Temperament merging: Difference between revisions
Cmloegcmluin (talk | contribs) →Grade-deficiencies: give names for examples |
Cmloegcmluin (talk | contribs) GCF back to GCD, for better distention from "greatest factor", and it's more popular anyway |
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The greatest factor of this matrix is 2, because we can produce the row {{map|24 38 56}} as a coprime linear combination of its rows (that's {{map|5 8 12}} + {{map|19 30 44}}), and the entries of this row have a | The greatest factor of this matrix is 2, because we can produce the row {{map|24 38 56}} as a coprime linear combination of its rows (that's {{map|5 8 12}} + {{map|19 30 44}}), and the entries of this row have a GCD of 2, so in other words this matrix is 2-enfactored. If we merely normalize it (again, using the Hermite normal form), we receive: | ||
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which is a 2-enfactored meantone mapping, and it reveals the greatest factor as the | which is a 2-enfactored meantone mapping, and it reveals the greatest factor as the GCD of the second row. But if we fully canonicalize it (defactor, and normalize), then we get: | ||