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>2012-01-~~03 21~~:13:32 UTC</tt>.

: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-01-04 00:25:14 UTC</tt>.

: The original revision id was <tt>~~289405529~~</tt>.

: The original revision id was <tt>289427619</tt>.

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<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.

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2048/2025: [[80edo]] 19.915

81/80: [[81edo]] 7.381

20000/19683: [[109edo]] dunno

393216/390625: [[164edo]] 40.603

2109375/2097152: [[296edo]] 40.807

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[[Meantone family#Godzilla-11-limit|Godzilla]]: [[19edo]] 14c&19 28.947

[[Meantone family#Undevigintone|Undevigintone]]: [[19edo]] 19&38d 36.387

[[Meantone family#Septimal ~~meantone~~-Meanundeci|Meanundeci]]: [[19edo|19e]] 12e&19e 31.539

[[Meantone family#Septimal%20meantone-Meanundeci|Meanundeci]]: [[19edo|19e]] 12e&19e 31.539

[[Diaschismic family#Pajara|Pajara]]: [[22edo]] 12&22 20.343

[[Diaschismic family#Pajara|Pajarous]]: [[22edo]] 10&22 28.349

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[[Meantone family#Liese-Liesel|Liesel]]: [[36edo]] 19&36 40.721

[[Meantone family#Liese-Elisa|Elisa]]: [[36edo|36e]] 19e&36e 41.592

[[Pythagorean family#Catler ~~temperament~~-Catcall|Catcall]]: [[36edo]] 12&24 34.478

[[Pythagorean family#Catler%20temperament-Catcall|Catcall]]: [[36edo]] 12&24 34.478

[[Archytas clan#Beatles|Beatles]]: [[37edo]] 27e&37 45.639

[[Augmented family|Triforce]]: [[39edo]] 6&9 20.248

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[[Kleismic family#Catalytic|Catalytic]]: [[72edo]] 53e&72 30.422

[[Marvel temperaments#Enneaportent|Enneaportent]]: [[72edo]] 9&54 30.426

[[Starling temperaments#Casablanca ~~temperament~~-Marrakesh|Marrakesh]]: [[73edo]] 31&73 40.539

[[Starling temperaments#Casablanca%20temperament-Marrakesh|Marrakesh]]: [[73edo]] 31&73 40.539

[[Starling temperaments|Valentine]]: [[77edo]] 15&31 16.687

[[Unicorn family#Alicorn|Camahueto]] [[77edo]] 19&77 65.940

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[[Schismatic family|Garibaldi]]: [[94edo]] 41&53 27.396

[[Ragismic microtemperaments|Hitchcock]]: [[99edo]] 7&39 35.187

[[Würschmidt family#~~Hemiwürschmidt~~|Hemiwur]]: [[99edo]] 6&31 29.270

[[Würschmidt family#Hemiw%FCrschmidt|Hemiwur]]: [[99edo]] 6&31 29.270

[[Starling temperaments|Nusecond]]: [[101edo]] 31&101 25.621

[[Magic family|Magic]]: [[104edo]] 19&22 25.621

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[[Marvel family|Spectacle]]: [[281edo]] 10&31&281 49.8669

[[Porwell family|Jupiter]]: [[282edo]] 9&22&108 56.2368

[[Sensamagic family#Sensamagic-Unidecimal ~~sensamagic~~|Sensamagic]]: [[283edo]] 5&17&19 72.231

[[Sensamagic family#Sensamagic-Unidecimal%20sensamagic|Sensamagic]]: [[283edo]] 5&17&19 72.231

[[Breed family|Agni]]: [[284edo]] 4&6&27 49.3790

[[Kleismic rank three family#Enlil|Enlil]]: [[284edo]] 4&15&38 79.8062

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[[Starling temperaments|Keemun]]: [[19edo]] 4&19 29.749

[[Meantone family|Meanenneadecal]]: [[19edo]] 12f&19 21.182

[[Meantone family#Septimal ~~meantone~~-Meanpop-Meanplop|Meanplop]] [[19edo]] 12f&19 27.666

[[Meantone family#Septimal%20meantone-Meanpop-Meanplop|Meanplop]] [[19edo]] 12f&19 27.666

[[Augmented family|August]]: [[21edo]] 9&21 18.448

[[Magic family#Magic-Telepathy-13-limit ~~telepathy~~|Telepathy]]: [[22edo]] 19e&22 25.522

[[Magic family#Magic-Telepathy-13-limit%20telepathy|Telepathy]]: [[22edo]] 19e&22 25.522

[[Magic family#Magic-13-limit-Sorcery|Sorcery]]: [[22edo]] 19&22 25.829

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

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

[[Marvel temperaments#Tritonic|Tritonic]]: [[31edo]] 29&31 22.993

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

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

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

[[Meantone family#Mohajira-13-limit|Mohajira]]: [[31edo]] 7&24 23.388

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[[Marvel temperaments|Lizard]]: [[72edo]] 22&50 21.781

[[Breedsmic temperaments#Neominor|Neominor]]: [[72edo]] 72&161f 26.942

[[Pythagorean family#Compton ~~temperament~~|Compton]]: [[72edo]] 72&228f 21.852

[[Pythagorean family#Compton%20temperament|Compton]]: [[72edo]] 72&228f 21.852

[[Pythagorean family#Compton ~~temperament~~|Comptone]]: [[72edo]] 12&72 25.144

[[Pythagorean family#Compton%20temperament|Comptone]]: [[72edo]] 12&72 25.144

[[Pythagorean family#Hours|Hours]]: [[72edo]] 24&72 26.931

[[Kleismic family#Bikleismic|Bikleismic]]: [[72edo]] 72&106 21.814

[[Marvel temperaments#Marvolo|Marvolo]]: [[72edo]] 29&43 21.470

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

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

[[Meantone family|Grosstone]]: [[74edo]] 12&31 25.899

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

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[[Diaschismic family|Echidna]]: [[80edo]] 22&58 23.679

