Aberschismic family: Difference between revisions

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__FORCETOC__
The '''hemifamity family''' of temperaments are rank-3 temperaments tempering out [[5120/5103]].
=Vital statistics=
 
[[Comma|Comma]] c = 5120/5103
= Hemifamity =
[[Comma]] c = 5120/5103


7-limit minimax: 3 and 7 1/7c sharp, 5 just
7-limit minimax: 3 and 7 1/7c sharp, 5 just
Line 8: Line 9:
|0 0 1 0>, |10/7 -6/7 1/7 6/7>]
|0 0 1 0>, |10/7 -6/7 1/7 6/7>]


[[Eigenmonzo|Eigenmonzos]]: 2, 5/4, 7/6
[[Eigenmonzo]]s: 2, 5/4, 7/6


9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp
9-limit minimax: 3 1/8c sharp, 5 just, 7 1/4c sharp
Line 15: Line 16:
|0 0 1 0>, |5/2 -3/2 1/4 3/4>]
|0 0 1 0>, |5/2 -3/2 1/4 3/4>]


[[Eigenmonzo|Eigenmonzos]]: 2, 5/4, 9/7
[[Eigenmonzo]]s: 2, 5/4, 9/7


Lattice basis: 3/2 length 0.5670, 10/9 length 1.8063
Lattice basis: 3/2 length 0.5670, 10/9 length 1.8063
Line 31: Line 32:
Badness: 0.000153
Badness: 0.000153


[[Projection_pair|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]


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|Commas]]: 441/440, 896/891
[[Comma]]s: 441/440, 896/891


[[Minimax_tuning|Minimax tuning]]
[[Minimax tuning]]


[|1 0 0 0 0>, |17/10 0 1/10 0 -1/10>,  
[|1 0 0 0 0>, |17/10 0 1/10 0 -1/10>,  
Line 51: Line 52:
|16/5 -2 3/5 0 2/5>, |17/5 -2 1/5 0 4/5>]
|16/5 -2 3/5 0 2/5>, |17/5 -2 1/5 0 4/5>]


[[Eigenmonzo|Eigenmonzos]]: 2, 10/9, 11/9
[[Eigenmonzo]]s: 2, 10/9, 11/9


Lattice basis: 3/2 length 0.3812 56/55 length 1.5893
Lattice basis: 3/2 length 0.3812 56/55 length 1.5893
Line 61: Line 62:
Map: [<1 0 0 10 17|, <0 1 0 -6 -10|, <0 0 1 1 1|]
Map: [<1 0 0 10 17|, <0 1 0 -6 -10|, <0 0 1 1 1|]


[[generator|Generators]]: 2, 3, 5
[[Generator]]s: 2, 3, 5


[[EDO|Edos]]: [[41edo|41]], [[46edo|46]], [[77edo|77e]], [[87edo|87]], [[99edo|99e]], [[128edo|128]], [[145edo|145]], [[186edo|186e]], [[232edo|232]], [[285edo|285e]], [[331edo|331e]]
[[EDO|Edos]]: [[41edo|41]], [[46edo|46]], [[77edo|77e]], [[87edo|87]], [[99edo|99e]], [[128edo|128]], [[145edo|145]], [[186edo|186e]], [[232edo|232]], [[285edo|285e]], [[331edo|331e]]
Line 69: Line 70:
Projection pairs: 7 5120/729 11 655360/59049
Projection pairs: 7 5120/729 11 655360/59049


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


Line 87: Line 88:


= Laka =
= Laka =
[[Comma|Commas]]: 5120/5103, 540/539
[[Comma]]s: 5120/5103, 540/539


[[Minimax tuning]]
[[Minimax tuning]]
Line 95: Line 96:
|2 0 3/7 -5/7 5/7>]
|2 0 3/7 -5/7 5/7>]


[[Eigenmonzo|Eigenmonzos]]: 2, 5/4, 14/11
[[Eigenmonzo]]s: 2, 5/4, 14/11


Projection pairs: 5120/729 11 14348907/1310720
Projection pairs: 5120/729 11 14348907/1310720
Line 103: Line 104:
EDOs: {{EDOs|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|Commas]]: 352/351, 540/539, 847/845
[[Comma]]s: 352/351, 540/539, 847/845


13 and 15 limit minimax tuning
13 and 15 limit minimax tuning
Line 113: Line 114:
|13/4 -3 1/4 0 0 5/4>]
|13/4 -3 1/4 0 0 5/4>]


