Development of Bore Reconstruction Techniques Applied to the Study of Brass Wind Instruments
Hendrie, Darren Alexander
The acoustic impedance is a valuable parameter in musical acoustics. Information contained within this frequency-domain parameter can be used to determine the acoustical behaviour of a musical wind instrument: the notes at which the instrument will play; the ease with which a particular note can be played; and the timbre of the instrument. The time-domain version of acoustic impedance - the input impulse response - gives us information on how sound waves propagate within an instrument under playing conditions and how sound is radiated from the open end or from other holes in the bore. Acoustic impedance data can also be used to calculate an accurate profile of the internal structure of the instrument - referred to as a bore reconstruction. This is very useful as the main bore is usually coiled and difficult to measure mechanically. An accurate reconstruction, however, is only possible if the impedance is measured over a large range of frequencies, typically of the order of tens of hertz up to many kilohertz. The bulk of this work follows on from research where the impedance of a short, closed, cylindrically-symmetric tube has been measured experimentally at high frequencies - 1 kHz up to 20 kHz - and compared with theory. The technique used is known as the Two-Microphone-Four-Calibration system, or TMFC system: two microphones are used to monitor the air pressure in the system, and measurement of four closed tubes of different length are required for calibration. The TMFC system has been modified so that impedance data far below 1 kHz (down to 10 Hz) can be attained for a full instrument as well as instrument components - for example trombone mouthpieces or French horn crooks. Suitable algorithms have been developed for processing the impedance data. Obtaining large bandwidth impedance data has allowed the possibility of accurate reconstructions of an instrument's internal profile. The results are compared with plane-wave theoretical models, which are derived in detail, and other well-documented methods of bore and impedance analysis: the acoustic pulse reflectometer (APR), and the brass instrument analysis system (BIAS). An in-depth discussion and analysis of the TMFC results for test objects and instruments of various lengths are presented. Simulations, whereby bore profiles are artificially altered, and a post-processing method utilising transmission matrix theory (TMT), are explored. A variety of orchestral French horn crooks dating from as early as the 18th-Century have been measured using APR and TMFC. A comparison is made between the capabilities of the two systems. Conclusions - of interest from a historical and manufacturing perspective - are drawn. The BIAS has been used to investigate how changes to the bore profile affect the behaviour of trumpets. The impedance of the trumpet is measured using a variety of leadpipes and mouthpieces.