[[Diaschismic family|Bidia]]: [[80edo]] 12&68 41.137

[[Ragismic microtemperaments#Parakleismic-Paradigmic-Paradigmic-13-limit|Paradigmic]]: [[80edo]] 19&80 35.781

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

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

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[[Breedsmic temperaments|Harry]]: [[130edo]] 58&72 13.046

[[Kleismic family|Countercata]]: [[140edo]] 34&53 20.156

[[Pythagorean family#Omicronbeta ~~temperament~~|Omicronbeta]]: [[144edo]] 72&144 29.956

[[Pythagorean family#Omicronbeta%20temperament|Omicronbeta]]: [[144edo]] 72&144 29.956

[[Sensipent family|Heinz]]: [[149edo]] 46&103 25.779

[[Hemifamity temperaments#Supers|Supers]]: [[152edo]] 58&94 21.644

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[[Breed family|Jovis]]: [[363edo]] 31&58&72 54.221

[[Lehmerismic temperaments#Hanuman|Hanuman]]: [[535edo]] 15&72&137 65.278

[[Swetismic temperaments#Hades|Hades]]: [[578edo]] 36&58&72

[[Breed family|Vili]]: [[643edo]] 37&93&103 73.821

[[Mirkwai family#Indra-Shibi|Shibi]]: [[703edo]] 41&72&111 72.094

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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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2048/2025: <a class="wiki_link" href="/80edo">80edo</a> 19.915

81/80: <a class="wiki_link" href="/81edo">81edo</a> 7.381

20000/19683: <a class="wiki_link" href="/109edo">109edo</a> dunno

393216/390625: <a class="wiki_link" href="/164edo">164edo</a> 40.603

2109375/2097152: <a class="wiki_link" href="/296edo">296edo</a> 40.807

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<a class="wiki_link" href="/Meantone%20family#Godzilla-11-limit">Godzilla</a>: <a class="wiki_link" href="/19edo">19edo</a> 14c&amp;19 28.947

<a class="wiki_link" href="/Meantone%20family#Undevigintone">Undevigintone</a>: <a class="wiki_link" href="/19edo">19edo</a> 19&amp;38d 36.387

<a class="wiki_link" href="/Meantone%20family#Septimal ~~meantone~~-Meanundeci">Meanundeci</a>: <a class="wiki_link" href="/19edo">19e</a> 12e&amp;19e 31.539

<a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Meanundeci">Meanundeci</a>: <a class="wiki_link" href="/19edo">19e</a> 12e&amp;19e 31.539

<a class="wiki_link" href="/Diaschismic%20family#Pajara">Pajara</a>: <a class="wiki_link" href="/22edo">22edo</a> 12&amp;22 20.343

<a class="wiki_link" href="/Diaschismic%20family#Pajara">Pajarous</a>: <a class="wiki_link" href="/22edo">22edo</a> 10&amp;22 28.349

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<a class="wiki_link" href="/Meantone%20family#Liese-Liesel">Liesel</a>: <a class="wiki_link" href="/36edo">36edo</a> 19&amp;36 40.721

<a class="wiki_link" href="/Meantone%20family#Liese-Elisa">Elisa</a>: <a class="wiki_link" href="/36edo">36e</a> 19e&amp;36e 41.592

<a class="wiki_link" href="/Pythagorean%20family#Catler ~~temperament~~-Catcall">Catcall</a>: <a class="wiki_link" href="/36edo">36edo</a> 12&amp;24 34.478

<a class="wiki_link" href="/Pythagorean%20family#Catler%20temperament-Catcall">Catcall</a>: <a class="wiki_link" href="/36edo">36edo</a> 12&amp;24 34.478

<a class="wiki_link" href="/Archytas%20clan#Beatles">Beatles</a>: <a class="wiki_link" href="/37edo">37edo</a> 27e&amp;37 45.639

<a class="wiki_link" href="/Augmented%20family">Triforce</a>: <a class="wiki_link" href="/39edo">39edo</a> 6&amp;9 20.248

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<a class="wiki_link" href="/Kleismic%20family#Catalytic">Catalytic</a>: <a class="wiki_link" href="/72edo">72edo</a> 53e&amp;72 30.422

<a class="wiki_link" href="/Marvel%20temperaments#Enneaportent">Enneaportent</a>: <a class="wiki_link" href="/72edo">72edo</a> 9&amp;54 30.426

<a class="wiki_link" href="/Starling%20temperaments#Casablanca ~~temperament~~-Marrakesh">Marrakesh</a>: <a class="wiki_link" href="/73edo">73edo</a> 31&amp;73 40.539

<a class="wiki_link" href="/Starling%20temperaments#Casablanca%20temperament-Marrakesh">Marrakesh</a>: <a class="wiki_link" href="/73edo">73edo</a> 31&amp;73 40.539

<a class="wiki_link" href="/Starling%20temperaments">Valentine</a>: <a class="wiki_link" href="/77edo">77edo</a> 15&amp;31 16.687

<a class="wiki_link" href="/Unicorn%20family#Alicorn">Camahueto</a> <a class="wiki_link" href="/77edo">77edo</a> 19&amp;77 65.940

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<a class="wiki_link" href="/Schismatic%20family">Garibaldi</a>: <a class="wiki_link" href="/94edo">94edo</a> 41&amp;53 27.396

<a class="wiki_link" href="/Ragismic%20microtemperaments">Hitchcock</a>: <a class="wiki_link" href="/99edo">99edo</a> 7&amp;39 35.187

<a class="wiki_link" href="/W%C3%BCrschmidt%20family#~~Hemiwürschmidt~~">Hemiwur</a>: <a class="wiki_link" href="/99edo">99edo</a> 6&amp;31 29.270