[[Eigenmonzo|Eigenmonzos]]: 2, 11/8, 14/13
[[Eigenmonzo]]s: 2, 11/8, 14/13


==17 limit==
== 17-limit ==
[[Comma|Commas]]: 352/351, 540/539, 847/845, 442/441
[[Comma]]s: 352/351, 540/539, 847/845, 442/441


17-limit minimax
17-limit minimax
Line 128: Line 129:
|35/12 0 0 23/12 5/6 -23/12 0>]
|35/12 0 0 23/12 5/6 -23/12 0>]


[[Eigenmonzo|Eigenmonzos]]: 2, 11/8, 14/13
[[Eigenmonzo]]s: 2, 11/8, 14/13


Map: [<1 0 0 10 -18 -13 32|,  
Map: [<1 0 0 10 -18 -13 32|,  
Line 134: Line 135:
<0 1 0 -6 15 12 -22|, <0 0 1 1 -1 -1 3|]
<0 1 0 -6 15 12 -22|, <0 0 1 1 -1 -1 3|]


[[generator|Generators]]: 2, 3, 5
[[Generator]]s: 2, 3, 5


[[EDO|Edos]]: [[94edo|94]], [[111edo|111]], [[152edo|152]], [[205edo|205]], [[345edo|345]]
[[EDO|Edos]]: [[94edo|94]], [[111edo|111]], [[152edo|152]], [[205edo|205]], [[345edo|345]]


=Akea=
= Akea =
[[Comma|Commas]]: 385/384, 2200/2187
[[Comma]]s: 385/384, 2200/2187


[[Minimax_tuning|Minimax tuning]]
[[Minimax tuning]]


[|1 0 0 0 0>, |5/3 0 1/6 -1/6 0>,  
[|1 0 0 0 0>, |5/3 0 1/6 -1/6 0>,  
Line 148: Line 149:
|26/9 0 -5/18 -7/18 2/3>]
|26/9 0 -5/18 -7/18 2/3>]


[[Eigenmonzo|Eigenmonzos]]: 2, 14/11, 7/5
[[Eigenmonzo]]s: 2, 14/11, 7/5


Map: [<1 0 0 10 -3|, <0 1 0 -6 7|, <0 0 1 1 -2|]
Map: [<1 0 0 10 -3|, <0 1 0 -6 7|, <0 0 1 1 -2|]


[[generator|Generators]]: 2, 3, 5
[[Generator]]s: 2, 3, 5


EDOs: 34, 41, 53, 87, 140, 181, 321
EDOs: 34, 41, 53, 87, 140, 181, 321
Line 187: Line 188:
Scales: [[akea46_13|akea46_13]]
Scales: [[akea46_13|akea46_13]]


=Kapo=
= Kapo =
[[Comma|Commas]]: 5120/5103, 3025/3024
[[Comma]]s: 3025/3024, 5120/5103


[[Minimax_tuning|Minimax tuning]]
[[Minimax tuning]]


[|1 0 0 0 0>, |8/5 2/5 0 -1/15 -2/15>,  
[|1 0 0 0 0>, |8/5 2/5 0 -1/15 -2/15>,  
Line 197: Line 198:
|16/5 -6/5 0 -2/15 11/15>]
|16/5 -6/5 0 -2/15 11/15>]


[[Eigenmonzo|Eigenmonzos]]: 2, 11/9, 9/7
[[Eigenmonzo]]s: 2, 11/9, 9/7


Map: [<1 0 0 10 7|, <0 1 1 -5 -2|, <0 0 2 2 -1|]
Map: [<1 0 0 10 7|, <0 1 1 -5 -2|, <0 0 2 2 -1|]


[[generator|Generators]]: 2, 3, 128/99
[[Generator]]s: 2, 3, 128/99


[[EDO|EDOs]]: [[152edo|152]], [[198edo|198]], [[239edo|239]], [[350edo|350]], [[391edo|391]], [[478edo|478]], [[589edo|589]]
[[EDO|EDOs]]: 41, 87, 111, [[152edo|152]], [[198edo|198]], [[239edo|239]], [[350edo|350]], [[391edo|391]], [[478edo|478]], [[589edo|589]]
 
EDOs: 41, 87, 111, 152, 239, 391


Badness: 0.000994
Badness: 0.000994


=Lono=
= Lono =
Commas: 176/175, 5120/5103
Commas: 176/175, 5120/5103


Line 218: Line 217:
Badness: 0.00118
Badness: 0.00118


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


Line 227: Line 226:
Badness: 0.00174
Badness: 0.00174


==13-limit==
== 13-limit ==
Commas: 352/351, 676/675, 847/845
Commas: 352/351, 676/675, 847/845


Line 238: Line 237:
[[Category:Theory]]
[[Category:Theory]]
[[Category:Temperament family]]
[[Category:Temperament family]]
[[Category:Planar temperament]]
[[Category:Hemifamity]]
[[Category:Hemifamity]]
[[Category:Rank 3]]

Revision as of 05:22, 6 January 2021

The hemifamity family of temperaments are rank-3 temperaments tempering out 5120/5103.

