User:Sintel/Validation of common consonance measures: Difference between revisions
→Continuous extension of the Tenney norm: Note on k |
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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 | Given ''s'', the sum of prime factors, and ''n'' the number of prime factors, Euler's gradus function is {{nowrap|''s'' - ''n'' + 1}}. | ||
For example <math>\text{Gradus}\left(\tfrac{15}{8}\right) = 14 - 5 + 1 = 10</math>. | For example <math>\text{Gradus}\left(\tfrac{15}{8}\right) = 14 - 5 + 1 = 10</math>. | ||