All the sounds can break up into a series of harmonics, in a rational or irrational relationship with the fundamental frequency. The whole of these harmonic or inharmonic frequencies represents the sound spectrum . The musical sounds have a harmonic spectral decomposition, where each frequency Harmonique is a multiple entirety of the fundamental frequency.

The discovery of this spectral decomposition goes back to the 19th century, and its study improved much.

Intellectual instruments

In 1822, the decomposition of periodic functions of the baron Joseph Fourier (1768-1830) provided the mathematical tool for decomposition of the complex vibratory phenomena. This technique indeed brings a mathematical modeling which replaces a function single, difficult to write mathematically, by a series much more handy of functions sine and cosine. But the decomposition of Fourier is limited to a finite series, and although mathematically validated by the operators whom it introduces, it is however only one approximation of reality, because all the sinusoids present in the analysis vary there like vibrations limited in their duration and their number. To however try to represent the real sounds as sums of sinusoidal waves energy of infinite of passed to that of the future, can be only one mathematical artifice; the decomposition of Fourier gives only one instantaneous where one would need a film.

Instruments of experimentation

Thanks to electronics, this purely intellectual construction and eminently rationalisatrice, were going to become an experimental conceptualization of first order while falling under the temporal evolution. One did not have yet of the “film”, but already instantaneous most precise, which was not only any more one fantastic notion.

Ernst Chladni has, by studying the propagation of the sound in the solids, provided since 1787 with its “Klangsbilder”, an image correct, but fixed, sound vibrations; starting from the distribution in the course of vibratory shock of a heap of sand on metal plates, Chladni got an acoustic figure of the nodes and bellies of the Vibration.

In 1936 the Vocoder of Homer Dudley provides a tool of coding and transmission, and by there, an analysis - voice synthesis carries out (especially on the level of the vowels); but it sticks to a rather coarse representation Formant ic.

The Sonagraphe whose discovery goes back to the years 1940 was the most important instrument in the visualition of the decomposition of the sound spectrum. This instrument of visual transcription of sound “reality” has provides the elements of an experimentation Acoustique more aguerrie to the taking into account of temporal dimension.

See also

• harmonic Spectrum

• Harmonic
• Acoustic
• Acoustics musical