Tenney–Euclidean metrics: Difference between revisions
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== TE logflat badness == | == TE logflat badness == | ||
Given a matrix A whose rows are linearly independent vals defining a regular temperament, then the rank ''r'' of the temperament is the number of rows, which equals the number of linearly independent vals. The dimension of the temperament is the number of primes it covers; if ''p'' is the largest such prime, then the dimension ''n'' is π(''p''), the number of primes to ''p''. If we define S(A) to be the simple badness (relative error) of A, and C(A) to be the complexity of A, then '''logflat badness''' is defined by the formula | Given a matrix A whose rows are linearly independent vals defining a regular temperament, then the rank ''r'' of the temperament is the number of rows, which equals the number of linearly independent vals. The dimension of the temperament is the number of primes it covers; if ''p'' is the largest such prime, then the dimension ''n'' is π(''p''), the number of primes to ''p''. If we define S(A) to be the simple badness ([[relative error]]) of A, and C(A) to be the complexity of A, then '''logflat badness''' is defined by the formula | ||
<math>\displaystyle | <math>\displaystyle | ||