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Hemifamity family: Difference between revisions

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= Hemifamity =
= Hemifamity =
[[Comma]] c = 5120/5103
Subgroup: 2.3.5.7


7-limit minimax: 3 and 7 1/7c sharp, 5 just
[[Comma list]] c = 5120/5103


[|1 0 0 0>, |10/7 1/7 1/7 -1/7>,
[[Mapping]]: [<1 0 0 10|, <0 1 0 -6|, <0 0 1 1|]
|0 0 1 0>, |10/7 -6/7 1/7 6/7>]


[[Eigenmonzo]]s: 2, 5/4, 7/6
Mapping generators: ~2, ~3, ~5
 
9-limit minimax: 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>]
 
[[Eigenmonzo]]s: 2, 5/4, 9/7
 
Lattice basis: 3/2 length 0.5670, 10/9 length 1.8063
 
Angle(3/2, 10/9) = 82.112 degrees


Map to lattice: [<0 1 2 -4|, <0 0 1 1|]
Map to lattice: [<0 1 2 -4|, <0 0 1 1|]


Map: [<1 0 0 10|, <0 1 0 -6|, <0 0 1 1|]
Lattice basis:  
: 3/2 length = 0.5670, 10/9 length = 1.8063
: Angle (3/2, 10/9) = 82.112 degrees


Generators: 2, 3, 5
[[Minimax tuning]]:
* [[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>]
: [[Eigenmonzo]]s: 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>]
: [[Eigenmonzo]]s: 2, 5/4, 9/7


[[EDO|EDOs]]: [[99edo|99]], [[140edo|140]], [[239edo|239]], [[292edo|292]], [[391edo|391]], [[490edo|490]], [[881edo|881bd]]
{{Val list|legend=1| 99, 140, 239, 292, 391, 490, 881bd }}


Badness: 0.000153
[[Badness]]: 0.153 × 10<sup>-3</sup>


[[Projection pair]]s: 7 5120/729
[[Projection pair]]s: 7 5120/729
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== 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]


By Chris Vaisvil
By Chris Vaisvil
* [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 =
[[Comma]]s: 441/440, 896/891
Subgroup: 2.3.5.7.11
 
[[Minimax tuning]]
 
[|1 0 0 0 0&gt;, |17/10 0 1/10 0 -1/10&gt;,
|17/5 -2 6/5 0 -1/5&gt;,
|16/5 -2 3/5 0 2/5&gt;, |17/5 -2 1/5 0 4/5&gt;]


[[Eigenmonzo]]s: 2, 10/9, 11/9
[[Comma list]]: 441/440, 896/891


Lattice basis: 3/2 length 0.3812 56/55 length 1.5893
[[Mapping]]: [&lt;1 0 0 10 17|, &lt;0 1 0 -6 -10|, &lt;0 0 1 1 1|]


Angle(3/2, 56/55) = 90.4578 degrees
[[Minimax tuning]]:
* [[11-odd-limit]]
: [|1 0 0 0 0&gt;, |17/10 0 1/10 0 -1/10&gt;, |17/5 -2 6/5 0 -1/5&gt;, |16/5 -2 3/5 0 2/5&gt;, |17/5 -2 1/5 0 4/5&gt;]
: [[Eigenmonzo]]s: 2, 10/9, 11/9


Map to lattice: [&lt;0 1 4 -2 -6|, &lt;0 0 -1 -1 -1|]
Map to lattice: [&lt;0 1 4 -2 -6|, &lt;0 0 -1 -1 -1|]


Map: [&lt;1 0 0 10 17|, &lt;0 1 0 -6 -10|, &lt;0 0 1 1 1|]
Lattice basis:  
 
: 3/2 length = 0.3812, 56/55 length = 1.5893
[[Generator]]s: 2, 3, 5
: Angle(3/2, 56/55) = 90.4578 degrees


[[EDO|Edos]]: [[41edo|41]], [[46edo|46]], [[77edo|77e]], [[87edo|87]], [[99edo|99e]], [[128edo|128]], [[145edo|145]], [[186edo|186e]], [[232edo|232]], [[285edo|285e]], [[331edo|331e]]
{{Val list|legend=1| 41, 46, 77e, 87, 99e, 128, 145, 186e, 232, 285e, 331e }}


Badness: 0.000648
[[Badness]]: 0.000648


Projection pairs: 7 5120/729 11 655360/59049
[[Projection pair]]s: 7 5120/729 11 655360/59049


== 13-limit ==
== 13-limit ==
Commas: 196/195, 352/351, 364/363
Subgroup: 2.3.5.7.11.13


