Tour of regular temperaments: Difference between revisions
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | 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>2010-10- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-10-04 18:13:54 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>167742567</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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===[[Starling family]]=== | ===[[Starling family]]=== | ||
Starling tempers out 126/125, and like marvel it has the same generators as the 5-limit. An excellent tuning for starling is [[77edo]], but 31, 46 or 58 also work nicely. | Starling tempers out 126/125, and like marvel it has the same generators as the 5-limit. An excellent tuning for starling is [[77edo]], but 31, 46 or 58 also work nicely. | ||
===[[Gamelismic family]]=== | |||
Not to be confused with the gamelismic clan of rank two temperaments, the gamelismic family are those rank three temperaments which temper out the gamelisma, 1029/1024. | |||
===[[Breed family]]=== | ===[[Breed family]]=== | ||
Breed is a 7-limit microtemperament which tempers out 2401/2400. While it is so accurate it hardly matters what is used to temper it, or whether it is even tempered at all, 2749et will certainly do the trick. Breed has generators of 2, a 49/40-cum-60/49 neutral third, and your choice of 8/7 or 10/7. | Breed is a 7-limit microtemperament which tempers out 2401/2400. While it is so accurate it hardly matters what is used to temper it, or whether it is even tempered at all, 2749et will certainly do the trick. Breed has generators of 2, a 49/40-cum-60/49 neutral third, and your choice of 8/7 or 10/7. | ||
===[[ | ===[[Ragisma family]]=== | ||
The 7-limit rank three microtemperament which tempers out the ragisma, 4375/4374, extends to various higher limit rank three temperaments such as thor. | |||
===[[Hemifamity family]]=== | ===[[Hemifamity family]]=== | ||
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* [[http://en.wikipedia.org/wiki/Regular_temperament|Regular temperaments - Wikipedia]]</pre></div> | * [[http://en.wikipedia.org/wiki/Regular_temperament|Regular temperaments - Wikipedia]]</pre></div> | ||
<h4>Original HTML content:</h4> | <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>Tour of Regular Temperaments</title></head><body><!-- ws:start:WikiTextTocRule: | <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>Tour of Regular Temperaments</title></head><body><!-- ws:start:WikiTextTocRule:78:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><a href="#Equal temperaments">Equal temperaments </a><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --> | <a href="#Rank 2 (including &quot;linear&quot;) temperaments">Rank 2 (including &quot;linear&quot;) temperaments</a><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --> | <a href="#Rank 3 temperaments">Rank 3 temperaments</a><!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Equal temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 --><a class="wiki_link" href="/edo">Equal temperaments</a> </h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Equal temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 --><a class="wiki_link" href="/edo">Equal temperaments</a> </h1> | ||
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<a class="wiki_link" href="/Equal%20Temperaments">Equal temperaments</a> (abbreviated ET or tET) and equal divisions of the octave (abbreviated EDO) are similar concepts, although there are distinctions in the way these terms are used. An EDO is simply a division of the octave into equal steps (specifically, steps of equal size in cents). An ET, on the other hand, is a temperament, an altered representation of some subset of the intervals of just intonation. The familiar 12-note equal temperament (12-ET) reduces the size of the perfect fifth (about 701.955 cents) by 1/12 of the Pythagorean comma, resulting in a fifth of 700.0 cents.<br /> | <a class="wiki_link" href="/Equal%20Temperaments">Equal temperaments</a> (abbreviated ET or tET) and equal divisions of the octave (abbreviated EDO) are similar concepts, although there are distinctions in the way these terms are used. An EDO is simply a division of the octave into equal steps (specifically, steps of equal size in cents). An ET, on the other hand, is a temperament, an altered representation of some subset of the intervals of just intonation. The familiar 12-note equal temperament (12-ET) reduces the size of the perfect fifth (about 701.955 cents) by 1/12 of the Pythagorean comma, resulting in a fifth of 700.0 cents.