- Guy Oldham,
- Murray Campbell
- and Clive Greated
Sets of musical notes whose frequencies are related by simple whole number ratios. A harmonic series is a set of frequencies which are successive integer multiples of the fundamental (or first harmonic). For example, the set of frequencies 100, 200, 300, 400, 500 Hz … is a harmonic series whose fundamental is 100 Hz and whose fifth harmonic is 500 Hz. In general, the nth harmonic of a series has a frequency which is n times the fundamental frequency.
The importance of harmonics in various branches of music theory and practice derives ultimately from the way in which sound is perceived by the human ear and brain. The pressure fluctuations at the eardrum of a listener, which give rise to the sensation of sound (musical or otherwise), normally have a complex pattern or waveform. In 1822 the French mathematician Fourier showed that any waveform, however complex, could be decomposed into a set of simple sine wave components. If the waveform is periodic, corresponding to a regularly repeating pattern of pressure variation, then its sine wave components are members of a harmonic series. In this case it is difficult to perceive the components separately; they are fused into a single sound with a definite musical pitch. In contrast, a sound which has a set of components which are not harmonics (or close approximations to harmonics) will not normally be perceived as having a clear pitch, and the components can be heard separately. The pitch associated with a harmonic series is that of the fundamental or first harmonic; the frequency spectrum, which describes the relative strengths of the frequency components, helps to determine the timbre of the note, with an increase in the strength of upper harmonics giving an increased brightness to the sound....