13-limit minimax
Comma list: 196/195, 352/351, 364/363


Eigenmonzos: 2, 10/9, 13/10
Mapping: [&lt;1 0 0 10 17 22|, &lt;0 1 0 -6 -10 -13|, &lt;0 0 1 1 1 1|]


15-limit minimax
Minimax tuning:
* 13-odd-limit
: Eigenmonzos: 2, 10/9, 13/10
* 15-odd-limit
: Eigenmonzos: 2, 15/13, 6/5


Eigenmonzos: 2, 15/13, 6/5
Vals: {{Val list| 29, 41, 46, 58, 87, 145, 232, 377cef }}


Map: [&lt;1 0 0 10 17 22|, &lt;0 1 0 -6 -10 -13|, &lt;0 0 1 1 1 1|]
Badness: 0.703 × 10<sup>-3</sup>


EDOs: 29, 41, 46, 58, 87, 145, 232, 377cef
= Laka =
Subgroup: 2.3.5.7.11


Badness: 0.000703
[[Comma list]]: 540/539, 5120/5103


= Laka =
[[Mapping]]: [&lt;1 0 0 10 -18|, &lt;0 1 0 -6 15|, &lt;0 0 1 1 -1|]
[[Comma]]s: 5120/5103, 540/539


[[Minimax tuning]]
[[Minimax tuning]]
 
: [|1 0 0 0 0&gt;, |4/3 0 2/21 -1/21 1/21&gt;, |0 0 1 0 0&gt;, |2 0 3/7 2/7 -2/7&gt;, |2 0 3/7 -5/7 5/7&gt;]
[|1 0 0 0 0&gt;, |4/3 0 2/21 -1/21 1/21&gt;,  
: [[Eigenmonzo]]s: 2, 5/4, 14/11
|0 0 1 0 0&gt;, |2 0 3/7 2/7 -2/7&gt;,  
|2 0 3/7 -5/7 5/7&gt;]
 
[[Eigenmonzo]]s: 2, 5/4, 14/11


Projection pairs: 5120/729 11 14348907/1310720
Projection pairs: 5120/729 11 14348907/1310720


Map: [&lt;1 0 0 10 -18|, &lt;0 1 0 -6 15|, &lt;0 0 1 1 -1|]
{{Val list|legend=1| 41, 53, 58, 94, 99e, 111, 152, 555de, 707de, 859bde }}
 
EDOs: {{EDOs|41, 53, 58, 94, 99e, 111, 152, 555de, 707de, 859bde}}


== 13-limit ==
== 13-limit ==
[[Comma]]s: 352/351, 540/539, 847/845
Subgroup: 2.3.5.7.11.13


13 and 15 limit minimax tuning
Comma list: 352/351, 540/539, 847/845


[|1 0 0 0 0 0&gt;, |13/8 -1/2 1/8 0 0 1/8&gt;,  
Minimax tuning:
|13/4 -3 5/4 0 0 1/4&gt;, |7/2 0 1/2 0 0 -1/2&gt;,  
* 13- and 15-odd-limit
|25/8 -9/2 5/8 0 0 13/8&gt;,  
: [|1 0 0 0 0 0&gt;, |13/8 -1/2 1/8 0 0 1/8&gt;, |13/4 -3 5/4 0 0 1/4&gt;, |7/2 0 1/2 0 0 -1/2&gt;, |25/8 -9/2 5/8 0 0 13/8&gt;, |13/4 -3 1/4 0 0 5/4&gt;]
|13/4 -3 1/4 0 0 5/4&gt;]
: [[Eigenmonzo]]s: 2, 11/8, 14/13
 
[[Eigenmonzo]]s: 2, 11/8, 14/13


== 17-limit ==
== 17-limit ==
[[Comma]]s: 352/351, 540/539, 847/845, 442/441
Subgroup: 2.3.5.7.11.13.17
 
17-limit minimax
 
[|1 0 0 0 0 0 0&gt;,
|13/12 0 0 1/12 1/6 -1/12 0&gt;,
|-7/4 0 0 5/4 3/2 -5/4 0&gt;,
|7/4 0 0 3/4 1/2 -3/4 0&gt;,
|0 0 0 0 1 0 0&gt;,
|7/4 0 0 -1/4 1/2 1/4 0&gt;,
|35/12 0 0 23/12 5/6 -23/12 0&gt;]
 
[[Eigenmonzo]]s: 2, 11/8, 14/13


Map: [&lt;1 0 0 10 -18 -13 32|,  
Comma list: 352/351, 540/539, 847/845, 442/441


&lt;0 1 0 -6 15 12 -22|, &lt;0 0 1 1 -1 -1 3|]
Mapping: [&lt;1 0 0 10 -18 -13 32|, &lt;0 1 0 -6 15 12 -22|, &lt;0 0 1 1 -1 -1 3|]


