A detailed study of the impedances of mouthpieces, flared bells, and curved pipes in brass instruments

The input impedance of a brass instrument provides information about quality and playing characteristics, such as intonation and response. Modeling the input impedance of an instrument with the transfer matrix and finite element methods based on its geometry is useful, as the calculations can be performed without a physical prototype. Previous work has determined that both the transfer matrix and finite element methods can determine the properties of the impedances of mouthpieces and flaring bells. These results will be more closely examined and compared with regard to relative peak locations. At present, the transfer matrix method can only be used for conical or cylindrical segments along a straight axis, so it is useful to add curvature as a parameter of the calculation. An adaptation to the transfer matrix calculation for curved pipes will be presented. Transfer matrix and finite element calculations will be compared with each other and with impedance measurements. The ultimate goal of this work is to accurately calculate the input impedance of a realistic brass instrument, with curved pipes, valves, water keys, and slides. This will allow for improvement of existing instruments and development of new instruments and instrument parts exhibiting particular acoustical characteristics.