Pentacircle clan: Difference between revisions
Get the tolerant temperament here, a little bit more inclusive place |
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This is a collection of [[rank-3 temperament]]s tempering out the pentacircle comma, [[896/891]]. | This is a collection of [[rank-3 temperament]]s tempering out the pentacircle comma, [[896/891]]. But we can start with the rank-4 temperament. | ||
Temperaments discussed elsewhere are: | |||
* ''[[Melpomene]]'', {56/55, 81/80} → [[Didymus rank three family #Melpomene]] | |||
* ''[[Apollo]]'', {100/99, 225/224} → [[Marvel family #Apollo]] | |||
* ''[[Julius]]'' or ''[[varda]]'', {176/175, 896/891} → [[Diaschismic rank three family #Julius aka varda]] | |||
* [[Sensamagic]], {245/243, 385/384} → [[Sensamagic family #Undecimal sensamagic]] | |||
* ''[[Pele]]'', {441/440, 896/891} → [[Hemifamity family #Pele]] | |||
* ''[[Uni]]'', {540/539, 896/891} → [[Hemimage family #Uni]] | |||
Considered below, in addition to the no-5 subgroup temperament ''parapyth'', is ''tolerant''. | |||
== Pentacircle == | |||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 896/891 | |||
[[Mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 0 0 -4 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 1 }}] | |||
{{Val list|legend=1| 12, 17c, 19e, 22, 34d, 39d, 41, 58, 80, 87, 99e, 121, 145, 167, 208, 266e, 699bbcdeee }} | |||
[[Badness]]: 0.0658 × 10<sup>-6</sup> | |||
== Parapyth == | |||
Subgroup: 2.3.7.11 | |||
[[Comma list]]: 896/891 | |||
[[Sval]] [[mapping]]: [{{val| 1 0 0 0 7 }}, {{val| 0 1 0 0 -4 }}, {{val| 0 0 0 1 1 }}] | |||
Sval mapping generators: ~2, ~3, ~7 | |||
{{Val list|legend=1| 12, 17, 36, 41, 58, 63, 104, 225e, 266e, 370bee, 699bbdeee }} | |||
[[Badness]]: 0.0205 × 10<sup>-3</sup> | |||
=== 2.3.7.11.13 === | |||
Subgroup: 2.3.7.11.13 | |||
[[Comma list]]: 352/351, 364/363 | |||
[[Sval]] [[mapping]]: [{{val| 1 0 0 0 7 12 }}, {{val| 0 1 0 0 -4 -7 }}, {{val| 0 0 0 1 1 1 }}] | |||
{{Val list|legend=1| 12f, 17, 41, 46, 58, 87, 104, 266ef, 329bef, 370beef, 474beef, 595bdeeeff, 699bbdeeeff }} | |||
[[Badness]]: 0.1099 × 10<sup>-3</sup> | |||
== Tolerant == | == Tolerant == | ||
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[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Temperament collection]] | [[Category:Temperament collection]] | ||
[[Category:Pentacircle temperaments| ]] | [[Category:Pentacircle temperaments| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
[[Category:Parapyth]] | |||
[[Category:Tolerant]] | [[Category:Tolerant]] | ||