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>2010-06-23 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-06-23 22:22:57 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>150286803</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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===[[Semicomma family|Orwell and the semicomma family]]=== | ===[[Semicomma family|Orwell and the semicomma family]]=== | ||
The semicomma 2109375/2097152 = |-21 3 7> is tempered out by the members of the semicomma family. It doesn't have much independent existence as a 5-limit temperament, since its generator has a natural interpretation as 7/6, leading to orwell temperament. | The semicomma 2109375/2097152 = |-21 3 7> is tempered out by the members of the semicomma family. It doesn't have much independent existence as a 5-limit temperament, since its generator has a natural interpretation as 7/6, leading to orwell temperament. | ||
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===[[Starling temperaments]]=== | ===[[Starling temperaments]]=== | ||
Not a family or clan, but related by the fact that 126/125, the septimal semicomma or starling comma is tempered out, are myna, sensi, valentine, casablanca and nusecond temperaments, not to mention meantone, keemun, muggles and opossum. | Not a family or clan, but related by the fact that 126/125, the septimal semicomma or starling comma is tempered out, are myna, sensi, valentine, casablanca and nusecond temperaments, not to mention meantone, keemun, muggles and opossum. | ||
===[[Ragismic microtemperaments]]=== | |||
By a ragismic temperament I mean one which tempers out 4375/4374. These are not by any means all microtemperaments, but those which are not highly accurate are probably best discussed under another heading. Accurate ones include ennealimmal, supermajor, enneadecal, amity, mitonic, parakleismic, gamera and vishnu. Pontiac belongs on the list but falls under the schismatic family rubric. | |||
===[[Turkish maqam music temperaments]]=== | ===[[Turkish maqam music temperaments]]=== | ||
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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> | ||
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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"><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:46:&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:46 --><!-- ws:start:WikiTextTocRule:47: --><a href="#Equal temperaments">Equal temperaments</a><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --> | <a href="#Rank 2 (including &quot;linear&quot;) temperaments">Rank 2 (including &quot;linear&quot;) temperaments</a><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --> | <a href="#Rank 3 temperaments">Rank 3 temperaments</a><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Equal temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->Equal temperaments</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Equal temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->Equal temperaments</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:71:&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:71 --></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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<!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Orwell and the semicomma family"></a><!-- ws:end:WikiTextHeadingRule:22 --><a class="wiki_link" href="/Semicomma%20family">Orwell and the semicomma family</a></h3> | <!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Orwell and the semicomma family"></a><!-- ws:end:WikiTextHeadingRule:22 --><a class="wiki_link" href="/Semicomma%20family">Orwell and the semicomma family</a></h3> | ||
The semicomma 2109375/2097152 = |-21 3 7&gt; is tempered out by the members of the semicomma family. It doesn't have much independent existence as a 5-limit temperament, since its generator has a natural interpretation as 7/6, leading to orwell temperament.<br /> | |||
The semicomma 2109375/2097152 = |-21 3 7&gt; is tempered out by the members of the semicomma family. It doesn't have much independent existence as a 5-limit temperament, since its generator has a natural interpretation as 7/6, leading to orwell temperament.<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Gamelismic clan"></a><!-- ws:end:WikiTextHeadingRule:24 --><a class="wiki_link" href="/Gamelismic%20clan">Gamelismic clan</a></h3> | <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Gamelismic clan"></a><!-- ws:end:WikiTextHeadingRule:24 --><a class="wiki_link" href="/Gamelismic%20clan">Gamelismic clan</a></h3> | ||
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Not a family or clan, but related by the fact that 126/125, the septimal semicomma or starling comma is tempered out, are myna, sensi, valentine, casablanca and nusecond temperaments, not to mention meantone, keemun, muggles and opossum.<br /> | Not a family or clan, but related by the fact that 126/125, the septimal semicomma or starling comma is tempered out, are myna, sensi, valentine, casablanca and nusecond temperaments, not to mention meantone, keemun, muggles and opossum.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Turkish maqam music temperaments"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Ragismic microtemperaments"></a><!-- ws:end:WikiTextHeadingRule:28 --><a class="wiki_link" href="/Ragismic%20microtemperaments">Ragismic microtemperaments</a></h3> | ||
