The Relationship Between Bore Resonance Frequencies and Playing Frequencies in Trumpets

The aim of this work is to study experimentally the relationship between the resonance frequencies of the trumpet, extracted from its input impedance, and the playing frequencies of notes, as played by musicians. Three different trumpets have been used for the experiment, obtained by changing only the leadpipe of the same instrument. After a measurement of the input impedance of these trumpets, four musicians were asked to play the first five regimes of the instrument, for four different fingerings. This was done for three dynamic levels and repeated three times. Statistical methods were implemented to assess the variability in the playing frequencies, and to study quantitatively their relationships with the bore resonance frequencies. A limited influence of the musician on the instrument overall intonation is observed, as well as a weak influence of the dynamic levels on the pitch of the notes. The results show that for most of the regimes, variations of the resonance frequency lead to same order variations of the playing frequency of the corresponding note. We noticed also that the sum function, derived from the input impedance, does not give a better prediction of the playing frequency than the input impedance itself.