Catalog of rank-4 temperaments: Difference between revisions

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==441/440==
==Werckismic (441/440)==
Map: [<1 0 0 0 -3|, <0 1 0 0 2|, <0 0 1 0 -1|, <0 0 0 1 2|]
Map: [<1 0 0 0 -3|, <0 1 0 0 2|, <0 0 1 0 -1|, <0 0 0 1 2|]


Line 44: Line 44:
EDOs: 26, 31, 46, 58, 72, 103, 130
EDOs: 26, 31, 46, 58, 72, 103, 130


===Commas 441/440, 352/351===
===Commas 196/195, 352/351===
Map: [<1 0 0 0 -3 2|, <0 1 0 0 2 -1|, <0 0 1 0 -1 -1|, <0 0 0 1 2 2|]
Map: [<1 0 0 0 -3 2|, <0 1 0 0 2 -1|, <0 0 1 0 -1 -1|, <0 0 0 1 2 2|]


Line 51: Line 51:
EDOs: 29, 31, 41, 46, 58, 77, 87
EDOs: 29, 31, 41, 46, 58, 77, 87


==385/384==
==Keenanismic (385/384)==
Map: [<1 0 0 0 7|, <0 1 0 0 1|, <0 0 1 0 -1|, <0 0 0 1 -1|]
 
Generators: 2, 3, 5, 7
 
EDOs: 15, 22, 31, 41, 46, 53, 72, 87, 94, 118


===Commas 385/384, 325/324===
===Commas 385/384, 325/324===
Line 71: Line 76:
Lattice basis: 4/3 1.0820 6/5 1.3935 10/9 1.6247
Lattice basis: 4/3 1.0820 6/5 1.3935 10/9 1.6247


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


<0 0 1 0 -1 -2|, <0 0 0 1 -1 0|]
Generators: 2, 3, 5, 7
 
EDOs: 7, 8, 15, 19, 26, 34, 41, 46, 53, 68, 72, 79, 87, 94, 99, 113, 140, 159, 212, 253
 
==Swetismic (540/539)==
Map: [<1 0 0 0 2|, <0 1 0 0 3|, <0 0 1 0 1|, <0 0 0 1 -2|]


Generators: 2, 3, 5, 7
Generators: 2, 3, 5, 7


Edos: 7, 8, 15, 19, 26, 34, 41, 46, 53, 68, 72, 79, 87, 94, 99, 113, 140, 159, 212, 253
EDOs: 22, 31, 41, 53, 58, 72, 80, 130, 152


==9801/9800==
==Lehmerismic (3025/3024)==
Map: [<1 0 0 0 2|, <0 1 0 1 2|, <0 0 1 0 -1|, <0 0 0 2 1|]
 
Generators: 2, 3, 5, 55/36
 
EDOs: 31, 72, 118, 152, 224, 270, 311, 342, 494, 612
 
==Kalismic (9801/9800)==
Map: [<2 0 0 0 3|, <0 1 0 0 -2|, <0 0 1 0 1|, <0 0 0 1 1|]
 
Generators: 99/70, 3, 5, 7
 
EDOs: 270, 342, 494, 612, 764, 836, 1106, 1236, 1578, 1848


===Commas 2080/2079, 1716/1715===
===Commas 2080/2079, 1716/1715===
Line 93: Line 115:
Lattice basis: 3/2 length 1.1956 7/4 length 1.4506 14/13 1.8299
Lattice basis: 3/2 length 1.1956 7/4 length 1.4506 14/13 1.8299


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


Generators: 99/70, 3, 5, 7
Generators: 99/70, 3, 5, 7


Edos: 26, 36, 46, 58, 68, 72, 84, 94, 130, 140, 166, 198, 224, 270, 494, 764, 1186, 1892
EDOs: 26, 36, 46, 58, 68, 72, 84, 94, 130, 140, 166, 198, 224, 270, 494, 764, 1186, 1892


[[Category:rank]]
[[Category:rank]]
[[Category:rank_4]]
[[Category:rank-four]]
[[Category:temperament]]
[[Category:temperament]]
[[Category:theory]]
[[Category:theory]]
[[category:todo:expand]]
[[category:todo:expand]]

Revision as of 05:16, 16 February 2019

Werckismic (441/440)