<a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiw%FCrschmidt">Hemiwur</a>: <a class="wiki_link" href="/99edo">99edo</a> 6&amp;31 29.270

<a class="wiki_link" href="/Starling%20temperaments">Nusecond</a>: <a class="wiki_link" href="/101edo">101edo</a> 31&amp;101 25.621

<a class="wiki_link" href="/Magic%20family">Magic</a>: <a class="wiki_link" href="/104edo">104edo</a> 19&amp;22 25.621

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<a class="wiki_link" href="/Marvel%20family">Spectacle</a>: <a class="wiki_link" href="/281edo">281edo</a> 10&amp;31&amp;281 49.8669

<a class="wiki_link" href="/Porwell%20family">Jupiter</a>: <a class="wiki_link" href="/282edo">282edo</a> 9&amp;22&amp;108 56.2368

<a class="wiki_link" href="/Sensamagic%20family#Sensamagic-Unidecimal ~~sensamagic~~">Sensamagic</a>: <a class="wiki_link" href="/283edo">283edo</a> 5&amp;17&amp;19 72.231

<a class="wiki_link" href="/Sensamagic%20family#Sensamagic-Unidecimal%20sensamagic">Sensamagic</a>: <a class="wiki_link" href="/283edo">283edo</a> 5&amp;17&amp;19 72.231

<a class="wiki_link" href="/Breed%20family">Agni</a>: <a class="wiki_link" href="/284edo">284edo</a> 4&amp;6&amp;27 49.3790

<a class="wiki_link" href="/Kleismic%20rank%20three%20family#Enlil">Enlil</a>: <a class="wiki_link" href="/284edo">284edo</a> 4&amp;15&amp;38 79.8062

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<a class="wiki_link" href="/Starling%20temperaments">Keemun</a>: <a class="wiki_link" href="/19edo">19edo</a> 4&amp;19 29.749

<a class="wiki_link" href="/Meantone%20family">Meanenneadecal</a>: <a class="wiki_link" href="/19edo">19edo</a> 12f&amp;19 21.182

<a class="wiki_link" href="/Meantone%20family#Septimal ~~meantone~~-Meanpop-Meanplop">Meanplop</a> <a class="wiki_link" href="/19edo">19edo</a> 12f&amp;19 27.666

<a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Meanpop-Meanplop">Meanplop</a> <a class="wiki_link" href="/19edo">19edo</a> 12f&amp;19 27.666

<a class="wiki_link" href="/Augmented%20family">August</a>: <a class="wiki_link" href="/21edo">21edo</a> 9&amp;21 18.448

<a class="wiki_link" href="/Magic%20family#Magic-Telepathy-13-limit ~~telepathy~~">Telepathy</a>: <a class="wiki_link" href="/22edo">22edo</a> 19e&amp;22 25.522

<a class="wiki_link" href="/Magic%20family#Magic-Telepathy-13-limit%20telepathy">Telepathy</a>: <a class="wiki_link" href="/22edo">22edo</a> 19e&amp;22 25.522

<a class="wiki_link" href="/Magic%20family#Magic-13-limit-Sorcery">Sorcery</a>: <a class="wiki_link" href="/22edo">22edo</a> 19&amp;22 25.829

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

Line 1,016:

<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="/Marvel%20temperaments#Tritonic">Tritonic</a>: <a class="wiki_link" href="/31edo">31edo</a> 29&amp;31 22.993

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

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

<a class="wiki_link" href="/Meantone%20family#Mohajira-13-limit">Mohajira</a>: <a class="wiki_link" href="/31edo">31edo</a> 7&amp;24 23.388

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<a class="wiki_link" href="/Marvel%20temperaments">Lizard</a>: <a class="wiki_link" href="/72edo">72edo</a> 22&amp;50 21.781

<a class="wiki_link" href="/Breedsmic%20temperaments#Neominor">Neominor</a>: <a class="wiki_link" href="/72edo">72edo</a> 72&amp;161f 26.942

<a class="wiki_link" href="/Pythagorean%20family#Compton ~~temperament~~">Compton</a>: <a class="wiki_link" href="/72edo">72edo</a> 72&amp;228f 21.852

<a class="wiki_link" href="/Pythagorean%20family#Compton%20temperament">Compton</a>: <a class="wiki_link" href="/72edo">72edo</a> 72&amp;228f 21.852

<a class="wiki_link" href="/Pythagorean%20family#Compton ~~temperament~~">Comptone</a>: <a class="wiki_link" href="/72edo">72edo</a> 12&amp;72 25.144

<a class="wiki_link" href="/Pythagorean%20family#Compton%20temperament">Comptone</a>: <a class="wiki_link" href="/72edo">72edo</a> 12&amp;72 25.144

<a class="wiki_link" href="/Pythagorean%20family#Hours">Hours</a>: <a class="wiki_link" href="/72edo">72edo</a> 24&amp;72 26.931

<a class="wiki_link" href="/Kleismic%20family#Bikleismic">Bikleismic</a>: <a class="wiki_link" href="/72edo">72edo</a> 72&amp;106 21.814

<a class="wiki_link" href="/Marvel%20temperaments#Marvolo">Marvolo</a>: <a class="wiki_link" href="/72edo">72edo</a> 29&amp;43 21.470

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

<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">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

Line 1,061:

<a class="wiki_link" href="/Diaschismic%20family">Echidna</a>: <a class="wiki_link" href="/80edo">80edo</a> 22&amp;58 23.679

<a class="wiki_link" href="/Diaschismic%20family">Bidia</a>: <a class="wiki_link" href="/80edo">80edo</a> 12&amp;68 41.137

<a class="wiki_link" href="/Ragismic%20microtemperaments#Parakleismic-Paradigmic-Paradigmic-13-limit">Paradigmic</a>: <a class="wiki_link" href="/80edo">80edo</a> 19&amp;80 35.781

