https://en.xen.wiki/index.php?action=history&feed=atom&title=User%3AHkm%2FFifive_family 2026-07-07T04:37:18Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=User:Hkm/Fifive_family&diff=192060&oldid=prev 2025-04-14T04:07:24Z

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Hkm https://en.xen.wiki/index.php?title=User:Hkm/Fifive_family&diff=192056&oldid=prev 2025-04-14T03:38:17Z

<p>Created page with &quot;{{Technical data page}} The &#039;&#039;&#039;fifive family&#039;&#039;&#039; of <a href="/w/Regular_temperament" title="Regular temperament">temperaments</a> <a href="/w/Tempering_out" title="Tempering out">tempers out</a> the <a href="/w/Fifive_comma" title="Fifive comma">fifive comma</a> ({{monzo|legend=1| -1 -14 10 }}, <a href="/w/Ratio" class="mw-redirect" title="Ratio">ratio</a>: 9765625/9565938). The name &#039;&#039;fifive&#039;&#039; was given by <a href="/w/Petr_Pa%C5%99%C3%ADzek" title="Petr Pařízek">Petr Pařízek</a> in 2011 for it splits the <a href="/w/3/2" title="3/2">perfect fifth</a> in five.&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | &#039;&#039;Suggested names for the unclasified temperaments&#039;&#039;]&lt;/ref&gt;...&quot;</p> <p><b>New page</b></p><div>{{Technical data page}}<br /> The &#039;&#039;&#039;fifive family&#039;&#039;&#039; of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[fifive comma]] ({{monzo|legend=1| -1 -14 10 }}, [[ratio]]: 9765625/9565938).<br /> <br /> The name &#039;&#039;fifive&#039;&#039; was given by [[Petr Pařízek]] in 2011 for it splits the [[3/2|perfect fifth]] in five.&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | &#039;&#039;Suggested names for the unclasified temperaments&#039;&#039;]&lt;/ref&gt;<br /> <br /> Considered below are crepuscular, fifives, and fourfives. <br /> <br /> == Fifive ==<br /> [[Subgroup]]: 2.3.5<br /> <br /> [[Comma list]]: 9765625/9565938<br /> <br /> {{Mapping|legend=1| 2 2 3 | 0 5 7 }}<br /> <br /> : mapping generators: ~78125/50421, ~27/25<br /> <br /> [[Optimal tuning]]s:<br /> * [[CTE]]: ~78125/50421 = 1\2, ~27/25 = 140.6349<br /> * [[POTE]]: ~78125/50421 = 1\2, ~27/25 = 140.624<br /> <br /> {{Optimal ET sequence|legend=1| 8, 18bc, 26, 34, 94, 128 }}<br /> <br /> [[Badness]]: <br /> * Smith: 0.205812<br /> * Dirichlet: 4.828<br /> <br /> === 2.3.5.13 subgroup ===<br /> Subgroup: 2.3.5.13<br /> <br /> Comma list: 325/324, 20000/19773<br /> <br /> Mapping: {{mapping| 2 2 3 6 | 0 5 7 6 }}<br /> <br /> : mapping generators: ~351/250, ~13/12<br /> <br /> Optimal tunings:<br /> * CTE: ~351/250 = 1\2, ~13/12 = 140.5685<br /> * CWE: ~351/250 = 1\2, ~13/12 = 140.6232<br /> <br /> Optimal ET sequence: {{Optimal ET sequence| 8, 18bcf, 26, 34, 94, 128 }}<br /> <br /> Badness: <br /> * Smith: 0.0240<br /> * Dirichlet: 0.800<br /> <br /> === 2.3.5.13.17 subgroup ===<br /> Subgroup: 2.3.5.13.17<br /> <br /> Comma list: 170/169, 289/288, 325/324<br /> <br /> Mapping: {{mapping| 2 2 3 6 7 | 0 5 7 6 5 }}<br /> <br /> : mapping generators: ~17/12, ~13/12<br /> <br /> Optimal tunings:<br /> * CTE: ~17/12 = 1\2, ~13/12 = 140.5958<br /> * CWE: ~17/12 = 1\2, ~13/12 = 140.6057<br /> <br /> Optimal ET sequence: {{Optimal ET sequence| 8, 18bcfg, 26, 34, 94, 128 }}<br /> <br /> Badness: <br /> * Smith: 0.0110<br /> * Dirichlet: 0.488<br /> <br /> == Crepuscular ==<br /> {{See also| Jubilismic clan #Crepuscular }}<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 50/49, 4375/4374<br /> <br /> {{Mapping|legend=1| 2 2 3 4 | 0 5 7 7 }}<br /> <br /> {{Multival|legend=1| 10 14 14 -1 -6 -7 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~27/25 = 140.349<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}<br /> <br /> [[Badness]]: 0.086669<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 50/49, 99/98, 864/847<br /> <br /> Mapping: {{mapping| 2 2 3 4 6 | 0 5 7 7 4 }}<br /> <br /> Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.587<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}<br /> <br /> Badness: 0.040758<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 50/49, 78/77, 99/98, 144/143<br /> <br /> Mapping: {{mapping| 2 2 3 4 6 6 | 0 5 7 7 4 6 }}<br /> <br /> Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.554<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}<br /> <br /> Badness: 0.024368<br /> <br /> === 17-limit ===<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 50/49, 78/77, 85/84, 99/98, 144/143<br /> <br /> Mapping: {{mapping| 2 2 3 4 6 6 7 | 0 5 7 7 4 6 5 }}<br /> <br /> Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.405<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 26, 34d, 60d }}<br /> <br /> Badness: 0.018567<br /> <br /> == Fifives ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 875/864, 83349/81920<br /> <br /> {{Mapping|legend=1| 2 2 3 7 | 0 5 7 -6 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~567/400 = 1\2, ~27/25 = 139.909<br /> <br /> {{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}<br /> <br /> [[Badness]]: 0.130589<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 100/99, 385/384, 3969/3872<br /> <br /> Mapping: {{mapping| 2 2 3 7 6 | 0 5 7 -6 4 }}<br /> <br /> Optimal tuning (POTE): ~63/44 = 1\2, ~12/11 = 139.884<br /> <br /> {{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}<br /> <br /> Badness: 0.080306<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 100/99, 105/104, 144/143, 1352/1331<br /> <br /> Mapping: {{mapping| 2 2 3 7 6 6 | 0 5 7 -6 4 6 }}<br /> <br /> Optimal tuning (POTE): ~55/39 = 1\2, ~12/11 = 139.867<br /> <br /> {{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}<br /> <br /> Badness: 0.044253<br /> <br /> === 17-limit ===<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 100/99, 105/104, 144/143, 170/169, 221/220<br /> <br /> Mapping: {{mapping| 2 2 3 7 6 6 7 | 0 5 7 -6 4 6 5 }}<br /> <br /> Optimal tuning (POTE): ~17/12 = 1\2, ~12/11 = 139.868<br /> <br /> {{Optimal ET sequence|legend=1| 8, 26, 34, 60 }}<br /> <br /> Badness: 0.029429<br /> <br /> == Fourfives ==<br /> {{See also| Sensamagic clan }}<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 245/243, 235298/234375<br /> <br /> {{Mapping|legend=1| 4 4 6 7 | 0 5 7 9 }}<br /> <br /> : mapping generators: ~25/21, ~27/25<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~25/21 = 1\4, ~27/25 = 140.754<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 60, 68, 128 }}<br /> <br /> [[Badness]]: 0.114143<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 245/243, 385/384, 235298/234375<br /> <br /> Mapping: {{mapping| 4 4 6 7 19 | 0 5 7 9 -11 }}<br /> <br /> Optimal tuning (POTE): ~25/21 = 1\4, ~27/25 = 140.771<br /> <br /> {{Optimal ET sequence|legend=1| 8de, 60, 68, 128, 196 }}<br /> <br /> Badness: 0.120165<br /> <br /> ==== 13-limit ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 196/195, 245/243, 385/384, 20000/19773<br /> <br /> Mapping: {{mapping| 4 4 6 7 19 12 | 0 5 7 9 -11 6 }}<br /> <br /> Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.760<br /> <br /> {{Optimal ET sequence|legend=1| 8de, 60, 68, 128, 196f }}<br /> <br /> Badness: 0.067365<br /> <br /> === Quadrafives ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 121/120, 245/243, 1375/1372<br /> <br /> Mapping: {{mapping| 4 4 6 7 11 | 0 5 7 9 6 }}<br /> <br /> Optimal tuning (POTE): ~25/21 = 1\4, ~27/25 = 140.630<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }}<br /> <br /> Badness: 0.057268<br /> <br /> ==== 13-limit ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 121/120, 196/195, 245/243, 275/273<br /> <br /> Mapping: {{mapping| 4 4 6 7 11 12 | 0 5 7 9 6 6 }}<br /> <br /> Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.728<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }}<br /> <br /> Badness: 0.036128<br /> <br /> ==== 17-limit ====<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 121/120, 154/153, 170/169, 196/195, 245/243<br /> <br /> Mapping: {{mapping| 4 4 6 7 11 12 14 | 0 5 7 9 6 6 5 }}<br /> <br /> Optimal tuning (POTE): ~25/21 = 1\4, ~13/12 = 140.718<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 60e, 68, 128e }}<br /> <br /> Badness: 0.024796<br /> <br /> == Notes ==<br /> <br /> [[Category:Temperament families]]<br /> [[Category:Fifive family| ]] &lt;!-- main article --&gt;<br /> [[Category:Fifive| ]] &lt;!-- key article --&gt;<br /> [[Category:Rank 2]]</div>

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