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: | : This revision was by author [[User:guest|guest]] and made on <tt>2010-08-28 12:06:07 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>158823061</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> | ||
<h4>Original Wikitext content:</h4> | <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]] | <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]] | ||
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=Equal temperaments= | =Equal temperaments= | ||
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The dicot family is a low-accuracy family of temperaments which temper out the chromatic semitone, 25/24, and hence identify major and minor thirds. [[7edo]] makes for a good dicot tuning. | The dicot family is a low-accuracy family of temperaments which temper out the chromatic semitone, 25/24, and hence identify major and minor thirds. [[7edo]] makes for a good dicot tuning. | ||
===[[Tetracot family]]=== | ===[[Tetracot family]]=== | ||
The tetracot family is a much higher accuracy affair than the dicot family. Instead of taking two neutral thirds to reach 3/2, it takes four minor (10/9) whole tones. Four of these exceed 3/2 by 20000/19683, the minimal diesis or tetracot comma. | The tetracot family is a much higher accuracy affair than the dicot family. Instead of taking two neutral thirds to reach 3/2, it takes four minor (10/9) whole tones. Four of these exceed 3/2 by 20000/19683, the minimal diesis or tetracot comma. | ||
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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. | ||
===[[Pythagorean family]]=== | ===[[Pythagorean family]]=== | ||
The Pythagorean family tempers out the Pythagorean comma, |-19 12 0>. Since this is a 3-limit comma, it is also a 5-limit comma and can stand as parent to a 7-limit or higher family, in this case containing compton temperament and catler temperament. | The Pythagorean family tempers out the Pythagorean comma, |-19 12 0>. Since this is a 3-limit comma, it is also a 5-limit comma and can stand as parent to a 7-limit or higher family, in this case containing compton temperament and catler temperament. | ||
===[[Gammic family]]=== | ===[[Gammic family]]=== | ||
The gammic family tempers out the gammic comma, |-29 -11 20>. The head of the family is 5-limit gammic, whose generator chain is [[Carlos Gamma]]. Another member is Neptune temperament. | The gammic family tempers out the gammic comma, |-29 -11 20>. The head of the family is 5-limit gammic, whose generator chain is [[Carlos Gamma]]. Another member is Neptune temperament. | ||
===[[Sycamore family]]=== | ===[[Sycamore family]]=== | ||
The sycamore family tempers out the sycamore comma, |-16 -6 11> = 48838125/47775744, which is the amount by which five stacked chromatic semitones, 25/24, exceed 6/5, and hence also the amount six exceeds 5/4. | The sycamore family tempers out the sycamore comma, |-16 -6 11> = 48838125/47775744, which is the amount by which five stacked chromatic semitones, 25/24, exceed 6/5, and hence also the amount six exceeds 5/4. | ||
===[[Mutt family]]=== | ===[[Mutt family]]=== | ||
This tempers out the mutt comma, |-44 -3 21>, leading to some strange properties. | This tempers out the mutt comma, |-44 -3 21>, leading to some strange properties. | ||
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Miracle temperament divides the fifth into 6 equal steps. A 21-note scale called "blackjack" and a 31-note scale called "canasta" have some useful properties. It's the most efficient 11-limit temperament for many purposes with a tuning close to 72-EDO. | Miracle temperament divides the fifth into 6 equal steps. A 21-note scale called "blackjack" and a 31-note scale called "canasta" have some useful properties. It's the most efficient 11-limit temperament for many purposes with a tuning close to 72-EDO. | ||
===[[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. | ||
===[[Marvel temperaments]]=== | ===[[Marvel temperaments]]=== | ||
These temper out 225/224, the marvel comma, and include negri, sharp, mavila, wizard, tritonic, septimin, slender, triton, escapade and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august and compton. | These temper out 225/224, the marvel comma, and include negri, sharp, mavila, wizard, tritonic, septimin, slender, triton, escapade and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august and compton. | ||
===[[Breedsmic temperaments]]=== | ===[[Breedsmic temperaments]]=== | ||
