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 ameasurement 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 wasd one 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. Alimited influence of the musician on the instrument overall intonation is observed, as well as aweak influence of the dynamic levels on the pitch of the notes. The results showthat for most of the regimes, variations of the resonance frequencylead to same order variations of the playing frequencyo ft he corresponding note. We noticed also that the sum function, derived from the input impedance, does not give ab etter prediction of the playing frequencyt han the input impedance itself.

The quality of a musical instrument embraces many aspects such as tuning, ease of play, tone, etc. This study aims to validate the use of the sum function (SF) proposed by Wogram from the measurement of input impedance as a descriptor of quality. This work is part of a wider project, PAFI (Aid Platform for Instrumental Making), supported by the French National Agency of Research. To validate the choice of the SF, we created a family of trumpets made from a basic instrument for which the leadpipe will be slightly modified for each model. The SF was calculated for a range of selected frequencies from the measurement of the input impedance of these different trumpets. The next step was to ask musicians experts to play these instruments, to measure the playing frequencies, and to note their feedback about quality. These tests were supplemented by comparative tests carried out this time with the help of a robotic artificial mouth. The final step involved was to try to identify correlations between the SF and the results of various tests and propose correction factors to be made to the formula of the SF, related to the nuance or range for example.