On the cutoff frequency of conical woodwind instruments
* Presenting author
Since Arthur Benade, the cutoff frequency of woodwind instruments is a well-known concept that is a result of the acoustic regularity of the tonehole lattice. The distinction between the global cutoff frequency and the local cutoff frequencies was recently introduced. The first one can be approximately defined from the input impedance curve, while the second are related to the different cells of the lattice and can be theoretically determined from their individual geometries. From the local cutoffs, it is possible to check the acoustic regularity of an instrument, as was done for the clarinet, even if the geometry is irregular. The present work aims at finding a generalization for conical instruments. The existence of a global cutoff is evident in the impedance curves of oboes, bassoons, and saxophones published by Benade. However, the existence of periodicity is not obvious for a conical geometry because the cells are a priori very different, due to the taper. The present work uses a change of variables to investigate an acoustic periodicity for conical resonators and, for the example of a saxophone, determines the local cutoffs, compared to the global one.