A breedsmic temperament is one which tempers out the breedsma, 2401/2400. Some which do not get discussed elsewhere are collected on a page [[Breedsmic temperaments|here]]. | A breedsmic temperament is one which tempers out the breedsma, 2401/2400. Some which do not get discussed elsewhere are collected on a page [[Breedsmic temperaments|here]]. | ||
===[[Ragismic microtemperaments]]=== | ===[[Ragismic microtemperaments]]=== | ||
A ragismic temperament is 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. | A ragismic temperament is 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. | ||
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===Jove, aka Wonder[[#wonder]]=== | ===Jove, aka Wonder[[#wonder]]=== | ||
Jove, formerly known as wonder, tempers out 243/242 and 441/440. Wonder has been | Jove, formerly known as wonder, tempers out 243/242 and 441/440. Wonder has been deprecated 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. | ||
===[[Gamelismic family]]=== | ===[[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. | 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. | ||
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== Links == | ==Links== | ||
* [[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:60:&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:60 --><!-- ws:start:WikiTextTocRule:61: --><a href="#Equal temperaments">Equal temperaments</a><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Rank 2 (including &quot;linear&quot;) temperaments">Rank 2 (including &quot;linear&quot;) temperaments</a><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- 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: --><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><!-- 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: --> | <a href="#Rank 3 temperaments">Rank 3 temperaments</a><!-- 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: --> | <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:60:&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:60 --><!-- ws:start:WikiTextTocRule:61: --><a href="#Equal temperaments">Equal temperaments</a><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Rank 2 (including &quot;linear&quot;) temperaments">Rank 2 (including &quot;linear&quot;) temperaments</a><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- 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: --><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><!-- 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: --> | <a href="#Rank 3 temperaments">Rank 3 temperaments</a><!-- 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: --> | ||
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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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<!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Tetracot family"></a><!-- ws:end:WikiTextHeadingRule:22 --><a class="wiki_link" href="/Tetracot%20family">Tetracot family</a></h3> | <!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Tetracot family"></a><!-- ws:end:WikiTextHeadingRule:22 --><a class="wiki_link" href="/Tetracot%20family">Tetracot family</a></h3> | ||
The tetracot family is a much higher accuracy affair than the dicot family. Instead of taking two neutral thirds to reach 3/2, it takes four minor (10/9) whole tones. Four of these exceed 3/2 by 20000/19683, the minimal diesis or tetracot comma.<br /> | The tetracot family is a much higher accuracy affair than the dicot family. Instead of taking two neutral thirds to reach 3/2, it takes four minor (10/9) whole tones. Four of these exceed 3/2 by 20000/19683, the minimal diesis or tetracot comma.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Orwell and the semicomma family"></a><!-- ws:end:WikiTextHeadingRule:24 --><a class="wiki_link" href="/Semicomma%20family">Orwell and the semicomma family</a></h3> | <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Orwell and the semicomma family"></a><!-- ws:end:WikiTextHeadingRule:24 --><a class="wiki_link" href="/Semicomma%20family">Orwell and the semicomma family</a></h3> | ||
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The Pythagorean family tempers out the Pythagorean comma, |-19 12 0&gt;. Since this is a 3-limit comma, it is also a 5-limit comma and can stand as parent to a 7-limit or higher family, in this case containing compton temperament and catler temperament.<br /> | The Pythagorean family tempers out the Pythagorean comma, |-19 12 0&gt;. Since this is a 3-limit comma, it is also a 5-limit comma and can stand as parent to a 7-limit or higher family, in this case containing compton temperament and catler temperament.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Gammic family"></a><!-- ws:end:WikiTextHeadingRule:28 --><a class="wiki_link" href="/Gammic%20family">Gammic family</a></h3> | <!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Gammic family"></a><!-- ws:end:WikiTextHeadingRule:28 --><a class="wiki_link" href="/Gammic%20family">Gammic family</a></h3> | ||
