Generic spectrum envelope functions for orchestral wind instruments
A. H. Benade · The Journal of the Acoustical Society of America · 1986
The basic behavior of the room-average spectrum envelopes E(f) = M(f)T(f) of orchestral winds is describable via a limited number of functional forms, each with a breakpoint frequency parameter characteristic of the instrument itself. At the mezzoforte playing level the internal (mouthpiece) spectrum envelope comprises two factors, M and T1 for the nonclarinet woodwinds and brasses. For woodwinds, Mw (x) = sin (πx)/(πx)2, where x = f/fbreak, and for the brasses the coresponding function is M>b = (1/x) (1 + x2)1/2. The clarinet odd harmonics fit Mco = (1/x)/(1 + x4)1/2, while Mce = x/(1 + x8)1/2 for the evens. The function T1 = [(1 − x)2 + Bx2]1/2 depends on the mouthpiece cavity-and-constriction plus main bore entrance taper. T1 = 1 for clarinets. The transfer out to room-average spectra involves a tonehole based transfer function Th = x/(1 + x2)1/2 for nonclarinet woodwinds, and a bell-controlled function Tb = x3/2/(1 + x3)1/2 for the brasses. For the clarinet odd harmonics Tco = Th, while Tce = 1 for the even components. Playing-level modifications to the envelopes are similarly describable for the various instrumental types. Numerous illustrative examples will be presented. [Work supported by NSF.]