Spectral envelopes of orchestral instruments
A. H. Benade, Spyros Kouzoupis · The Journal of the Acoustical Society of America · 1985
Dependable techniques are available for the measurement of musical spectra. The oscillation and radiation dynamics of wind, bow, hammer, and plectrum excited instruments is well understood. Most of an instrument's dynamical system is shared by the production processes of all its notes, so that similar spectrum envelopes are expected for many notes in its scale. Measured spectra confirm the expectation, and show that these similarities are also shared by most instruments of the same playing range. Thus the notes of violin, piano, trumpet, oboe, and clarinet (odd partials) scales have envelopes caricatured by E0(f) = [1 + (f/fc)2β]−1/2, with β = 3 and fc = 1500 Hz. Corresponding alto instruments, e.g., English horn, alto sax, and alto clarinet, tend to have fc close to 1000 Hz, and β = 3. Several mechanisms, each with its own slope and breakpoint, combine in each instrument to produce its E(f), yet makers and players normally choose combinations that approximate E0(f). This suggests perceptual constraints on desirable tone color, e.g., via the “sharpness” integral of v. Bismarck, refined by Terhardt et al. Numerous measured envelopes will be presented, and discussed via their sharpness functions for treble, soprano, alto, and bass instruments. [Work supported by NSF.]