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Catalog of rank-4 temperaments: Difference between revisions

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== Werckismic (441/440) ==
== Werckismic (441/440) ==
[[Mapping]]: [<1 0 0 0 -3|, <0 1 0 0 2|, <0 0 1 0 -1|, <0 0 0 1 2|]
Subgroup: 2.3.5.7.11
 
[[Mapping]]: [{{val| 1 0 0 0 -3 }}, {{val| 0 1 0 0 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 1 2 }}]


Generators: ~2, ~3, ~5, ~7
Generators: ~2, ~3, ~5, ~7
Line 6: Line 8:
{{Val list|legend=1| 12, 31, 41, 46, 58, 72, 87, 118, 130 }}
{{Val list|legend=1| 12, 31, 41, 46, 58, 72, 87, 118, 130 }}


=== Commas 441/440, 364/363 ===
=== Commas 364/363, 441/440 ===
Subgroup: 2.3.5.7.11.13


[[Mapping]]: [<1 0 0 0 -3 -8|, <0 1 0 0 2 5|, <0 0 1 0 -1 -2|, <0 0 0 1 2 3|]
[[Mapping]]: [{{val| 1 0 0 0 -3 -8 }}, {{val| 0 1 0 0 2 5 }}, {{val| 0 0 1 0 -1 -2 }}, {{val| 0 0 0 1 2 3 }}]


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


Map to lattice: [<0 1 1 -1 -1 0|, <0 0 1 0 -1 -2|, <0 0 1 1 1 1|]
Map to lattice: [{{val| 0 1 1 -1 -1 0 }}, {{val| 0 0 1 0 -1 -2 }}, {{val| 0 0 1 1 1 1 }}]


Lattice basis:  
Lattice basis:  
Line 19: Line 22:
[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[13-odd-limit]]
* [[13-odd-limit]]
: [|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>]
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 5/3 0 1/3 -1/3 -1/3 1/3 }}, {{monzo| 1/6 0 5/6 2/3 -5/6 1/3 }}, {{monzo| 0 0 0 1 0 0 }}, {{monzo| 1/6 0 -1/6 2/3 1/6 1/3 }}, {{monzo| 0 0 0 0 0 1 }}]
: Eigenmonzos: 2, 11/10, 8/7, 16/13
: Eigenmonzos: 2, 11/10, 8/7, 16/13
* [[15-odd-limit]]
* [[15-odd-limit]]
: [|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>]
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 5/4 1/4 1/4 -1/4 -1/4 1/4 }}, {{monzo| 5/4 -3/4 5/4 -1/4 -1/4 1/4 }}, {{monzo| 17/8 -11/8 5/8 -1/8 3/8 1/8 }}, {{monzo| 5/2 -3/2 1/2 -1/2 1/2 1/2 }}, {{monzo| 17/8 -11/8 5/8 -9/8 3/8 9/8 }}]
: Eigenmonzos: 2, 14/13, 6/5, 11/9
: Eigenmonzos: 2, 14/13, 6/5, 11/9


{{Val list|legend=1| 15, 23, 26, 29, 41, 43, 46, 58, 113, 130, 159, 217, 289, 393 }}
{{Val list|legend=1| 15, 23, 26, 29, 41, 43, 46, 58, 113, 130, 159, 217, 289, 393 }}


=== Commas 441/440, 351/350 ===
=== Commas 351/350, 441/440 ===
[[Mapping]]: [<1 0 0 0 -3 1|, <0 1 0 0 2 -3|, <0 0 1 0 -1 2|, <0 0 0 1 2 1|]
Subgroup: 2.3.5.7.11.13
 
[[Mapping]]: [{{val| 1 0 0 0 -3 1 }}, {{val| 0 1 0 0 2 -3 }}, {{val| 0 0 1 0 -1 2 }}, {{val| 0 0 0 1 2 1 }}]


Generators: ~2, ~3, ~5, ~7
Generators: ~2, ~3, ~5, ~7
Line 35: Line 40:


