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>2010-06-20 00: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-06-20 07:00:28 UTC</tt>.<br> | ||
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Even less familiar than rank 2 temperaments are the [[Planar Temperament|rank 3 temperaments]], 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. | Even less familiar than rank 2 temperaments are the [[Planar Temperament|rank 3 temperaments]], 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. | ||
===Marvel | ===Marvel family=== | ||
Tempers out 225/224. An excellent tuning for marvel is [[240edo]]. It extends in a natural way to unidecimal marvel, which tempers out 385/384, for which the slightly less accurate tuning of [[72edo]] works well. Marvel is generated by 2, 3, and 5, the same generators as the [[Harmonic Limit|5-limit]], which means a scale can be converted to marvel or unidecimal marvel simply by tempering it. | Tempers out 225/224. An excellent tuning for marvel is [[240edo]]. It extends in a natural way to unidecimal marvel, which tempers out 385/384, for which the slightly less accurate tuning of [[72edo]] works well. Marvel is generated by 2, 3, and 5, the same generators as the [[Harmonic Limit|5-limit]], which means a scale can be converted to marvel or unidecimal marvel simply by tempering it. | ||
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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:32:&lt;h3&gt; --><h3 id="toc16"><a name="Rank 3 temperaments--Marvel"></a><!-- ws:end:WikiTextHeadingRule:32 -->Marvel | <!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="Rank 3 temperaments--Marvel family"></a><!-- ws:end:WikiTextHeadingRule:32 -->Marvel family</h3> | ||
Tempers out 225/224. An excellent tuning for marvel is <a class="wiki_link" href="/240edo">240edo</a>. It extends in a natural way to unidecimal marvel, which tempers out 385/384, for which the slightly less accurate tuning of <a class="wiki_link" href="/72edo">72edo</a> works well. Marvel is generated by 2, 3, and 5, the same generators as the <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a>, which means a scale can be converted to marvel or unidecimal marvel simply by tempering it.<br /> | Tempers out 225/224. An excellent tuning for marvel is <a class="wiki_link" href="/240edo">240edo</a>. It extends in a natural way to unidecimal marvel, which tempers out 385/384, for which the slightly less accurate tuning of <a class="wiki_link" href="/72edo">72edo</a> works well. Marvel is generated by 2, 3, and 5, the same generators as the <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a>, which means a scale can be converted to marvel or unidecimal marvel simply by tempering it.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Rank 3 temperaments--Starling"></a><!-- ws:end:WikiTextHeadingRule:34 -->Starling<!-- ws:start:WikiTextAnchorRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Rank 3 temperaments--Starling"></a><!-- ws:end:WikiTextHeadingRule:34 -->Starling<!-- ws:start:WikiTextAnchorRule:70:&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:70 --></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:36:&lt;h2&gt; --><h2 id="toc18"><a name="Rank 3 temperaments-Breed"></a><!-- ws:end:WikiTextHeadingRule:36 -->Breed<!-- ws:start:WikiTextAnchorRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Rank 3 temperaments-Breed"></a><!-- ws:end:WikiTextHeadingRule:36 -->Breed<!-- ws:start:WikiTextAnchorRule:71:&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:71 --></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:38:&lt;h3&gt; --><h3 id="toc19"><a name="Rank 3 temperaments-Breed-Jove, aka Wonder"></a><!-- ws:end:WikiTextHeadingRule:38 -->Jove, aka Wonder<!-- ws:start:WikiTextAnchorRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h3&gt; --><h3 id="toc19"><a name="Rank 3 temperaments-Breed-Jove, aka Wonder"></a><!-- ws:end:WikiTextHeadingRule:38 -->Jove, aka Wonder<!-- ws:start:WikiTextAnchorRule:72:&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:72 --></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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