Validation of a descriptor, the “sum function", related to “quality” and derived from the input impedance of wind instruments

Abstract

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.