Gradus suavitatis: Difference between revisions
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Created page with "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. == Definition == 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 <mat..." |
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The '''gradus suavitatis''' (Latin for ''degree of sweetness''), also known as '''Euler complexity''' is probably the first complexity measure historically.<ref>Leonhard Euler (1739) ''Tentamen novae theoriae musicae'' (Attempt at a New Theory of Music), St. Petersburg.</ref> | |||
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. | ||
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[[Category:Interval complexity measures]] | |||
Latest revision as of 16:55, 19 June 2025
The gradus suavitatis (Latin for degree of sweetness), also known as Euler complexity is probably the first complexity measure historically.[1] It is somewhat similar to the Wilson norm, in that it depends on the prime factorization.
Definition
Given s, the sum of prime factors, and n the number of prime factors, Euler's gradus function is s - n + 1. For example [math]\displaystyle{ \text{Gradus}\left(\tfrac{15}{8}\right) = 14 - 5 + 1 = 10 }[/math].
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- ↑ Leonhard Euler (1739) Tentamen novae theoriae musicae (Attempt at a New Theory of Music), St. Petersburg.