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Analysis and Synthesis of Cornet Tones Using Nonlinear Interharmonic Relationships

Instantaneous levels (in decibels) of the harmonics of cornet tones are plotted as functions of the first-harmonic (fundamental) level. The resulting graphs are called nonlinear-interharmonic-relationship (NIHR) graphs. Smooth, nearly one-to-one (isomorphic) NIHR graphs result for the same played pitch, regardless of dynamic level, even when the attack and decay data of the tones are included. Therefore it is possible to synthesize cornet tones which sound very close to the originals by using the original first-harmonic envelope to generate several other harmonics (up to 16) by means of least-square polynomial approximations to the original NIHR curves. Simplified linear approximations which relate harmonic levels allow for a comparison of -offset- and -slope- parameters, and it is found that both offsets and slopes generally increase monotonically according to an orderly relationship with the harmonic number. The author suspects that the perceived -brassy- character of the cornet tones is due in large part to the types of nonlinear relationships which exist between their harmonic levels. This suspicion is strengthened by recently developed techniques of acoustical analysis and by brass tone synthesis by other researchers and by professional musicians utilizing electronic music synthesizers.


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