## Spectrum |

The frequency content of a sound or audio signal, often displayed as a graphic representation of amplitude (or intensity level) against frequency. Three-dimensional displays of a spectrum add the time variation on the third axis (see below). The spectrum of a sound is a primary determinant of its perceived timbre.

A partial spectrum consists of discrete
frequencies known as overtones, harmonics or inharmonics.
A
*continuous spectrum* consists of noise
components. The spectrum of a sound may be determined by a sound analyser or by Fourier analysis and is distributed
over the audible range (20 to 20,000 Hz). A partial spectrum is also
known as a *line spectrum,* where discrete frequencies are
present. A continuous spectrum, on the other hand, shows frequencies
continuously distributed over the audible range.

See: diagrams under Broad Band Noise, Fourier Analysis, Infrasonic, Spectrograph, White Noise.

Analyzing the spectrum of a sound is a way of understanding its
behaviour in the *frequency domain,* as opposed to its behaviour
in the *time domain,* according to its waveform
or envelope. The auditory system is
designed to balance the simultaneous resolution of detail in both
domains, as expressed by the law of
uncertainty.

The *spectral envelope* refers to the contour or shape of the
spectrum, particularly when it shows the maximum strength of each
frequency component during the sound.

The spectrum of a sound may be altered electronically by filtering or equalization.

Spectrum may also refer to a range of
frequencies, as in the *audio spectrum* (see audio frequency) or the radio spectrum.

The first 32 partials of a harmonic series shown as a line spectrum. The amplitude of each partial is inversely proportional to the partial number.

Line spectrum of the partials of a viola string, omitting their time variation.

Third-octave spectrum of the Salvatore Mundi bell, Salzburg. Peak intensities occur in the frequency bands centred on 200, 315 and 630 Hz, with a fundamental about 80 Hz.

Salvatore Mundi.

Three-dimensional plot of a trumpet tone showing
the amplitude envelope of the first 20 harmonics. From J. Beauchamp
& A. Horner, "Synthesis of trumpet tones using a fixed wavetable
and a centroid-controlled second order filter," *Proceedings of the
1994 International Computer Music Conference,* used by permission of
the authors*.*