Harmonics and Overtones

A string or an air column, once set vibrating, reflects waves at its ends and can support stationary waves -- but only certain specific wavelengths (or, equivalently, frequencies) are actually possible, fixed by the system's own BOUNDARY CONDITIONS (essentially, where nodes and antinodes are forced to sit by the physical constraints at each end). These allowed frequencies are called the NATURAL FREQUENCIES of the system's NORMAL MODES of oscillation. The lowest of these natural frequencies is called the FUNDAMENTAL FREQUENCY (or FIRST HARMONIC), and its corresponding mode of vibration is the FUNDAMENTAL MODE (or fundamental tone). Any frequency higher than the fundamental that is actually PRESENT in the resulting sound is called an OVERTONE -- the first (lowest) such higher frequency is the FIRST OVERTONE, the next is the SECOND OVERTONE, and so on, always numbered in increasing order. An overtone is additionally termed a HARMONIC specifically when its frequency happens to be an exact integer multiple of the fundamental frequency; for both strings and air columns (as this chapter goes on to show), the overtones that actually occur ARE always integer multiples of the fundamental, so they can equally be called ha …