Mirkwai family: Difference between revisions
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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 | Subgroup: 2.3.5.7 | ||
| Line 24: | Line 24: | ||
[[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 | Subgroup: 2.3.5.7.11 | ||
| Line 52: | Line 52: | ||
Scales: [[indra31]] | Scales: [[indra31]] | ||
== Shibi == | === Shibi === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 63: | Line 63: | ||
Badness: 0.721 × 10<sup>-3</sup> | Badness: 0.721 × 10<sup>-3</sup> | ||
== Yajna == | === Yajna === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 84: | Line 84: | ||
Badness: 0.700 × 10<sup>-3</sup> | Badness: 0.700 × 10<sup>-3</sup> | ||
== Vibhu == | === Vibhu === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 95: | Line 95: | ||
Badness: 0.826 × 10<sup>-3</sup> | Badness: 0.826 × 10<sup>-3</sup> | ||
== Vish == | === Vish === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Revision as of 21:48, 1 June 2021
The mirkwai family of planar temperaments tempers out the mirkwai comma, 16875/16807.
Mirkwai
Subgroup: 2.3.5.7
Comma list: 16875/16807 (mirkwai)
Mapping: [⟨1 0 0 0], ⟨0 1 3 3], ⟨0 0 -5 -4]]
Mapping generators: ~2, ~3, ~7/5
- [[1 0 0 0⟩, [0 4/7 -4/7 5/7⟩, [0 -3/7 3/7 5/7⟩, [0 0 0 1⟩]
- Eigenmonzos: 2, 8/7, 6/5
- [[1 0 0 0⟩, [0 8/11 -4/11 5/11⟩, [0 -6/11 3/11 10/11⟩, [0 0 0 1⟩]
- Eigenmonzos: 2, 10/9, 8/7
Badness: 0.342 × 10-3
Projection pairs: 5 84375/16807 7 16875/2401 to 2.3.7/5
Indra
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372
Mapping: [⟨1 0 0 0 2], ⟨0 1 3 3 0], ⟨0 0 -5 -4 3]]
Mapping generators: ~2, ~3, ~7/5
Map to lattice: [⟨0 2 1 2 3], ⟨0 -1 2 1 -3]]
Lattice basis:
- 15/14 length = 0.6184, 55/36 length = 0.7585
- Angle (15/14, 55/36) = 68.1048 deg
- [[1 0 0 0 0⟩, [10 10 -3 0 -5⟩, [0 0 1 0 0⟩, [6 6 -1 0 -3⟩, [20 18 -6 0 -9⟩]
- Eigenmonzos: 2, 11/9, 5/4
Badness: 0.266 × 10-3
Projection pairs: 5 84375/16807 7 16875/2401 11 1372/125 to 2.3.7/5
Scales: indra31
Shibi
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1375/1372
Mapping: [⟨1 0 0 0 2 -4 -3], ⟨0 1 3 3 0 11 3], ⟨0 0 -5 -4 3 4]]
Vals: Template:Val list
Badness: 0.721 × 10-3
Yajna
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 625/624, 1375/1372
Mapping: [⟨1 0 0 0 2 -4], ⟨0 1 3 3 0 11], ⟨0 0 -5 -4 3 -20]]
Mapping generators: ~2, ~3, ~7/5
Minimax tuning:
- 13-odd-limit
- [[1 0 0 0 0 0⟩, [4/5 6/5 -4/5 0 0 1/5⟩, [8/5 2/5 -3/5 0 0 2/5⟩, [44/25 26/25 -24/25 0 0 11/25⟩, [62/25 48/25 -27/25 0 0 3/25⟩, [8/5 2/5 -8/5 0 0 7/5⟩]
- Eigenmonzos: 2, 10/9, 13/10
- 15-odd-limit minimax
- [[1 0 0 0 0 0⟩, [0 1 0 0 0 0⟩, [5/4 1/2 0 -5/16 0 5/16⟩, [1 1 0 -1/4 0 1/4⟩, [5/4 3/2 0 3/16 0 -3/16⟩, [1 1 0 -5/4 0 5/4⟩]
- Eigenmonzos: 2, 14/13, 4/3
Vals: Template:Val list
Badness: 0.700 × 10-3
Vibhu
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 1375/1372
Mapping: [⟨1 0 0 0 2 1], ⟨0 1 3 3 0 6], ⟨0 0 -5 -4 3 -14]]
Vals: Template:Val list
Badness: 0.826 × 10-3
Vish
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 540/539
Mapping: [⟨1 0 0 0 2 2], ⟨0 1 3 3 0 -2], ⟨0 0 -5 -4 3 10]]
Vals: Template:Val list
Badness: 0.930 × 10-3