Whitney L. Coyle

Predicting playing frequencies for clarinets: A comparison between numerical simulations and simplified analytical formulas

When designing a wind instrument such as a clarinet, it can be useful to be able to predict the playing frequencies. This paper presents an analytical method to deduce these playing frequencies using the input impedance curve. Specifically there are two control parameters that have a significant influence on the playing frequency, the blowing pressure and reed opening. Four effects are known to alter the playing frequency and are examined separately: the flow rate due to the reed motion, the reed dynamics, the inharmonicity of the resonator, and the temperature gradient within the clarinet. The resulting playing frequencies for the first register of a particular professional level clarinet are found using the analytical formulas presented in this paper. The analytical predictions are then compared to numerically simulated results to validate the prediction accuracy. The main conclusion is that in general the playing frequency decreases above the oscillation threshold because of inharmonicity, then increases above the beating reed regime threshold because of the decrease of the flow rate effect.

Clarinet playing frequency predictions: Comparison between analytic and numerical simulations

The input impedance measurement can provide the resonance frequencies of an instrument and is a standard method used by wind instrument makers in designing modifications. For a complete design, it is necessary to know the playing frequencies themselves, which depend on several control parameters, such as the blowing pressure and reed opening and the input impedance. Using the values of these parameters, we can determine the playing frequencies. This research will analytically deduce these frequencies from the different control parameters and from the input impedance curve. Four effects are known to influence the playing frequency and are examined separately: the flow rate due to the reed motion, the reed dynamics, the inharmonicity of the resonator, and the temperature gradient in the clarinet. The results for a particular clarinet are given and compared to numerically simulated playing frequencies. Experimental methods are also presented and discussed.

Studying the clarinet with an artificial mouth: Comparison of playing frequencies between model and measurement

In the field of musical acoustics, instruments, such as the clarinet, are often played with the use of an artificial mouth or playing machine in order to objectively measure the playing characteristics such as sound levels, playing frequency, regime changes, etc. The purpose of this research was to study the tuning tendencies of the clarinet experimentally and compare this to the models found in literature. A clarinet was artificially blown to determine the playing frequencies for varying levels of blowing pressure and reed opening. These measurements could then be compared to computational models of the clarinet. The experimental results will be presented and compared with the theoretical values from past studies that predicted playing frequencies both analytically and computationally. Finally, suggestions for improving the models will be presented and discussed.In the field of musical acoustics, instruments, such as the clarinet, are often played with the use of an artificial mouth or playing machine in order to objectively measure the playing characteristics such as sound levels, playing frequency, regime changes, etc. The purpose of this research was to study the tuning tendencies of the clarinet experimentally and compare this to the models found in literature. A clarinet was artificially blown to determine the playing frequencies for varying levels of blowing pressure and reed opening. These measurements could then be compared to computational models of the clarinet. The experimental results will be presented and compared with the theoretical values from past studies that predicted playing frequencies both analytically and computationally. Finally, suggestions for improving the models will be presented and discussed.

Flow visualizations using electronic speckle pattern interferometry

Imaging air flow in and around a musical instrument is a difficult task, but it can be important for understanding the physics associated with sound production as well as verifying the accuracy of computer simulations. Particle image velocimetry (PIV) has been successfully used to image air flow, but it requires expensive equipment, extensive technical expertise, and sophisticated software. Furthermore, PIV is usually restricted to observing only a small area of the flow. As an alternative to PIV, we demonstrate a method based on electronic speckle pattern interferometry that allows large-area real-time imaging of air flow using minimal optical equipment.

Velocity analysis of the vacuum-driven clarinet reed

A vacuumed artificial mouth has been assembled and tested to measure reed velocity for a Bb clarinet along the width of the reed. Reed velocity measurements may be useful for better estimation of parameters in physical models, such as the relevant surface area of the vibrating reed. Use of a vacuum system instead of a pressurized mouth chamber allows straightforward observation and manipulation of the mouthpiece apparatus. Point measurements of reed velocity were obtained via a laser-Doppler vibrometer directed at the reed surface when artificially blown. Simultaneous high-speed exposures were recorded to visualize reed motion. Preliminary results indicate that the velocity amplitude of any torsional motion in the reed is negligible compared to an asymmetric reed velocity, likely caused by natural limitations of the clarinet ligature. Velocity measurements also indicate that the reed may sometimes rebound against the mouthpiece in its oscillatory period. High-speed exposures support this conclusion by vis...

