Brass instruments as a cascade of two-port networks: Transfer functions, chain parameters, and power efficiency in theory and practice.

This paper investigates how two-port network theory as a means for system identification can be applied to the analysis of brass instruments. A special focus is placed on the energy conversion efficiency as this is limited by inner damping, which receives much attention by expert players and makers of brasses. Theory suggests that a reconstruction of the 2 × 2 matrix representing the network requires input impedance and transfer function for two different boundary conditions. Besides the normal case of free sound radiation, instruments are also analyzed with the bell closed by a spherical cap. For this purpose, a customized 3D-printed spherical cap was fabricated and attached to the bell. Four measured spectra and the passivity condition over-determine the set of system equations. It is shown how to take advantage of this freedom when analyzing wind instruments. Measurements and simulations of a trumpet and a trombone are presented and compared.

Detection of time-varying harmonic amplitude alterations due to spectral interpolations between musical instrument tones.

Gradated spectral interpolations between musical instrument tone pairs were used to investigate discrimination as a function of time-averaged spectral difference. All possible nonidentical pairs taken from a collection of eight musical instrument sounds consisting of bassoon, clarinet, flute, horn, oboe, saxophone, trumpet, and violin were tested. For each pair, several tones were generated with different balances between the primary and secondary instruments, where the balance was fixed across the duration of each tone. Among primary instruments it was found that changes to horn and bassoon [corrected] were most easily discriminable, while changes to saxophone and trumpet timbres were least discriminable. Among secondary instruments, the clarinet had the strongest effect on discrimination, whereas the bassoon had the least effect. For primary instruments, strong negative correlations were found between discrimination and their spectral incoherences, suggesting that the presence of dynamic spectral variations tends to increase the difficulty of detecting time-varying alterations such as spectral interpolation.