overtones

If I sit at the piano and play that low C, you may think you're hearing only that one tone—a dark, rich bass note—but you're not; you are simultaneously hearing a whole series of higher tones that are sounding at the same time. These are arranged in an order preordained by nature and ruled by universal physical laws . . . All these upper notes of which you may be unaware result from a phenomenon of nature whereby any sound-producing source, or I should say "pitch-producing source," such as that piano string, vibrates not only as the whole string, in all its whatever-inch glory, sounding that low C, but also in fractional segments of that string—each vibrating separately. It's as though the string were infinitely divisible, into two halves, into three thirds, four quarters, and so on. And the smaller those segments are, the faster they vibrate, producing higher and higher frequencies and therefore higher and higher tones—OVERtones. And these overtones, or harmonics, as they're also called, are all sounding together with the fundamental sound of the full string. This is the basic principle by which the entire harmonic series is generated, starting on any fundamental tone . . . Any note I strike will contain its own series of overtones, but the lower the note I strike, the more abundantly audible will be its harmonic series, which accounts in part for the comparative richness of that low C.

-- Leonard Bernstein The Unanswered Question