Spectrogramm of a Risset's bell sound, showing the 11 basic sounds included inside it.
Risset's bell modelling
Music is an art that has alwoays been numerical, since it has always used numbers.
Jean-Claude Risset (1938-2016) both a composer and a researcher has imagined new ways of investigation into sound that transformed music composition thanks to computerized processes that appeared during the 20th century. In his catalogue of sounds synthetizezd by computer released in 1969, Risset put the emphasis on the understanding, the modelling and the synthses of complex sounds. New technologies that appeared in the 1960s enabled to measure the components inside sounds and to give mathematical and physical modelling of them.
Risset proposes a first model of a bell sound as a sum of 11 basic sounds, that are sinusoids with frequencies (in Herz, Hz) from the bass to the treble register that are not regularly spread: it is an inharmonic sound.
One can notice that sounds # 1 and 2, as well as sounds # 3 and 4 are nearly the same: it is their overlapping that produces a beat that is characteristic of the bell, a slow variation of sound amplitude in the bass register that can be heard during the resonance.
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