Mirkwai family: Difference between revisions
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{{Technical data page}} | |||
The '''mirkwai family''' of [[planar temperament]]s tempers out the [[mirkwai comma]], 16875/16807. | The '''mirkwai family''' of [[planar temperament]]s tempers out the [[mirkwai comma]], 16875/16807. | ||
= Mirkwai = | == Mirkwai == | ||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 16875/16807 (mirkwai) | [[Comma list]]: 16875/16807 (mirkwai) | ||
[[Mapping]]: [ | [[Mapping]]: [{{val| 1 0 0 0 }}, {{val| 0 1 3 3 }}, {{val| 0 0 -5 -4 }}] | ||
Mapping generators: ~2, ~3, ~7/5 | Mapping generators: ~2, ~3, ~7/5 | ||
| Line 10: | Line 13: | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit]] | * [[7-odd-limit]] | ||
: [|1 0 0 0 | : [{{monzo| 1 0 0 0 }}, {{monzo| 0 4/7 -4/7 5/7 }}, {{monzo| 0 -3/7 3/7 5/7 }}, {{monzo| 0 0 0 1 }}] | ||
: [[Eigenmonzo]]s: 2, 8/7, 6/5 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 8/7, 6/5 | ||
* [[9-odd-limit]] | * [[9-odd-limit]] | ||
: [|1 0 0 0 | : [{{monzo| 1 0 0 0 }}, {{monzo| 0 8/11 -4/11 5/11 }}, {{monzo| 0 -6/11 3/11 10/11 }}, {{monzo| 0 0 0 1 }}] | ||
: [[Eigenmonzo]]s: 2, 10/9, 8/7 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9, 8/7 | ||
{{ | {{Optimal ET sequence|legend=1| 31, 41, 72, 152, 224 }} | ||
[[Badness]]: 0.342 × 10<sup>-3</sup> | [[Badness]]: 0.342 × 10<sup>-3</sup> | ||
| Line 22: | Line 25: | ||
[[Projection pair]]s: 5 84375/16807 7 16875/2401 to 2.3.7/5 | [[Projection pair]]s: 5 84375/16807 7 16875/2401 to 2.3.7/5 | ||
= Indra = | == Indra == | ||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 540/539, 1375/1372 | [[Comma list]]: 540/539, 1375/1372 | ||
Mapping: [ | [[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 3 3 0 }}, {{val| 0 0 -5 -4 3 }}] | ||
Mapping generators: ~2, ~3, ~7/5 | Mapping generators: ~2, ~3, ~7/5 | ||
[[ | [[Mapping to lattice]]: [{{val| 0 2 1 2 3 }}, {{val| 0 -1 2 1 -3 }}] | ||
: [| | |||
Lattice basis: | Lattice basis: | ||
| Line 40: | Line 40: | ||
: Angle (15/14, 55/36) = 68.1048 deg | : Angle (15/14, 55/36) = 68.1048 deg | ||
{{ | [[Minimax tuning]]: | ||
* [[11-odd-limit]] | |||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10 10 -3 0 -5 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 6 6 -1 0 -3 }}, {{monzo| 20 18 -6 0 -9 }}] | |||
: [[Eigenmonzo]]s (unchanged-intervals): 2, 11/9, 5/4 | |||
{{Optimal ET sequence|legend=1| 31, 41, 72, 152, 224, 631d, 855d }} | |||
[[Badness]]: 0.266 × 10<sup>-3</sup> | [[Badness]]: 0.266 × 10<sup>-3</sup> | ||
| Line 48: | Line 53: | ||
Scales: [[indra31]] | Scales: [[indra31]] | ||
== Shibi == | === Shibi === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 540/539, 729/728, 1375/1372 | Comma list: 540/539, 729/728, 1375/1372 | ||
Mapping: [ | Mapping: [{{val| 1 0 0 0 2 -3 }}, {{val| 0 1 3 3 0 3 }}, {{val| 0 0 -5 -4 4 }}] | ||
{{Optimal ET sequence|legend=1| 31f, 39df, 41, 72, 111, 152f, 183, 224, 631d, 855d }} | |||
Badness: 0.721 × 10<sup>-3</sup> | Badness: 0.721 × 10<sup>-3</sup> | ||
== Yajna == | === Yajna === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 540/539, 625/624, 1375/1372 | Comma list: 540/539, 625/624, 1375/1372 | ||
Mapping: [ | Mapping: [{{val| 1 0 0 0 2 -4 }}, {{val| 0 1 3 3 0 11 }}, {{val| 0 0 -5 -4 3 -20 }}] | ||
Mapping generators: ~2, ~3, ~7/5 | Mapping generators: ~2, ~3, ~7/5 | ||
| Line 66: | Line 75: | ||
Minimax tuning: | Minimax tuning: | ||
* 13-odd-limit | * 13-odd-limit | ||
: [|1 0 0 0 0 0 | : [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 4/5 6/5 -4/5 0 0 1/5 }}, {{monzo| 8/5 2/5 -3/5 0 0 2/5 }}, {{monzo| 44/25 26/25 -24/25 0 0 11/25 }}, {{monzo| 62/25 48/25 -27/25 0 0 3/25 }}, {{monzo| 8/5 2/5 -8/5 0 0 7/5 }}] | ||
: [[Eigenmonzo]]s: 2, 10/9, 13/10 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9, 13/10 | ||
* 15-odd-limit minimax | * 15-odd-limit minimax | ||
: [|1 0 0 0 0 0 | : [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 0 1 0 0 0 0 }}, {{monzo| 5/4 1/2 0 -5/16 0 5/16 }}, {{monzo| 1 1 0 -1/4 0 1/4 }}, {{monzo| 5/4 3/2 0 3/16 0 -3/16 }}, {{monzo| 1 1 0 -5/4 0 5/4 }}] | ||
: [[Eigenmonzo]]s: 2, 14/13, 4/3 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 14/13, 4/3 | ||
{{Optimal ET sequence|legend=1| 31, 49f, 72, 103, 121, 152f, 193, 224 }} | |||
Badness: 0.700 × 10<sup>-3</sup> | Badness: 0.700 × 10<sup>-3</sup> | ||
== Vibhu == | === Vibhu === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 351/350, 540/539, 1375/1372 | Comma list: 351/350, 540/539, 1375/1372 | ||
Mapping: [ | Mapping: [{{val| 1 0 0 0 2 1 }}, {{val| 0 1 3 3 0 6 }}, {{val| 0 0 -5 -4 3 -14 }}] | ||
{{Optimal ET sequence|legend=1| 31, 64cdf, 72, 103, 111, 152, 175f, 183, 469f }} | |||
Badness: 0.826 × 10<sup>-3</sup> | Badness: 0.826 × 10<sup>-3</sup> | ||
== Vish == | === Vish === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 325/324, 364/363, 540/539 | Comma list: 325/324, 364/363, 540/539 | ||
Mapping: [ | Mapping: [{{val| 1 0 0 0 2 2 }}, {{val| 0 1 3 3 0 -2 }}, {{val| 0 0 -5 -4 3 10 }}] | ||
{{Optimal ET sequence|legend=1| 31f, 41, 72, 121, 193 }} | |||
Badness: 0.930 × 10<sup>-3</sup> | Badness: 0.930 × 10<sup>-3</sup> | ||
[[Category: | [[Category:Temperament families]] | ||
[[Category: | [[Category:Pages with mostly numerical content]] | ||
[[Category:Mirkwai]] | [[Category:Mirkwai family]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||