Optimal patent val: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>2012-05-~~09 16~~:04:14 UTC</tt>.

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-05-13 13:49:41 UTC</tt>.

: The original revision id was <tt>~~332652360~~</tt>.

: The original revision id was <tt>334534992</tt>.

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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]

Given any collection of p-limit commas, there is a finite list of p-limit [[Patent val|patent vals]] tempering out the commas. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the unique patent val which has the lowest [[Tenney-Euclidean temperament measures|TE error]]; this is the //optimal (TE) patent val// for the temperament defined by the commas. Note that other definitions of error, such as maximum p-limit error, or maximum q-limit error where q is the largest odd number less than the prime above p, lead to different results.

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[[Archytas clan#Fervor|Fervor]]: [[2edo]] 2&27e 52.054

[[Dicot family#Decimal|Decimated]]: [[4edo]] 4&10e 31.456

[[Starling temperaments#Myna ~~temperament~~-Coleto|Coleto]]: [[4edo]] 4&27e 48.687

[[Starling temperaments#Myna%20temperament-Coleto|Coleto]]: [[4edo]] 4&27e 48.687

[[Meantone family#Godzilla-Semafour|Semafour]]: [[5edo]] 5&14c 28.510

[[Meantone family#Maqamic|Maqamic]]: [[7edo]] 7&10c 40.240

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[[Marvel temperaments|Tritonic]]: [[31edo]] 2&29 23.659

[[Starling temperaments|Casablanca]]: [[31edo]] 31&42 67.291

[[Starling temperaments#Myna ~~temperament~~-Myno|Myno]]: [[31edo]] 4&27 33.434

[[Starling temperaments#Myna%20temperament-Myno|Myno]]: [[31edo]] 4&27 33.434

[[Starling temperaments#Cypress-11-limit|Cypress]]: [[31edo]] 20cde&31 42.719

[[Gamelismic clan#Miracle|Revelation]]: [[31edo]] 21&31 32.946

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[[Porcupine family#Nautilus|Belauensis]]: [[15edo]] 14c&15 29.816

[[Kleismic family#Keemun-13-limit-Kumbaya|Kumbaya]]: [[15edo]] 4&15 31.633

[[Kleismic family#Keemun-Darjeeling-13-limit ~~Darjeeling~~|Darjeeling]]: [[15edo]] 15&19e 21.445

[[Kleismic family#Keemun-Darjeeling-13-limit%20Darjeeling|Darjeeling]]: [[15edo]] 15&19e 21.445

[[Augmented family#Augene-11-limit-13-limit|Augene]]: [[15edo]] 3&15 20.785

[[Augmented family#Augene-11-limit-Ogene|Ogene]]: [[15edo]] 12&15 22.890

[[Pelogic family#Armodue-13-limit ~~Armodue~~|Armodue]]: [[16edo]] 7&9 19.351

[[Pelogic family#Armodue-13-limit%20Armodue|Armodue]]: [[16edo]] 7&9 19.351

[[Meantone family#Dominant-Domination-13-limit|Domination]]: [[17edo|17c]] 5e&12e 27.435

[[Archytas clan#Progress|Progressive]]: [[17edo|17c]] 2f&15f 32.721

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[[Comic family#Comic-13-limit|Comic]]: [[22edo]] 2cde&22 41.470

[[Magic family#Astrology-13-limit|Astrology]]: [[22edo]] 6&16 34.376

[[Pythagorean family#Catler ~~temperament~~|Catcall]]: [[24edo]] 12f&24 28.363

[[Pythagorean family#Catler%20temperament|Catcall]]: [[24edo]] 12f&24 28.363

[[Augmented family|Triforce]]: [[24edo]] 9&15 20.248

[[Augmented family#Hemiaug-13-limit|Hemiaug]]: [[24edo]] 3de&24 30.159

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[[Archytas clan#Fervor|Fervor]]: [[27edo]] 2f&27e 39.705

[[Tetracot family#Octacot|Octocat]]: [[27edo|27e]] 14cf&27e 27.601

[[Starling temperaments#Myna ~~temperament~~-Minah|Minah]]: [[27edo|27e]] 4ef&27e

[[Starling temperaments#Myna%20temperament-Minah|Minah]]: [[27edo|27e]] 4ef&27e

[[Avicennmic temperaments|Roman]]: [[29edo]] 3&23 30.043

[[Porcupine family|Nautilus]]: [[29edo]] 15&29 22.285

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[[Starling temperaments|Lupercalia]]: [[31edo]] 15&31 21.328

[[Starling temperaments#Casablanca%20temperament-Marrakesh-Murakuc|Murakuc]]: [[31edo]] 31&73f 41.394

[[Starling temperaments#Nusecond ~~temperament~~-13-limit|Nusecond]]: [[31edo]] 31&70f 23.323

[[Starling temperaments#Nusecond%20temperament-13-limit|Nusecond]]: [[31edo]] 31&70f 23.323

[[Starling temperaments#Cypress-13-limit|Cypress]]: [[31edo]] 11cdeef&31 37.849

[[Starling temperaments#x5-limit-Maneh|Maneh]]: [[31edo]] 4ef&31 29.868

[[31 comma temperaments#Prajapati|Prajapati]]: [[31edo]] 31&93f 37.885

[[Würschmidt family#~~Würschmidt~~-13-limit|Würschmidt]]: [[31edo]] 31&65d 23.593

[[Würschmidt family#W%C3%BCrschmidt-13-limit|Würschmidt]]: [[31edo]] 31&65d 23.593

[[Würschmidt family#~~Würschmidt~~-Worseschmidt|Worseschmidt]]: [[31edo]] 3def&31 34.382

[[Würschmidt family#W%C3%BCrschmidt-Worseschmidt|Worseschmidt]]: [[31edo]] 3def&31 34.382

[[Würschmidt family#~~Hemiwürschmidt~~-11-limit-Hemithir|Hemithir]]: [[31edo]] 31&68e 31.199

[[Würschmidt family#Hemiw%C3%BCrschmidt-11-limit-Hemithir|Hemithir]]: [[31edo]] 31&68e 31.199

[[Würschmidt family#~~Hemiwürschmidt~~-Hemiwur-Hemiwar|Hemiwar]]: [[31edo]] 6f&31 44.886

[[Würschmidt family#Hemiw%C3%BCrschmidt-Hemiwur-Hemiwar|Hemiwar]]: [[31edo]] 6f&31 44.886

[[Orwellismic temperaments#Sentinel-13-limit|Sentinel]]: [[31edo]] 14&17 37.408

[[Orwellismic temperaments#Diesic-13-limit|Diesic]]: [[31edo]] 1ce&31 38.116

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[[Meantone family#Jerome|Jerome]]: [[43edo]] 26&43 29.285

[[Marvel temperaments#Amavil|Amavil]]: [[43edo]] 9&43 25.791

[[Meantone family#Septimal ~~meantone~~-Unidecimal ~~meantone aka Huygens~~-Meridetone|Meridetone]]: [[43edo]] 43&117df 26.421

[[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Meridetone|Meridetone]]: [[43edo]] 43&117df 26.421

[[Starling temperaments#Kumonga-13-limit|Kumonga]]: [[43edo]] 16&43 28.920

[[Starling temperaments|Sensor]]: [[46edo]] 19&27 25.474

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[[Kleismic family#Kleiboh-13-limit]]: [[53edo]] 4ef&53 31.074

[[Maja family#Maja-13-limit|Maja]]: [[53edo]] 45ef&53 27.532

[[Schismatic family#Garibaldi-Helenus-13-limit ~~Helenus~~|Helenus]]: [[53edo]] 53&118d 26.284

[[Schismatic family#Garibaldi-Helenus-13-limit%20Helenus|Helenus]]: [[53edo]] 53&118d 26.284

[[Schismatic family#Hemigari-13-limit|Hemigari]]: [[53edo]] 29&53 27.464

[[Orwellismic temperaments#Quartonic-Quartz-13-limit|Quartz]]: [[53edo]] 26&53 28.818

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[[31 comma temperaments#Gallium|Gallium]]: [[62edo]] 31&62 25.484

[[Porcupine family|Ammonite]]: [[66edo]] 29&37 27.168

[[Würschmidt family#~~Hemiwürschmidt~~-Hemiwur-13-limit|Hemiwur]]: [[68edo]] 6&31 28.432

[[Würschmidt family#Hemiw%C3%BCrschmidt-Hemiwur-13-limit|Hemiwur]]: [[68edo]] 6&31 28.432

