1/6-comma meantone

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Revision as of 17:33, 17 June 2011 by Wikispaces>genewardsmith (**Imported revision 237371211 - Original comment: **)
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This revision was by author genewardsmith and made on 2011-06-17 17:33:15 UTC.
The original revision id was 237371211.
The revision comment was:

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Original Wikitext content:

1/6 comma meantone is the tuning of [[Meantone family|meantone temperament]] which tunes the fifth as the sixth root of 45/4, or in other words 698.371 cents. This means the fifth is flattened by 1/6 of the syntonic comma (81/80 ratio) of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. It is closely related to [[55edo]] in terms of its tuning.

=Fractional projection matrix=
The [[Fractional monzos|fractional projection map]] defining 7-limit 1/6 comma meantone is
|| [1 || 0 || 0 || 0> ||
|| [2/3 || 1/3 || 1/6 || 0> ||
|| [-4/3 || 4/3 || 2/3 || 0> || 
|| [-19/3 || 10/3 || 5/3 || 0> ||

=Links=
[[http://music.case.edu/~rwd/baroquetemp/XMT.intro.html|Baroque Ensemble Tuning in Extended 1/6 Syntonic Comma Meantone]] by Ross W. Duffin [[http://www.webcitation.org/5zW8FuybZ|permalink]]
[[http://sonic-arts.org/monzo/55edo/55edo.htm|Mozart's tuning: 55-EDO and its close relative, 1/6-comma meantone]] by [[Joe Monzo]] [[http://www.webcitation.org/5zW910Jax|permalink]]

Original HTML content:

<html><head><title>1-6 Syntonic Comma Meantone</title></head><body>1/6 comma meantone is the tuning of <a class="wiki_link" href="/Meantone%20family">meantone temperament</a> which tunes the fifth as the sixth root of 45/4, or in other words 698.371 cents. This means the fifth is flattened by 1/6 of the syntonic comma (81/80 ratio) of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. It is closely related to <a class="wiki_link" href="/55edo">55edo</a> in terms of its tuning.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Fractional projection matrix"></a><!-- ws:end:WikiTextHeadingRule:0 -->Fractional projection matrix</h1>
The <a class="wiki_link" href="/Fractional%20monzos">fractional projection map</a> defining 7-limit 1/6 comma meantone is<br />


<table class="wiki_table">
    <tr>
        <td>[1<br />
</td>
        <td>0<br />
</td>
        <td>0<br />
</td>
        <td>0&gt;<br />
</td>
    </tr>
    <tr>
        <td>[2/3<br />
</td>
        <td>1/3<br />
</td>
        <td>1/6<br />
</td>
        <td>0&gt;<br />
</td>
    </tr>
    <tr>
        <td>[-4/3<br />
</td>
        <td>4/3<br />
</td>
        <td>2/3<br />
</td>
        <td>0&gt;<br />
</td>
        <td><br />
</td>
        <td>[-19/3<br />
</td>
        <td>10/3<br />
</td>
        <td>5/3<br />
</td>
        <td>0&gt;<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:2 -->Links</h1>
<a class="wiki_link_ext" href="http://music.case.edu/~rwd/baroquetemp/XMT.intro.html" rel="nofollow">Baroque Ensemble Tuning in Extended 1/6 Syntonic Comma Meantone</a> by Ross W. Duffin <a class="wiki_link_ext" href="http://www.webcitation.org/5zW8FuybZ" rel="nofollow">permalink</a><br />
<a class="wiki_link_ext" href="http://sonic-arts.org/monzo/55edo/55edo.htm" rel="nofollow">Mozart's tuning: 55-EDO and its close relative, 1/6-comma meantone</a> by <a class="wiki_link" href="/Joe%20Monzo">Joe Monzo</a> <a class="wiki_link_ext" href="http://www.webcitation.org/5zW910Jax" rel="nofollow">permalink</a></body></html>
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