User:Sintel/Validation of common consonance measures: Difference between revisions
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* The Wilson norm is the sum of prime factors (with repetition). That gives <math>\text{Wilson}\left(\tfrac{15}{8}\right) = 5 + 3 + 2 + 2 + 2 = 14</math>. | * The Wilson norm is the sum of prime factors (with repetition). That gives <math>\text{Wilson}\left(\tfrac{15}{8}\right) = 5 + 3 + 2 + 2 + 2 = 14</math>. | ||
I have also included Euler's ''gradus suavitatis'',<ref>Leonhard Euler (1739) ''Tentamen novae theoriae musicae'' (Attempt at a New Theory of Music), St. Petersburg.</ref> which is probably the first complexity measure historically. | I have also included Euler's ''[[gradus suavitatis]]'',<ref>Leonhard Euler (1739) ''Tentamen novae theoriae musicae'' (Attempt at a New Theory of Music), St. Petersburg.</ref> which is probably the first complexity measure historically. | ||
It is somewhat similar to the Wilson norm, in that it depends on the prime factorization. | It is somewhat similar to the Wilson norm, in that it depends on the prime factorization. | ||
Given ''s'', the sum of prime factors, and ''n'' the number of prime factors, Euler's gradus function is {{nowrap|''s'' - ''n'' + 1}}. | Given ''s'', the sum of prime factors, and ''n'' the number of prime factors, Euler's gradus function is {{nowrap|''s'' - ''n'' + 1}}. | ||