How can we deduce playing frequencies from measured resonance frequencies for trumpets?

Abstract

Lip-type valve (“striking outwards” type) is responsible for sound production for brass instruments. The operation of the valve is controlled by feedback from a passive resonator. The purpose of this study is to compare experimentally how far the resonance frequencies of instrument, taken from their input impedance (which does not involve the intervention of the player's lips) are able to give informations about the playing frequencies. A family of three trumpets made from a basic instrument for which the lead pipe will be slightly modified for each model, were considered for the experiment. Four expert musicians were asked to play the first five playable notes, for four different fingerings and for three nuances. This exercise was repeated three times. All these notes allow to make a quantitative assessment of the relation between the resonance frequencies and the playing frequencies, using in particular statistical methods. Several results will be presented: the influence of the player on the overall intonation, the effect of nuances on the pitch and the relation between small changes of geometry and playing frequencies. Functions made from the input impedance, such as the « sum function » proposed by Wogram, do not bring more relevant informations than the input impedance itself.