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

Generators: 2, 3, 5

EDOs: 12, 31, 41, 46, 58, 72, 87, 118, 130

Commas 441/440, 364/363

13-limit minimax

[|1 0 0 0 0 0>, |5/3 0 1/3 -1/3 -1/3 1/3>, |1/6 0 5/6 2/3 -5/6 1/3>, |0 0 0 1 0 0>, |1/6 0 -1/6 2/3 1/6 1/3>, |0 0 0 0 0 1>]

Eigenmonzos: 2, 11/10, 8/7, 16/13

15-limit minimax

[|1 0 0 0 0 0>, |5/4 1/4 1/4 -1/4 -1/4 1/4>, |5/4 -3/4 5/4 -1/4 -1/4 1/4>, |17/8 -11/8 5/8 -1/8 3/8 1/8>, |5/2 -3/2 1/2 -1/2 1/2 1/2>, |17/8 -11/8 5/8 -9/8 3/8 9/8>]

Eigenmonzos: 2, 14/13, 6/5, 11/9

Lattice basis: 3/2 1.2263 14/11 1.4629 21/16 1.4657

Map to lattice: [<0 1 1 -1 -1 0|,

<0 0 1 0 -1 -2|, <0 0 1 1 1 1|]

Map: [<1 0 0 0 -3 -8|, <0 1 0 0 2 5|, <0 0 1 0 -1 -2|, <0 0 0 1 2 3|]

Generators: 2, 3, 5

EDOs: 15, 23, 26, 29, 41, 43, 46, 58, 113, 130, 159, 217, 289, 393

Commas 441/440, 351/350

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

Generators: 2, 3, 5

EDOs: 26, 31, 46, 58, 72, 103, 130

Commas 196/195, 352/351

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

Generators: 2, 3, 5

EDOs: 29, 31, 41, 46, 58, 77, 87

Keenanismic (385/384)

Map: [<1 0 0 0 7|, <0 1 0 0 1|, <0 0 1 0 -1|, <0 0 0 1 -1|]

Generators: 2, 3, 5, 7

EDOs: 15, 22, 31, 41, 46, 53, 72, 87, 94, 118

Commas 385/384, 325/324

13 and 15 limit minimax

[<1 0 0 0 0 0|, <0 1 0 0 0 0|,

<2/3 4/3 1/3 0 0 -1/3|,

<19/6 -1/6 -1/6 1/2 -1/2 1/6|,

<19/6 -1/6 -1/6 -1/2 1/2 1/6|,

<2/3 4/3 -2/3 0 0 2/3|]

Eigenmonzos: 2, 14/11, 13/10, 4/3

Lattice basis: 4/3 1.0820 6/5 1.3935 10/9 1.6247

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

Generators: 2, 3, 5, 7

EDOs: 7, 8, 15, 19, 26, 34, 41, 46, 53, 68, 72, 79, 87, 94, 99, 113, 140, 159, 212, 253

Swetismic (540/539)

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

Generators: 2, 3, 5, 7

EDOs: 22, 31, 41, 53, 58, 72, 80, 130, 152

Lehmerismic (3025/3024)

Map: [<1 0 0 0 2|, <0 1 0 1 2|, <0 0 1 0 -1|, <0 0 0 2 1|]

Generators: 2, 3, 5, 55/36

EDOs: 31, 72, 118, 152, 224, 270, 311, 342, 494, 612

Kalismic (9801/9800)

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

Generators: 99/70, 3, 5, 7

EDOs: 270, 342, 494, 612, 764, 836, 1106, 1236, 1578, 1848

Commas 2080/2079, 1716/1715

13 and 15 limit minimax

[|1 0 0 0 0 0>, |7/10 4/5 0 -2/5 0 1/5>, |7/10 -1/5 1 -2/5 0 1/5>, |7/5 -2/5 0 1/5 0 2/5>, |11/5 -11/5 1 3/5 0 1/5>, |0 0 0 0 0 1>]

Eigenmonzos: 2, 6/5, 16/13, 9/7

Lattice basis: 3/2 length 1.1956 7/4 length 1.4506 14/13 1.8299

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

Generators: 99/70, 3, 5, 7

EDOs: 26, 36, 46, 58, 68, 72, 84, 94, 130, 140, 166, 198, 224, 270, 494, 764, 1186, 1892

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