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Rank 2 (including &quot;linear&quot;) temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->Rank 2 (including &quot;linear&quot;) temperaments<!-- ws:start:WikiTextAnchorRule: | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Rank 2 (including &quot;linear&quot;) temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->Rank 2 (including &quot;linear&quot;) temperaments<!-- ws:start:WikiTextAnchorRule:119:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@lineartemperaments&quot; title=&quot;Anchor: lineartemperaments&quot;/&gt; --><a name="lineartemperaments"></a><!-- ws:end:WikiTextAnchorRule:119 --></h1> | ||
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<a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a> has given us a <a class="wiki_link" href="/Catalog%20of%20five-limit%20rank%20two%20temperaments">catalog of 5-limit rank two temperaments</a>, and we also have a <a class="wiki_link" href="/Proposed%20names%20for%20rank%202%20temperaments">page</a> listing higher limit temperaments.<br /> | <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a> has given us a <a class="wiki_link" href="/Catalog%20of%20five-limit%20rank%20two%20temperaments">catalog of 5-limit rank two temperaments</a>, and we also have a <a class="wiki_link" href="/Proposed%20names%20for%20rank%202%20temperaments">page</a> listing higher limit temperaments.<br /> | ||
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Starling tempers out 126/125, and like marvel it has the same generators as the 5-limit. An excellent tuning for starling is <a class="wiki_link" href="/77edo">77edo</a>, but 31, 46 or 58 also work nicely.<br /> | Starling tempers out 126/125, and like marvel it has the same generators as the 5-limit. An excellent tuning for starling is <a class="wiki_link" href="/77edo">77edo</a>, but 31, 46 or 58 also work nicely.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:52:&lt;h3&gt; --><h3 id="toc26"><a name="Rank 3 temperaments--Breed family"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h3&gt; --><h3 id="toc26"><a name="Rank 3 temperaments--Gamelismic family"></a><!-- ws:end:WikiTextHeadingRule:52 --><a class="wiki_link" href="/Gamelismic%20family">Gamelismic family</a></h3> | ||
Not to be confused with the gamelismic clan of rank two temperaments, the gamelismic family are those rank three temperaments which temper out the gamelisma, 1029/1024. <br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:54:&lt;h3&gt; --><h3 id="toc27"><a name="Rank 3 temperaments--Breed family"></a><!-- ws:end:WikiTextHeadingRule:54 --><a class="wiki_link" href="/Breed%20family">Breed family</a></h3> | |||
Breed is a 7-limit microtemperament which tempers out 2401/2400. While it is so accurate it hardly matters what is used to temper it, or whether it is even tempered at all, 2749et will certainly do the trick. Breed has generators of 2, a 49/40-cum-60/49 neutral third, and your choice of 8/7 or 10/7.<br /> | Breed is a 7-limit microtemperament which tempers out 2401/2400. While it is so accurate it hardly matters what is used to temper it, or whether it is even tempered at all, 2749et will certainly do the trick. Breed has generators of 2, a 49/40-cum-60/49 neutral third, and your choice of 8/7 or 10/7.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:56:&lt;h3&gt; --><h3 id="toc28"><a name="Rank 3 temperaments--Ragisma family"></a><!-- ws:end:WikiTextHeadingRule:56 --><a class="wiki_link" href="/Ragisma%20family">Ragisma family</a></h3> | ||
The 7-limit rank three microtemperament which tempers out the ragisma, 4375/4374, extends to various higher limit rank three temperaments such as thor.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:58:&lt;h3&gt; --><h3 id="toc29"><a name="Rank 3 temperaments--Hemifamity family"></a><!-- ws:end:WikiTextHeadingRule:58 --><a class="wiki_link" href="/Hemifamity%20family">Hemifamity family</a></h3> | ||