[[Gamelismic clan|Manna]]: [[72edo]] 41&72 17.012

[[Gamelismic clan|Hendec]]: [[72edo]] 26&46 17.707

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[[Marvel temperaments#Enneaportent-13-limit|Enneaportent]]: [[72edo]] 9&54 22.322

[[Starling temperaments#Casablanca%20temperament-Marrakesh-13-limit|Marrakesh]]: [[73edo]] 31&73 40.774

[[Meantone family#Septimal ~~meantone~~-Unidecimal ~~meantone aka Huygens~~-Grosstone|Grosstone]]: [[74edo]] 12&31 25.899

[[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Grosstone|Grosstone]]: [[74edo]] 12&31 25.899

[[Starling temperaments|Valentino]]: [[77edo]] 31&46 20.665

[[Unicorn family#Alicorn|Camahueto]] [[77edo]] 19&77 36.155

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[[Orwellismic temperaments#Quartonic-13-limit|Quartonic]]: [[80edo]] 53&80 23.875

[[Meantone family|Meanpop]]: [[81edo]] 19&31 20.883

[[Magic family#~~Divination~~|~~Divination~~]]: [[82edo]] 22&60 55.443

[[Magic family#Soothsaying|Soothsaying]]: [[82edo]] 22&60 55.443

[[Orwellismic temperaments#Secant-13-limit|Secant]]: [[84edo]] 26&58 46.373

[[Gamelismic clan|Rodan]]: [[87edo]] 41&46 18.448

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[[Hemimean clan#Subpental|Subpental]]: [[241edo]] 19&111 23.940

[[Ragismic microtemperaments#Ennealimmal|Ennealimmic]]: [[243edo]] 72&171 20.250

[[Mirkwai clan#Subsemifourth|Subsemifourth]]: [[255edo]] 103&255 28.387

[[Ragismic microtemperaments|Hemiennealimmal]]: [[270edo]] 72&198 12.505

[[Ragismic microtemperaments#Acrokleismic-13-limit|Acrokleismic]]: [[270edo]] 19&251 26.818

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[[Schismatic family|Sextilififths]]: [[289edo]] 29&130 25.276

[[Ragismic microtemperaments#Quincy|Quincy]]: [[289edo]] 72&145 23.862

[[Würschmidt family#~~Hemiwürschmidt~~-11-limit-13-limit|Hemiwürschmidt]]: [[291edo]] 31&130 23.074

[[Würschmidt family#Hemiw%C3%BCrschmidt-11-limit-13-limit|Hemiwürschmidt]]: [[291edo]] 31&130 23.074

[[Porwell temperaments|Hemischis]]: [[313edo]] 53&130 20.816

[[Werckismic temperaments#Octowerck|Octowerck]]: [[320edo]] 72&248 27.632

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<h4>Original HTML content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Optimal patent val</title></head><body><a href="#x5-limit rank two">5-limit rank two</a> | <a href="#x7-limit rank two">7-limit rank two</a> | <a href="#x7-limit rank three">7-limit rank three</a> | <a href="#x11-limit rank two">11-limit rank two</a> | <a href="#x11-limit rank three">11-limit rank three</a> | <a href="#x13-limit rank two">13-limit rank two</a> | <a href="#x13-limit rank three">13-limit rank three</a>

~~ ~~

Given any collection of p-limit commas, there is a finite list of p-limit <a class="wiki_link" href="/Patent%20val">patent vals</a> tempering out the commas. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the unique patent val which has the lowest <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures">TE error</a>; this is the optimal (TE) patent val for the temperament defined by the commas. Note that other definitions of error, such as maximum p-limit error, or maximum q-limit error where q is the largest odd number less than the prime above p, lead to different results.

Given any collection of p-limit commas, there is a finite list of p-limit <a class="wiki_link" href="/Patent%20val">patent vals</a> tempering out the commas. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the unique patent val which has the lowest <a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures">TE error</a>; this is the optimal (TE) patent val for the temperament defined by the commas. Note that other definitions of error, such as maximum p-limit error, or maximum q-limit error where q is the largest odd number less than the prime above p, lead to different results.

By tempering a JI scale using N-edo found on the list below we automatically temper it to the corresponding temperament. This can be done in <a class="wiki_link_ext" href="http://www.huygens-fokker.org/scala/" rel="nofollow">Scala</a> using the Quantize command: either type in &quot;Quantize/consistent N&quot; on the bottom, or use the pull-down menu under &quot;Modify&quot;, check the box saying &quot;Consistent&quot; and type N (without a decimal point) into &quot;Resolution&quot;.

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<a class="wiki_link" href="/Archytas%20clan#Fervor">Fervor</a>: <a class="wiki_link" href="/2edo">2edo</a> 2&amp;27e 52.054

<a class="wiki_link" href="/Dicot%20family#Decimal">Decimated</a>: <a class="wiki_link" href="/4edo">4edo</a> 4&amp;10e 31.456

<a class="wiki_link" href="/Starling%20temperaments#Myna ~~temperament~~-Coleto">Coleto</a>: <a class="wiki_link" href="/4edo">4edo</a> 4&amp;27e 48.687

<a class="wiki_link" href="/Starling%20temperaments#Myna%20temperament-Coleto">Coleto</a>: <a class="wiki_link" href="/4edo">4edo</a> 4&amp;27e 48.687

<a class="wiki_link" href="/Meantone%20family#Godzilla-Semafour">Semafour</a>: <a class="wiki_link" href="/5edo">5edo</a> 5&amp;14c 28.510

<a class="wiki_link" href="/Meantone%20family#Maqamic">Maqamic</a>: <a class="wiki_link" href="/7edo">7edo</a> 7&amp;10c 40.240

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<a class="wiki_link" href="/Marvel%20temperaments">Tritonic</a>: <a class="wiki_link" href="/31edo">31edo</a> 2&amp;29 23.659

<a class="wiki_link" href="/Starling%20temperaments">Casablanca</a>: <a class="wiki_link" href="/31edo">31edo</a> 31&amp;42 67.291

<a class="wiki_link" href="/Starling%20temperaments#Myna ~~temperament~~-Myno">Myno</a>: <a class="wiki_link" href="/31edo">31edo</a> 4&amp;27 33.434

<a class="wiki_link" href="/Starling%20temperaments#Myna%20temperament-Myno">Myno</a>: <a class="wiki_link" href="/31edo">31edo</a> 4&amp;27 33.434

<a class="wiki_link" href="/Starling%20temperaments#Cypress-11-limit">Cypress</a>: <a class="wiki_link" href="/31edo">31edo</a> 20cde&amp;31 42.719

<a class="wiki_link" href="/Gamelismic%20clan#Miracle">Revelation</a>: <a class="wiki_link" href="/31edo">31edo</a> 21&amp;31 32.946

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<a class="wiki_link" href="/Porcupine%20family#Nautilus">Belauensis</a>: <a class="wiki_link" href="/15edo">15edo</a> 14c&amp;15 29.816

<a class="wiki_link" href="/Kleismic%20family#Keemun-13-limit-Kumbaya">Kumbaya</a>: <a class="wiki_link" href="/15edo">15edo</a> 4&amp;15 31.633

<a class="wiki_link" href="/Kleismic%20family#Keemun-Darjeeling-13-limit ~~Darjeeling~~">Darjeeling</a>: <a class="wiki_link" href="/15edo">15edo</a> 15&amp;19e 21.445

<a class="wiki_link" href="/Kleismic%20family#Keemun-Darjeeling-13-limit%20Darjeeling">Darjeeling</a>: <a class="wiki_link" href="/15edo">15edo</a> 15&amp;19e 21.445

<a class="wiki_link" href="/Augmented%20family#Augene-11-limit-13-limit">Augene</a>: <a class="wiki_link" href="/15edo">15edo</a> 3&amp;15 20.785

<a class="wiki_link" href="/Augmented%20family#Augene-11-limit-Ogene">Ogene</a>: <a class="wiki_link" href="/15edo">15edo</a> 12&amp;15 22.890

<a class="wiki_link" href="/Pelogic%20family#Armodue-13-limit ~~Armodue~~">Armodue</a>: <a class="wiki_link" href="/16edo">16edo</a> 7&amp;9 19.351

<a class="wiki_link" href="/Pelogic%20family#Armodue-13-limit%20Armodue">Armodue</a>: <a class="wiki_link" href="/16edo">16edo</a> 7&amp;9 19.351

<a class="wiki_link" href="/Meantone%20family#Dominant-Domination-13-limit">Domination</a>: <a class="wiki_link" href="/17edo">17c</a> 5e&amp;12e 27.435

