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A Method of Generating and Controlling Musical Asymmetrical Spectra

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Using a very simple modification of classical frequency modulation (FM), it is possible to control nicely the sideband asymmetry. The new synthesis formula creates an asymmetric spectrum generalizing the FM spectrum (r=1): : (formula-see printed page): : The mathematical formulas that generate new spectra are developed in detail, and several applications relevant to sound synthesis are carefully examined. A second synthesis formula has also been derived using modified Bessel functions of the first kind. The new algorithms meet satisfactorily the acoustic requirements necessary to generate formants, to control reflected side frequencies, and to achieve selective filtering.

JAES Volume 36 Issue 9 pp. 671-685; September 1988
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AES - Audio Engineering Society