1/6-comma meantone
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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]]
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<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:<h1> --><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 /> [|1 0 0 0> <br /> |2/3 1/3 1/6 0> <br /> |-4/3 4/3 2/3 0> <br /> |-19/3 10/3 5/3 0>]<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><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>