<a class="wiki_link" href="/Ragismic%20microtemperaments#Parakleismic-Paradigmic-Paradigmic-13-limit">Paradigmic</a>: <a class="wiki_link" href="/80edo">80edo</a> 19&amp;80 35.781

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

Line 1,078:

<a class="wiki_link" href="/Breedsmic%20temperaments">Harry</a>: <a class="wiki_link" href="/130edo">130edo</a> 58&amp;72 13.046

<a class="wiki_link" href="/Kleismic%20family">Countercata</a>: <a class="wiki_link" href="/140edo">140edo</a> 34&amp;53 20.156

<a class="wiki_link" href="/Pythagorean%20family#Omicronbeta ~~temperament~~">Omicronbeta</a>: <a class="wiki_link" href="/144edo">144edo</a> 72&amp;144 29.956

<a class="wiki_link" href="/Pythagorean%20family#Omicronbeta%20temperament">Omicronbeta</a>: <a class="wiki_link" href="/144edo">144edo</a> 72&amp;144 29.956

<a class="wiki_link" href="/Sensipent%20family">Heinz</a>: <a class="wiki_link" href="/149edo">149edo</a> 46&amp;103 25.779

<a class="wiki_link" href="/Hemifamity%20temperaments#Supers">Supers</a>: <a class="wiki_link" href="/152edo">152edo</a> 58&amp;94 21.644

Line 1,161:

<a class="wiki_link" href="/Breed%20family">Jovis</a>: <a class="wiki_link" href="/363edo">363edo</a> 31&amp;58&amp;72 54.221

<a class="wiki_link" href="/Lehmerismic%20temperaments#Hanuman">Hanuman</a>: <a class="wiki_link" href="/535edo">535edo</a> 15&amp;72&amp;137 65.278

<a class="wiki_link" href="/Swetismic%20temperaments#Hades">Hades</a>: <a class="wiki_link" href="/578edo">578edo</a> 36&amp;58&amp;72

<a class="wiki_link" href="/Swetismic%20temperaments#Hades">Hades</a>: <a class="wiki_link" href="/578edo">578edo</a> 36&amp;58&amp;72

<a class="wiki_link" href="/Breed%20family">Vili</a>: <a class="wiki_link" href="/643edo">643edo</a> 37&amp;93&amp;103 73.821

<a class="wiki_link" href="/Mirkwai%20family#Indra-Shibi">Shibi</a>: <a class="wiki_link" href="/703edo">703edo</a> 41&amp;72&amp;111 72.094

