Porwell family: Difference between revisions
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{{Technical data page}} | {{Technical data page}} | ||
The '''porwell family''' of [[rank-3 temperament]]s tempers out the porwell comma | The '''porwell family''' of [[rank-3 temperament|rank-3]] [[regular temperament]]s [[tempering out|tempers out]] the [[porwell comma]] ({{monzo|legend=1| 11 1 -3 -2 }}, [[ratio]]: 6144/6125). | ||
== Porwell a.k.a. hewuermity == | == Porwell a.k.a. hewuermity == | ||
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{{Mapping|legend=1| 1 0 1 4 | 0 1 1 -1 | 0 0 -2 3 }} | {{Mapping|legend=1| 1 0 1 4 | 0 1 1 -1 | 0 0 -2 3 }} | ||
: mapping generators: ~2, ~3, ~35/32 | : mapping generators: ~2, ~3, ~35/32 | ||
[[Optimal tuning]] ([[POTE]]): ~2 = | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.3482{{c}}, ~35/32 = 157.4677{{c}} | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* 7- and [[9-odd-limit]] | * [[7-odd-limit|7-]] and [[9-odd-limit]] | ||
: {{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 }} | : {{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 basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5 | ||
{{Optimal ET sequence|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 }} | ||
[[Badness]]: 0.142 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.142 × 10<sup>-3</sup> | ||
[[Projection pair]]s: 3 6125/2048 to 2.5.7 | [[Projection pair]]s: <code>3 6125/2048</code> to 2.5.7 | ||
== Zeus == | == Zeus == | ||
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{{Optimal ET sequence|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 }} | ||
[[Badness]]: 0.562 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.562 × 10<sup>-3</sup> | ||
== Hera == | == Hera == | ||
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{{Mapping|legend=1| 1 0 1 4 9 | 0 1 1 -1 -3 | 0 0 -2 3 -6 }} | {{Mapping|legend=1| 1 0 1 4 9 | 0 1 1 -1 -3 | 0 0 -2 3 -6 }} | ||
[[Optimal tuning]] ([[POTE]]): ~2 = | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 701.8035{{c}}, ~35/32 = 157.1649{{c}} | ||
{{Optimal ET sequence|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 }} | ||
[[Badness]]: 2.23 × 10<sup>-3</sup> | [[Badness]] (Smith): 2.23 × 10<sup>-3</sup> | ||
=== 13-limit === | === 13-limit === | ||
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Mapping: {{mapping| 1 0 1 4 9 7 | 0 1 1 -1 -3 -2 | 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 }} | ||
Optimal tuning (POTE): ~2 = | Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 701.6641{{c}}, ~35/32 = 157.1899{{c}} | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 46, 53, 84, 99, 130, 183, 313 }} | ||
Badness: 1.30 × 10<sup>-3</sup> | Badness (Smith): 1.30 × 10<sup>-3</sup> | ||
== Semiporwell == | == Semiporwell == | ||
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{{Mapping|legend=1| 2 0 0 11 14 | 0 1 1 -1 -2 | 0 0 2 -3 -1 }} | {{Mapping|legend=1| 2 0 0 11 14 | 0 1 1 -1 -2 | 0 0 2 -3 -1 }} | ||
: mapping generators: ~99/70, ~3, ~128/99 | : mapping generators: ~99/70, ~3, ~128/99 | ||
[[Optimal tuning]] ([[POTE]]): ~99/70 = | [[Optimal tuning]] ([[POTE]]): ~99/70 = 600.0000{{c}}, ~3/2 = 702.4613{{c}}, ~128/99 = 442.4903{{c}} | ||
{{Optimal ET sequence|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 }} | ||
[[Badness]]: 1.25 × 10<sup>-3</sup> | [[Badness]] (Smith): 1.25 × 10<sup>-3</sup> | ||
=== 13-limit === | === 13-limit === | ||
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Mapping: {{mapping| 2 0 0 11 14 15 | 0 1 1 -1 -2 -1 | 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 }} | ||
Optimal tuning (POTE): ~99/70 = | Optimal tuning (POTE): ~99/70 = 600.0000{{c}}, ~3/2 = 702.3964{{c}}, ~84/65 = 442.5902{{c}} | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 22f, 38e, 46, 68, 84, 130, 198, 282, 328, 480f, 610cdef, 808cdeff, 1090ccdeefff, 1418bcccddeeefff }} | ||
Badness: 1.22 × 10<sup>-3</sup> | Badness (Smith): 1.22 × 10<sup>-3</sup> | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Porwell family| ]] <!-- main article --> | [[Category:Porwell family| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Revision as of 10:38, 22 April 2026
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The porwell family of rank-3 regular temperaments tempers out the porwell comma (monzo: [11 1 -3 -2⟩, ratio: 6144/6125).