=== Commas 196/195, 352/351 ===
=== Commas 196/195, 352/351 ===
[[Mapping]]: [<1 0 0 0 -3 2|, <0 1 0 0 2 -1|, <0 0 1 0 -1 -1|, <0 0 0 1 2 2|]
Subgroup: 2.3.5.7.11.13
 
[[Mapping]]: [{{val| 1 0 0 0 -3 2 }}, {{val| 0 1 0 0 2 -1 }}, {{val| 0 0 1 0 -1 -1 }}, {{val| 0 0 0 1 2 2 }}]


Generators: ~2, ~3, ~5, ~7
Generators: ~2, ~3, ~5, ~7
Line 42: Line 49:


=== Commas 441/440, 847/845 ===
=== Commas 441/440, 847/845 ===
[[Mapping]]: [<1 0 0 0 -3 -3|, <0 1 0 0 2 2|, <0 0 1 1 1 1|, <0 0 0 2 4 5|]
Subgroup: 2.3.5.7.11.13
 
[[Mapping]]: [{{val| 1 0 0 0 -3 -3 }}, {{val| 0 1 0 0 2 2 }}, {{val| 0 0 1 1 1 1 }}, {{val| 0 0 0 2 4 5 }}]


Generators: ~2, ~3, ~5, ~13/11
Generators: ~2, ~3, ~5, ~13/11
Line 51: Line 60:
{{Main| Keenanismic family }}
{{Main| Keenanismic family }}


[[Mapping]]: [<1 0 0 0 7|, <0 1 0 0 1|, <0 0 1 0 -1|, <0 0 0 1 -1|]
Subgroup: 2.3.5.7.11
 
[[Mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 0 0 1 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 1 -1 }}]


Generators: ~2, ~3, ~5, ~7
Generators: ~2, ~3, ~5, ~7
Line 57: Line 68:
{{Val list|legend=1| 15, 22, 31, 41, 46, 53, 72, 87, 94, 118 }}
{{Val list|legend=1| 15, 22, 31, 41, 46, 53, 72, 87, 94, 118 }}


=== Commas 385/384, 325/324 ===
=== Commas 325/324, 385/384 ===
Subgroup: 2.3.5.7.11.13


Mapping: [<1 0 0 0 7 2|, <0 1 0 0 1 4|, <0 0 1 0 -1 -2|, <0 0 0 1 -1 0|]
Mapping: [{{val| 1 0 0 0 7 2 }}, {{val| 0 1 0 0 1 4 }}, {{val| 0 0 1 0 -1 -2 }}, {{val| 0 0 0 1 -1 0 }}]


Generators: ~2, ~3, ~5, ~7
Generators: ~2, ~3, ~5, ~7
Line 68: Line 80:
[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[13-odd-limit|13-]] and [[15-odd-limit]]
* [[13-odd-limit|13-]] and [[15-odd-limit]]
: [<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|]
: [{{val| 1 0 0 0 0 0 }}, {{val| 0 1 0 0 0 0 }}, {{val| 2/3 4/3 1/3 0 0 -1/3 }}, {{val| 19/6 -1/6 -1/6 1/2 -1/2 1/6 }}, {{val| 19/6 -1/6 -1/6 -1/2 1/2 1/6 }}, {{val| 2/3 4/3 -2/3 0 0 2/3 }}]
: Eigenmonzos: 2, 14/11, 13/10, 4/3
: Eigenmonzos: 2, 14/11, 13/10, 4/3


{{Val list|legend=1| 7, 8, 15, 19, 26, 34, 41, 46, 53, 68, 72, 79, 87, 94, 99, 113, 140, 159, 212, 253 }}
{{Val list|legend=1| 7, 8, 15, 19, 26, 34, 41, 46, 53, 68, 72, 79, 87, 94, 99, 113, 140, 159, 212, 253 }}


=== Commas 385/384, 351/350 ===
=== Commas 351/350, 385/384 ===
[[Mapping]]: [<1 0 0 0 7 1|, <0 1 0 0 1 -3|, <0 0 1 0 -1 2|, <0 0 0 1 -1 1|]
Subgroup: 2.3.5.7.11.13
 
