Mirkwai family: Difference between revisions
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Cmloegcmluin (talk | contribs) adding parenthetical "(unchanged intervals)" to eigenmonzo lists |
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* [[7-odd-limit]] | * [[7-odd-limit]] | ||
: [{{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 }}] | : [{{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]] | ||
: [{{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 }}] | : [{{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 | ||
{{Val list|legend=1| 31, 41, 72, 152, 224 }} | {{Val list|legend=1| 31, 41, 72, 152, 224 }} | ||
| Line 42: | Line 42: | ||
* [[11-odd-limit]] | * [[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 }}] | : [{{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: 2, 11/9, 5/4 | : [[Eigenmonzo]]s (unchanged intervals): 2, 11/9, 5/4 | ||
{{Val list|legend=1| 31, 41, 72, 152, 224, 631d, 855d }} | {{Val list|legend=1| 31, 41, 72, 152, 224, 631d, 855d }} | ||
| Line 75: | Line 75: | ||
* 13-odd-limit | * 13-odd-limit | ||
: [{{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 }}] | : [{{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 | ||
: [{{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 }}] | : [{{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 | ||
Vals: {{Val list| 31, 49f, 72, 103, 121, 152f, 193, 224 }} | Vals: {{Val list| 31, 49f, 72, 103, 121, 152f, 193, 224 }} | ||
Revision as of 18:33, 23 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 (unchanged intervals): 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 (unchanged intervals): 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 (unchanged intervals): 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 (unchanged intervals): 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 (unchanged intervals): 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