@@ 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>2012-01-03 21:13:32 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-01-04 00:25:14 UTC</tt>.<br>
-: The original revision id was <tt>289405529</tt>.<br>
+: The original revision id was <tt>289427619</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 28: / Line 27: @@
 /2025: [[80edo]] 19.915
 /80: [[81edo]] 7.381
+/19683: [[109edo]] dunno
 /390625: [[164edo]] 40.603
 2109375/2097152: [[296edo]] 40.807
@@ Line 203: / Line 203: @@
 [[Meantone family#Godzilla-11-limit|Godzilla]]: [[19edo]] 14c&amp;19 28.947
 [[Meantone family#Undevigintone|Undevigintone]]: [[19edo]] 19&amp;38d 36.387
-[[Meantone family#Septimal meantone-Meanundeci|Meanundeci]]: [[19edo|19e]] 12e&amp;19e 31.539
+[[Meantone family#Septimal%20meantone-Meanundeci|Meanundeci]]: [[19edo|19e]] 12e&amp;19e 31.539
 [[Diaschismic family#Pajara|Pajara]]: [[22edo]] 12&amp;22 20.343
 [[Diaschismic family#Pajara|Pajarous]]: [[22edo]] 10&amp;22 28.349
@@ Line 225: / Line 225: @@
 [[Meantone family#Liese-Liesel|Liesel]]: [[36edo]] 19&amp;36 40.721
 [[Meantone family#Liese-Elisa|Elisa]]: [[36edo|36e]] 19e&amp;36e 41.592
-[[Pythagorean family#Catler temperament-Catcall|Catcall]]: [[36edo]] 12&amp;24 34.478
+[[Pythagorean family#Catler%20temperament-Catcall|Catcall]]: [[36edo]] 12&amp;24 34.478
 [[Archytas clan#Beatles|Beatles]]: [[37edo]] 27e&amp;37 45.639
 [[Augmented family|Triforce]]: [[39edo]] 6&amp;9 20.248
@@ Line 266: / Line 266: @@
 [[Kleismic family#Catalytic|Catalytic]]: [[72edo]] 53e&amp;72 30.422
 [[Marvel temperaments#Enneaportent|Enneaportent]]: [[72edo]] 9&amp;54 30.426
-[[Starling temperaments#Casablanca temperament-Marrakesh|Marrakesh]]: [[73edo]] 31&amp;73 40.539
+[[Starling temperaments#Casablanca%20temperament-Marrakesh|Marrakesh]]: [[73edo]] 31&amp;73 40.539
 [[Starling temperaments|Valentine]]: [[77edo]] 15&amp;31 16.687
 [[Unicorn family#Alicorn|Camahueto]] [[77edo]] 19&amp;77 65.940
@@ Line 283: / Line 283: @@
 [[Schismatic family|Garibaldi]]: [[94edo]] 41&amp;53 27.396
 [[Ragismic microtemperaments|Hitchcock]]: [[99edo]] 7&amp;39 35.187
-[[Würschmidt family#Hemiwürschmidt|Hemiwur]]: [[99edo]] 6&amp;31 29.270
+[[Würschmidt family#Hemiw%FCrschmidt|Hemiwur]]: [[99edo]] 6&amp;31 29.270
 [[Starling temperaments|Nusecond]]: [[101edo]] 31&amp;101 25.621
 [[Magic family|Magic]]: [[104edo]] 19&amp;22 25.621
@@ Line 386: / Line 386: @@
 [[Marvel family|Spectacle]]: [[281edo]] 10&amp;31&amp;281 49.8669
 [[Porwell family|Jupiter]]: [[282edo]] 9&amp;22&amp;108 56.2368
-[[Sensamagic family#Sensamagic-Unidecimal sensamagic|Sensamagic]]: [[283edo]] 5&amp;17&amp;19 72.231
+[[Sensamagic family#Sensamagic-Unidecimal%20sensamagic|Sensamagic]]: [[283edo]] 5&amp;17&amp;19 72.231
 [[Breed family|Agni]]: [[284edo]] 4&amp;6&amp;27 49.3790
 [[Kleismic rank three family#Enlil|Enlil]]: [[284edo]] 4&amp;15&amp;38 79.8062
@@ Line 417: / Line 417: @@
 [[Starling temperaments|Keemun]]: [[19edo]] 4&amp;19 29.749
 [[Meantone family|Meanenneadecal]]: [[19edo]] 12f&amp;19 21.182
-[[Meantone family#Septimal meantone-Meanpop-Meanplop|Meanplop]] [[19edo]] 12f&amp;19 27.666
+[[Meantone family#Septimal%20meantone-Meanpop-Meanplop|Meanplop]] [[19edo]] 12f&amp;19 27.666
 [[Augmented family|August]]: [[21edo]] 9&amp;21 18.448
-[[Magic family#Magic-Telepathy-13-limit telepathy|Telepathy]]: [[22edo]] 19e&amp;22 25.522
+[[Magic family#Magic-Telepathy-13-limit%20telepathy|Telepathy]]: [[22edo]] 19e&amp;22 25.522
 [[Magic family#Magic-13-limit-Sorcery|Sorcery]]: [[22edo]] 19&amp;22 25.829
 [[Augmented family|Triforce]]: [[24edo]] 9&amp;15 20.248
@@ Line 432: / Line 432: @@
 [[Starling temperaments|Lupercalia]]: [[31edo]] 15&amp;31 21.328
 [[Marvel temperaments#Tritonic|Tritonic]]: [[31edo]] 29&amp;31 22.993
-[[Starling temperaments#Casablanca temperament-Marrakesh-Murakuc|Murakuc]]: [[31edo]] 31&amp;73f 41.394
+[[Starling temperaments#Casablanca%20temperament-Marrakesh-Murakuc|Murakuc]]: [[31edo]] 31&amp;73f 41.394
 [[31 comma temperaments#Prajapati|Prajapati]]: [[31edo]] 31&amp;93f 37.885
 [[Meantone family#Mohajira-13-limit|Mohajira]]: [[31edo]] 7&amp;24 23.388
@@ Line 466: / Line 466: @@
 [[Marvel temperaments|Lizard]]: [[72edo]] 22&amp;50 21.781
 [[Breedsmic temperaments#Neominor|Neominor]]: [[72edo]] 72&amp;161f 26.942
-[[Pythagorean family#Compton temperament|Compton]]: [[72edo]] 72&amp;228f 21.852
+[[Pythagorean family#Compton%20temperament|Compton]]: [[72edo]] 72&amp;228f 21.852
-[[Pythagorean family#Compton temperament|Comptone]]: [[72edo]] 12&amp;72 25.144
+[[Pythagorean family#Compton%20temperament|Comptone]]: [[72edo]] 12&amp;72 25.144
 [[Pythagorean family#Hours|Hours]]: [[72edo]] 24&amp;72 26.931
 [[Kleismic family#Bikleismic|Bikleismic]]: [[72edo]] 72&amp;106 21.814
 [[Marvel temperaments#Marvolo|Marvolo]]: [[72edo]] 29&amp;43 21.470
