Vals: {{Val list| 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: [{{val| 1 0 1 4 2 2 }}, {{val| 0 1 1 -1 1 1 }}, {{val| 0 0 -2 3 -1 -1 }}]
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| POTE generators: ~3/2 = 699.3420, ~11/10 = 155.3666
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| Vals: {{Val list| 7, 9, 15, 22f, 24, 31 }}
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| Badness: 0.808 × 10<sup>-3</sup>
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| == Jupiter == | | == Jupiter == |
| Subgroup: 2.3.5.7.11 | | [[Subgroup]]: 2.3.5.7.11 |
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| [[Comma list]]: 540/539, 5632/5625 | | [[Comma list]]: 540/539, 5632/5625 |
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| [[Mapping]]: [{{val| 1 0 1 4 -5 }}, {{val| 0 1 1 -1 6 }}, {{val| 0 0 -2 3 -8 }}]
| | {{Mapping|legend=1| 1 0 1 4 -5 | 0 1 1 -1 6 | 0 0 -2 3 -8 }} |
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| Mapping generators: ~2, ~3, ~35/32
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| {{Val list|legend=1| 22, 31, 53, 84e, 99e, 121, 130, 152, 282, 434de, 465d, 617de, 747cde, 899cdde }} | | {{Optimal ET sequence|legend=1| 22, 31, 53, 84e, 99e, 121, 130, 152, 282, 434de, 465d, 617de, 747cde, 899cdde }} |
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| [[Badness]]: 0.562 × 10<sup>-3</sup> | | [[Badness]]: 0.562 × 10<sup>-3</sup> |
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| == Hera == | | == Hera == |
| Subgroup: 2.3.5.7.11 | | [[Subgroup]]: 2.3.5.7.11 |
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| [[Comma list]]: 6144/6125, 8019/8000 | | [[Comma list]]: 6144/6125, 8019/8000 |
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| [[Mapping]]: [{{val| 1 0 1 4 9 }}, {{val| 0 1 1 -1 -3 }}, {{val| 0 0 -2 3 -6 }}]
| | {{Mapping|legend=1| 1 0 1 4 9 | 0 1 1 -1 -3 | 0 0 -2 3 -6 }} |
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| Mapping generators: ~2, ~3, ~35/32
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| [[POTE generator]]s: ~3/2 = 701.8035, ~35/32 = 157.1649 | | [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 701.8035, ~35/32 = 157.1649 |
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| {{Val list|legend=1| 46, 53, 84, 99, 130, 183, 313, 359, 542c, 672c }} | | {{Optimal ET sequence|legend=1| 46, 53, 84, 99, 130, 183, 313, 359, 542c, 672c }} |
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| [[Badness]]: 2.23 × 10<sup>-3</sup> | | [[Badness]]: 2.23 × 10<sup>-3</sup> |
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| Comma list: 351/350, 2080/2079, 4096/4095 | | Comma list: 351/350, 2080/2079, 4096/4095 |
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| Mapping: [{{val| 1 0 1 4 9 7 }}, {{val| 0 1 1 -1 -3 -2 }}, {{val| 0 0 -2 3 -6 -1 }}] | | Mapping: {{mapping| 1 0 1 4 9 7 | 0 1 1 -1 -3 -2 | 0 0 -2 3 -6 -1 }} |
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| POTE generators: ~3/2 = 701.6641, ~35/32 = 157.1899 | | Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 701.6641, ~35/32 = 157.1899 |
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| Vals: {{Val list| 46, 53, 84, 99, 130, 183, 313 }}
| | {{Optimal ET sequence|legend=1| 46, 53, 84, 99, 130, 183, 313 }} |
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| Badness: 1.30 × 10<sup>-3</sup> | | Badness: 1.30 × 10<sup>-3</sup> |
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| == Semiporwell == | | == Semiporwell == |
| Subgroup: 2.3.5.7.11 | | [[Subgroup]]: 2.3.5.7.11 |
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| [[Comma list]]: 6144/6125, 9801/9800 | | [[Comma list]]: 6144/6125, 9801/9800 |
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| [[Mapping]]: [{{val| 2 0 0 11 14 }}, {{val| 0 1 1 -1 -2 }}, {{val| 0 0 2 -3 -1 }}]
| | {{Mapping|legend=1| 2 0 0 11 14 | 0 1 1 -1 -2 | 0 0 2 -3 -1 }} |
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| Mapping generators: ~99/70, ~3, ~128/99
| | : mapping generators: ~99/70, ~3, ~128/99 |
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| [[POTE generator]]s: ~3/2 = 702.4613, ~128/99 = 442.4903 | | [[Optimal tuning]] ([[POTE]]): ~99/70 = 1\2, ~3/2 = 702.4613, ~128/99 = 442.4903 |
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| {{Val list|legend=1| 22, 46, 68, 84, 106, 130, 152, 282, 328, 480, 1112bccddee, 1242ccddee, 1722bcccdddeee }} | | {{Optimal ET sequence|legend=1| 22, 46, 68, 84, 106, 130, 152, 282, 328, 480, 1112bccddee, 1242ccddee, 1722bcccdddeee }} |
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| [[Badness]]: 1.25 × 10<sup>-3</sup> | | [[Badness]]: 1.25 × 10<sup>-3</sup> |
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| Comma list: 1716/1715, 2080/2079, 3584/3575 | | Comma list: 1716/1715, 2080/2079, 3584/3575 |
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| Mapping: [{{val| 2 0 0 11 14 15 }}, {{val| 0 1 1 -1 -2 -1 }}, {{val| 0 0 2 -3 -1 -6 }}] | | Mapping: {{mapping| 2 0 0 11 14 15 | 0 1 1 -1 -2 -1 | 0 0 2 -3 -1 -6 }} |
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| POTE generators: ~3/2 = 702.3964, ~84/65 = 442.5902 | | Optimal tuning (POTE): ~99/70 = 1\2, ~3/2 = 702.3964, ~84/65 = 442.5902 |
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| Vals: {{Val list| 22f, 38e, 46, 68, 84, 130, 198, 282, 328, 480f, 610cdef, 808cdeff, 1090ccdeefff, 1418bcccddeeefff }}
| | {{Optimal ET sequence|legend=1| 22f, 38e, 46, 68, 84, 130, 198, 282, 328, 480f, 610cdef, 808cdeff, 1090ccdeefff, 1418bcccddeeefff }} |
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| Badness: 1.22 × 10<sup>-3</sup> | | Badness: 1.22 × 10<sup>-3</sup> |
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| [[Category:Temperament families]] | | [[Category:Temperament families]] |
| | [[Category:Pages with mostly numerical content]] |
| [[Category:Porwell family| ]] <!-- main article --> | | [[Category:Porwell family| ]] <!-- main article --> |
| | [[Category:Porwell| ]] <!-- key article --> |
| [[Category:Rank 3]] | | [[Category:Rank 3]] |