The hemifamity family of rank three temperaments tempers out the hemifamity comma, 5120/5103.<br /> | The hemifamity family of rank three temperaments tempers out the hemifamity comma, 5120/5103.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:60:&lt;h3&gt; --><h3 id="toc30"><a name="Rank 3 temperaments--Porwell family"></a><!-- ws:end:WikiTextHeadingRule:60 --><a class="wiki_link" href="/Porwell%20family">Porwell family</a></h3> | ||
The porwell family of rank three temperaments tempers out the porwell comma, 6144/6125.<br /> | The porwell family of rank three temperaments tempers out the porwell comma, 6144/6125.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:62:&lt;h3&gt; --><h3 id="toc31"><a name="Rank 3 temperaments--Hemimage family"></a><!-- ws:end:WikiTextHeadingRule:62 --><a class="wiki_link" href="/Hemimage%20family">Hemimage family</a></h3> | ||
The hemimage family of rank three temperaments tempers out the hemimage comma, 10976/10935.<br /> | The hemimage family of rank three temperaments tempers out the hemimage comma, 10976/10935.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:64:&lt;h3&gt; --><h3 id="toc32"><a name="Rank 3 temperaments--Octagar family"></a><!-- ws:end:WikiTextHeadingRule:64 --><a class="wiki_link" href="/Octagar%20family">Octagar family</a></h3> | ||
The octagar family of rank three temperaments tempers out the octagar comma, 4000/3969.<br /> | The octagar family of rank three temperaments tempers out the octagar comma, 4000/3969.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:66:&lt;h3&gt; --><h3 id="toc33"><a name="Rank 3 temperaments--Mirkwai family"></a><!-- ws:end:WikiTextHeadingRule:66 --><a class="wiki_link" href="/Mirkwai%20family">Mirkwai family</a></h3> | ||
The mirkwai family of rank three temperaments tempers out the mirkwai comma, 16875/16807.<br /> | The mirkwai family of rank three temperaments tempers out the mirkwai comma, 16875/16807.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:68:&lt;h3&gt; --><h3 id="toc34"><a name="Rank 3 temperaments--Hemimean family"></a><!-- ws:end:WikiTextHeadingRule:68 --><a class="wiki_link" href="/Hemimean%20family">Hemimean family</a></h3> | ||
The hemimean family of rank three temperaments tempers out the hemimean comma, 3136/3125.<br /> | The hemimean family of rank three temperaments tempers out the hemimean comma, 3136/3125.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:70:&lt;h3&gt; --><h3 id="toc35"><a name="Rank 3 temperaments--Archytas family"></a><!-- ws:end:WikiTextHeadingRule:70 --><a class="wiki_link" href="/Archytas%20family">Archytas family</a></h3> | ||
Archytas temperament tempers out 64/63, and thereby identifies the otonal tetrad with the dominant seventh chord.<br /> | Archytas temperament tempers out 64/63, and thereby identifies the otonal tetrad with the dominant seventh chord.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:72:&lt;h3&gt; --><h3 id="toc36"><a name="Rank 3 temperaments--Kleismic rank three family"></a><!-- ws:end:WikiTextHeadingRule:72 --><a class="wiki_link" href="/Kleismic%20rank%20three%20family">Kleismic rank three family</a></h3> | ||
These are the rank three temperaments tempering out the kleisma, 15625/15552. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.<br /> | These are the rank three temperaments tempering out the kleisma, 15625/15552. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:74:&lt;h3&gt; --><h3 id="toc37"><a name="Rank 3 temperaments--Jubilismic temperament"></a><!-- ws:end:WikiTextHeadingRule:74 --><a class="wiki_link" href="/Jubilismic%20temperament">Jubilismic temperament</a></h3> | ||
Jubilismic temperament tempers out 50/49 and thereby identifies the two septimal tritones, 7/5 and 10/7.<br /> | Jubilismic temperament tempers out 50/49 and thereby identifies the two septimal tritones, 7/5 and 10/7.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:76:&lt;h2&gt; --><h2 id="toc38"><a name="Rank 3 temperaments-Links"></a><!-- ws:end:WikiTextHeadingRule:76 -->Links</h2> | ||
<ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Regular_temperament" rel="nofollow">Regular temperaments - Wikipedia</a></li></ul></body></html></pre></div> | <ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Regular_temperament" rel="nofollow">Regular temperaments - Wikipedia</a></li></ul></body></html></pre></div> | ||