1/6-comma meantone: Difference between revisions
Jump to navigation
Jump to search
Wikispaces>genewardsmith **Imported revision 237370859 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 237371211 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2011-06-17 17: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-17 17:33:15 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>237371211</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> | ||
| Line 10: | Line 10: | ||
=Fractional projection matrix= | =Fractional projection matrix= | ||
The [[Fractional monzos|fractional projection map]] defining 7-limit 1/6 comma meantone is | The [[Fractional monzos|fractional projection map]] defining 7-limit 1/6 comma meantone is | ||
|| [1 0 0 0> || | || [1 || 0 || 0 || 0> || | ||
|| [2/3 1/3 1/6 0> || | || [2/3 || 1/3 || 1/6 || 0> || | ||
|| [-4/3 4/3 2/3 0> || | || [-4/3 || 4/3 || 2/3 || 0> || | ||
|| [-19/3 10/3 5/3 0> || | || [-19/3 || 10/3 || 5/3 || 0> || | ||
=Links= | =Links= | ||
| Line 27: | Line 27: | ||
<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td>[1 0 0 0&gt;<br /> | <td>[1<br /> | ||
</td> | |||
<td>0<br /> | |||
</td> | |||
<td>0<br /> | |||
</td> | |||
<td>0&gt;<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>[2/3 1/3 1/6 0&gt;<br /> | <td>[2/3<br /> | ||
</td> | |||
<td>1/3<br /> | |||
</td> | |||
<td>1/6<br /> | |||
</td> | |||
<td>0&gt;<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>[-4/3 4/3 2/3 0&gt;<br /> | <td>[-4/3<br /> | ||
</td> | |||
<td>4/3<br /> | |||
</td> | |||
<td>2/3<br /> | |||
</td> | |||
<td>0&gt;<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>[-19/3 10/3 5/3 0&gt;<br /> | <td>[-19/3<br /> | ||
</td> | |||
<td>10/3<br /> | |||
</td> | |||
<td>5/3<br /> | |||
</td> | |||
<td>0&gt;<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
Revision as of 17:33, 17 June 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- 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:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
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:<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 />
<table class="wiki_table">
<tr>
<td>[1<br />
</td>
<td>0<br />
</td>
<td>0<br />
</td>
<td>0><br />
</td>
</tr>
<tr>
<td>[2/3<br />
</td>
<td>1/3<br />
</td>
<td>1/6<br />
</td>
<td>0><br />
</td>
</tr>
<tr>
<td>[-4/3<br />
</td>
<td>4/3<br />
</td>
<td>2/3<br />
</td>
<td>0><br />
</td>
<td><br />
</td>
<td>[-19/3<br />
</td>
<td>10/3<br />
</td>
<td>5/3<br />
</td>
<td>0><br />
</td>
</tr>
</table>
<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>