Gradus suavitatis: Difference between revisions
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The '''gradus suavitatis''', 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]] | |||
Revision as of 16:46, 19 June 2025
The gradus suavitatis, 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.