<a class="wiki_link" href="/Archytas%20clan#Progress">Progressive</a>: <a class="wiki_link" href="/17edo">17c</a> 2f&amp;15f 32.721

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<a class="wiki_link" href="/Comic%20family#Comic-13-limit">Comic</a>: <a class="wiki_link" href="/22edo">22edo</a> 2cde&amp;22 41.470

<a class="wiki_link" href="/Magic%20family#Astrology-13-limit">Astrology</a>: <a class="wiki_link" href="/22edo">22edo</a> 6&amp;16 34.376

<a class="wiki_link" href="/Pythagorean%20family#Catler ~~temperament~~">Catcall</a>: <a class="wiki_link" href="/24edo">24edo</a> 12f&amp;24 28.363

<a class="wiki_link" href="/Pythagorean%20family#Catler%20temperament">Catcall</a>: <a class="wiki_link" href="/24edo">24edo</a> 12f&amp;24 28.363

<a class="wiki_link" href="/Augmented%20family">Triforce</a>: <a class="wiki_link" href="/24edo">24edo</a> 9&amp;15 20.248

<a class="wiki_link" href="/Augmented%20family#Hemiaug-13-limit">Hemiaug</a>: <a class="wiki_link" href="/24edo">24edo</a> 3de&amp;24 30.159

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<a class="wiki_link" href="/Archytas%20clan#Fervor">Fervor</a>: <a class="wiki_link" href="/27edo">27edo</a> 2f&amp;27e 39.705

<a class="wiki_link" href="/Tetracot%20family#Octacot">Octocat</a>: <a class="wiki_link" href="/27edo">27e</a> 14cf&amp;27e 27.601

<a class="wiki_link" href="/Starling%20temperaments#Myna ~~temperament~~-Minah">Minah</a>: <a class="wiki_link" href="/27edo">27e</a> 4ef&amp;27e

<a class="wiki_link" href="/Starling%20temperaments#Myna%20temperament-Minah">Minah</a>: <a class="wiki_link" href="/27edo">27e</a> 4ef&amp;27e

<a class="wiki_link" href="/Avicennmic%20temperaments">Roman</a>: <a class="wiki_link" href="/29edo">29edo</a> 3&amp;23 30.043

<a class="wiki_link" href="/Porcupine%20family">Nautilus</a>: <a class="wiki_link" href="/29edo">29edo</a> 15&amp;29 22.285

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<a class="wiki_link" href="/Starling%20temperaments">Lupercalia</a>: <a class="wiki_link" href="/31edo">31edo</a> 15&amp;31 21.328

<a class="wiki_link" href="/Starling%20temperaments#Casablanca%20temperament-Marrakesh-Murakuc">Murakuc</a>: <a class="wiki_link" href="/31edo">31edo</a> 31&amp;73f 41.394

<a class="wiki_link" href="/Starling%20temperaments#Nusecond ~~temperament~~-13-limit">Nusecond</a>: <a class="wiki_link" href="/31edo">31edo</a> 31&amp;70f 23.323

<a class="wiki_link" href="/Starling%20temperaments#Nusecond%20temperament-13-limit">Nusecond</a>: <a class="wiki_link" href="/31edo">31edo</a> 31&amp;70f 23.323

<a class="wiki_link" href="/Starling%20temperaments#Cypress-13-limit">Cypress</a>: <a class="wiki_link" href="/31edo">31edo</a> 11cdeef&amp;31 37.849

<a class="wiki_link" href="/Starling%20temperaments#x5-limit-Maneh">Maneh</a>: <a class="wiki_link" href="/31edo">31edo</a> 4ef&amp;31 29.868

<a class="wiki_link" href="/31%20comma%20temperaments#Prajapati">Prajapati</a>: <a class="wiki_link" href="/31edo">31edo</a> 31&amp;93f 37.885

<a class="wiki_link" href="/W%C3%BCrschmidt%20family#~~Würschmidt~~-13-limit">Würschmidt</a>: <a class="wiki_link" href="/31edo">31edo</a> 31&amp;65d 23.593

<a class="wiki_link" href="/W%C3%BCrschmidt%20family#W%C3%BCrschmidt-13-limit">Würschmidt</a>: <a class="wiki_link" href="/31edo">31edo</a> 31&amp;65d 23.593

<a class="wiki_link" href="/W%C3%BCrschmidt%20family#~~Würschmidt~~-Worseschmidt">Worseschmidt</a>: <a class="wiki_link" href="/31edo">31edo</a> 3def&amp;31 34.382

<a class="wiki_link" href="/W%C3%BCrschmidt%20family#W%C3%BCrschmidt-Worseschmidt">Worseschmidt</a>: <a class="wiki_link" href="/31edo">31edo</a> 3def&amp;31 34.382

<a class="wiki_link" href="/W%C3%BCrschmidt%20family#~~Hemiwürschmidt~~-11-limit-Hemithir">Hemithir</a>: <a class="wiki_link" href="/31edo">31edo</a> 31&amp;68e 31.199

<a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiw%C3%BCrschmidt-11-limit-Hemithir">Hemithir</a>: <a class="wiki_link" href="/31edo">31edo</a> 31&amp;68e 31.199

<a class="wiki_link" href="/W%C3%BCrschmidt%20family#~~Hemiwürschmidt~~-Hemiwur-Hemiwar">Hemiwar</a>: <a class="wiki_link" href="/31edo">31edo</a> 6f&amp;31 44.886

<a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiw%C3%BCrschmidt-Hemiwur-Hemiwar">Hemiwar</a>: <a class="wiki_link" href="/31edo">31edo</a> 6f&amp;31 44.886

<a class="wiki_link" href="/Orwellismic%20temperaments#Sentinel-13-limit">Sentinel</a>: <a class="wiki_link" href="/31edo">31edo</a> 14&amp;17 37.408

<a class="wiki_link" href="/Orwellismic%20temperaments#Diesic-13-limit">Diesic</a>: <a class="wiki_link" href="/31edo">31edo</a> 1ce&amp;31 38.116

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<a class="wiki_link" href="/Meantone%20family#Jerome">Jerome</a>: <a class="wiki_link" href="/43edo">43edo</a> 26&amp;43 29.285

<a class="wiki_link" href="/Marvel%20temperaments#Amavil">Amavil</a>: <a class="wiki_link" href="/43edo">43edo</a> 9&amp;43 25.791

<a class="wiki_link" href="/Meantone%20family#Septimal ~~meantone~~-Unidecimal ~~meantone aka Huygens~~-Meridetone">Meridetone</a>: <a class="wiki_link" href="/43edo">43edo</a> 43&amp;117df 26.421

<a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Meridetone">Meridetone</a>: <a class="wiki_link" href="/43edo">43edo</a> 43&amp;117df 26.421

<a class="wiki_link" href="/Starling%20temperaments#Kumonga-13-limit">Kumonga</a>: <a class="wiki_link" href="/43edo">43edo</a> 16&amp;43 28.920

<a class="wiki_link" href="/Starling%20temperaments">Sensor</a>: <a class="wiki_link" href="/46edo">46edo</a> 19&amp;27 25.474

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Line 1,567:

<a class="wiki_link" href="/Kleismic%20family#Kleiboh-13-limit">Kleismic family</a>: <a class="wiki_link" href="/53edo">53edo</a> 4ef&amp;53 31.074

<a class="wiki_link" href="/Maja%20family#Maja-13-limit">Maja</a>: <a class="wiki_link" href="/53edo">53edo</a> 45ef&amp;53 27.532

<a class="wiki_link" href="/Schismatic%20family#Garibaldi-Helenus-13-limit ~~Helenus~~">Helenus</a>: <a class="wiki_link" href="/53edo">53edo</a> 53&amp;118d 26.284

<a class="wiki_link" href="/Schismatic%20family#Garibaldi-Helenus-13-limit%20Helenus">Helenus</a>: <a class="wiki_link" href="/53edo">53edo</a> 53&amp;118d 26.284

<a class="wiki_link" href="/Schismatic%20family#Hemigari-13-limit">Hemigari</a>: <a class="wiki_link" href="/53edo">53edo</a> 29&amp;53 27.464

<a class="wiki_link" href="/Orwellismic%20temperaments#Quartonic-Quartz-13-limit">Quartz</a>: <a class="wiki_link" href="/53edo">53edo</a> 26&amp;53 28.818

Line 1,584:

Line 1,582:

<a class="wiki_link" href="/31%20comma%20temperaments#Gallium">Gallium</a>: <a class="wiki_link" href="/62edo">62edo</a> 31&amp;62 25.484