Hemifamity

Comma c = 5120/5103

7-limit minimax: 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-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>]

Eigenmonzos: 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: [<1 0 0 10|, <0 1 0 -6|, <0 0 1 1|]

Generators: 2, 3, 5

EDOs: 99, 140, 239, 292, 391, 490, 881bd

Badness: 0.000153

Projection pairs: 7 5120/729

Music

By Gene Ward Smith

By Chris Vaisvil

Pele

Commas: 441/440, 896/891

Minimax tuning

[|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

Lattice basis: 3/2 length 0.3812 56/55 length 1.5893

Angle(3/2, 56/55) = 90.4578 degrees

Map to lattice: [<0 1 4 -2 -6|, <0 0 -1 -1 -1|]

Map: [<1 0 0 10 17|, <0 1 0 -6 -10|, <0 0 1 1 1|]

Generators: 2, 3, 5

Edos: 41, 46, 77e, 87, 99e, 128, 145, 186e, 232, 285e, 331e

Badness: 0.000648

Projection pairs: 7 5120/729 11 655360/59049

13-limit

Commas: 196/195, 352/351, 364/363

13-limit minimax

Eigenmonzos: 2, 10/9, 13/10

15-limit minimax

Eigenmonzos: 2, 15/13, 6/5

Map: [<1 0 0 10 17 22|, <0 1 0 -6 -10 -13|, <0 0 1 1 1 1|]

EDOs: 29, 41, 46, 58, 87, 145, 232, 377cef

Badness: 0.000703

Laka

Commas: 5120/5103, 540/539

Minimax tuning

[|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

Map: [<1 0 0 10 -18|, <0 1 0 -6 15|, <0 0 1 1 -1|]

EDOs: 41, 53, 58, 94, 99e, 111, 152, 555de, 707de, 859bde

13-limit

Commas: 352/351, 540/539, 847/845

13 and 15 limit minimax tuning

[|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

Commas: 352/351, 540/539, 847/845, 442/441

17-limit minimax

[|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

Map: [<1 0 0 10 -18 -13 32|,

<0 1 0 -6 15 12 -22|, <0 0 1 1 -1 -1 3|]

Generators: 2, 3, 5

Edos: 94, 111, 152, 205, 345

Akea

Commas: 385/384, 2200/2187

Minimax tuning

[|1 0 0 0 0>, |5/3 0 1/6 -1/6 0>, |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

Map: [<1 0 0 10 -3|, <0 1 0 -6 7|, <0 0 1 1 -2|]

Generators: 2, 3, 5

EDOs: 34, 41, 53, 87, 140, 181, 321

Badness: 0.000998

13-limit

Commas: 325/324, 352/351, 385/384

13 and 15 limit minimax

[|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|]

Map: [<1 0 0 10 -3 2|, <0 1 0 -6 7 4|, <0 0 1 1 -2 -2|]

Generators: 2, 3, 5

EDOs: 7, 41, 46, 53, 87, 94, 140, 181, 321, 408

Badness: 0.000822

Scales: akea46_13

Kapo

Commas: 3025/3024, 5120/5103

Minimax tuning

[|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

Map: [<1 0 0 10 7|, <0 1 1 -5 -2|, <0 0 2 2 -1|]

Generators: 2, 3, 128/99

EDOs: 41, 87, 111, 152, 198, 239, 350, 391, 478, 589

Badness: 0.000994

Lono

Commas: 176/175, 5120/5103

Map: [<1 0 0 10 6|, <0 1 0 -6 -6|, <0 0 1 1 3|]

EDOs: 7, 12, 39, 46, 53, 58, 99, 111

Badness: 0.00118

Namaka

Commas: 3388/3375, 5120/5103

Map: [<1 0 0 10 -6|, <0 2 0 -12 9|, <0 0 1 1 1|]

EDOs: 29, 53, 58, 87, 111, 140, 198

Badness: 0.00174

13-limit

Commas: 352/351, 676/675, 847/845

Map: [<1 0 0 10 -6 -1|, <0 2 0 -12 9 3|, <0 0 1 1 1 1|]

EDOs: 29, 53, 58, 87, 111, 140, 198

Badness: 0.000781

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