The saxophone spectrum Available to Purchase

The geometrical nature of the saxophone air column is outlined, along with a sketch of the theory of sound production and radiation of saxophones. The discussion is based upon a similar but somewhat more detailed discussion of the clarinet and its spectrum published recently by Benade and Kouzoupis [J. Acoust. Soc. Am. 83, 292–304 (1988)]. Room‐averaged spectra were measured for essentially all notes in the low and second registers of a B‐flat tenor and an E‐flat alto saxophone played at a mezzoforte level (so that the reed was beating steadily). It is shown that the observed spectra have a great regularity of pattern that is in good agreement with theoretical expectation. All amplitudes of spectral components of all notes fit the same spectrum envelope function, E(x)=[Nx/(1+x⁷)]^1/2. Here, N is a normalizing constant and x=f/f_b, where f_b is a break frequency characteristic of the instrument. This break frequency is closely related to the instrument’s tonehole lattice cutoff frequency f_c. In addition to the f^1/2 (3‐dB/oct) spectral rise below f_b and the 1/f³ fall (18 dB/oct) above f_b, we find one or more ‘‘spectral notches’’ in the envelope. These are associated with the fact that the reed is beating, and they may lie almost anywhere in the upper part of the spectrum. The values of f_b for the tenor and the alto saxophones are 618 and 837 Hz. These lie about a semitone below the break frequencies that would be calculated for such transposing instruments on the basis of the 1500‐Hz f_c that belongs to essentially all of the nontransposing soprano instruments. The systematic behavior of the spectrum when the instruments are played at a stronger or weaker dynamic level is also outlined and explained.