<a class="wiki_link" href="/Porcupine%20family">Ammonite</a>: <a class="wiki_link" href="/66edo">66edo</a> 29&amp;37 27.168

<a class="wiki_link" href="/W%C3%BCrschmidt%20family#~~Hemiwürschmidt~~-Hemiwur-13-limit">Hemiwur</a>: <a class="wiki_link" href="/68edo">68edo</a> 6&amp;31 28.432

<a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiw%C3%BCrschmidt-Hemiwur-13-limit">Hemiwur</a>: <a class="wiki_link" href="/68edo">68edo</a> 6&amp;31 28.432

<a class="wiki_link" href="/Gamelismic%20clan">Manna</a>: <a class="wiki_link" href="/72edo">72edo</a> 41&amp;72 17.012

<a class="wiki_link" href="/Gamelismic%20clan">Hendec</a>: <a class="wiki_link" href="/72edo">72edo</a> 26&amp;46 17.707

Line 1,599:

Line 1,597:

<a class="wiki_link" href="/Marvel%20temperaments#Enneaportent-13-limit">Enneaportent</a>: <a class="wiki_link" href="/72edo">72edo</a> 9&amp;54 22.322

<a class="wiki_link" href="/Starling%20temperaments#Casablanca%20temperament-Marrakesh-13-limit">Marrakesh</a>: <a class="wiki_link" href="/73edo">73edo</a> 31&amp;73 40.774

<a class="wiki_link" href="/Meantone%20family#Septimal ~~meantone~~-Unidecimal ~~meantone aka Huygens~~-Grosstone">Grosstone</a>: <a class="wiki_link" href="/74edo">74edo</a> 12&amp;31 25.899

<a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Grosstone">Grosstone</a>: <a class="wiki_link" href="/74edo">74edo</a> 12&amp;31 25.899

<a class="wiki_link" href="/Starling%20temperaments">Valentino</a>: <a class="wiki_link" href="/77edo">77edo</a> 31&amp;46 20.665

<a class="wiki_link" href="/Unicorn%20family#Alicorn">Camahueto</a> <a class="wiki_link" href="/77edo">77edo</a> 19&amp;77 36.155

Line 1,607:

Line 1,605:

<a class="wiki_link" href="/Orwellismic%20temperaments#Quartonic-13-limit">Quartonic</a>: <a class="wiki_link" href="/80edo">80edo</a> 53&amp;80 23.875

<a class="wiki_link" href="/Meantone%20family">Meanpop</a>: <a class="wiki_link" href="/81edo">81edo</a> 19&amp;31 20.883

<a class="wiki_link" href="/Magic%20family#~~Divination~~">~~Divination~~</a>: <a class="wiki_link" href="/82edo">82edo</a> 22&amp;60 55.443

<a class="wiki_link" href="/Magic%20family#Soothsaying">Soothsaying</a>: <a class="wiki_link" href="/82edo">82edo</a> 22&amp;60 55.443

<a class="wiki_link" href="/Orwellismic%20temperaments#Secant-13-limit">Secant</a>: <a class="wiki_link" href="/84edo">84edo</a> 26&amp;58 46.373

<a class="wiki_link" href="/Gamelismic%20clan">Rodan</a>: <a class="wiki_link" href="/87edo">87edo</a> 41&amp;46 18.448

Line 1,652:

Line 1,650:

<a class="wiki_link" href="/Hemimean%20clan#Subpental">Subpental</a>: <a class="wiki_link" href="/241edo">241edo</a> 19&amp;111 23.940

<a class="wiki_link" href="/Ragismic%20microtemperaments#Ennealimmal">Ennealimmic</a>: <a class="wiki_link" href="/243edo">243edo</a> 72&amp;171 20.250

<a class="wiki_link" href="/Mirkwai%20clan#Subsemifourth">Subsemifourth</a>: <a class="wiki_link" href="/255edo">255edo</a> 103&amp;255 28.387

<a class="wiki_link" href="/Ragismic%20microtemperaments">Hemiennealimmal</a>: <a class="wiki_link" href="/270edo">270edo</a> 72&amp;198 12.505

<a class="wiki_link" href="/Ragismic%20microtemperaments#Acrokleismic-13-limit">Acrokleismic</a>: <a class="wiki_link" href="/270edo">270edo</a> 19&amp;251 26.818

Line 1,659:

Line 1,657:

<a class="wiki_link" href="/Schismatic%20family">Sextilififths</a>: <a class="wiki_link" href="/289edo">289edo</a> 29&amp;130 25.276

<a class="wiki_link" href="/Ragismic%20microtemperaments#Quincy">Quincy</a>: <a class="wiki_link" href="/289edo">289edo</a> 72&amp;145 23.862

<a class="wiki_link" href="/W%C3%BCrschmidt%20family#~~Hemiwürschmidt~~-11-limit-13-limit">Hemiwürschmidt</a>: <a class="wiki_link" href="/291edo">291edo</a> 31&amp;130 23.074

<a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiw%C3%BCrschmidt-11-limit-13-limit">Hemiwürschmidt</a>: <a class="wiki_link" href="/291edo">291edo</a> 31&amp;130 23.074

<a class="wiki_link" href="/Porwell%20temperaments">Hemischis</a>: <a class="wiki_link" href="/313edo">313edo</a> 53&amp;130 20.816

<a class="wiki_link" href="/Werckismic%20temperaments#Octowerck">Octowerck</a>: <a class="wiki_link" href="/320edo">320edo</a> 72&amp;248 27.632

