Canonical extension: Difference between revisions
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(The page is marked as problematic because the definition of naturalness needs to be made more rigorous) | (The page is marked as problematic because the definition of naturalness needs to be made more rigorous) | ||
Let ''T'' be a regular temperament on JI group ''G''. A [[strong extension]] ''U'' of ''T'', on a JI group ''H'' of one rank higher than ''G'' is '''natural''' if the commas tempered out by ''T'' induces the presence of the added basis element of ''H''. A strong extension is | Let ''T'' be a regular temperament on JI group ''G''. A [[strong extension]] ''U'' of ''T'', on a JI group ''H'' of one rank higher than ''G'' is '''natural''' if the commas tempered out by ''T'' induces the presence of the added basis element of ''H''. A strong extension is (less formally) '''canonical''' if it is agreed that it is an efficient (accurate and low-complexity) extension. | ||
Revision as of 01:45, 4 February 2026
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This is a technical or mathematical page. While the subject may be of some relevance to music, the page treats the subject in technical language.
(The page is marked as problematic because the definition of naturalness needs to be made more rigorous)
Let T be a regular temperament on JI group G. A strong extension U of T, on a JI group H of one rank higher than G is natural if the commas tempered out by T induces the presence of the added basis element of H. A strong extension is (less formally) canonical if it is agreed that it is an efficient (accurate and low-complexity) extension.
