Regular temperament: Difference between revisions
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<span style="display: block; text-align: right;">Other languages: [[:de:Verallgemeinerte reguläre Temperatur|Deutsch]]</span> | <span style="display: block; text-align: right;">Other languages: [[:de:Verallgemeinerte reguläre Temperatur|Deutsch]]</span> | ||
{{See also| Tour of Regular Temperaments}} | |||
=Characterizing a regular temperament= | =Characterizing a regular temperament= | ||
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Grassmannians have the structure of a smooth, homogenous [http://en.wikipedia.org/wiki/Metric_space metric space], and hence represent a distinctly geometric mathematical object. In the 5-limit, the Grassmannian '''Gr'''(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. | Grassmannians have the structure of a smooth, homogenous [http://en.wikipedia.org/wiki/Metric_space metric space], and hence represent a distinctly geometric mathematical object. In the 5-limit, the Grassmannian '''Gr'''(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. | ||
[[File:dualzoom.gif|alt=dualzoom.gif|dualzoom.gif]] | [[File:dualzoom.gif|alt=dualzoom.gif|dualzoom.gif]] | ||
= See also = | |||
* [[Tour of Regular Temperaments]] | |||
* [[Wikipedia: Regular temperament]] | |||
[[Category:Math]] | |||
[[Category:Temperament]] | [[Category:Temperament]] | ||
[[Category:Theory]] | [[Category:Theory]] | ||
[[Category:Todo:reduce mathslang]] | [[Category:Todo:reduce mathslang]] | ||