Hemifamity family: Difference between revisions
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The '''hemifamity family''' of temperaments are rank-3 temperaments tempering out [[5120/5103]]. | The '''hemifamity family''' of temperaments are rank-3 temperaments tempering out [[5120/5103]]. | ||
= Hemifamity = | == Hemifamity == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Projection pair]]s: 7 5120/729 | [[Projection pair]]s: 7 5120/729 | ||
== Music == | === Music === | ||
By Gene Ward Smith | By Gene Ward Smith | ||
* [http://www.archive.org/details/Choraled Choraled] [http://www.archive.org/download/Choraled/Genewardsmith-Choraled.mp3 play] | * [http://www.archive.org/details/Choraled Choraled] [http://www.archive.org/download/Choraled/Genewardsmith-Choraled.mp3 play] | ||
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* [http://clones.soonlabel.com/public/micro/hemifamity27/hemifamity27-IF-20100917.mp3 Hemifamity27] | * [http://clones.soonlabel.com/public/micro/hemifamity27/hemifamity27-IF-20100917.mp3 Hemifamity27] | ||
= Pele = | == Pele == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Projection pair]]s: 7 5120/729 11 655360/59049 | [[Projection pair]]s: 7 5120/729 11 655360/59049 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 78: | Line 78: | ||
Badness: 0.703 × 10<sup>-3</sup> | Badness: 0.703 × 10<sup>-3</sup> | ||
= Laka = | == Laka == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 94: | Line 94: | ||
Projection pairs: 5120/729 11 14348907/1310720 | Projection pairs: 5120/729 11 14348907/1310720 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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: [[Eigenmonzo]]s: 2, 11/8, 14/13 | : [[Eigenmonzo]]s: 2, 11/8, 14/13 | ||
== 17-limit == | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | Subgroup: 2.3.5.7.11.13.17 | ||
| Line 118: | Line 118: | ||
Vals: {{Val list| 58, 94, 111, 152f, 205 }} | Vals: {{Val list| 58, 94, 111, 152f, 205 }} | ||
= Akea = | == Akea == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Badness: 0.998 × 10<sup>-3</sup> | Badness: 0.998 × 10<sup>-3</sup> | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 160: | Line 160: | ||
Scales: [[akea46_13]] | Scales: [[akea46_13]] | ||
= Kapo = | == Kapo == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Badness]]: 0.994 × 10<sup>-3</sup> | [[Badness]]: 0.994 × 10<sup>-3</sup> | ||
= Lono = | == Lono == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 189: | Line 189: | ||
[[Badness]]: 1.18 × 10<sup>-3</sup> | [[Badness]]: 1.18 × 10<sup>-3</sup> | ||
= Namaka = | == Namaka == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 200: | Line 200: | ||
[[Badness]]: 1.74 × 10<sup>-3</sup> | [[Badness]]: 1.74 × 10<sup>-3</sup> | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Revision as of 21:32, 1 June 2021
The hemifamity family of temperaments are rank-3 temperaments tempering out 5120/5103.
Hemifamity
Subgroup: 2.3.5.7
Comma list c = 5120/5103
Mapping: [⟨1 0 0 10], ⟨0 1 0 -6], ⟨0 0 1 1]]
Mapping generators: ~2, ~3, ~5
Map to lattice: [⟨0 1 2 -4], ⟨0 0 1 1]]
Lattice basis:
- 3/2 length = 0.5670, 10/9 length = 1.8063
- Angle (3/2, 10/9) = 82.112 degrees
- 7-odd-limit: 3 and 7 1/7c sharp, 5 just
- [[1 0 0 0⟩, [10/7 1/7 1/7 -1/7⟩, [0 0 1 0⟩, [10/7 -6/7 1/7 6/7⟩]
- Eigenmonzos: 2, 5/4, 7/6
- 9-odd-limit: 3 1/8c sharp, 5 just, 7 1/4c sharp
- [[1 0 0 0⟩, [5/4 1/4 1/8 -1/8⟩, [0 0 1 0⟩, [5/2 -3/2 1/4 3/4⟩]
