Minkowski reduced bases for Fokker groups of certain vals

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This revision was by author genewardsmith and made on 2012-03-08 13:05:46 UTC.
The original revision id was 309119184.
The revision comment was:

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Original Wikitext content:

For some purposes, eg Fokker blocks, it is convenient to have a good basis for the wedgies of rank two temperaments supported by a given val. Below are listed some Minkowski reduced bases relative to [[generator complexity]] as a metric, with TE complexity used to break any ties.

=5-limit=

<12 19 28|: <<1 4 4||, <<3 0 -7||

<15 24 35|: <<3 0 -7||, <<3 5 1||

<17 27 39|: <<2 1 -3||, <<1 9 12||

<17 27 40|: <<1 4 4||, <<4 -1 -11||

<19 30 44|: <<1 4 4||, <<5 1 -10||

<22 35 51|: <<3 5 1||, <<2 -4 -11||

<31 49 72|: <<1 4 4||, <<8 1 -17||

<34 54 79|: <<2 -4 -11||, <<6 5 -6||

<41 65 95|: <<5 1 -10||, <<4 9 5||

<46 73 107|: <<2 -4 -11||, <<7 9 -2||

<53 84 123|: <<6 5 -6||, <<1 -8 -15||

Original HTML content:

<html><head><title>Minkowski reduced bases for Fokker groups of certain vals</title></head><body>For some purposes, eg Fokker blocks, it is convenient to have a good basis for the wedgies of rank two temperaments supported by a given val. Below are listed some Minkowski reduced bases relative to <a class="wiki_link" href="/generator%20complexity">generator complexity</a> as a metric, with TE complexity used to break any ties.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x5-limit"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit</h1>
<br />
&lt;12 19 28|: &lt;&lt;1 4 4||, &lt;&lt;3 0 -7||<br />
<br />
&lt;15 24 35|: &lt;&lt;3 0 -7||, &lt;&lt;3 5 1||<br />
<br />
&lt;17 27 39|: &lt;&lt;2 1 -3||, &lt;&lt;1 9 12||<br />
<br />
&lt;17 27 40|: &lt;&lt;1 4 4||, &lt;&lt;4 -1 -11||<br />
<br />
&lt;19 30 44|: &lt;&lt;1 4 4||, &lt;&lt;5 1 -10||<br />
<br />
&lt;22 35 51|: &lt;&lt;3 5 1||, &lt;&lt;2 -4 -11||<br />
<br />
&lt;31 49 72|: &lt;&lt;1 4 4||, &lt;&lt;8 1 -17||<br />
<br />
&lt;34 54 79|: &lt;&lt;2 -4 -11||, &lt;&lt;6 5 -6||<br />
<br />
&lt;41 65 95|: &lt;&lt;5 1 -10||, &lt;&lt;4 9 5||<br />
<br />
&lt;46 73 107|: &lt;&lt;2 -4 -11||, &lt;&lt;7 9 -2||<br />
<br />
&lt;53 84 123|: &lt;&lt;6 5 -6||, &lt;&lt;1 -8 -15||</body></html>
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