Our ideas about music and Harmony have for the longest time been dominated by Pythagoras' philosophy: Harmony is number. The problem with this philosophy is not that it is wrong, but that it is hopelessly narrow. Any deeper dwelling on the nature of music - of its meaning, its inner-workings, its relation to our existence - is restricted to the realm of number mysticism. Even the greatest philsophers turn shallow whenever they attempt to incorporate music into their writings (See Schopenhauer, Montaigne, Spengler, etc.). Watch how, the moment the topic of music comes up, they all suddenly and bizarrely transform into insipid Pythagoreans.

The notion that "Harmony is number" really says nothing at all about the nature of Harmony, other than the fact that it is measurable, but it gives one the impression that he understands it. Its an idea that appeals to the learned pedant, the dork who thinks that because he has measured something out that he has a good idea of what it is. "This scale is composed of the ratios 2/1, 15/8, 5/3, 3/2, 4/3, and 9/8" says the music theorist, and he smiles as if he has unraveled all the secrets of music. But it is nothing. One does not "get" Mozart's mass in C minor by reducing it to a set of mathematical proportions; in fact, he maybe understands it less.