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-09 16:04:14 UTC</tt>.<br>
+: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2012-05-13 13:49:41 UTC</tt>.<br>
-: The original revision id was <tt>332652360</tt>.<br>
+: The original revision id was <tt>334534992</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]
 Given any collection of p-limit commas, there is a finite list of p-limit [[Patent val|patent vals]] tempering out the commas. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the unique patent val which has the lowest [[Tenney-Euclidean temperament measures|TE error]]; this is the //optimal (TE) patent val// for the temperament defined by the commas. Note that other definitions of error, such as maximum p-limit error, or maximum q-limit error where q is the largest odd number less than the prime above p, lead to different results.
@@ Line 224: / Line 223: @@
 [[Archytas clan#Fervor|Fervor]]: [[2edo]] 2&amp;27e 52.054
 [[Dicot family#Decimal|Decimated]]: [[4edo]] 4&amp;10e 31.456
-[[Starling temperaments#Myna temperament-Coleto|Coleto]]: [[4edo]] 4&amp;27e 48.687
+[[Starling temperaments#Myna%20temperament-Coleto|Coleto]]: [[4edo]] 4&amp;27e 48.687
 [[Meantone family#Godzilla-Semafour|Semafour]]: [[5edo]] 5&amp;14c 28.510
 [[Meantone family#Maqamic|Maqamic]]: [[7edo]] 7&amp;10c 40.240
@@ Line 310: / Line 309: @@
 [[Marvel temperaments|Tritonic]]: [[31edo]] 2&amp;29 23.659
 [[Starling temperaments|Casablanca]]: [[31edo]] 31&amp;42 67.291
-[[Starling temperaments#Myna temperament-Myno|Myno]]: [[31edo]] 4&amp;27 33.434
+[[Starling temperaments#Myna%20temperament-Myno|Myno]]: [[31edo]] 4&amp;27 33.434
 [[Starling temperaments#Cypress-11-limit|Cypress]]: [[31edo]] 20cde&amp;31 42.719
 [[Gamelismic clan#Miracle|Revelation]]: [[31edo]] 21&amp;31 32.946
@@ Line 582: / Line 581: @@
 [[Porcupine family#Nautilus|Belauensis]]: [[15edo]] 14c&amp;15 29.816
 [[Kleismic family#Keemun-13-limit-Kumbaya|Kumbaya]]: [[15edo]] 4&amp;15 31.633
-[[Kleismic family#Keemun-Darjeeling-13-limit Darjeeling|Darjeeling]]: [[15edo]] 15&amp;19e 21.445
+[[Kleismic family#Keemun-Darjeeling-13-limit%20Darjeeling|Darjeeling]]: [[15edo]] 15&amp;19e 21.445
 [[Augmented family#Augene-11-limit-13-limit|Augene]]: [[15edo]] 3&amp;15 20.785
 [[Augmented family#Augene-11-limit-Ogene|Ogene]]: [[15edo]] 12&amp;15 22.890
-[[Pelogic family#Armodue-13-limit Armodue|Armodue]]: [[16edo]] 7&amp;9 19.351
+[[Pelogic family#Armodue-13-limit%20Armodue|Armodue]]: [[16edo]] 7&amp;9 19.351
 [[Meantone family#Dominant-Domination-13-limit|Domination]]: [[17edo|17c]] 5e&amp;12e 27.435
 [[Archytas clan#Progress|Progressive]]: [[17edo|17c]] 2f&amp;15f 32.721
@@ Line 615: / Line 614: @@
 [[Comic family#Comic-13-limit|Comic]]: [[22edo]] 2cde&amp;22 41.470
 [[Magic family#Astrology-13-limit|Astrology]]: [[22edo]] 6&amp;16 34.376
-[[Pythagorean family#Catler temperament|Catcall]]: [[24edo]] 12f&amp;24 28.363
+[[Pythagorean family#Catler%20temperament|Catcall]]: [[24edo]] 12f&amp;24 28.363
 [[Augmented family|Triforce]]: [[24edo]] 9&amp;15 20.248
 [[Augmented family#Hemiaug-13-limit|Hemiaug]]: [[24edo]] 3de&amp;24 30.159
@@ Line 634: / Line 633: @@
 [[Archytas clan#Fervor|Fervor]]: [[27edo]] 2f&amp;27e 39.705
 [[Tetracot family#Octacot|Octocat]]: [[27edo|27e]] 14cf&amp;27e 27.601
-[[Starling temperaments#Myna temperament-Minah|Minah]]: [[27edo|27e]] 4ef&amp;27e
+[[Starling temperaments#Myna%20temperament-Minah|Minah]]: [[27edo|27e]] 4ef&amp;27e
 [[Avicennmic temperaments|Roman]]: [[29edo]] 3&amp;23 30.043
 [[Porcupine family|Nautilus]]: [[29edo]] 15&amp;29 22.285
@@ Line 649: / Line 648: @@
 [[Starling temperaments|Lupercalia]]: [[31edo]] 15&amp;31 21.328
 [[Starling temperaments#Casablanca%20temperament-Marrakesh-Murakuc|Murakuc]]: [[31edo]] 31&amp;73f 41.394
-[[Starling temperaments#Nusecond temperament-13-limit|Nusecond]]: [[31edo]] 31&amp;70f 23.323
+[[Starling temperaments#Nusecond%20temperament-13-limit|Nusecond]]: [[31edo]] 31&amp;70f 23.323
 [[Starling temperaments#Cypress-13-limit|Cypress]]: [[31edo]] 11cdeef&amp;31 37.849
 [[Starling temperaments#x5-limit-Maneh|Maneh]]: [[31edo]] 4ef&amp;31 29.868
 [[31 comma temperaments#Prajapati|Prajapati]]: [[31edo]] 31&amp;93f 37.885
-[[Würschmidt family#Würschmidt-13-limit|Würschmidt]]: [[31edo]] 31&amp;65d 23.593
+[[Würschmidt family#W%C3%BCrschmidt-13-limit|Würschmidt]]: [[31edo]] 31&amp;65d 23.593
-[[Würschmidt family#Würschmidt-Worseschmidt|Worseschmidt]]: [[31edo]] 3def&amp;31 34.382
+[[Würschmidt family#W%C3%BCrschmidt-Worseschmidt|Worseschmidt]]: [[31edo]] 3def&amp;31 34.382
-[[Würschmidt family#Hemiwürschmidt-11-limit-Hemithir|Hemithir]]: [[31edo]] 31&amp;68e 31.199
+[[Würschmidt family#Hemiw%C3%BCrschmidt-11-limit-Hemithir|Hemithir]]: [[31edo]] 31&amp;68e 31.199
-[[Würschmidt family#Hemiwürschmidt-Hemiwur-Hemiwar|Hemiwar]]: [[31edo]] 6f&amp;31 44.886
+[[Würschmidt family#Hemiw%C3%BCrschmidt-Hemiwur-Hemiwar|Hemiwar]]: [[31edo]] 6f&amp;31 44.886
 [[Orwellismic temperaments#Sentinel-13-limit|Sentinel]]: [[31edo]] 14&amp;17 37.408
 [[Orwellismic temperaments#Diesic-13-limit|Diesic]]: [[31edo]] 1ce&amp;31 38.116
@@ Line 683: / Line 682: @@
 [[Meantone family#Jerome|Jerome]]: [[43edo]] 26&amp;43 29.285
 [[Marvel temperaments#Amavil|Amavil]]: [[43edo]] 9&amp;43 25.791
-[[Meantone family#Septimal meantone-Unidecimal meantone aka Huygens-Meridetone|Meridetone]]: [[43edo]] 43&amp;117df 26.421
+[[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Meridetone|Meridetone]]: [[43edo]] 43&amp;117df 26.421
 [[Starling temperaments#Kumonga-13-limit|Kumonga]]: [[43edo]] 16&amp;43 28.920
 [[Starling temperaments|Sensor]]: [[46edo]] 19&amp;27 25.474
@@ Line 699: / Line 698: @@
 [[Kleismic family#Kleiboh-13-limit]]: [[53edo]] 4ef&amp;53 31.074
 [[Maja family#Maja-13-limit|Maja]]: [[53edo]] 45ef&amp;53 27.532
-[[Schismatic family#Garibaldi-Helenus-13-limit Helenus|Helenus]]: [[53edo]] 53&amp;118d 26.284
+[[Schismatic family#Garibaldi-Helenus-13-limit%20Helenus|Helenus]]: [[53edo]] 53&amp;118d 26.284
 [[Schismatic family#Hemigari-13-limit|Hemigari]]: [[53edo]] 29&amp;53 27.464
 [[Orwellismic temperaments#Quartonic-Quartz-13-limit|Quartz]]: [[53edo]] 26&amp;53 28.818
@@ Line 714: / Line 713: @@
 [[31 comma temperaments#Gallium|Gallium]]: [[62edo]] 31&amp;62 25.484
 [[Porcupine family|Ammonite]]: [[66edo]] 29&amp;37 27.168
-[[Würschmidt family#Hemiwürschmidt-Hemiwur-13-limit|Hemiwur]]: [[68edo]] 6&amp;31 28.432
+[[Würschmidt family#Hemiw%C3%BCrschmidt-Hemiwur-13-limit|Hemiwur]]: [[68edo]] 6&amp;31 28.432
 [[Gamelismic clan|Manna]]: [[72edo]] 41&amp;72 17.012
 [[Gamelismic clan|Hendec]]: [[72edo]] 26&amp;46 17.707
@@ Line 729: / Line 728: @@
 [[Marvel temperaments#Enneaportent-13-limit|Enneaportent]]: [[72edo]] 9&amp;54 22.322
 [[Starling temperaments#Casablanca%20temperament-Marrakesh-13-limit|Marrakesh]]: [[73edo]] 31&amp;73 40.774
-[[Meantone family#Septimal meantone-Unidecimal meantone aka Huygens-Grosstone|Grosstone]]: [[74edo]] 12&amp;31 25.899
+[[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Grosstone|Grosstone]]: [[74edo]] 12&amp;31 25.899
 [[Starling temperaments|Valentino]]: [[77edo]] 31&amp;46 20.665
 [[Unicorn family#Alicorn|Camahueto]] [[77edo]] 19&amp;77 36.155
@@ Line 737: / Line 736: @@
