The dual influence of the reed resonance frequency and tonehole lattice cutoff frequency on sound production and radiation of a clarinet-like instrument

Abstract

The internal and external spectra of woodwind reed instruments are partially determined by the tonehole lattice cutoff and reed resonance frequencies. Because they can impact the spectrum in similar ways, a study of one without accounting for the other risks incomplete or false conclusions. Here, the dual effects of the cutoff and reed resonance frequencies are investigated using digital synthesis with clarinet-like academic resonators. It is shown that the odd and even harmonics have similar amplitudes at and above the cutoff frequency or reed resonance frequency, whichever is lowest. However, because the resonators radiate efficiently at the cutoff, it has the additional role of reinforcing the amplitude of both the odd and even harmonics in the external spectrum. The spectra are analyzed using the single value descriptors playing frequency, spectral centroid (SC), odd/even ratio (OER), and brightness as a function of the musician mouth pressure. Higher reed resonances correspond to higher values for all descriptors. The OER and brightness increase with resonator cutoff frequency, whereas the SC exhibits more complicated trends. The reed resonance has a larger impact on the “playing condition oscillation threshold,” implying that it may have a more important role in sustaining auto-oscillation.