-[[Starling temperaments#Casablanca temperament-Marrakesh-13-limit|Marrakesh]]: [[73edo]] 31&amp;73 40.774
+[[Starling temperaments#Casablanca%20temperament-Marrakesh-13-limit|Marrakesh]]: [[73edo]] 31&amp;73 40.774
 [[Meantone family|Grosstone]]: [[74edo]] 12&amp;31 25.899
 [[Starling temperaments|Valentino]]: [[77edo]] 31&amp;46 20.665
@@ Line 477: / Line 477: @@
 [[Diaschismic family|Echidna]]: [[80edo]] 22&amp;58 23.679
 [[Diaschismic family|Bidia]]: [[80edo]] 12&amp;68 41.137
 [[Ragismic microtemperaments#Parakleismic-Paradigmic-Paradigmic-13-limit|Paradigmic]]: [[80edo]] 19&amp;80 35.781
 [[Meantone family|Meanpop]]: [[81edo]] 19&amp;31 20.883
 [[Gamelismic clan|Rodan]]: [[87edo]] 41&amp;46 18.448
@@ Line 494: / Line 494: @@
 [[Breedsmic temperaments|Harry]]: [[130edo]] 58&amp;72 13.046
 [[Kleismic family|Countercata]]: [[140edo]] 34&amp;53 20.156
-[[Pythagorean family#Omicronbeta temperament|Omicronbeta]]: [[144edo]] 72&amp;144 29.956
+[[Pythagorean family#Omicronbeta%20temperament|Omicronbeta]]: [[144edo]] 72&amp;144 29.956
 [[Sensipent family|Heinz]]: [[149edo]] 46&amp;103 25.779
 [[Hemifamity temperaments#Supers|Supers]]: [[152edo]] 58&amp;94 21.644
@@ Line 577: / Line 577: @@
 [[Breed family|Jovis]]: [[363edo]] 31&amp;58&amp;72 54.221
 [[Lehmerismic temperaments#Hanuman|Hanuman]]: [[535edo]] 15&amp;72&amp;137 65.278
 [[Swetismic temperaments#Hades|Hades]]: [[578edo]] 36&amp;58&amp;72
 [[Breed family|Vili]]: [[643edo]] 37&amp;93&amp;103 73.821
 [[Mirkwai family#Indra-Shibi|Shibi]]: [[703edo]] 41&amp;72&amp;111 72.094
@@ Line 591: / Line 591: @@
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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;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 612: / Line 611: @@
 /2025: &lt;a class="wiki_link" href="/80edo"&gt;80edo&lt;/a&gt; 19.915&lt;br /&gt;
 /80: &lt;a class="wiki_link" href="/81edo"&gt;81edo&lt;/a&gt; 7.381&lt;br /&gt;
+/19683: &lt;a class="wiki_link" href="/109edo"&gt;109edo&lt;/a&gt; dunno&lt;br /&gt;
 /390625: &lt;a class="wiki_link" href="/164edo"&gt;164edo&lt;/a&gt; 40.603&lt;br /&gt;
 2109375/2097152: &lt;a class="wiki_link" href="/296edo"&gt;296edo&lt;/a&gt; 40.807&lt;br /&gt;
@@ Line 787: / Line 787: @@
 &lt;a class="wiki_link" href="/Meantone%20family#Godzilla-11-limit"&gt;Godzilla&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 14c&amp;amp;19 28.947&lt;br /&gt;
 &lt;a class="wiki_link" href="/Meantone%20family#Undevigintone"&gt;Undevigintone&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 19&amp;amp;38d 36.387&lt;br /&gt;
-&lt;a class="wiki_link" href="/Meantone%20family#Septimal meantone-Meanundeci"&gt;Meanundeci&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19e&lt;/a&gt; 12e&amp;amp;19e 31.539&lt;br /&gt;
+&lt;a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Meanundeci"&gt;Meanundeci&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19e&lt;/a&gt; 12e&amp;amp;19e 31.539&lt;br /&gt;
 &lt;a class="wiki_link" href="/Diaschismic%20family#Pajara"&gt;Pajara&lt;/a&gt;: &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; 12&amp;amp;22 20.343&lt;br /&gt;
 &lt;a class="wiki_link" href="/Diaschismic%20family#Pajara"&gt;Pajarous&lt;/a&gt;: &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; 10&amp;amp;22 28.349&lt;br /&gt;
@@ Line 809: / Line 809: @@
 &lt;a class="wiki_link" href="/Meantone%20family#Liese-Liesel"&gt;Liesel&lt;/a&gt;: &lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt; 19&amp;amp;36 40.721&lt;br /&gt;
 &lt;a class="wiki_link" href="/Meantone%20family#Liese-Elisa"&gt;Elisa&lt;/a&gt;: &lt;a class="wiki_link" href="/36edo"&gt;36e&lt;/a&gt; 19e&amp;amp;36e 41.592&lt;br /&gt;
-&lt;a class="wiki_link" href="/Pythagorean%20family#Catler temperament-Catcall"&gt;Catcall&lt;/a&gt;: &lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt; 12&amp;amp;24 34.478&lt;br /&gt;
+&lt;a class="wiki_link" href="/Pythagorean%20family#Catler%20temperament-Catcall"&gt;Catcall&lt;/a&gt;: &lt;a class="wiki_link" href="/36edo"&gt;36edo&lt;/a&gt; 12&amp;amp;24 34.478&lt;br /&gt;
 &lt;a class="wiki_link" href="/Archytas%20clan#Beatles"&gt;Beatles&lt;/a&gt;: &lt;a class="wiki_link" href="/37edo"&gt;37edo&lt;/a&gt; 27e&amp;amp;37 45.639&lt;br /&gt;
 &lt;a class="wiki_link" href="/Augmented%20family"&gt;Triforce&lt;/a&gt;: &lt;a class="wiki_link" href="/39edo"&gt;39edo&lt;/a&gt; 6&amp;amp;9 20.248&lt;br /&gt;
@@ Line 850: / Line 850: @@
 &lt;a class="wiki_link" href="/Kleismic%20family#Catalytic"&gt;Catalytic&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 53e&amp;amp;72 30.422&lt;br /&gt;
 &lt;a class="wiki_link" href="/Marvel%20temperaments#Enneaportent"&gt;Enneaportent&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 9&amp;amp;54 30.426&lt;br /&gt;
-&lt;a class="wiki_link" href="/Starling%20temperaments#Casablanca temperament-Marrakesh"&gt;Marrakesh&lt;/a&gt;: &lt;a class="wiki_link" href="/73edo"&gt;73edo&lt;/a&gt; 31&amp;amp;73 40.539&lt;br /&gt;
