Fifive family: Difference between revisions
Review (restore POTE tuning since the replacement was based on a wrong assessment: CWE is ~140.629 not .623) |
m Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content" Tags: Mobile edit Mobile web edit |
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The '''fifive family''' tempers out the [[fifive comma]] | {{Technical data page}} | ||
The '''fifive family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[fifive comma]] ({{monzo|legend=1| -1 -14 10 }}, [[ratio]]: 9765625/9565938). | |||
The name ''fifive'' was given by [[Petr Pařízek]] in 2011 for it splits the [[3/2|perfect fifth]] in five.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref> | |||
Considered below are crepuscular and | Considered below are crepuscular, fifives, and fourfives. | ||
== Fifive == | == Fifive == | ||
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{{Mapping|legend=1| 2 2 3 4 | 0 5 7 7 }} | {{Mapping|legend=1| 2 2 3 4 | 0 5 7 7 }} | ||
[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~27/25 = 140.349 | [[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~27/25 = 140.349 | ||
| Line 170: | Line 168: | ||
Badness: 0.029429 | Badness: 0.029429 | ||
== Fourfives == | |||
{{See also| Sensamagic clan }} | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 245/243, 235298/234375 | |||
{{Mapping|legend=1| 4 4 6 7 | 0 5 7 9 }} | |||
: mapping generators: ~25/21, ~27/25 | |||
[[Optimal tuning]] ([[POTE]]): ~25/21 = 1\4, ~27/25 = 140.754 | |||
{{Optimal ET sequence|legend=1| 8d, 60, 68, 128 }} | |||
[[Badness]]: 0.114143 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 245/243, 385/384, 235298/234375 | |||
Mapping: {{mapping| 4 4 6 7 19 | 0 5 7 9 -11 }} | |||
Optimal tuning (POTE): ~25/21 = 1\4, ~27/25 = 140.771 | |||
{{Optimal ET sequence|legend=1| 8de, 60, 68, 128, 196 }} | |||
Badness: 0.120165 | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 196/195, 245/243, 385/384, 20000/19773 | |||
Mapping: {{mapping| 4 4 6 7 19 12 | 0 5 7 9 -11 6 }} | |||
Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.760 | |||
{{Optimal ET sequence|legend=1| 8de, 60, 68, 128, 196f }} | |||
Badness: 0.067365 | |||
=== Quadrafives === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 121/120, 245/243, 1375/1372 | |||
Mapping: {{mapping| 4 4 6 7 11 | 0 5 7 9 6 }} | |||
Optimal tuning (POTE): ~25/21 = 1\4, ~27/25 = 140.630 | |||
{{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }} | |||
Badness: 0.057268 | |||
==== 13-limit ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 121/120, 196/195, 245/243, 275/273 | |||
Mapping: {{mapping| 4 4 6 7 11 12 | 0 5 7 9 6 6 }} | |||
Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.728 | |||
{{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }} | |||
Badness: 0.036128 | |||
==== 17-limit ==== | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 121/120, 154/153, 170/169, 196/195, 245/243 | |||
Mapping: {{mapping| 4 4 6 7 11 12 14 | 0 5 7 9 6 6 5 }} | |||
Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.718 | |||
{{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }} | |||
Badness: 0.024796 | |||
== Notes == | |||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Fifive family| ]] <!-- main article --> | [[Category:Fifive family| ]] <!-- main article --> | ||
[[Category:Fifive| ]] <!-- key article --> | [[Category:Fifive| ]] <!-- key article --> | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||