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Swetismic temperaments: Difference between revisions

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These are rank-3 temperaments tempering out [[540/539]], but we can begin by looking at the rank-4 temperament.
These are rank three temperaments tempering out [[540/539]], but we can begin by looking at the rank four temperament.


Comma: 540/539
== Swetismic ==
[[Comma list]]: 540/539


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


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


EDOs: 9, 10, 19, 22, 31, 41, 53, 58, 72, 130, 152, 224, 354, 537, 578
{{Val list|legend=1| 9, 10, 19, 22, 31, 41, 53, 58, 72, 130, 152, 224, 354, 537, 578 }}


== Hades ==
== Hades ==
Commas: 540/539, 4000/3993
[[Comma list]]: 540/539, 4000/3993


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


Generators: 99/70, 9/7, 5
Mapping generators: ~99/70, ~9/7, ~5


EDOs: 22, 50, 58, 72, 130, 152, 224, 354, 578
{{Val list|legend=1| 22, 50, 58, 72, 130, 152, 224, 354, 578 }}


Badness: 0.000361
[[Badness]]: 0.361 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Commas: 540/539, 729/728, 1575/1573
Comma list: 540/539, 729/728, 1575/1573


Map: [&lt;2 1 0 2 3 -2 |, &lt;0 3 0 5 -1 13|, &lt;0 0 1 0 1 0|]
Mapping: [{{val| 2 1 0 2 3 -2 }}, {{val| 0 3 0 5 -1 13 }}, {{val| 0 0 1 0 1 0 }}]


Generators: 99/70, 9/7, 5
Mapping generators: ~99/70, ~9/7, ~5


EDOs: 36, 58, 72, 130, 224, 354, 578
Vals: {{val list| 36, 58, 72, 130, 224, 354, 578 }}


Badness: 0.000535
Badness: 0.535 × 10<sup>-3</sup>


=== Cerberus ===
=== Cerberus ===
Commas: 351/350, 364/363, 540/539
Comma list: 351/350, 364/363, 540/539


Map: [&lt;2 1 0 2 3 1|, &lt;0 3 0 5 -1 -4|, &lt;0 0 1 0 1 2|]
Mapping: [{{val| 2 1 0 2 3 1 }}, {{val| 0 3 0 5 -1 -4 }}, {{val| 0 0 1 0 1 2 }}]


Generators: 55/39.9/7.5
Mapping generators: ~55/39, ~9/7, ~5


EDOs: 22, 50, 58, 72, 130
Vals: {{val list| 22, 50, 58, 72, 130 }}


Badness: 0.000766
Badness: 0.766 × 10<sup>-3</sup>


== Minos ==
== Minos ==
Commas: 540/539, 12005/11979
[[Comma list]]: 540/539, 12005/11979


Map: [&lt;1 0 2 1 2|, &lt;0 2 4 3 4|, &lt;0 0 -5 -1 -3|]
[[Mapping]]: [{{val| 1 0 2 1 2 }}, {{val| 0 2 4 3 4 }}, {{val| 0 0 -5 -1 -3 }}]


Generators: 2.121/70.49/33
Mapping generators: ~2, ~121/70, ~49/33


EDOs: 9, 49, 58, 72, 130, 193, 202, 467
{{Val list|legend=1| 9, 49, 58, 72, 130, 193, 202, 467 }}


Badness: 0.000886
[[Badness]]: 0.886 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Commas: 364/363, 540/539, 676/675
Comma list: 364/363, 540/539, 676/675


Map: [&lt;1 0 2 1 2 1|, &lt;0 2 4 3 4 7|, &lt;0 0 -5 -1 -3 -5|]
Mapping: [{{val| 1 0 2 1 2 1 }}, {{val| 0 2 4 3 4 7 }}, {{val| 0 0 -5 -1 -3 -5 }}]


Generators: 2.26/15.49/33
Mapping generators: ~2, ~26/15, ~49/33


EDOs: 9, 54, 58, 72, 121, 130, 193
Vals: {{val list| 9, 54, 58, 72, 121, 130, 193 }}


Badness: 0.000724
Badness: 0.724 × 10<sup>-3</sup>


== Persephone ==
== Persephone ==
Commas: 540/539, 88209/87500
[[Comma list]]: 540/539, 88209/87500


Map: [&lt;1 0 4 -2 10|, &lt;0 1 4 0 7|, &lt;0 0 -5 3 -11|]
[[Mapping]]: [{{val| 1 0 4 -2 10 }}, {{val| 0 1 4 0 7 }}, {{val| 0 0 -5 3 -11 }}]


EDOs: 50, 53, 58, 103, 108, 111, 161, 214, 272, 375, 1022bcde, 1236bcde, 1397bcde
{{Val list|legend=1| 50, 53, 58, 103, 108, 111, 161, 214, 272, 375, 1022bcde, 1236bcde, 1397bcde }}


Badness: 0.002015
[[Badness]]: 2.015 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Commas: 351/350, 540/539, 847/845
Comma list: 351/350, 540/539, 847/845


Map: [&lt;1 0 4 -2 10 7|, &lt;0 1 4 0 7 5|, &lt;0 0 -5 3 -11 -7|]
Mapping: [{{val| 1 0 4 -2 10 7 }}, {{val| 0 1 4 0 7 5 }}, {{val| 0 0 -5 3 -11 -7 }}]


EDOs: 50, 53, 58, 103, 108, 111, 161, 214, 375, 700cdef, 861bcdef, 1075bcdef, 1236bcdef, 1450bcdef
Vals: {{val list| 50, 53, 58, 103, 108, 111, 161, 214, 375, 700cdef, 861bcdef, 1075bcdef, 1236bcdef, 1450bcdef }}


Badness: 0.000997
Badness: 0.997 × 10<sup>-3</sup>


== Hypnos ==
== Hypnos ==
Commas: 540/539, 72171/71680
[[Comma list]]: 540/539, 72171/71680


Map: [&lt;1 0 0 -3 8|, &lt;0 3 0 11 -13|, &lt;0 0 1 0 1|]
[[Mapping]]: [{{val| 1 0 0 -3 8 }}, {{val| 0 3 0 11 -13 }}, {{val| 0 0 1 0 1 }}]


EDOs: 19, 36, 53, 72, 161, 197e, 214, 233, 286, 358, 591be, 663be, 949bce
{{Val list|legend=1| 19, 36, 53, 72, 161, 197e, 214, 233, 286, 358, 591be, 663be, 949bce }}


Badness: 0.001629
[[Badness]]: 1.629 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
Commas: 169/168, 540/539, 729/728
Comma list: 169/168, 540/539, 729/728


Map: [&lt;1 0 0 -3 8 0|, &lt;0 3 0 11 -13 7|, &lt;0 0 1 0 1 0|]
Mapping: [{{val| 1 0 0 -3 8 0 }}, {{val| 0 3 0 11 -13 7 }}, {{val| 0 0 1 0 1 0 }}]


EDOs: 19, 36, 53, 72, 125f, 197ef
Vals: {{val list| 19, 36, 53, 72, 125f, 197ef }}


Badness: 0.001439
Badness: 1.439 × 10<sup>-3</sup>


[[Category:Theory]]
[[Category:Regular temperament theory]]
[[Category:Temperament]]
[[Category:Temperament collection]]
[[Category:Swetismic]]
[[Category:Swetismic temperaments| ]] <!-- main article -->
[[Category:Rank 3]]
[[Category:Rank 3]]
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