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It's a pretty defensible claim on its own for one simple reason - overtones. A string, pipe, or other resonating component of a musical instrument, if it resonates at some frequency X, will also resonate at frequencies 2X, 3X, 4X, etc. (Picture a taut string: you can get a standing wave where the whole thing vibrates back and forth, or you can get a standing wave where there's a node in the middle and it looks like the left and right sides are vibrating in opposite directions, or you can get a standing wave where there are two nodes and three components, or so forth.) These frequencies are exact pitches in just intonation. Let's say that you play a C at octave 3. Its overtones are C at octave 4 (twice the pitch), G at octave 4 (3x the pitch, or 3/2 the pitch of C4), C at octave 5 (4x the pitch), E at octave 5 (5x the pitch, or 5/2 the pitch of C5). When you play a note on any instrument except a pure sine generator, there are natural overtones because of the construction of the instrument. A guitar or a piano basically introduces random noise into the string when you pluck/hammer it, and the standing waves stay around and resonate, producing the "bright" sound of these instruments from their overtones. If you play a chord on an instrument, the overtones of the various notes in the chord will line up - if you play a C3 major chord, both the C3 and the G3 have overtones at G4, both the C3 and the E3 have overtones at E5, etc. If you're playing an instrument in C-major just intonation, those notes will line up perfectly. (Moreover, for e.g. a piano with the sustain pedal down, the strings for those upper keys will resonate by receiving the vibrations in the air, even if you're not playing them!) If the instrument is in equal temperament, they won't exactly line up. That is perceptible, even if only slightly, to the non-musical listener. Of course, the tradeoff is that if you play a C# major chord on an instrument tuned to C major just intonation, they'll line up even worse than they would in equal temperament. Which is why "modern" instruments - which is to say, from at least around Bach's time - have avoided tuning to a just intonation. |