By a ragismic temperament I mean one which tempers out 4375/4374. These are not by any means all microtemperaments, but those which are not highly accurate are probably best discussed under another heading. Accurate ones include ennealimmal, supermajor, enneadecal, amity, mitonic, parakleismic, gamera and vishnu. Pontiac belongs on the list but falls under the schismatic family rubric.<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Turkish maqam music temperaments"></a><!-- ws:end:WikiTextHeadingRule:30 --><a class="wiki_link" href="/Turkish%20maqam%20music%20temperaments">Turkish maqam music temperaments</a></h3> | |||
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Vsrious theoretical solutions have been put forward for the vexing problem of how to indicate and define the tuning of Turkish <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">maqam music</a> in a systematic way. This includes, in effect, certain linear temperaments.<br /> | Vsrious theoretical solutions have been put forward for the vexing problem of how to indicate and define the tuning of Turkish <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">maqam music</a> in a systematic way. This includes, in effect, certain linear temperaments.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Rank 3 temperaments"></a><!-- ws:end:WikiTextHeadingRule:32 -->Rank 3 temperaments</h1> | ||
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Even less familiar than rank 2 temperaments are the <a class="wiki_link" href="/Planar%20Temperament">rank 3 temperaments</a>, based on a set of three intervals. Since these temperaments may be mapped in many different ways, it is more common to identify rank 3 temperaments by the commas they temper out.<br /> | Even less familiar than rank 2 temperaments are the <a class="wiki_link" href="/Planar%20Temperament">rank 3 temperaments</a>, based on a set of three intervals. Since these temperaments may be mapped in many different ways, it is more common to identify rank 3 temperaments by the commas they temper out.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Rank 3 temperaments--Marvel family"></a><!-- ws:end:WikiTextHeadingRule:34 --><a class="wiki_link" href="/Marvel%20family">Marvel family</a></h3> | ||
The head of the marvel family is marvel, which tempers out 225/224. It has a number of 11-limit children, including unidecimal marvel, prodigy, minerva and spectacle.<br /> | The head of the marvel family is marvel, which tempers out 225/224. It has a number of 11-limit children, including unidecimal marvel, prodigy, minerva and spectacle.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h3&gt; --><h3 id="toc18"><a name="Rank 3 temperaments--Starling"></a><!-- ws:end:WikiTextHeadingRule:36 -->Starling<!-- ws:start:WikiTextAnchorRule:72:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@starling&quot; title=&quot;Anchor: starling&quot;/&gt; --><a name="starling"></a><!-- ws:end:WikiTextAnchorRule:72 --></h3> | ||
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: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Rank 3 temperaments-Breed"></a><!-- ws:end:WikiTextHeadingRule:38 -->Breed<!-- ws:start:WikiTextAnchorRule:73:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@breed&quot; title=&quot;Anchor: breed&quot;/&gt; --><a name="breed"></a><!-- ws:end:WikiTextAnchorRule:73 --></h2> | ||
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, 2578et will certainly do the trick. Breed has generators of a 49/40 neutral third, and 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, 2578et will certainly do the trick. Breed has generators of a 49/40 neutral third, and 10/7.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h3&gt; --><h3 id="toc20"><a name="Rank 3 temperaments-Breed-Jove, aka Wonder"></a><!-- ws:end:WikiTextHeadingRule:40 -->Jove, aka Wonder<!-- ws:start:WikiTextAnchorRule:74:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@wonder&quot; title=&quot;Anchor: wonder&quot;/&gt; --><a name="wonder"></a><!-- ws:end:WikiTextAnchorRule:74 --></h3> | ||
Jove, formerly known as wonder, tempers out 243/242 and 441/440. Wonder has been depreciated as a name due to conflict with another temperament also given that name. Jove converts breed into an 11-limit temperament via 441/440, which equates 49/40 with 11/9, and 243/242, which tells us 11/9 can serve as a neutral third. While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. 72 and 130 are good edos for jove, and if that doesn't suit there's 476edo.<br /> | Jove, formerly known as wonder, tempers out 243/242 and 441/440. Wonder has been depreciated as a name due to conflict with another temperament also given that name. Jove converts breed into an 11-limit temperament via 441/440, which equates 49/40 with 11/9, and 243/242, which tells us 11/9 can serve as a neutral third. While jove is no longer a super-accurate microtemperament like breed, it has the advantage of adjusting its tuning to deal with the 11-limit. 72 and 130 are good edos for jove, and if that doesn't suit there's 476edo.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h3&gt; --><h3 id="toc21"><a name="Rank 3 temperaments-Breed-Gamelismic family"></a><!-- ws:end:WikiTextHeadingRule:42 --><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 /> | 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 /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Rank 3 temperaments-Links"></a><!-- ws:end:WikiTextHeadingRule:44 --> 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> | ||