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Predicting playing frequencies for clarinets: A comparison between numerical simulations and simplified analytical
Whitney L Coyle1, Philippe Guillemain2, Jean Kergomard2
1Graduate Program in Acoustics, The Pennsylvania State University, 201 Applied Science Building, University Park, Pennsylvania 16802, USA.
The Journal of the Acoustical Society of America
|December 3, 2015
Summary
This study presents an analytical method to predict clarinet playing frequencies using input impedance. The method considers blowing pressure, reed opening, and four key physical effects for accurate frequency prediction.
Area of Science:
- Acoustics
- Musical Instrument Design
- Fluid Dynamics
Background:
- Predicting wind instrument playing frequencies is crucial for design.
- Input impedance curves offer a basis for frequency analysis.
- Blowing pressure and reed opening are key control parameters.
Purpose of the Study:
- To develop an analytical method for predicting clarinet playing frequencies.
- To investigate the influence of blowing pressure and reed opening.
- To analyze four specific effects altering playing frequency.
Main Methods:
- Utilized input impedance curves for frequency prediction.
- Developed analytical formulas for playing frequencies.
- Examined effects of flow rate, reed dynamics, inharmonicity, and temperature gradients.
- Validated predictions against numerical simulations.
Main Results:
- Analytical formulas derived for playing frequencies in the first register.
- Predictions show frequency decreases due to inharmonicity above oscillation threshold.
- Frequency increases above beating reed threshold due to flow rate changes.
Conclusions:
- The analytical method accurately predicts clarinet playing frequencies.
- Inharmonicity and flow rate effects significantly influence frequency.
- The study provides a tool for optimizing clarinet design and performance.
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