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A brief introduction to Regular Temperament Theory: Difference between revisions

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initial version, adapted from Facebook post on Dave's request
 
Dave Keenan (talk | contribs)
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Moved "Alternatively, you can avoid wedge products ..." to the 3rd footnote
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We can then institute computer searches to find optimum mappings, with our desired balance of error versus complexity. Many such searches have been done and [[Tour_of_Regular_Temperaments|many resulting temperaments named and catalogued]].
We can then institute computer searches to find optimum mappings, with our desired balance of error versus complexity. Many such searches have been done and [[Tour_of_Regular_Temperaments|many resulting temperaments named and catalogued]].
Alternatively, you can avoid wedge products, by agreeing on rules that determine a canonical set of generators. For example, the first generator alone should generate the lowest prime using a positive count. Then the first and second generators alone should generate the next prime using a positive count of the second generator, and so on. This is equivalent to requiring the mapping matrix to be in a certain form. I don't know if this form has a name. I note that an RT mapping matrix is never a square matrix (otherwise it would be JI).


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