Porwell a.k.a. hewuermity
Subgroup: 2.3.5.7
Mapping: [⟨1 0 1 4], ⟨0 1 1 -1], ⟨0 0 -2 3]]
- mapping generators: ~2, ~3, ~35/32
Optimal tuning (POTE): ~2 = 1200.0000 ¢, ~3/2 = 702.3482 ¢, ~35/32 = 157.4677 ¢
- 7- and 9-odd-limit
- [[1 0 0 0⟩, [0 1 0 0⟩, [11/5 1/5 2/5 -2/5⟩, [11/5 1/5 -3/5 3/5⟩]
- unchanged-interval (eigenmonzo) basis: 2.3.7/5
Optimal ET sequence: 15, 22, 31, 46, 53, 84, 99, 229, 251, 282, 381
Badness (Smith): 0.142 × 10-3
Projection pairs: 3 6125/2048 to 2.5.7
Zeus
Zeus tempers out 121/120, 176/175, and 385/384. See Biyatismic clan #Zeus.
Jupiter
Subgroup: 2.3.5.7.11
Comma list: 540/539, 5632/5625
Mapping: [⟨1 0 1 4 -5], ⟨0 1 1 -1 6], ⟨0 0 -2 3 -8]]
Optimal ET sequence: 22, 31, 53, 84e, 99e, 121, 130, 152, 282, 434de, 465d, 617de, 747cde, 899cdde
Badness (Smith): 0.562 × 10-3
Hera
Subgroup: 2.3.5.7.11
Comma list: 6144/6125, 8019/8000
Mapping: [⟨1 0 1 4 9], ⟨0 1 1 -1 -3], ⟨0 0 -2 3 -6]]
Optimal tuning (POTE): ~2 = 1200.0000 ¢, ~3/2 = 701.8035 ¢, ~35/32 = 157.1649 ¢
Optimal ET sequence: 46, 53, 84, 99, 130, 183, 313, 359, 542c, 672c
Badness (Smith): 2.23 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 2080/2079, 4096/4095
Mapping: [⟨1 0 1 4 9 7], ⟨0 1 1 -1 -3 -2], ⟨0 0 -2 3 -6 -1]]
Optimal tuning (POTE): ~2 = 1200.0000 ¢, ~3/2 = 701.6641 ¢, ~35/32 = 157.1899 ¢
Optimal ET sequence: 46, 53, 84, 99, 130, 183, 313
Badness (Smith): 1.30 × 10-3
Semiporwell
Subgroup: 2.3.5.7.11
Comma list: 6144/6125, 9801/9800
Mapping: [⟨2 0 0 11 14], ⟨0 1 1 -1 -2], ⟨0 0 2 -3 -1]]
- mapping generators: ~99/70, ~3, ~128/99
Optimal tuning (POTE): ~99/70 = 600.0000 ¢, ~3/2 = 702.4613 ¢, ~128/99 = 442.4903 ¢
Optimal ET sequence: 22, 46, 68, 84, 106, 130, 152, 282, 328, 480, 1112bccddee, 1242ccddee, 1722bcccdddeee
Badness (Smith): 1.25 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 3584/3575
Mapping: [⟨2 0 0 11 14 15], ⟨0 1 1 -1 -2 -1], ⟨0 0 2 -3 -1 -6]]
Optimal tuning (POTE): ~99/70 = 600.0000 ¢, ~3/2 = 702.3964 ¢, ~84/65 = 442.5902 ¢
Optimal ET sequence: 22f, 38e, 46, 68, 84, 130, 198, 282, 328, 480f, 610cdef, 808cdeff, 1090ccdeefff, 1418bcccddeeefff
Badness (Smith): 1.22 × 10-3