Er, all respects to your high-school physics teacher, but that what makes notes discordant is quite well known, and it has nothing to do with jangling air molecules! Or, at least they jangle pretty much the same way with any sound, and jangle quite well with no sound at all.

What makes a note sound "musical" is that its components are more or less equally spaced in frequency (how close they need to be depends at least partly on duration); in fact, this has to be true to some degree for the ear to perceive a definite pitch for the sound as a whole. What makes it consonant (not dissonant) with another note is that none of its components and hetrodyne frequencies beat with any of the components and hetrodyne frequencies of the other note. This more or less happens when the fundamental frequencies have certain small integer ratios, as a previous poster said. This is *why* those ratios sound good.

Said more simply, a musical note contains a whole array of frequencies, and more are generated inside the ear. Your ear likes it (hears them as consonant) if the frequencies from two different notes are either the same or far away from each other, and it dislikes it whenever two of them fall very close, but not quite, together. Think of the beating sound of two strings when you tune a guitar. If a lot of the component frequencies are all doing that at the same time, and all at different beat frequencies, the notes sound very dissonant together. That might even be good, if say we're talking about blues and the two dissonant notes are the minor and the major thirds. That is a matter of artistic choice and learned preference. But the degree of consonance or dissonance is not, or at least not only learned.

This is actually even why single notes need to have (very close to) evenly spaced components to sound musical; your ear generates equally-spaced hetrodyne frequencies for each of the original components, and if the original components are evenly spaced the new components the ear generates fall right on top of them. If they are not evenly spaced, they will probably beat like mad with the internally generated frequencies.

These rules aren't really true for very brief sounds--percussion instruments do just fine without evenly spaced components. But the longer the duration, the more discriminating the ear is about the harmonic structure.

Dustin