Regular temperament: Difference between revisions

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=Characterizing an abstract regular temperament=  

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  An &lt;em&gt;abstract regular temperament&lt;/em&gt; is a &lt;a class="wiki_link" href="/regular%20temperament"&gt;regular temperament&lt;/a&gt; considered apart from any consideration of tuning, which classifies all of its tunings as tunings of the single abstract temperament. Various methods have been proposed for uniquely characterizing an abstract regular temperament. Among these are&lt;br /&gt;

Grassmannians have the structure of a smooth, homogenous &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Metric_space" rel="nofollow"&gt;metric space&lt;/a&gt;, and hence represent a distinctly geometric mathematical object. In the 5-limit, the Grassmannian &lt;strong&gt;Gr&lt;/strong&gt;(2, 3), consisting of the planes through the origin in three dimensional space, may be identified with the projective plane, and hence 5-limit rank two temperaments may be pictured as points in a projective plane, as below.&lt;br /&gt;

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