The definition of music as “sound” wrongly suggests that music, like all natural phenomena, adheres to the laws of nature. In this case, the laws would be the acoustical patterns of sound such as the (harmonic) relationships in the structure of the dominant tones, which determine the timbre. This is an idea that has preoccupied primarily the mathematically oriented music scientists, from Pythagoras to Hermann von Helmholtz.
The first, and oldest, of these scientists, Pythagoras, observed, for example, that “beautiful” consonant intervals consist of simple frequency relationships (such as 2:3 or 3:4). Several centuries later, Galileo Galilei wrote that complex frequency relationships only “tormented” the eardrum.
But, for all their wisdom, Pythagoras, Galilei, and like-minded thinkers got it wrong. In music, the “beautiful,” so-called “whole-number” frequency relationships rarely occur—in fact, only when a composer dictates them. The composer often even has to have special instruments built to achieve them, as American composer Harry Partch did in the twentieth century.