Harmonics

Harmonics, series of subsidiary vibrations that accompany a primary, or fundamental, wave-motion vibration, most notably in musical instruments. They result when the vibrating body, for example, a stretched string or an enclosed air column, vibrates simultaneously as a whole and in equal parts (halves, thirds, fourths, and so on), producing wave frequencies that are in simple ratios with the fundamental frequency (2:1, 3:1, 4:1, and so on). In musical sound the full-length vibration produces the fundamental note (or first harmonic or first partial), which is usually perceived as the basic pitch of the musical sound. The subsidiary vibrations produce faint overtones (second and higher harmonics or partials). As the series progresses, the vibrating segments become smaller, the frequencies higher, and the musical pitches closer together. The harmonic series for the tone C is given in the accompanying notation; black notes show pitches that do not correspond exactly with the standard Western tuning system known as equal temperament. Harmonics contribute to the ear's perception of the quality, or timbre, of a sound: On a flute, certain harmonics of the series are most prominent; on a clarinet, others.

In “overblowing” a wind instrument, the player isolates and makes predominant one of the higher harmonics, thus extending the range of the instrument upwards. Unvalved brass instruments, such as the bugle, produce only the notes of the harmonic series; the valves of the trumpet and the slide of a trombone add extra tubing, giving the player a new fundamental wavelength with a new harmonic series; the instrument can thus produce more notes. The harmonics of string players are flutelike tones produced when they cause the string to vibrate solely in halves (or thirds, and so on). Vibrating membranes and solids, such as bells, produce complex partials that lie outside the harmonic series.