[[Mapping]]: [{{val| 1 0 0 0 7 1 }}, {{val| 0 1 0 0 1 -3 }}, {{val| 0 0 1 0 -1 2 }}, {{val| 0 0 0 1 -1 1 }}]


Generators: ~2, ~3, ~5, ~7
Generators: ~2, ~3, ~5, ~7
Line 80: Line 94:
{{Val list|legend=1| 19, 22, 26, 31, 46, 50, 53, 72, 77, 103 }}
{{Val list|legend=1| 19, 22, 26, 31, 46, 50, 53, 72, 77, 103 }}


=== Commas 385/384, 352/351 ===
=== Commas 352/351, 385/384 ===
[[Mapping]]: [<1 0 0 0 7 12|, <0 1 0 0 1 -2|, <0 0 1 0 -1 -1|, <0 0 0 1 -1 -1|]
Subgroup: 2.3.5.7.11.13
 
[[Mapping]]: [{{val| 1 0 0 0 7 12 }}, {{val| 0 1 0 0 1 -2 }}, {{val| 0 0 1 0 -1 -1 }}, {{val| 0 0 0 1 -1 -1 }}]


Generators: ~2, ~3, ~5, ~7
Generators: ~2, ~3, ~5, ~7
Line 87: Line 103:
{{Val list|legend=1| 10, 22, 31, 41, 46, 53, 63, 77, 87, 94 }}
{{Val list|legend=1| 10, 22, 31, 41, 46, 53, 63, 77, 87, 94 }}


=== Commas 385/384, 364/363 ===
=== Commas 364/363, 385/384 ===
[[Mapping]]: [<1 0 0 0 7 12|, <0 1 0 0 1 3|, <0 0 1 0 -1 -2|, <0 0 0 1 -1 -3|]
Subgroup: 2.3.5.7.11.13
 
[[Mapping]]: [{{val| 1 0 0 0 7 12 }}, {{val| 0 1 0 0 1 3 }}, {{val| 0 0 1 0 -1 -2 }}, {{val| 0 0 0 1 -1 -3 }}]


Generators: ~2, ~3, ~5, ~7
Generators: ~2, ~3, ~5, ~7
Line 95: Line 113:


=== Commas 385/384, 847/845 ===
=== Commas 385/384, 847/845 ===
[[Mapping]]: [<1 0 0 0 7 7|, <0 1 0 0 1 1|, <0 0 1 1 -2 -2|, <0 0 0 2 -2 -1|]
Subgroup: 2.3.5.7.11.13
 
[[Mapping]]: [{{val| 1 0 0 0 7 7 }}, {{val| 0 1 0 0 1 1 }}, {{val| 0 0 1 1 -2 -2 }}, {{val| 0 0 0 2 -2 -1 }}]


Generators: ~2, ~3, ~5, ~13/11
Generators: ~2, ~3, ~5, ~13/11
Line 102: Line 122:


== Swetismic (540/539) ==
== Swetismic (540/539) ==
[[Mapping]]: [<1 0 0 0 2|, <0 1 0 0 3|, <0 0 1 0 1|, <0 0 0 1 -2|]
Subgroup: 2.3.5.7.11
 
[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 0 3 }}, {{val| 0 0 1 0 1 }}, {{val| 0 0 0 1 -2 }}]


Generators: ~2, ~3, ~5, ~7
Generators: ~2, ~3, ~5, ~7
Line 109: Line 131:


=== Commas 540/539, 847/845 ===
=== Commas 540/539, 847/845 ===
[[Mapping]]: [<1 0 0 0 2 2|, <0 1 0 0 3 3|, <0 0 1 1 -1 -1|, <0 0 0 2 -4 -3|]
Subgroup: 2.3.5.7.11.13
 
[[Mapping]]: [{{val| 1 0 0 0 2 2 }}, {{val| 0 1 0 0 3 3 }}, {{val| 0 0 1 1 -1 -1 }}, {{val| 0 0 0 2 -4 -3 }}]


