Marveltwin
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2011-06-21 14:49:27 UTC.
- The original revision id was 238012277.
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Original Wikitext content:
[[toc|flat]] =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 version of marvel, tempering 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. =Rank five= Comma: 325/324 Map: || <1 0 0 0 0 2] || || <0 1 0 0 0 4] || || <0 0 1 0 0 -2] || || <0 0 0 1 0 0] || || <0 0 0 0 1 0] || Edos: 7, 12, 15, 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 299, 333
Original HTML content:
<html><head><title>Marveltwin</title></head><body><!-- ws:start:WikiTextTocRule:4:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:4 --><!-- ws:start:WikiTextTocRule:5: --><a href="#Marveltwin and Marvel">Marveltwin and Marvel</a><!-- ws:end:WikiTextTocRule:5 --><!-- ws:start:WikiTextTocRule:6: --> | <a href="#Rank five">Rank five</a><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: -->
<!-- ws:end:WikiTextTocRule:7 --><br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><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<br />
version of marvel, tempering 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.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Rank five"></a><!-- ws:end:WikiTextHeadingRule:2 -->Rank five</h1>
Comma: 325/324<br />
<br />
Map: <br />
<table class="wiki_table">
<tr>
<td><1 0 0 0 0 2]<br />
</td>
</tr>
<tr>
<td><0 1 0 0 0 4]<br />
</td>
</tr>
<tr>
<td><0 0 1 0 0 -2]<br />
</td>
<td><br />
</td>
<td><0 0 0 1 0 0]<br />
</td>
</tr>
<tr>
<td><0 0 0 0 1 0]<br />
</td>
</tr>
</table>
<br />
Edos: 7, 12, 15, 19, 26, 34, 41, 46, 53, 72, 87, 121, 140, 159, 193, 212, 299, 333</body></html>