 [[Orwellismic temperaments#Quartonic-13-limit|Quartonic]]: [[80edo]] 53&amp;80 23.875
 [[Meantone family|Meanpop]]: [[81edo]] 19&amp;31 20.883
-[[Magic family#Divination|Divination]]: [[82edo]] 22&amp;60 55.443
+[[Magic family#Soothsaying|Soothsaying]]: [[82edo]] 22&amp;60 55.443
 [[Orwellismic temperaments#Secant-13-limit|Secant]]: [[84edo]] 26&amp;58 46.373
 [[Gamelismic clan|Rodan]]: [[87edo]] 41&amp;46 18.448
@@ Line 782: / Line 781: @@
 [[Hemimean clan#Subpental|Subpental]]: [[241edo]] 19&amp;111 23.940
 [[Ragismic microtemperaments#Ennealimmal|Ennealimmic]]: [[243edo]] 72&amp;171 20.250
-[[Mirkwai clan#Subsemifourth|Subsemifourth]]: [[255edo]] 103&amp;255  28.387
+[[Mirkwai clan#Subsemifourth|Subsemifourth]]: [[255edo]] 103&amp;255 28.387
 [[Ragismic microtemperaments|Hemiennealimmal]]: [[270edo]] 72&amp;198 12.505
 [[Ragismic microtemperaments#Acrokleismic-13-limit|Acrokleismic]]: [[270edo]] 19&amp;251 26.818
@@ Line 789: / Line 788: @@
 [[Schismatic family|Sextilififths]]: [[289edo]] 29&amp;130 25.276
 [[Ragismic microtemperaments#Quincy|Quincy]]: [[289edo]] 72&amp;145 23.862
-[[Würschmidt family#Hemiwürschmidt-11-limit-13-limit|Hemiwürschmidt]]: [[291edo]] 31&amp;130 23.074
+[[Würschmidt family#Hemiw%C3%BCrschmidt-11-limit-13-limit|Hemiwürschmidt]]: [[291edo]] 31&amp;130 23.074
 [[Porwell temperaments|Hemischis]]: [[313edo]] 53&amp;130 20.816
 [[Werckismic temperaments#Octowerck|Octowerck]]: [[320edo]] 72&amp;248 27.632
@@ Line 877: / Line 876: @@
 <h4>Original HTML content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Optimal patent val&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:14:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;a href="#x5-limit rank two"&gt;5-limit rank two&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#x7-limit rank two"&gt;7-limit rank two&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt; | &lt;a href="#x7-limit rank three"&gt;7-limit rank three&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#x11-limit rank two"&gt;11-limit rank two&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt; | &lt;a href="#x11-limit rank three"&gt;11-limit rank three&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt; | &lt;a href="#x13-limit rank two"&gt;13-limit rank two&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt; | &lt;a href="#x13-limit rank three"&gt;13-limit rank three&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:22 --&gt;Given any collection of p-limit commas, there is a finite list of p-limit &lt;a class="wiki_link" href="/Patent%20val"&gt;patent vals&lt;/a&gt; tempering out the commas. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the unique patent val which has the lowest &lt;a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures"&gt;TE error&lt;/a&gt;; this is the &lt;em&gt;optimal (TE) patent val&lt;/em&gt; for the temperament defined by the commas. Note that other definitions of error, such as maximum p-limit error, or maximum q-limit error where q is the largest odd number less than the prime above p, lead to different results.&lt;br /&gt;
-Given any collection of p-limit commas, there is a finite list of p-limit &lt;a class="wiki_link" href="/Patent%20val"&gt;patent vals&lt;/a&gt; tempering out the commas. The list is not guaranteed to contain any members, but in most actual circumstances it will. If the list is not empty, then among these patent vals will be found the unique patent val which has the lowest &lt;a class="wiki_link" href="/Tenney-Euclidean%20temperament%20measures"&gt;TE error&lt;/a&gt;; this is the &lt;em&gt;optimal (TE) patent val&lt;/em&gt; for the temperament defined by the commas. Note that other definitions of error, such as maximum p-limit error, or maximum q-limit error where q is the largest odd number less than the prime above p, lead to different results.&lt;br /&gt;
 &lt;br /&gt;
 By tempering a JI scale using N-edo found on the list below we automatically temper it to the corresponding temperament. This can be done in &lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/scala/" rel="nofollow"&gt;Scala&lt;/a&gt; using the Quantize command: either type in &amp;quot;Quantize/consistent N&amp;quot; on the bottom, or use the pull-down menu under &amp;quot;Modify&amp;quot;, check the box saying &amp;quot;Consistent&amp;quot; and type N (without a decimal point) into &amp;quot;Resolution&amp;quot;.&lt;br /&gt;
@@ Line 1,094: / Line 1,092: @@
 &lt;a class="wiki_link" href="/Archytas%20clan#Fervor"&gt;Fervor&lt;/a&gt;: &lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt; 2&amp;amp;27e 52.054&lt;br /&gt;
 &lt;a class="wiki_link" href="/Dicot%20family#Decimal"&gt;Decimated&lt;/a&gt;: &lt;a class="wiki_link" href="/4edo"&gt;4edo&lt;/a&gt; 4&amp;amp;10e 31.456&lt;br /&gt;
-&lt;a class="wiki_link" href="/Starling%20temperaments#Myna temperament-Coleto"&gt;Coleto&lt;/a&gt;: &lt;a class="wiki_link" href="/4edo"&gt;4edo&lt;/a&gt; 4&amp;amp;27e 48.687&lt;br /&gt;
+&lt;a class="wiki_link" href="/Starling%20temperaments#Myna%20temperament-Coleto"&gt;Coleto&lt;/a&gt;: &lt;a class="wiki_link" href="/4edo"&gt;4edo&lt;/a&gt; 4&amp;amp;27e 48.687&lt;br /&gt;
 &lt;a class="wiki_link" href="/Meantone%20family#Godzilla-Semafour"&gt;Semafour&lt;/a&gt;: &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt; 5&amp;amp;14c 28.510&lt;br /&gt;
 &lt;a class="wiki_link" href="/Meantone%20family#Maqamic"&gt;Maqamic&lt;/a&gt;: &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt; 7&amp;amp;10c 40.240&lt;br /&gt;
@@ Line 1,180: / Line 1,178: @@
 &lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;Tritonic&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 2&amp;amp;29 23.659&lt;br /&gt;
 &lt;a class="wiki_link" href="/Starling%20temperaments"&gt;Casablanca&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 31&amp;amp;42 67.291&lt;br /&gt;
-&lt;a class="wiki_link" href="/Starling%20temperaments#Myna temperament-Myno"&gt;Myno&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 4&amp;amp;27 33.434&lt;br /&gt;
+&lt;a class="wiki_link" href="/Starling%20temperaments#Myna%20temperament-Myno"&gt;Myno&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 4&amp;amp;27 33.434&lt;br /&gt;
 &lt;a class="wiki_link" href="/Starling%20temperaments#Cypress-11-limit"&gt;Cypress&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 20cde&amp;amp;31 42.719&lt;br /&gt;
 &lt;a class="wiki_link" href="/Gamelismic%20clan#Miracle"&gt;Revelation&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 21&amp;amp;31 32.946&lt;br /&gt;
@@ Line 1,452: / Line 1,450: @@
 &lt;a class="wiki_link" href="/Porcupine%20family#Nautilus"&gt;Belauensis&lt;/a&gt;: &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt; 14c&amp;amp;15 29.816&lt;br /&gt;
 &lt;a class="wiki_link" href="/Kleismic%20family#Keemun-13-limit-Kumbaya"&gt;Kumbaya&lt;/a&gt;: &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt; 4&amp;amp;15 31.633&lt;br /&gt;
-&lt;a class="wiki_link" href="/Kleismic%20family#Keemun-Darjeeling-13-limit Darjeeling"&gt;Darjeeling&lt;/a&gt;: &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt; 15&amp;amp;19e 21.445&lt;br /&gt;
+&lt;a class="wiki_link" href="/Kleismic%20family#Keemun-Darjeeling-13-limit%20Darjeeling"&gt;Darjeeling&lt;/a&gt;: &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt; 15&amp;amp;19e 21.445&lt;br /&gt;
