Flute acoustics: measurement, modelling and design

Abstract

A well-made flute is always a compromise and the job of flute makers is to achieve a musically and aesthetically satisfying compromise; a task that involves much trial and-error. The practical aim of this thesis is to develop a mathematical model of the flute and a computer program that assists in the flute design process.

Many musical qualities of a woodwind instrument may be calculated from the acoustic impedance spectrum of the instrument. A technique for fast and accurate measurement of this quantity is developed. The technique is based on the multiple-microphone technique, and uses resonance-free impedance loads to calibrate the system and spectral shaping to improve the precision at impedance extrema. The impedance spectra of the flute and clarinet are measured over a wide range of fingerings, yielding a comprehensive and accurate database. The impedance properties of single finger holes are measured using a related technique, and fitformulae are derived for the length corrections of closed finger holes for a typical range of hole sizes and lengths.

The bore surface of wooden instruments can change over time with playing and this can affect the acoustic impedance, and therefore the playing quality. Such changes in acoustic impedance are explored using wooden test pipes. To account for the effect of a typical player on flute tuning, an empirical correction is determined from the measured tuning of both modern and classical flutes as played by several professional and semi-professional players. By combining the measured impedance database with the player effects and various results in the literature a mathematical model of the input impedance of flutes is developed and implemented in command-line programs written in the software language C.

A user-friendly graphical interface is created using the flute impedance model for the purposes of flute acoustical design and analysis. The program calculates the tuning and other acoustical properties for any given geometry. The program is applied to a modern flute and a classical flute. The capabilities and limitations of the software are thereby illustrated and possible contributions of the program to contemporary flute design are explored.