The gammic family tempers out the gammic comma, |-29 -11 20&gt;. The head of the family is 5-limit gammic, whose generator chain is <a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>. Another member is Neptune temperament.<br /> | The gammic family tempers out the gammic comma, |-29 -11 20&gt;. The head of the family is 5-limit gammic, whose generator chain is <a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>. Another member is Neptune temperament.<br /> | ||
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The sycamore family tempers out the sycamore comma, |-16 -6 11&gt; = 48838125/47775744, which is the amount by which five stacked chromatic semitones, 25/24, exceed 6/5, and hence also the amount six exceeds 5/4. <br /> | The sycamore family tempers out the sycamore comma, |-16 -6 11&gt; = 48838125/47775744, which is the amount by which five stacked chromatic semitones, 25/24, exceed 6/5, and hence also the amount six exceeds 5/4. <br /> | ||
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This tempers out the mutt comma, |-44 -3 21&gt;, leading to some strange properties.<br /> | This tempers out the mutt comma, |-44 -3 21&gt;, leading to some strange properties.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Gamelismic clan"></a><!-- ws:end:WikiTextHeadingRule:34 --><a class="wiki_link" href="/Gamelismic%20clan">Gamelismic clan</a></h3> | <!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Gamelismic clan"></a><!-- ws:end:WikiTextHeadingRule:34 --><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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These temper out 225/224, the marvel comma, and include negri, sharp, mavila, wizard, tritonic, septimin, slender, triton, escapade and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august and compton.<br /> | These temper out 225/224, the marvel comma, and include negri, sharp, mavila, wizard, tritonic, septimin, slender, triton, escapade and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august and compton.<br /> | ||
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A breedsmic temperament is one which tempers out the breedsma, 2401/2400. Some which do not get discussed elsewhere are collected on a page <a class="wiki_link" href="/Breedsmic%20temperaments">here</a>.<br /> | A breedsmic temperament is one which tempers out the breedsma, 2401/2400. Some which do not get discussed elsewhere are collected on a page <a class="wiki_link" href="/Breedsmic%20temperaments">here</a>.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:42:&lt;h3&gt; --><h3 id="toc21"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Ragismic microtemperaments"></a><!-- ws:end:WikiTextHeadingRule:42 --><a class="wiki_link" href="/Ragismic%20microtemperaments">Ragismic microtemperaments</a></h3> | <!-- ws:start:WikiTextHeadingRule:42:&lt;h3&gt; --><h3 id="toc21"><a name="Rank 2 (including &quot;linear&quot;) temperaments--Ragismic microtemperaments"></a><!-- ws:end:WikiTextHeadingRule:42 --><a class="wiki_link" href="/Ragismic%20microtemperaments">Ragismic microtemperaments</a></h3> | ||
A ragismic temperament is 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 /> | A ragismic temperament is 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:54:&lt;h3&gt; --><h3 id="toc27"><a name="Rank 3 temperaments-Breed-Jove, aka Wonder"></a><!-- ws:end:WikiTextHeadingRule:54 -->Jove, aka Wonder<!-- ws:start:WikiTextAnchorRule:94:&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:94 --></h3> | <!-- ws:start:WikiTextHeadingRule:54:&lt;h3&gt; --><h3 id="toc27"><a name="Rank 3 temperaments-Breed-Jove, aka Wonder"></a><!-- ws:end:WikiTextHeadingRule:54 -->Jove, aka Wonder<!-- ws:start:WikiTextAnchorRule:94:&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:94 --></h3> | ||
Jove, formerly known as wonder, tempers out 243/242 and 441/440. Wonder has been | Jove, formerly known as wonder, tempers out 243/242 and 441/440. Wonder has been deprecated 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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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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<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> | ||