 &lt;a class="wiki_link" href="/Augmented%20family#Augene-11-limit-13-limit"&gt;Augene&lt;/a&gt;: &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt; 3&amp;amp;15 20.785&lt;br /&gt;
 &lt;a class="wiki_link" href="/Augmented%20family#Augene-11-limit-Ogene"&gt;Ogene&lt;/a&gt;: &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt; 12&amp;amp;15 22.890&lt;br /&gt;
-&lt;a class="wiki_link" href="/Pelogic%20family#Armodue-13-limit Armodue"&gt;Armodue&lt;/a&gt;: &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt; 7&amp;amp;9 19.351&lt;br /&gt;
+&lt;a class="wiki_link" href="/Pelogic%20family#Armodue-13-limit%20Armodue"&gt;Armodue&lt;/a&gt;: &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt; 7&amp;amp;9 19.351&lt;br /&gt;
 &lt;a class="wiki_link" href="/Meantone%20family#Dominant-Domination-13-limit"&gt;Domination&lt;/a&gt;: &lt;a class="wiki_link" href="/17edo"&gt;17c&lt;/a&gt; 5e&amp;amp;12e 27.435&lt;br /&gt;
 &lt;a class="wiki_link" href="/Archytas%20clan#Progress"&gt;Progressive&lt;/a&gt;: &lt;a class="wiki_link" href="/17edo"&gt;17c&lt;/a&gt; 2f&amp;amp;15f 32.721&lt;br /&gt;
@@ Line 1,485: / Line 1,483: @@
 &lt;a class="wiki_link" href="/Comic%20family#Comic-13-limit"&gt;Comic&lt;/a&gt;: &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; 2cde&amp;amp;22 41.470&lt;br /&gt;
 &lt;a class="wiki_link" href="/Magic%20family#Astrology-13-limit"&gt;Astrology&lt;/a&gt;: &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; 6&amp;amp;16 34.376&lt;br /&gt;
-&lt;a class="wiki_link" href="/Pythagorean%20family#Catler temperament"&gt;Catcall&lt;/a&gt;: &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt; 12f&amp;amp;24 28.363&lt;br /&gt;
+&lt;a class="wiki_link" href="/Pythagorean%20family#Catler%20temperament"&gt;Catcall&lt;/a&gt;: &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt; 12f&amp;amp;24 28.363&lt;br /&gt;
 &lt;a class="wiki_link" href="/Augmented%20family"&gt;Triforce&lt;/a&gt;: &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt; 9&amp;amp;15 20.248&lt;br /&gt;
 &lt;a class="wiki_link" href="/Augmented%20family#Hemiaug-13-limit"&gt;Hemiaug&lt;/a&gt;: &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt; 3de&amp;amp;24 30.159&lt;br /&gt;
@@ Line 1,504: / Line 1,502: @@
 &lt;a class="wiki_link" href="/Archytas%20clan#Fervor"&gt;Fervor&lt;/a&gt;: &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt; 2f&amp;amp;27e 39.705&lt;br /&gt;
 &lt;a class="wiki_link" href="/Tetracot%20family#Octacot"&gt;Octocat&lt;/a&gt;: &lt;a class="wiki_link" href="/27edo"&gt;27e&lt;/a&gt; 14cf&amp;amp;27e 27.601&lt;br /&gt;
-&lt;a class="wiki_link" href="/Starling%20temperaments#Myna temperament-Minah"&gt;Minah&lt;/a&gt;: &lt;a class="wiki_link" href="/27edo"&gt;27e&lt;/a&gt; 4ef&amp;amp;27e&lt;br /&gt;
+&lt;a class="wiki_link" href="/Starling%20temperaments#Myna%20temperament-Minah"&gt;Minah&lt;/a&gt;: &lt;a class="wiki_link" href="/27edo"&gt;27e&lt;/a&gt; 4ef&amp;amp;27e&lt;br /&gt;
 &lt;a class="wiki_link" href="/Avicennmic%20temperaments"&gt;Roman&lt;/a&gt;: &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt; 3&amp;amp;23 30.043&lt;br /&gt;
 &lt;a class="wiki_link" href="/Porcupine%20family"&gt;Nautilus&lt;/a&gt;: &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt; 15&amp;amp;29 22.285&lt;br /&gt;
@@ Line 1,519: / Line 1,517: @@
 &lt;a class="wiki_link" href="/Starling%20temperaments"&gt;Lupercalia&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 15&amp;amp;31 21.328&lt;br /&gt;
 &lt;a class="wiki_link" href="/Starling%20temperaments#Casablanca%20temperament-Marrakesh-Murakuc"&gt;Murakuc&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 31&amp;amp;73f 41.394&lt;br /&gt;
-&lt;a class="wiki_link" href="/Starling%20temperaments#Nusecond temperament-13-limit"&gt;Nusecond&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 31&amp;amp;70f 23.323&lt;br /&gt;
+&lt;a class="wiki_link" href="/Starling%20temperaments#Nusecond%20temperament-13-limit"&gt;Nusecond&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 31&amp;amp;70f 23.323&lt;br /&gt;
 &lt;a class="wiki_link" href="/Starling%20temperaments#Cypress-13-limit"&gt;Cypress&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 11cdeef&amp;amp;31 37.849&lt;br /&gt;
 &lt;a class="wiki_link" href="/Starling%20temperaments#x5-limit-Maneh"&gt;Maneh&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 4ef&amp;amp;31 29.868&lt;br /&gt;
 &lt;a class="wiki_link" href="/31%20comma%20temperaments#Prajapati"&gt;Prajapati&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 31&amp;amp;93f 37.885&lt;br /&gt;
-&lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family#Würschmidt-13-limit"&gt;Würschmidt&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 31&amp;amp;65d 23.593&lt;br /&gt;
+&lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family#W%C3%BCrschmidt-13-limit"&gt;Würschmidt&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 31&amp;amp;65d 23.593&lt;br /&gt;
-&lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family#Würschmidt-Worseschmidt"&gt;Worseschmidt&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 3def&amp;amp;31 34.382&lt;br /&gt;
+&lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family#W%C3%BCrschmidt-Worseschmidt"&gt;Worseschmidt&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 3def&amp;amp;31 34.382&lt;br /&gt;
-&lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiwürschmidt-11-limit-Hemithir"&gt;Hemithir&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 31&amp;amp;68e 31.199&lt;br /&gt;
+&lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiw%C3%BCrschmidt-11-limit-Hemithir"&gt;Hemithir&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 31&amp;amp;68e 31.199&lt;br /&gt;
-&lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiwürschmidt-Hemiwur-Hemiwar"&gt;Hemiwar&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 6f&amp;amp;31 44.886&lt;br /&gt;
+&lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiw%C3%BCrschmidt-Hemiwur-Hemiwar"&gt;Hemiwar&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 6f&amp;amp;31 44.886&lt;br /&gt;
 &lt;a class="wiki_link" href="/Orwellismic%20temperaments#Sentinel-13-limit"&gt;Sentinel&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 14&amp;amp;17 37.408&lt;br /&gt;
 &lt;a class="wiki_link" href="/Orwellismic%20temperaments#Diesic-13-limit"&gt;Diesic&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 1ce&amp;amp;31 38.116&lt;br /&gt;
@@ Line 1,553: / Line 1,551: @@
 &lt;a class="wiki_link" href="/Meantone%20family#Jerome"&gt;Jerome&lt;/a&gt;: &lt;a class="wiki_link" href="/43edo"&gt;43edo&lt;/a&gt; 26&amp;amp;43 29.285&lt;br /&gt;
 &lt;a class="wiki_link" href="/Marvel%20temperaments#Amavil"&gt;Amavil&lt;/a&gt;: &lt;a class="wiki_link" href="/43edo"&gt;43edo&lt;/a&gt; 9&amp;amp;43 25.791&lt;br /&gt;
-&lt;a class="wiki_link" href="/Meantone%20family#Septimal meantone-Unidecimal meantone aka Huygens-Meridetone"&gt;Meridetone&lt;/a&gt;: &lt;a class="wiki_link" href="/43edo"&gt;43edo&lt;/a&gt; 43&amp;amp;117df 26.421&lt;br /&gt;
+&lt;a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Meridetone"&gt;Meridetone&lt;/a&gt;: &lt;a class="wiki_link" href="/43edo"&gt;43edo&lt;/a&gt; 43&amp;amp;117df 26.421&lt;br /&gt;
