The overtone series occurs naturally in non-synthetic tone production. When a person sings, the overtone series is present above every pitch. When any woodwind, string, or brass instrument creates a pitch, the overtone series is present above every pitch. Perhaps even more importantly for our discussions, the mathematics behind creating the overtone series are not only fascinating, but also explain the fundamentals of Western harmony
To put it succinctly, the overtone series explains why music evolved as it did.