Generators: ~2, ~3, ~5, ~13/11
Generators: ~2, ~3, ~5, ~13/11
Line 116: Line 140:


=== Commas 540/539, 625/624 ===
=== Commas 540/539, 625/624 ===
[[Mapping]]: [<1 0 0 0 2 -4|, <0 1 0 0 3 -1|, <0 0 1 0 1 4|, <0 0 0 1 -2 0|]
Subgroup: 2.3.5.7.11.13
 
[[Mapping]]: [{{val| 1 0 0 0 2 -4 }}, {{val| 0 1 0 0 3 -1 }}, {{val| 0 0 1 0 1 4 }}, {{val| 0 0 0 1 -2 0 }}]


Generators: ~2, ~3, ~5, ~7
Generators: ~2, ~3, ~5, ~7
Line 123: Line 149:


=== Commas 540/539, 676/675 ===
=== Commas 540/539, 676/675 ===
[[Mapping]]: [<1 0 0 0 2 -1|, <0 2 0 0 6 3|, <0 0 1 0 1 1|, <0 0 0 1 -2 0|]
Subgroup: 2.3.5.7.11
 
[[Mapping]]: [{{val| 1 0 0 0 2 -1 }}, {{val| 0 2 0 0 6 3 }}, {{val| 0 0 1 0 1 1 }}, {{val| 0 0 0 1 -2 0 }}]


Generators: ~2, ~26/15, ~5, ~7
Generators: ~2, ~26/15, ~5, ~7
Line 130: Line 158:


== Lehmerismic (3025/3024) ==
== Lehmerismic (3025/3024) ==
[[Mapping]]: [<1 0 0 0 2|, <0 1 0 1 2|, <0 0 1 0 -1|, <0 0 0 2 1|]
Subgroup: 2.3.5.7.11
 
[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 1 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 2 1 }}]


Generators: ~2, ~3, ~5, ~55/36
Generators: ~2, ~3, ~5, ~55/36
Line 137: Line 167:


== Kalismic (9801/9800) ==
== Kalismic (9801/9800) ==
[[Mapping]]: [<2 0 0 0 3|, <0 1 0 0 -2|, <0 0 1 0 1|, <0 0 0 1 1|]
Subgroup: 2.3.5.7.11
 
[[Mapping]]: [{{val| 2 0 0 0 3 }}, {{val| 0 1 0 0 -2 }}, {{val| 0 0 1 0 1 }}, {{val| 0 0 0 1 1 }}]


Generators: ~99/70, ~3, ~5, ~7
Generators: ~99/70, ~3, ~5, ~7
Line 144: Line 176:


=== Commas 1716/1715, 2080/2079 ===
=== Commas 1716/1715, 2080/2079 ===
Subgroup: 2.3.5.7.11.13


[[Mapping]]: [<2 0 0 0 3 -7|, <0 1 0 0 -2 1|, <0 0 1 0 1 0|, <0 0 0 1 1 2|]
[[Mapping]]: [{{val| 2 0 0 0 3 -7 }}, {{val| 0 1 0 0 -2 1 }}, {{val| 0 0 1 0 1 0 }}, {{val| 0 0 0 1 1 2 }}]


Generators: ~99/70, ~3, ~5, ~7
Generators: ~99/70, ~3, ~5, ~7
Line 154: Line 187:
[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[13-odd-limit|13-]] and [[15-odd-limit]]
* [[13-odd-limit|13-]] and [[15-odd-limit]]
: [|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>]
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 7/10 4/5 0 -2/5 0 1/5 }}, {{monzo| 7/10 -1/5 1 -2/5 0 1/5 }}, {{monzo| 7/5 -2/5 0 1/5 0 2/5 }}, {{monzo| 11/5 -11/5 1 3/5 0 1/5 }}, {{monzo| 0 0 0 0 0 1 }}]
: Eigenmonzos: 2, 6/5, 16/13, 9/7
: Eigenmonzos: 2, 6/5, 16/13, 9/7


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