+&lt;a class="wiki_link" href="/Starling%20temperaments#Casablanca%20temperament-Marrakesh"&gt;Marrakesh&lt;/a&gt;: &lt;a class="wiki_link" href="/73edo"&gt;73edo&lt;/a&gt; 31&amp;amp;73 40.539&lt;br /&gt;
 &lt;a class="wiki_link" href="/Starling%20temperaments"&gt;Valentine&lt;/a&gt;: &lt;a class="wiki_link" href="/77edo"&gt;77edo&lt;/a&gt; 15&amp;amp;31 16.687&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 65.940&lt;br /&gt;
@@ Line 867: / Line 867: @@
 &lt;a class="wiki_link" href="/Schismatic%20family"&gt;Garibaldi&lt;/a&gt;: &lt;a class="wiki_link" href="/94edo"&gt;94edo&lt;/a&gt; 41&amp;amp;53 27.396&lt;br /&gt;
 &lt;a class="wiki_link" href="/Ragismic%20microtemperaments"&gt;Hitchcock&lt;/a&gt;: &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; 7&amp;amp;39 35.187&lt;br /&gt;
-&lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiwürschmidt"&gt;Hemiwur&lt;/a&gt;: &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; 6&amp;amp;31 29.270&lt;br /&gt;
+&lt;a class="wiki_link" href="/W%C3%BCrschmidt%20family#Hemiw%FCrschmidt"&gt;Hemiwur&lt;/a&gt;: &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; 6&amp;amp;31 29.270&lt;br /&gt;
 &lt;a class="wiki_link" href="/Starling%20temperaments"&gt;Nusecond&lt;/a&gt;: &lt;a class="wiki_link" href="/101edo"&gt;101edo&lt;/a&gt; 31&amp;amp;101 25.621&lt;br /&gt;
 &lt;a class="wiki_link" href="/Magic%20family"&gt;Magic&lt;/a&gt;: &lt;a class="wiki_link" href="/104edo"&gt;104edo&lt;/a&gt; 19&amp;amp;22 25.621&lt;br /&gt;
@@ Line 970: / Line 970: @@
 &lt;a class="wiki_link" href="/Marvel%20family"&gt;Spectacle&lt;/a&gt;: &lt;a class="wiki_link" href="/281edo"&gt;281edo&lt;/a&gt; 10&amp;amp;31&amp;amp;281 49.8669&lt;br /&gt;
 &lt;a class="wiki_link" href="/Porwell%20family"&gt;Jupiter&lt;/a&gt;: &lt;a class="wiki_link" href="/282edo"&gt;282edo&lt;/a&gt; 9&amp;amp;22&amp;amp;108 56.2368&lt;br /&gt;
-&lt;a class="wiki_link" href="/Sensamagic%20family#Sensamagic-Unidecimal sensamagic"&gt;Sensamagic&lt;/a&gt;: &lt;a class="wiki_link" href="/283edo"&gt;283edo&lt;/a&gt; 5&amp;amp;17&amp;amp;19 72.231&lt;br /&gt;
+&lt;a class="wiki_link" href="/Sensamagic%20family#Sensamagic-Unidecimal%20sensamagic"&gt;Sensamagic&lt;/a&gt;: &lt;a class="wiki_link" href="/283edo"&gt;283edo&lt;/a&gt; 5&amp;amp;17&amp;amp;19 72.231&lt;br /&gt;
 &lt;a class="wiki_link" href="/Breed%20family"&gt;Agni&lt;/a&gt;: &lt;a class="wiki_link" href="/284edo"&gt;284edo&lt;/a&gt; 4&amp;amp;6&amp;amp;27 49.3790&lt;br /&gt;
 &lt;a class="wiki_link" href="/Kleismic%20rank%20three%20family#Enlil"&gt;Enlil&lt;/a&gt;: &lt;a class="wiki_link" href="/284edo"&gt;284edo&lt;/a&gt; 4&amp;amp;15&amp;amp;38 79.8062&lt;br /&gt;
@@ Line 1,001: / Line 1,001: @@
 &lt;a class="wiki_link" href="/Starling%20temperaments"&gt;Keemun&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 4&amp;amp;19 29.749&lt;br /&gt;
 &lt;a class="wiki_link" href="/Meantone%20family"&gt;Meanenneadecal&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 12f&amp;amp;19 21.182&lt;br /&gt;
-&lt;a class="wiki_link" href="/Meantone%20family#Septimal meantone-Meanpop-Meanplop"&gt;Meanplop&lt;/a&gt; &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 12f&amp;amp;19 27.666&lt;br /&gt;
+&lt;a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Meanpop-Meanplop"&gt;Meanplop&lt;/a&gt; &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; 12f&amp;amp;19 27.666&lt;br /&gt;
 &lt;a class="wiki_link" href="/Augmented%20family"&gt;August&lt;/a&gt;: &lt;a class="wiki_link" href="/21edo"&gt;21edo&lt;/a&gt; 9&amp;amp;21 18.448&lt;br /&gt;
-&lt;a class="wiki_link" href="/Magic%20family#Magic-Telepathy-13-limit telepathy"&gt;Telepathy&lt;/a&gt;: &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; 19e&amp;amp;22 25.522&lt;br /&gt;
+&lt;a class="wiki_link" href="/Magic%20family#Magic-Telepathy-13-limit%20telepathy"&gt;Telepathy&lt;/a&gt;: &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; 19e&amp;amp;22 25.522&lt;br /&gt;
 &lt;a class="wiki_link" href="/Magic%20family#Magic-13-limit-Sorcery"&gt;Sorcery&lt;/a&gt;: &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; 19&amp;amp;22 25.829&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;
@@ Line 1,016: / Line 1,016: @@
 &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="/Marvel%20temperaments#Tritonic"&gt;Tritonic&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 29&amp;amp;31 22.993&lt;br /&gt;
-&lt;a class="wiki_link" href="/Starling%20temperaments#Casablanca temperament-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#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="/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="/Meantone%20family#Mohajira-13-limit"&gt;Mohajira&lt;/a&gt;: &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; 7&amp;amp;24 23.388&lt;br /&gt;
@@ Line 1,050: / Line 1,050: @@