 &lt;a class="wiki_link" href="/Starling%20temperaments#Kumonga-13-limit"&gt;Kumonga&lt;/a&gt;: &lt;a class="wiki_link" href="/43edo"&gt;43edo&lt;/a&gt; 16&amp;amp;43 28.920&lt;br /&gt;
 &lt;a class="wiki_link" href="/Starling%20temperaments"&gt;Sensor&lt;/a&gt;: &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt; 19&amp;amp;27 25.474&lt;br /&gt;
@@ Line 1,569: / Line 1,567: @@
 &lt;a class="wiki_link" href="/Kleismic%20family#Kleiboh-13-limit"&gt;Kleismic family&lt;/a&gt;: &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; 4ef&amp;amp;53 31.074&lt;br /&gt;
 &lt;a class="wiki_link" href="/Maja%20family#Maja-13-limit"&gt;Maja&lt;/a&gt;: &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; 45ef&amp;amp;53 27.532&lt;br /&gt;
-&lt;a class="wiki_link" href="/Schismatic%20family#Garibaldi-Helenus-13-limit Helenus"&gt;Helenus&lt;/a&gt;: &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; 53&amp;amp;118d 26.284&lt;br /&gt;
+&lt;a class="wiki_link" href="/Schismatic%20family#Garibaldi-Helenus-13-limit%20Helenus"&gt;Helenus&lt;/a&gt;: &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; 53&amp;amp;118d 26.284&lt;br /&gt;
 &lt;a class="wiki_link" href="/Schismatic%20family#Hemigari-13-limit"&gt;Hemigari&lt;/a&gt;: &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; 29&amp;amp;53 27.464&lt;br /&gt;
 &lt;a class="wiki_link" href="/Orwellismic%20temperaments#Quartonic-Quartz-13-limit"&gt;Quartz&lt;/a&gt;: &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; 26&amp;amp;53 28.818&lt;br /&gt;
@@ Line 1,584: / Line 1,582: @@
 &lt;a class="wiki_link" href="/31%20comma%20temperaments#Gallium"&gt;Gallium&lt;/a&gt;: &lt;a class="wiki_link" href="/62edo"&gt;62edo&lt;/a&gt; 31&amp;amp;62 25.484&lt;br /&gt;
 &lt;a class="wiki_link" href="/Porcupine%20family"&gt;Ammonite&lt;/a&gt;: &lt;a class="wiki_link" href="/66edo"&gt;66edo&lt;/a&gt; 29&amp;amp;37 27.168&lt;br /&gt;
-&lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiwürschmidt-Hemiwur-13-limit"&gt;Hemiwur&lt;/a&gt;: &lt;a class="wiki_link" href="/68edo"&gt;68edo&lt;/a&gt; 6&amp;amp;31 28.432&lt;br /&gt;
+&lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiw%C3%BCrschmidt-Hemiwur-13-limit"&gt;Hemiwur&lt;/a&gt;: &lt;a class="wiki_link" href="/68edo"&gt;68edo&lt;/a&gt; 6&amp;amp;31 28.432&lt;br /&gt;
 &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;Manna&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 41&amp;amp;72 17.012&lt;br /&gt;
 &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;Hendec&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 26&amp;amp;46 17.707&lt;br /&gt;
@@ Line 1,599: / Line 1,597: @@
 &lt;a class="wiki_link" href="/Marvel%20temperaments#Enneaportent-13-limit"&gt;Enneaportent&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 9&amp;amp;54 22.322&lt;br /&gt;
 &lt;a class="wiki_link" href="/Starling%20temperaments#Casablanca%20temperament-Marrakesh-13-limit"&gt;Marrakesh&lt;/a&gt;: &lt;a class="wiki_link" href="/73edo"&gt;73edo&lt;/a&gt; 31&amp;amp;73 40.774&lt;br /&gt;
-&lt;a class="wiki_link" href="/Meantone%20family#Septimal meantone-Unidecimal meantone aka Huygens-Grosstone"&gt;Grosstone&lt;/a&gt;: &lt;a class="wiki_link" href="/74edo"&gt;74edo&lt;/a&gt; 12&amp;amp;31 25.899&lt;br /&gt;
+&lt;a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Grosstone"&gt;Grosstone&lt;/a&gt;: &lt;a class="wiki_link" href="/74edo"&gt;74edo&lt;/a&gt; 12&amp;amp;31 25.899&lt;br /&gt;
 &lt;a class="wiki_link" href="/Starling%20temperaments"&gt;Valentino&lt;/a&gt;: &lt;a class="wiki_link" href="/77edo"&gt;77edo&lt;/a&gt; 31&amp;amp;46 20.665&lt;br /&gt;
 &lt;a class="wiki_link" href="/Unicorn%20family#Alicorn"&gt;Camahueto&lt;/a&gt; &lt;a class="wiki_link" href="/77edo"&gt;77edo&lt;/a&gt; 19&amp;amp;77 36.155&lt;br /&gt;
@@ Line 1,607: / Line 1,605: @@
 &lt;a class="wiki_link" href="/Orwellismic%20temperaments#Quartonic-13-limit"&gt;Quartonic&lt;/a&gt;: &lt;a class="wiki_link" href="/80edo"&gt;80edo&lt;/a&gt; 53&amp;amp;80 23.875&lt;br /&gt;
 &lt;a class="wiki_link" href="/Meantone%20family"&gt;Meanpop&lt;/a&gt;: &lt;a class="wiki_link" href="/81edo"&gt;81edo&lt;/a&gt; 19&amp;amp;31 20.883&lt;br /&gt;
-&lt;a class="wiki_link" href="/Magic%20family#Divination"&gt;Divination&lt;/a&gt;: &lt;a class="wiki_link" href="/82edo"&gt;82edo&lt;/a&gt; 22&amp;amp;60 55.443&lt;br /&gt;
+&lt;a class="wiki_link" href="/Magic%20family#Soothsaying"&gt;Soothsaying&lt;/a&gt;: &lt;a class="wiki_link" href="/82edo"&gt;82edo&lt;/a&gt; 22&amp;amp;60 55.443&lt;br /&gt;
 &lt;a class="wiki_link" href="/Orwellismic%20temperaments#Secant-13-limit"&gt;Secant&lt;/a&gt;: &lt;a class="wiki_link" href="/84edo"&gt;84edo&lt;/a&gt; 26&amp;amp;58 46.373&lt;br /&gt;
 &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;Rodan&lt;/a&gt;: &lt;a class="wiki_link" href="/87edo"&gt;87edo&lt;/a&gt; 41&amp;amp;46 18.448&lt;br /&gt;
@@ Line 1,652: / Line 1,650: @@
 &lt;a class="wiki_link" href="/Hemimean%20clan#Subpental"&gt;Subpental&lt;/a&gt;: &lt;a class="wiki_link" href="/241edo"&gt;241edo&lt;/a&gt; 19&amp;amp;111 23.940&lt;br /&gt;
 &lt;a class="wiki_link" href="/Ragismic%20microtemperaments#Ennealimmal"&gt;Ennealimmic&lt;/a&gt;: &lt;a class="wiki_link" href="/243edo"&gt;243edo&lt;/a&gt; 72&amp;amp;171 20.250&lt;br /&gt;
-&lt;a class="wiki_link" href="/Mirkwai%20clan#Subsemifourth"&gt;Subsemifourth&lt;/a&gt;: &lt;a class="wiki_link" href="/255edo"&gt;255edo&lt;/a&gt; 103&amp;amp;255  28.387&lt;br /&gt;
+&lt;a class="wiki_link" href="/Mirkwai%20clan#Subsemifourth"&gt;Subsemifourth&lt;/a&gt;: &lt;a class="wiki_link" href="/255edo"&gt;255edo&lt;/a&gt; 103&amp;amp;255 28.387&lt;br /&gt;
 &lt;a class="wiki_link" href="/Ragismic%20microtemperaments"&gt;Hemiennealimmal&lt;/a&gt;: &lt;a class="wiki_link" href="/270edo"&gt;270edo&lt;/a&gt; 72&amp;amp;198 12.505&lt;br /&gt;
 &lt;a class="wiki_link" href="/Ragismic%20microtemperaments#Acrokleismic-13-limit"&gt;Acrokleismic&lt;/a&gt;: &lt;a class="wiki_link" href="/270edo"&gt;270edo&lt;/a&gt; 19&amp;amp;251 26.818&lt;br /&gt;
@@ Line 1,659: / Line 1,657: @@
 &lt;a class="wiki_link" href="/Schismatic%20family"&gt;Sextilififths&lt;/a&gt;: &lt;a class="wiki_link" href="/289edo"&gt;289edo&lt;/a&gt; 29&amp;amp;130 25.276&lt;br /&gt;
 &lt;a class="wiki_link" href="/Ragismic%20microtemperaments#Quincy"&gt;Quincy&lt;/a&gt;: &lt;a class="wiki_link" href="/289edo"&gt;289edo&lt;/a&gt; 72&amp;amp;145 23.862&lt;br /&gt;
-&lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiwürschmidt-11-limit-13-limit"&gt;Hemiwürschmidt&lt;/a&gt;: &lt;a class="wiki_link" href="/291edo"&gt;291edo&lt;/a&gt; 31&amp;amp;130 23.074&lt;br /&gt;
+&lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiw%C3%BCrschmidt-11-limit-13-limit"&gt;Hemiwürschmidt&lt;/a&gt;: &lt;a class="wiki_link" href="/291edo"&gt;291edo&lt;/a&gt; 31&amp;amp;130 23.074&lt;br /&gt;
 &lt;a class="wiki_link" href="/Porwell%20temperaments"&gt;Hemischis&lt;/a&gt;: &lt;a class="wiki_link" href="/313edo"&gt;313edo&lt;/a&gt; 53&amp;amp;130 20.816&lt;br /&gt;
 &lt;a class="wiki_link" href="/Werckismic%20temperaments#Octowerck"&gt;Octowerck&lt;/a&gt;: &lt;a class="wiki_link" href="/320edo"&gt;320edo&lt;/a&gt; 72&amp;amp;248 27.632&lt;br /&gt;