This is, wait, Eb can't be approximated in rational values at all, um.Īnd if you just have sine waves, rather than sawtooth or whatnot, they consist of a single partial so there's never any overlap - you're back to the pythagorean square 1. Now consider Eb, a minor 3 and also consonant. Now consider E, a major 3 and also considered highly consonant. That's pretty thin gruel given how fast these partials drop of in amplitude (for a sawtooth, a partial at xf drops off as 1/x) G, at a perfect fifth, is 3/2 the frequency of C. Harmonic sounds have partials at f, 2f, 3f, 4f, and so on. But it always has seemed the existing theory regarding consonance and partials is half baked at best. I believe that consonance probably has something to do with partial relationships. I've always had problems with existing consonance theories along these lines, probably out of ignorance. The overtones of several of these sounds will match when their fundamental frequencies are related by simple whole-number ratios. > Most Western instruments produce “harmonic” sounds that, when analyzed as Fourier described, have relatively strong lower overtones f, 2f, 3f, 4f. plenty of professionals are experts at something without being able to describe it perfectly in words but that doesn't mean that they don't understand the distinction when using them in musical contexts, or that the distinction is not meaningful. You are, of course, correct that many very competent musicians would not correctly name this distinction using the official theory terms. in other words, it's not just when writing them out in english that we treat those two intervals differently - we treat them differently while using them during music You would build different chords around them, you would play different melodies around them, etc. Or, perhaps to keep it within the artistic sphere, they're like and other "same color" illusions - they are technically the same, but taken in context they signify different things. The reason they are named differently and are notated differently is that they serve different functions.
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