[[Generator]]s: 2, 3, 5
Minimax tuning:
* 17-odd-limit
: [|1 0 0 0 0 0 0&gt;, |13/12 0 0 1/12 1/6 -1/12 0&gt;, |-7/4 0 0 5/4 3/2 -5/4 0&gt;, |7/4 0 0 3/4 1/2 -3/4 0&gt;, |0 0 0 0 1 0 0&gt;, |7/4 0 0 -1/4 1/2 1/4 0&gt;, |35/12 0 0 23/12 5/6 -23/12 0&gt;]
: [[Eigenmonzo]]s: 2, 11/8, 14/13


[[EDO|Edos]]: [[94edo|94]], [[111edo|111]], [[152edo|152]], [[205edo|205]], [[345edo|345]]
Vals: {{Val list| 94, 111, 152, 205, 345 }}


= Akea =
= Akea =
[[Comma]]s: 385/384, 2200/2187
Subgroup: 2.3.5.7.11


[[Minimax tuning]]
[[Comma list]]: 385/384, 2200/2187


[|1 0 0 0 0&gt;, |5/3 0 1/6 -1/6 0&gt;,
[[Mapping]]: [&lt;1 0 0 10 -3|, &lt;0 1 0 -6 7|, &lt;0 0 1 1 -2|]
|26/9 0 13/18 -7/18 -1/3&gt;,
|26/9 0 -5/18 11/18 -1/3&gt;,
|26/9 0 -5/18 -7/18 2/3&gt;]


[[Eigenmonzo]]s: 2, 14/11, 7/5
Mapping generators: ~2, ~3, ~5


Map: [&lt;1 0 0 10 -3|, &lt;0 1 0 -6 7|, &lt;0 0 1 1 -2|]
[[Minimax tuning]]:  
* [[11-odd-limit]]
: [|1 0 0 0 0&gt;, |5/3 0 1/6 -1/6 0&gt;, |26/9 0 13/18 -7/18 -1/3&gt;, |26/9 0 -5/18 11/18 -1/3&gt;, |26/9 0 -5/18 -7/18 2/3&gt;]
: [[Eigenmonzo]]s: ~2, ~14/11, ~7/5


[[Generator]]s: 2, 3, 5
{{Val list|legend=1| 34, 41, 53, 87, 140, 181, 321 }}


EDOs: 34, 41, 53, 87, 140, 181, 321
Badness: 0.998 × 10<sup>-3</sup>


Badness: 0.000998
== 13-limit ==
 
Subgroup: 2.3.5.7.11.13
==13-limit==
Commas: 325/324, 352/351, 385/384


13 and 15 limit minimax
Comma list: 325/324, 352/351, 385/384


[|1 0 0 0 0 0&gt;, |5/3 0 1/6 -1/6 0 0&gt;,
Mapping: [&lt;1 0 0 10 -3 2|, &lt;0 1 0 -6 7 4|, &lt;0 0 1 1 -2 -2|]
|26/9 0 13/18 -7/18 -1/3 0&gt;,
|26/9 0 -5/18 11/18 -1/3 0&gt;,
|26/9 0 -5/18 -7/18 2/3 0&gt;,
|26/9 0 -7/9 1/9 2/3 0&gt;]


Eigenmonzos: 2, 14/11, 7/5
Minimax tuning:
* 13- and 15-odd-limit
: [|1 0 0 0 0 0&gt;, |5/3 0 1/6 -1/6 0 0&gt;, |26/9 0 13/18 -7/18 -1/3 0&gt;, |26/9 0 -5/18 11/18 -1/3 0&gt;, |26/9 0 -5/18 -7/18 2/3 0&gt;, |26/9 0 -7/9 1/9 2/3 0&gt;]
: Eigenmonzos: 2, 14/11, 7/5


Lattice basis: 3/2 length 0.5354 27/20 length 1.0463
Lattice basis:
 
: 3/2 length = 0.5354, 27/20 length = 1.0463
Angle(3/2, 27/20) = 80.5628 degrees
: Angle (3/2, 27/20) = 80.5628 degrees


Map to lattice: [&lt;0 1 3 -3 1 -2|, &lt;0 0 -1 -1 2 2|]
Map to lattice: [&lt;0 1 3 -3 1 -2|, &lt;0 0 -1 -1 2 2|]


Map: [&lt;1 0 0 10 -3 2|, &lt;0 1 0 -6 7 4|, &lt;0 0 1 1 -2 -2|]
Vals: {{Val list| 7, 41, 46, 53, 87, 94, 140, 181, 321, 408 }}


