Influence of bore shape on the resonant frequencies and spectral envelope of a French horn

Abstract

The harmonicity of the resonant frequencies, and the shape of the spectral envelope of the input impedance curve, are two important indicators that might be used in predicting the usefulness of a given air column as a brass wind instrument. These can be determined by approximating the air column as a large number of concatenated lossy cylindrical increments, and computing and plotting the input impedance of the configuration as a function of frequency. In this paper the results of such calculations are described for a number of bore shapes related to the French horn, and the effects of changing various dimensional parameters are illustrated. The contributions of the bell, the leadpipe, and the mouthpiece of a typical open B‐flat horn are first examined. Then the horn is idealized and represented by 14 dimensional parameters, so that each can be varied independently to study its effects on harmonicity and spectral envelope, and an optimum configuration is determined. Finally, the effects of inserting the hand into the bell are examined.