Tour of regular temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 147200685 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 147243493 - Original comment: ** |
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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>2010-06-06 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-06-06 14:06:33 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>147243493</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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The wuerschmidt family tempers out Wuerschmidt's comma, 393216/390625 = |17 1 -8>. Wuerschmidt itself has a generator of a major third, eight of which give a 6; that is, (5/4)^8 * (393216/390625) = 6. Both [[31edo]] and [[34edo]] can be used as wuerschmit tunings, as can [[65edo]], which is quite accurate. | The wuerschmidt family tempers out Wuerschmidt's comma, 393216/390625 = |17 1 -8>. Wuerschmidt itself has a generator of a major third, eight of which give a 6; that is, (5/4)^8 * (393216/390625) = 6. Both [[31edo]] and [[34edo]] can be used as wuerschmit tunings, as can [[65edo]], which is quite accurate. | ||
===Augmented family=== | ===[[Augmented family]]=== | ||
The augmented family tempers out the limma of 128/125, and so identifies the major third with 1/3 octave. Hence it has the same 400 cent thirds as [[12edo]], which is an excellent tuning for augmented. | The augmented family tempers out the limma of 128/125, and so identifies the major third with 1/3 octave. Hence it has the same 400 cent thirds as [[12edo]], which is an excellent tuning for augmented. | ||
===Dicot family=== | ===[[Dicot family]]=== | ||
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. | ||
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The wuerschmidt family tempers out Wuerschmidt's comma, 393216/390625 = |17 1 -8&gt;. Wuerschmidt itself has a generator of a major third, eight of which give a 6; that is, (5/4)^8 * (393216/390625) = 6. Both <a class="wiki_link" href="/31edo">31edo</a> and <a class="wiki_link" href="/34edo">34edo</a> can be used as wuerschmit tunings, as can <a class="wiki_link" href="/65edo">65edo</a>, which is quite accurate.<br /> | The wuerschmidt family tempers out Wuerschmidt's comma, 393216/390625 = |17 1 -8&gt;. Wuerschmidt itself has a generator of a major third, eight of which give a 6; that is, (5/4)^8 * (393216/390625) = 6. Both <a class="wiki_link" href="/31edo">31edo</a> and <a class="wiki_link" href="/34edo">34edo</a> can be used as wuerschmit tunings, as can <a class="wiki_link" href="/65edo">65edo</a>, which is quite accurate.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="x-Rank 2 (including &quot;linear&quot;) temperaments-Augmented family"></a><!-- ws:end:WikiTextHeadingRule:18 -->Augmented family</h3> | <!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="x-Rank 2 (including &quot;linear&quot;) temperaments-Augmented family"></a><!-- ws:end:WikiTextHeadingRule:18 --><a class="wiki_link" href="/Augmented%20family">Augmented family</a></h3> | ||
The augmented family tempers out the limma of 128/125, and so identifies the major third with 1/3 octave. Hence it has the same 400 cent thirds as <a class="wiki_link" href="/12edo">12edo</a>, which is an excellent tuning for augmented.<br /> | The augmented family tempers out the limma of 128/125, and so identifies the major third with 1/3 octave. Hence it has the same 400 cent thirds as <a class="wiki_link" href="/12edo">12edo</a>, which is an excellent tuning for augmented.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="x-Rank 2 (including &quot;linear&quot;) temperaments-Dicot family"></a><!-- ws:end:WikiTextHeadingRule:20 -->Dicot family</h3> | <!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="x-Rank 2 (including &quot;linear&quot;) temperaments-Dicot family"></a><!-- ws:end:WikiTextHeadingRule:20 --><a class="wiki_link" href="/Dicot%20family">Dicot family</a></h3> | ||
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. <a class="wiki_link" href="/7edo">7edo</a> makes for a good dicot tuning.<br /> | 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. <a class="wiki_link" href="/7edo">7edo</a> makes for a good dicot tuning.<br /> | ||
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