QUALITY
If A above middle C is played on a violin, a piano, and a tuning fork, all at the same volume, the tones are identical in frequency and amplitude, but different in quality. Of these three sources, the simplest tone is produced by the tuning fork; the sound in this case consists almost entirely of vibrations having frequencies of 440 Hz. Because of the acoustical properties of the ear and the resonance properties of the ear's vibrating membrane (ear drum or tympanic membrane), however, it is doubtful that a pure tone reaches the inner hearing mechanism in an unmodified form. The principal component of the note produced by the piano or violin also has a frequency of 440 Hz, but these notes also contain components with frequencies that are exact multiples of 440, called overtones, at 880, 1320, and 1760 Hz, for example. The exact intensity of these other components, which are called harmonics (i.e., formant frequencies or formants), determines the quality, or timbre, of the note. The technical term "harmonics" refers to a series of subsidiary vibrations that accompany a primary, or fundamental (i.e., wave-motion) vibration.
Harmonics are most notably observed 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 tone (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 Western tuning system. 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 upward. Unvalved brass instruments, such as the bugle, produce only the tones 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 tones. The harmonics of string players are flutelike tones produced when they cause the string to vibrate solely in halves (or thirds, and so on). Harmonics are a specialized class of overtones; vibrating membranes and solids, such as bells, produce complex partials that lie outside the harmonic series.
