Marveltwin: Difference between revisions
Wikispaces>genewardsmith **Imported revision 238012277 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 238014607 - 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>2011-06-21 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-21 15:00:02 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>238014607</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 9: | Line 9: | ||
=Marveltwin and Marvel= | =Marveltwin and Marvel= | ||
The //marveltwin comma//, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the 11-limit | The //marveltwin comma//, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the [[11-limit]] version of marvel, which tempers out 225/224 and 385/384, to get [[13-limit]] marvel. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15. | ||
version of marvel, | |||
=Rank five= | =Rank five= | ||
Comma: 325/324 | Comma: 325/324 | ||
13 and 15 limit minimax tuning | |||
|| [1 0 0 0 0 0> || | |||
|| [0 1 0 0 0 0> || | |||
|| [2/3 4/3 1/3 0 0 -1/3> || | |||
|| [2/3 4/3 -2/3 1 0 -1/3> || | |||
|| [2/3 4/3 -2/3 0 1 -1/3> || | |||
|| [2/3 4/3 -2/3 0 0 2/3> || | |||
Eigenmonzo subgroup: 2.3.7/5.11/5.13/5 | |||
Map: | Map: | ||
| Line 28: | Line 37: | ||
<!-- ws:end:WikiTextTocRule:7 --><br /> | <!-- ws:end:WikiTextTocRule:7 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Marveltwin and Marvel"></a><!-- ws:end:WikiTextHeadingRule:0 -->Marveltwin and Marvel</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Marveltwin and Marvel"></a><!-- ws:end:WikiTextHeadingRule:0 -->Marveltwin and Marvel</h1> | ||
The <em>marveltwin comma</em>, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the 11-limit< | The <em>marveltwin comma</em>, 325/324, bears a curiously close analogy to the marvel comma, 225/224. 325/324 can be added to the <a class="wiki_link" href="/11-limit">11-limit</a> version of marvel, which tempers out 225/224 and 385/384, to get <a class="wiki_link" href="/13-limit">13-limit</a> marvel. But it's also interesting to leave 11 out of it. From 225/224 we get that a 5-limit approximation for 7 is 225/224 * 7 = 225/32. Similarly from 325/324 we get a 5-limit approximation of 13 from 324/325 * 13 = 324/25. If we define the major/minor transformation of the 5-limit as the result of fixing 2 and 3 and replacing 5 by 24/5, then major/minor applied to 225/32 is 162/25, which is (324/25)/2. Similarly, major/minor applied to 324/25 is 225/16 = 2 * (225/32). 225/224 tells us that two 16/15 in a row are an approximate 8/7, and 325/324 tells us two 10/9 in a row are an approximate 16/13. Needless to say, major/minor applied to 16/15 is 10/9, and applied to 10/9 is 16/15.<br /> | ||
version of marvel, | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Rank five"></a><!-- ws:end:WikiTextHeadingRule:2 -->Rank five</h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Rank five"></a><!-- ws:end:WikiTextHeadingRule:2 -->Rank five</h1> | ||
Comma: 325/324<br /> | Comma: 325/324<br /> | ||
<br /> | |||
13 and 15 limit minimax tuning<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td>[1 0 0 0 0 0&gt;<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>[0 1 0 0 0 0&gt;<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>[2/3 4/3 1/3 0 0 -1/3&gt;<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>[2/3 4/3 -2/3 1 0 -1/3&gt;<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>[2/3 4/3 -2/3 0 1 -1/3&gt;<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>[2/3 4/3 -2/3 0 0 2/3&gt;<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
Eigenmonzo subgroup: 2.3.7/5.11/5.13/5<br /> | |||
<br /> | <br /> | ||
Map: <br /> | Map: <br /> | ||