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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.
{{Technical data page}}
This is a collection of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out]] the [[swetisma]], 540/539 = {{monzo| 2 3 1 -2 -1 }}. For the rank-4 swetismic temperament, see [[Catalog of rank-4 temperaments #Swetismic (540/539)]].  


== Swetismic ==
Temperaments discussed elsewhere are:
[[Comma list]]: 540/539
* ''[[Terpsichore]]'' (+81/80) → [[Didymus rank three family #Terpsichore|Didymus rank-3 family]]
* ''[[Big brother]]'' (+99/98 or 121/120) → [[Nuwell family #Big brother|Nuwell family]]
* ''[[Octarod]]'' (+100/99 or 245/243) → [[Sensamagic family #Octarod|Sensamagic family]]
* ''[[Aplonis]]'' (+126/125) → [[Starling family #Aplonis|Starling family]]
* ''[[Guanyin]]'' (+176/175) → [[Orwellismic family #Guanyin|Orwellismic family]]
* [[Marvel]] (+225/224 or 385/384) → [[Marvel family #Undecimal marvel|Marvel family]]
* [[Jove]] (+243/242 or 441/440) → [[Breed family #Jove|Breed family]]
* ''[[Uni]]'' (+896/891) → [[Hemimage family #Uni|Hemimage family]]
* ''[[Gamel]]'' (+1029/1024) → [[Gamelismic family #Gamel|Gamelismic family]]
* ''[[Indra]]'' (+1375/1372) → [[Mirkwai family #Indra|Mirkwai family]]
* ''[[Claudius]]'' (+2048/2025) → [[Diaschismic rank three family #Claudius|Diaschismic rank-3 family]]
* ''[[Octasand]]'' (+2200/2187) → [[Octagar family #Octasand|Octagar family]]
* ''[[Gariboh]]'' (+3125/3087) → [[Gariboh family #Undecimal gariboh|Gariboh family]]
* ''[[Siebog]]'' (+3136/3125) → [[Hemimean family #Siebog|Hemimean family]]
* ''[[Laka]]'' (+5120/5103) → [[Hemifamity family #Laka|Hemifamity family]]
* ''[[Jupiter]]'' (+5632/5625) → [[Porwell family #Jupiter|Porwell family]]
* ''[[Albus]]'' (+8019/8000) → [[Cataharry family #Albus|Cataharry family]]


[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 0 3 }}, {{val| 0 0 0 1 -2 }}]
Considered below are hades, minos, persephone and hypnos.


Generators: ~2, ~3, ~5, ~7
== Hades ==
=== 7-limit (stearnsmic) ===
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 118098/117649
 
{{Mapping|legend=1| 2 1 0 2 | 0 3 0 5 | 0 0 1 0 }}
 
: mapping generators: ~343/243, ~9/7, ~5


{{Val list|legend=1| 9, 10, 19, 22, 31, 41, 53, 58, 72, 130, 152, 224, 354, 537, 578 }}
{{Optimal ET sequence|legend=1| 22, 50, 58, 72, 130, 152, 202, 224, 354 }}
 
[[Badness]]: 0.748 × 10<sup>-3</sup>
 
=== 11-limit ===
[[Subgroup]]: 2.3.5.7.11


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


[[Mapping]]: [{{val| 2 1 0 2 3 }}, {{val| 0 3 0 5 -1 }}, {{val| 0 0 1 0 1 }}]
{{Mapping|legend=1| 2 1 0 2 3 | 0 3 0 5 -1 | 0 0 1 0 1 }}


Mapping generators: ~99/70, ~9/7, ~5
{{Optimal ET sequence|legend=1| 22, 50, 58, 72, 130, 152, 224, 354, 506e, 578, 730e, 1084de, 1308dee }}
 
{{Val list|legend=1| 22, 50, 58, 72, 130, 152, 224, 354, 578 }}


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


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1575/1573
Comma list: 540/539, 729/728, 1575/1573


Mapping: [{{val| 2 1 0 2 3 -2 }}, {{val| 0 3 0 5 -1 13 }}, {{val| 0 0 1 0 1 0 }}]
Mapping: {{mapping| 2 1 0 2 3 -2 | 0 3 0 5 -1 13 | 0 0 1 0 1 0 }}


Mapping generators: ~99/70, ~9/7, ~5
{{Optimal ET sequence|legend=1| 22f, 36, 58, 72, 130, 224, 354, 578 }}
 
Vals: {{val list| 36, 58, 72, 130, 224, 354, 578 }}


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


=== Cerberus ===
=== Cerberus ===
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 540/539
Comma list: 351/350, 364/363, 540/539


Mapping: [{{val| 2 1 0 2 3 1 }}, {{val| 0 3 0 5 -1 -4 }}, {{val| 0 0 1 0 1 2 }}]
Mapping: {{mapping| 2 1 0 2 3 1 | 0 3 0 5 -1 -4 | 0 0 1 0 1 2 }}