- Eigenmonzos: 2, 5/4, 9/7
Badness: 0.153 × 10-3
Projection pairs: 7 5120/729
Music
By Gene Ward Smith
By Chris Vaisvil
Pele
Subgroup: 2.3.5.7.11
Comma list: 441/440, 896/891
Mapping: [⟨1 0 0 10 17], ⟨0 1 0 -6 -10], ⟨0 0 1 1 1]]
- [[1 0 0 0 0⟩, [17/10 0 1/10 0 -1/10⟩, [17/5 -2 6/5 0 -1/5⟩, [16/5 -2 3/5 0 2/5⟩, [17/5 -2 1/5 0 4/5⟩]
- Eigenmonzos: 2, 10/9, 11/9
Map to lattice: [⟨0 1 4 -2 -6], ⟨0 0 -1 -1 -1]]
Lattice basis:
- 3/2 length = 0.3812, 56/55 length = 1.5893
- Angle(3/2, 56/55) = 90.4578 degrees
Badness: 0.648 × 10-3
Projection pairs: 7 5120/729 11 655360/59049
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 364/363
Mapping: [⟨1 0 0 10 17 22], ⟨0 1 0 -6 -10 -13], ⟨0 0 1 1 1 1]]
Minimax tuning:
- 13-odd-limit eigenmonzos: 2, 10/9, 13/10
- 15-odd-limit eigenmonzos: 2, 15/13, 6/5
Vals: Template:Val list
Badness: 0.703 × 10-3
Laka
Subgroup: 2.3.5.7.11
Comma list: 540/539, 5120/5103
Mapping: [⟨1 0 0 10 -18], ⟨0 1 0 -6 15], ⟨0 0 1 1 -1]]
- [[1 0 0 0 0⟩, [4/3 0 2/21 -1/21 1/21⟩, [0 0 1 0 0⟩, [2 0 3/7 2/7 -2/7⟩, [2 0 3/7 -5/7 5/7⟩]
- Eigenmonzos: 2, 5/4, 14/11
Projection pairs: 5120/729 11 14348907/1310720
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 847/845
Minimax tuning:
- 13- and 15-odd-limit
- [[1 0 0 0 0 0⟩, [13/8 -1/2 1/8 0 0 1/8⟩, [13/4 -3 5/4 0 0 1/4⟩, [7/2 0 1/2 0 0 -1/2⟩, [25/8 -9/2 5/8 0 0 13/8⟩, [13/4 -3 1/4 0 0 5/4⟩]
- Eigenmonzos: 2, 11/8, 14/13
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 352/351, 442/441, 540/539, 847/845
Mapping: [⟨1 0 0 10 -18 -13 32], ⟨0 1 0 -6 15 12 -22], ⟨0 0 1 1 -1 -1 3]]
Minimax tuning:
- 17-odd-limit
- [[1 0 0 0 0 0 0⟩, [13/12 0 0 1/12 1/6 -1/12 0⟩, [-7/4 0 0 5/4 3/2 -5/4 0⟩, [7/4 0 0 3/4 1/2 -3/4 0⟩, [0 0 0 0 1 0 0⟩, [7/4 0 0 -1/4 1/2 1/4 0⟩, [35/12 0 0 23/12 5/6 -23/12 0⟩]
- Eigenmonzos: 2, 11/8, 14/13
Vals: Template:Val list
Akea
Subgroup: 2.3.5.7.11
Comma list: 385/384, 2200/2187
Mapping: [⟨1 0 0 10 -3], ⟨0 1 0 -6 7], ⟨0 0 1 1 -2]]
Mapping generators: ~2, ~3, ~5
- [[1 0 0 0 0⟩, [5/3 0 1/6 -1/6 0⟩, {{monzo| 26/9 0 13/18 -7/18 -1/3>, [26/9 0 -5/18 11/18 -1/3⟩, [26/9 0 -5/18 -7/18 2/3⟩]
- Eigenmonzos: ~2, ~14/11, ~7/5
Badness: 0.998 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 352/351, 385/384
Mapping: [⟨1 0 0 10 -3 2], ⟨0 1 0 -6 7 4], ⟨0 0 1 1 -2 -2]]
Minimax tuning:
- 13- and 15-odd-limit
- [[1 0 0 0 0 0⟩, [5/3 0 1/6 -1/6 0 0⟩, [26/9 0 13/18 -7/18 -1/3 0⟩, [26/9 0 -5/18 11/18 -1/3 0⟩, [26/9 0 -5/18 -7/18 2/3 0⟩, [26/9 0 -7/9 1/9 2/3 0⟩]
- Eigenmonzos: 2, 14/11, 7/5
Lattice basis:
- 3/2 length = 0.5354, 27/20 length = 1.0463
- Angle (3/2, 27/20) = 80.5628 degrees
Map to lattice: [⟨0 1 3 -3 1 -2], ⟨0 0 -1 -1 2 2]]
Vals: Template:Val list
Badness: 0.822 × 10-3
Scales: akea46_13
Kapo
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 5120/5103
Mapping: [⟨1 0 0 10 7], ⟨0 1 1 -5 -2], ⟨0 0 2 2 -1]]
Mapping generators: ~2, ~3, ~128/99
- [[1 0 0 0 0⟩, [8/5 2/5 0 -1/15 -2/15⟩, [14/5 6/5 0 7/15 -16/15⟩, [16/5 -6/5 0 13/15 -4/15⟩, [16/5 -6/5 0 -2/15 11/15⟩]
- Eigenmonzos: 2, 11/9, 9/7
Badness: 0.994 × 10-3
Lono
Subgroup: 2.3.5.7.11
Comma list: 176/175, 5120/5103
Mapping: [⟨1 0 0 10 6], ⟨0 1 0 -6 -6], ⟨0 0 1 1 3]]
Badness: 1.18 × 10-3
Namaka
Subgroup: 2.3.5.7.11
Comma list: 3388/3375, 5120/5103
Mapping: [⟨1 0 0 10 -6], ⟨0 2 0 -12 9], ⟨0 0 1 1 1]]
Badness: 1.74 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 676/675, 847/845
Mapping: [⟨1 0 0 10 -6 -1], ⟨0 2 0 -12 9 3], ⟨0 0 1 1 1 1]]
Vals: Template:Val list
Badness: 0.781 × 10-3