Spectrum transformation properties of the clarinet and saxophone
Douglas H. Keefe, A. H. Benade · The Journal of the Acoustical Society of America · 1980
The spectrum transformation function T mr(f) transforms the mouthpiece pressure spectrum into the room-averaged spectrum. One part of T mr is T1(f), proportional to the pressure ratio p1/p0 between the first open tone hole and the mouthpiece. T1(f) is measurable in a lab setup or in a playing experiment. We measured T1(f) at harmonics of the playing frequency f0, with T1(f0) normalized to unity. Odd harmonics of the clarinet's written B♭3, T1(f) = (f/f0)1.25 for 1 ⩽ f/f0 ⩽ 7 and T1(f) = 10 for 7 < f/f0 < 10. By chance, even harmonics show similar behavior in the lower range. They are very irregular above. For the alto sax written G4, T1(f) = [1 + 0.4(f/f0 − 1)2.8] for 1 ⩽ f/f0 ⩽ 4. There is an unexplained discrepancy between lab and played T1(f) for, 4 < f/f0 ⩽ 10. In the lab T1(f) = 10, played T1(f) = 0.024(f/f0)2.4. Throughout all experiments the break in functional form is associated with the tone hole cutoff frequency fc. For the clarinet note fc ≃ 7f0, for the sax note fc ≃ 3.7f0. [Work supported by NSF.]