The clarinet: Past, present, and future

The modern clarinet is the result of several hundreds of years of research and craftsmanship. This paper will discuss where the clarinet has been acoustically by studying some input impedance spectrum characteristics of historical instruments (the Baroque Chalumeau, 13-key, etc.). The paper will then present where we are at present—focusing on the same measurement information for a full Boehm system (multiple models of Bb clarinets) and a comparison of the modern French vs. German system clarinet. Finally, a few words will be given on the possible future of the instrument—where we are going, what are we doing to continue improving the instruments quality and playability.

From musical acoustics to outdoor sound and back

My musical acoustics student paper award was given in 2009 at ASA San Antonio after an NSF summer research experience at Coe College with Dr. James Cottingham. I was a junior at Murray State University in Kentucky studying the clarinet and mathematics. Though I was not the most qualified applicant, lacking the physics background necessary in this field, I had a passion for acoustics and wanted my future to go in this direction. This summer was my introduction to acoustics research and the reason I was able to continue in the field. Since, I have been attending Penn State in the Graduate Program in Acoustics and have earned my Masters in Acoustics focusing on outdoor sound propagation modeling and now, with the help of an NSF-GRFP, I have found my way back to musical acoustics—clarinet acoustics. Since the San Antonio ASA I have attended seven more ASA conferences, been the musical acoustics student council representative and am now the student council chair. I now split my time between Penn State and Marseille, France, at CNRS-LMA. This talk will detail each step along the path that retuned me to musical acoustics and give a look into my current research as well.

Descriptive maps to illustrate the quality of a clarinet

Generally, subjective opinions and decisions are made when judging the quality of musical instruments. In an attempt to become more objective, this research presents methods to numerically and experimentally create maps, over a range of control parameters, that describe instrument behavior for a variety of different sounds features or “quality markers” (playing regime, intonation, loudness, etc.). The behavior of instruments is highly dependent on the control parameters that are adjusted by the musician. Observing this behavior as a function of one control parameter (e.g., blowing pressure) can hide diversity of the overall behavior. An isovalue quality marker can be obtained for a multitude of control parameter combinations. Using multidimensional maps, where quality markers are a function of two or more control parameters, can solve this problem. Numerically: in two dimensions, a regular discretization on a subspace of control parameters can be implemented while conserving a reasonable calculation time....

Using simplified terrain and weather mapping in outdoor sound propagation predictions

A complementary experimental and computational study was undertaken to assess the variability due to model sensitivities when predicting propagation in realistic outdoor environments by using a Green’s Function Parabolic Equation (GFPE) method and including realistic weather and terrain profiles. In order to test the validity of the basic and enhanced model including real terrain and weather data, field measurements were conducted at Hogan’s Mountain, North Carolina. By incorporating USGS terrain and measured weather profiles, this project further developed a Hogan’s Mountain specific GFPE to include a stair-step terrain mapping capability and linearly interpolated sound speed profiles. This Hogan’s Mountain GFPE uses matching conditions for comparison to the measured received levels from the field test data. Due to the vast data set acquired, which allows for comparison of the model to measurement in a multitude of propagation situations, several comments are made regarding the choice of calculation para...

Vibrational modes of accordion reeds.

Some new measurements made of the oscillation of air‐driven accordion reeds show that higher transverse modes through the fourth mode are present as well as the first torsional mode. The second and third transverse modes are observable even at low amplitudes of oscillation. All of these have been previously observed in reed organ reeds [Paquette et al., J. Acoust. Soc. Am. 114, 2348 (2003)]. Additionally, for the first time a lateral mode of vibration (transverse vibration perpendicular to the usual first transverse mode) has been observed. For airflow in a given direction, only one of the two reeds mounted in each wind chamber is the primary source of sound production, but the vibration of the secondary reed has also been studied. The amplitudes of higher‐frequency modes relative to the fundamental are observed to be higher in the secondary reed than in the primary reed. Finite element calculations of the reed modes have been made, and the calculated mode frequencies and node locations were used to verif...