 &lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;Lizard&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 22&amp;amp;50 21.781&lt;br /&gt;
 &lt;a class="wiki_link" href="/Breedsmic%20temperaments#Neominor"&gt;Neominor&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 72&amp;amp;161f 26.942&lt;br /&gt;
-&lt;a class="wiki_link" href="/Pythagorean%20family#Compton temperament"&gt;Compton&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 72&amp;amp;228f 21.852&lt;br /&gt;
+&lt;a class="wiki_link" href="/Pythagorean%20family#Compton%20temperament"&gt;Compton&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 72&amp;amp;228f 21.852&lt;br /&gt;
-&lt;a class="wiki_link" href="/Pythagorean%20family#Compton temperament"&gt;Comptone&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 12&amp;amp;72 25.144&lt;br /&gt;
+&lt;a class="wiki_link" href="/Pythagorean%20family#Compton%20temperament"&gt;Comptone&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 12&amp;amp;72 25.144&lt;br /&gt;
 &lt;a class="wiki_link" href="/Pythagorean%20family#Hours"&gt;Hours&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 24&amp;amp;72 26.931&lt;br /&gt;
 &lt;a class="wiki_link" href="/Kleismic%20family#Bikleismic"&gt;Bikleismic&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 72&amp;amp;106 21.814&lt;br /&gt;
 &lt;a class="wiki_link" href="/Marvel%20temperaments#Marvolo"&gt;Marvolo&lt;/a&gt;: &lt;a class="wiki_link" href="/72edo"&gt;72edo&lt;/a&gt; 29&amp;amp;43 21.470&lt;br /&gt;
-&lt;a class="wiki_link" href="/Starling%20temperaments#Casablanca temperament-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="/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"&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;
@@ Line 1,061: / Line 1,061: @@
 &lt;a class="wiki_link" href="/Diaschismic%20family"&gt;Echidna&lt;/a&gt;: &lt;a class="wiki_link" href="/80edo"&gt;80edo&lt;/a&gt; 22&amp;amp;58 23.679&lt;br /&gt;
 &lt;a class="wiki_link" href="/Diaschismic%20family"&gt;Bidia&lt;/a&gt;: &lt;a class="wiki_link" href="/80edo"&gt;80edo&lt;/a&gt; 12&amp;amp;68 41.137&lt;br /&gt;
-&lt;a class="wiki_link" href="/Ragismic%20microtemperaments#Parakleismic-Paradigmic-Paradigmic-13-limit"&gt;Paradigmic&lt;/a&gt;: &lt;a class="wiki_link" href="/80edo"&gt;80edo&lt;/a&gt; 19&amp;amp;80 35.781 &lt;br /&gt;
+&lt;a class="wiki_link" href="/Ragismic%20microtemperaments#Parakleismic-Paradigmic-Paradigmic-13-limit"&gt;Paradigmic&lt;/a&gt;: &lt;a class="wiki_link" href="/80edo"&gt;80edo&lt;/a&gt; 19&amp;amp;80 35.781&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="/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 1,078: / Line 1,078: @@
 &lt;a class="wiki_link" href="/Breedsmic%20temperaments"&gt;Harry&lt;/a&gt;: &lt;a class="wiki_link" href="/130edo"&gt;130edo&lt;/a&gt; 58&amp;amp;72 13.046&lt;br /&gt;
 &lt;a class="wiki_link" href="/Kleismic%20family"&gt;Countercata&lt;/a&gt;: &lt;a class="wiki_link" href="/140edo"&gt;140edo&lt;/a&gt; 34&amp;amp;53 20.156&lt;br /&gt;
-&lt;a class="wiki_link" href="/Pythagorean%20family#Omicronbeta temperament"&gt;Omicronbeta&lt;/a&gt;: &lt;a class="wiki_link" href="/144edo"&gt;144edo&lt;/a&gt; 72&amp;amp;144 29.956&lt;br /&gt;
+&lt;a class="wiki_link" href="/Pythagorean%20family#Omicronbeta%20temperament"&gt;Omicronbeta&lt;/a&gt;: &lt;a class="wiki_link" href="/144edo"&gt;144edo&lt;/a&gt; 72&amp;amp;144 29.956&lt;br /&gt;
 &lt;a class="wiki_link" href="/Sensipent%20family"&gt;Heinz&lt;/a&gt;: &lt;a class="wiki_link" href="/149edo"&gt;149edo&lt;/a&gt; 46&amp;amp;103 25.779&lt;br /&gt;
 &lt;a class="wiki_link" href="/Hemifamity%20temperaments#Supers"&gt;Supers&lt;/a&gt;: &lt;a class="wiki_link" href="/152edo"&gt;152edo&lt;/a&gt; 58&amp;amp;94 21.644&lt;br /&gt;
@@ Line 1,161: / Line 1,161: @@
 &lt;a class="wiki_link" href="/Breed%20family"&gt;Jovis&lt;/a&gt;: &lt;a class="wiki_link" href="/363edo"&gt;363edo&lt;/a&gt; 31&amp;amp;58&amp;amp;72 54.221&lt;br /&gt;
 &lt;a class="wiki_link" href="/Lehmerismic%20temperaments#Hanuman"&gt;Hanuman&lt;/a&gt;: &lt;a class="wiki_link" href="/535edo"&gt;535edo&lt;/a&gt; 15&amp;amp;72&amp;amp;137 65.278&lt;br /&gt;
-&lt;a class="wiki_link" href="/Swetismic%20temperaments#Hades"&gt;Hades&lt;/a&gt;: &lt;a class="wiki_link" href="/578edo"&gt;578edo&lt;/a&gt; 36&amp;amp;58&amp;amp;72 &lt;br /&gt;
+&lt;a class="wiki_link" href="/Swetismic%20temperaments#Hades"&gt;Hades&lt;/a&gt;: &lt;a class="wiki_link" href="/578edo"&gt;578edo&lt;/a&gt; 36&amp;amp;58&amp;amp;72&lt;br /&gt;
 &lt;a class="wiki_link" href="/Breed%20family"&gt;Vili&lt;/a&gt;: &lt;a class="wiki_link" href="/643edo"&gt;643edo&lt;/a&gt; 37&amp;amp;93&amp;amp;103 73.821&lt;br /&gt;
 &lt;a class="wiki_link" href="/Mirkwai%20family#Indra-Shibi"&gt;Shibi&lt;/a&gt;: &lt;a class="wiki_link" href="/703edo"&gt;703edo&lt;/a&gt; 41&amp;amp;72&amp;amp;111 72.094&lt;br /&gt;