Lec 17 MIT 18.03 Differential Equations, Spring 2006
I'd like to talk. Thank you. One of the things I'd like to give a little insight into today is the mathematical basis for hearing. For example, if a musical tone, a pure musical tone would consist of a pure oscillation in terms of the vibration of the air. It would be a pure oscillation. So, [SINGS], and if you superimpose upon that, suppose you sing a triad, [SINGS], those are three tones. Each has its own period of oscillation, and then another one, which is the top one, which is even faster. The higher it is, the faster the thing. Anyway, what you hear, then, is the sum of those things. So, C plus E plus G, let's say, what you hear is the wave form. It's periodics, still, but it's a mess. I don't know, I can't draw it. So, this is periodic, but a mess, some sort of mess. Now, of course, if you hear the three tones together, most people, if they are not tone deaf, anyway, can hear the three tones that make up that. So, in other words, if this...