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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{interwiki |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | de = Sechstelkomma-mitteltönig |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-17 17:28:30 UTC</tt>.<br>
| | | en = 1/6-comma meantone |
| : The original revision id was <tt>237370707</tt>.<br>
| | | es = |
| : The revision comment was: <tt></tt><br>
| | | ja = |
| 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>
| | '''1/6-comma meantone''' is the tuning of [[meantone]] temperament which tunes the fifth as the sixth root of 45/4, or in other words 698.371 [[cent]]s. This means the fifth is flattened by 1/6 of the [[81/80|syntonic comma (81/80)]] of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone [[45/32]] is tuned justly, and it can be characterized fully as the regular tuning [[tempering out]] 81/80 and tuning 2 and 45/32 justly. [[55edo]] and [[67edo]] approximate it flatly and sharply, respectively, while [[122edo]] using the c val does so near perfectly. Leopold Mozart and Wolfgang Amadeus Mozart recommended this tuning (implemented as 55edo or something close to it), with a subset and further approximation used for keyboard instruments which (apart from an experimental instrument) did not have enough notes per octave to accommodate it in full.<ref>Chesnut, John (1977) ''Mozart's Teaching of Intonation'', '''Journal of the American Musicological Society''' Vol. 30, No. 2 (Summer, 1977), pp. 254-271 (Published By: University of California Press) [https://doi.org/10.2307/831219 doi.org/10.2307/831219], [http://www.jstor.org/stable/831219 https://www.jstor.org/stable/831219]</ref> |
| <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">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.
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| =Fractional projection matrix= | | == Tuning profile == |
| The [[Fractional monzos|fractional projection map]] defining 7-limit 1/6 comma meantone is
| | [[Projection map]]: |
| || [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> ||
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| =Links= | | {| class="right-all" |
| [[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]]</pre></div>
| | | [⟨ || 1 || 2/3 || -4/3 || -19/3 || ] |
| <h4>Original HTML content:</h4>
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| <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>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 />
| | | ⟨ || 0 || 1/3 || 4/3 || 10/3 || ] |
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| | |- |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Fractional projection matrix"></a><!-- ws:end:WikiTextHeadingRule:0 -->Fractional projection matrix</h1>
| | | ⟨ || 0 || 1/6 || 2/3 || 5/3 || ] |
| The <a class="wiki_link" href="/Fractional%20monzos">fractional projection map</a> defining 7-limit 1/6 comma meantone is<br />
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| | | ⟨ || 0 || 0 || 0 || 0 || ]] |
| | |} |
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| | [[Tuning map]]: {{val| 1200 1898.3706 2793.4825 3383.7062 }} |
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| <table class="wiki_table">
| | [[Error map]]: {{val| 0 -3.5844 +7.1688 +14.8803 }} |
| <tr>
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| <td>[1 0 0 0&gt;<br />
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| </td>
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| <td>[2/3 1/3 1/6 0&gt;<br />
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| </td>
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| <td>[-4/3 4/3 2/3 0&gt;<br />
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| </td>
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| <td>[-19/3 10/3 5/3 0&gt;<br />
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| </td>
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| </tr>
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| </table>
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| <br />
| | == Links == |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:2 -->Links</h1>
| | * ''Baroque Ensemble Tuning in Extended 1/6 Syntonic Comma Meantone'' by [[Ross W. Duffin]] ([https://www.webcitation.org/5zW8FuybZ WebCite]) |
| <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 />
| | * ''Mozart's tuning: 55-EDO and its close relative, 1/6-comma meantone'' by [[Joseph Monzo]] ([https://web.archive.org/web/20120214163510/sonic-arts.org/monzo/55edo/55edo.htm Internet Archive] [https://www.webcitation.org/5zW910Jax WebCite]) |
| <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></pre></div>
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| | == References == |
| | <references /> |
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| | [[Category:Meantone]] |
| | [[Category:Historical]] |