A study of the acoustical properties of the clarinet in order to predict playing frequencies

The modern clarinet has been in use for nearly 100 years, however, there remains much concerning the physics of the instrument that researchers have yet to understand. One of the more important aspects of the instrument that concerns musicians, is the quality of the instrument. There are many aspects of this study of instrument quality that could be subjective. This dissertation takes a step towards an objective acoustical quality marker of the clarinet by focusing on analytical predictions of playing frequencies given certain variable inputs such as blowing pressure and reed opening at rest. This research offers a study of this acoustical property by means of simplified mathematical formulas, numerical simulations, and experimental methods in order to create tuning maps of the clarinet over a normal range of playing parameters.;The dissertation begins by offering an introduction to the concept of impedance as perhaps the most important and applicable concept in musical instrument acoustics. In this work, the resonance frequencies of the instrument provide a basis for all playing frequency predictions and these resonance frequencies are found by analyzing the measured input impedance. The dissertation then describes the analytical methods for predicting playing frequencies by considering changes from the instrument's resonance frequencies due to a number of fairly complicated effects including: reed induced flow, reed dynamics, instrument inharmonicity, and a player introduced temperature gradient. Numerical prediction methods are also described in order to provide a benchmark for the newly defined analytical formulas. Next, experimental validation methods and preliminary data are detailed in which an artificial mouth and instrumented mouthpiece were used to create tuning maps in order to further test the bounds of the analytical formulas. Finally, tuning maps are created using the simplified analytical formulas. These tuning maps can show, for all combinations of possible blowing pressures and reed openings, the resulting clarinet playing frequencies. These tuning maps could eventually give musicians and instrument makers fast, reliable, and perhaps more importantly, objective information about the quality of their clarinets.