Mapping generators: ~55/39, ~9/7, ~5
{{Optimal ET sequence|legend=1| 22, 50, 58, 72, 130 }}
 
Vals: {{val list| 22, 50, 58, 72, 130 }}


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


== Minos ==
== Minos ==
[[Subgroup]]: 2.3.5.7.11
[[Comma list]]: 540/539, 12005/11979
[[Comma list]]: 540/539, 12005/11979


[[Mapping]]: [{{val| 1 0 2 1 2 }}, {{val| 0 2 4 3 4 }}, {{val| 0 0 -5 -1 -3 }}]
{{Mapping|legend=1| 1 0 2 1 2 | 0 2 4 3 4 | 0 0 -5 -1 -3 }}


Mapping generators: ~2, ~121/70, ~49/33
: mapping generators: ~2, ~121/70, ~49/33


{{Val list|legend=1| 9, 49, 58, 72, 130, 193, 202, 467 }}
{{Optimal ET sequence|legend=1| 9, 49, 58, 72, 130, 193, 202, 467 }}


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


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 540/539, 676/675
Comma list: 364/363, 540/539, 676/675


Mapping: [{{val| 1 0 2 1 2 1 }}, {{val| 0 2 4 3 4 7 }}, {{val| 0 0 -5 -1 -3 -5 }}]
Mapping: {{mapping| 1 0 2 1 2 1 | 0 2 4 3 4 7 | 0 0 -5 -1 -3 -5 }}


Mapping generators: ~2, ~26/15, ~49/33
{{Optimal ET sequence|legend=1| 9, 54, 58, 72, 121, 130, 193 }}
 
Vals: {{val list| 9, 54, 58, 72, 121, 130, 193 }}


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


== Persephone ==
== Persephone ==
[[Subgroup]]: 2.3.5.7.11
[[Comma list]]: 540/539, 88209/87500
[[Comma list]]: 540/539, 88209/87500


[[Mapping]]: [{{val| 1 0 4 -2 10 }}, {{val| 0 1 4 0 7 }}, {{val| 0 0 -5 3 -11 }}]
{{Mapping|legend=1| 1 0 4 -2 10 | 0 1 4 0 7 | 0 0 -5 3 -11 }}
 
: mapping generators: ~2, ~3, ~100/33


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


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


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 847/845
Comma list: 351/350, 540/539, 847/845


Mapping: [{{val| 1 0 4 -2 10 7 }}, {{val| 0 1 4 0 7 5 }}, {{val| 0 0 -5 3 -11 -7 }}]
Mapping: {{mapping| 1 0 4 -2 10 7 | 0 1 4 0 7 5 | 0 0 -5 3 -11 -7 }}


Vals: {{val list| 50, 53, 58, 103, 108, 111, 161, 214, 375, 700cdef, 861bcdef, 1075bcdef, 1236bcdef, 1450bcdef }}
{{Optimal ET sequence|legend=1| 50, 53, 58, 103, 108, 111, 161, 214, 375, 700cdef, 861bcdef, 1075bcdef, 1236bcdef, 1450bcdef }}


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


== Hypnos ==
== Hypnos ==
[[Subgroup]]: 2.3.5.7.11
[[Comma list]]: 540/539, 72171/71680
[[Comma list]]: 540/539, 72171/71680


[[Mapping]]: [{{val| 1 0 0 -3 8 }}, {{val| 0 3 0 11 -13 }}, {{val| 0 0 1 0 1 }}]
{{Mapping|legend=1| 1 0 0 -3 8 | 0 3 0 11 -13 | 0 0 1 0 1 }}


{{Val list|legend=1| 19, 36, 53, 72, 161, 197e, 214, 233, 286, 358, 591be, 663be, 949bce }}
: mapping generators: ~2, ~81/56, ~5
 
{{Optimal ET sequence|legend=1| 19, 36, 53, 72, 161, 197e, 214, 233, 286, 358, 591be, 663be, 949bce }}


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


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 540/539, 729/728
Comma list: 169/168, 540/539, 729/728


Mapping: [{{val| 1 0 0 -3 8 0 }}, {{val| 0 3 0 11 -13 7 }}, {{val| 0 0 1 0 1 0 }}]
Mapping: {{mapping| 1 0 0 -3 8 0 | 0 3 0 11 -13 7 | 0 0 1 0 1 0 }}


Vals: {{val list| 19, 36, 53, 72, 125f, 197ef }}
{{Optimal ET sequence|legend=1| 19, 36, 53, 72, 125f, 197ef }}


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


[[Category:Regular temperament theory]]
[[Category:Temperament collections]]
[[Category:Temperament collection]]
[[Category:Pages with mostly numerical content]]
[[Category:Swetismic temperaments| ]] <!-- main article -->
[[Category:Swetismic temperaments| ]] <!-- main article -->
[[Category:Rank 3]]
[[Category:Rank 3]]
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