Generators: 2, 3, 5
Badness: 0.822 × 10<sup>-3</sup>


[[EDO|EDOs]]: 7, 41, 46, 53, 87, [[94edo|94]], [[140edo|140]], [[181edo|181]], [[321edo|321]], [[408edo|408]]
Scales: [[akea46_13]]
 
Badness: 0.000822
 
Scales: [[akea46_13|akea46_13]]


= Kapo =
= Kapo =
[[Comma]]s: 3025/3024, 5120/5103
Subgroup: 2.3.5.7.11


[[Minimax tuning]]
[[Comma list]]: 3025/3024, 5120/5103


[|1 0 0 0 0&gt;, |8/5 2/5 0 -1/15 -2/15&gt;,
[[Mapping]]: [&lt;1 0 0 10 7|, &lt;0 1 1 -5 -2|, &lt;0 0 2 2 -1|]
|14/5 6/5 0 7/15 -16/15&gt;,
|16/5 -6/5 0 13/15 -4/15&gt;,
|16/5 -6/5 0 -2/15 11/15&gt;]


[[Eigenmonzo]]s: 2, 11/9, 9/7
Mapping generators: ~2, ~3, ~128/99


Map: [&lt;1 0 0 10 7|, &lt;0 1 1 -5 -2|, &lt;0 0 2 2 -1|]
[[Minimax tuning]]:  
* [[11-odd-limit]]:
: [|1 0 0 0 0&gt;, |8/5 2/5 0 -1/15 -2/15&gt;, |14/5 6/5 0 7/15 -16/15&gt;, |16/5 -6/5 0 13/15 -4/15&gt;, |16/5 -6/5 0 -2/15 11/15&gt;]
: [[Eigenmonzo]]s: 2, 11/9, 9/7


[[Generator]]s: 2, 3, 128/99
Vals: {{Val list| 41, 87, 111, 152, 198, 239, 350, 391, 478, 589 }}


[[EDO|EDOs]]: 41, 87, 111, [[152edo|152]], [[198edo|198]], [[239edo|239]], [[350edo|350]], [[391edo|391]], [[478edo|478]], [[589edo|589]]
[[Badness]]: 0.994 × 10<sup>-3</sup>


Badness: 0.000994
= Lono =
Subgroup: 2.3.5.7.11


= Lono =
[[Comma list]]: 176/175, 5120/5103
Commas: 176/175, 5120/5103


Map: [&lt;1 0 0 10 6|, &lt;0 1 0 -6 -6|, &lt;0 0 1 1 3|]
[[Mapping]]: [&lt;1 0 0 10 6|, &lt;0 1 0 -6 -6|, &lt;0 0 1 1 3|]


EDOs: 7, 12, 39, 46, 53, 58, 99, 111
{{Val list|legend=1| 7, 12, 39, 46, 53, 58, 99, 111 }}


Badness: 0.00118
[[Badness]]: 1.18 × 10<sup>-3</sup>


= Namaka =
= Namaka =
Commas: 3388/3375, 5120/5103
Subgroup: 2.3.5.7.11


Map: [&lt;1 0 0 10 -6|, &lt;0 2 0 -12 9|, &lt;0 0 1 1 1|]
[[Comma list]]: 3388/3375, 5120/5103


EDOs: 29, 53, 58, 87, 111, 140, 198
[[Mapping]]: [&lt;1 0 0 10 -6|, &lt;0 2 0 -12 9|, &lt;0 0 1 1 1|]


Badness: 0.00174
{{Val list|legend=1| 29, 53, 58, 87, 111, 140, 198 }}
 
[[Badness]]: 1.74 × 10<sup>-3</sup>


== 13-limit ==
== 13-limit ==
Commas: 352/351, 676/675, 847/845
Subgroup: 2.3.5.7.11.13
 
Comma list: 352/351, 676/675, 847/845


Map: [&lt;1 0 0 10 -6 -1|, &lt;0 2 0 -12 9 3|, &lt;0 0 1 1 1 1|]
Mapping: [&lt;1 0 0 10 -6 -1|, &lt;0 2 0 -12 9 3|, &lt;0 0 1 1 1 1|]


EDOs: 29, 53, 58, 87, 111, 140, 198
Vals: {{Val list| 29, 53, 58, 87, 111, 140, 198 }}


Badness: 0.000781
Badness: 0.781 × 10<sup>-3</sup>


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Hemifamity]]
[[Category:Hemifamity]]
[[Category:Rank 3]]
[[Category:Rank 3]]
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