The capacity of a brass instrument to generate sounds with strong high-frequency components is dependent on the extent to which its bore profile supports nonlinear sound propagation. At high dynamic levels some instruments are readily sounded in a "cuivré" (brassy) manner: this phenomenon is due to the nonlinear propagation of sound in ducts of the proportions typical of labrosones (lip-reed aerophones). The effect is also evident at lower dynamic levels and contributes to the overall tonal character of the various kinds of brass instrument. This paper defines a brassiness potential parameter derived from the bore geometries of brass instruments. The correlation of the brassiness potential parameter with spectral enrichment as measured by the spectral centroid of the radiated sound is examined in playing tests using musicians, experiments using sine-wave excitation of instruments, and simulations using a computational tool. The complementary effects of absolute bore size on spectral enrichment are investigated using sine-wave excitation of cylindrical tubes and of instruments, establishing the existence of a trade-off between bore size and brassiness potential. The utility of the brassiness potential parameter in characterizing labrosones is established, and the graphical presentation of results in a 2D space defined by bore size and brassiness potential demonstrated.
Some authors writing about brass musical instruments have used the term ’’effective length,’’ usually meaning the length of a cylindrical tube having the same resonance frequencies as a given horn, but possibly with different end conditions. In this paper, alternative definitions of effective length are considered, and one definition is chosen and generalized to all frequencies, not just discrete resonance frequencies. Within the framework of lossless plane-wave horn theory, a nonlinear first-order differential equation is derived that yields effective length as a function of frequency and horn contour. Effective length has been calculated for some horn contours resembling French horns and trumpets. The solutions are qualitatively consistent with the experience of instrument makers and players, and with the effective lengths of actual instruments, determined from measured resonance frequencies. Subject Classification: 85.60; 75.40.
The propagation of torsional waves in tapered solid elastic rods is examined both theoretically and experimentally from the viewpoint of acoustic horn theory. Such tapered rods in torsional vibration are dubbed torsional horns. Two differential equations are derived that describe the propagation of torsional waves. One of these is an “exact” wave equation that can be readily solved only when the horn boundaries fit a separable coordinate system. The other is an approximate wave equation based on the assumption that the wavefronts are plane cross sections of the horn. This equation is very similar to Webster's plane-wave equation for compressional waves in an acoustic horn. Experimentally determined standing-wave patterns and resonance frequencies of torsional horns are compared with the solutions of the two wave equations for selected horn contours. A quantitative estimate of the error introduced by the plane-wave approximation is obtained for the exponential horn.
input impedances of six excised dog lungs were computed from Fourier analysis of their response to a transient pulse pressure excitation. Impcdances, between 156 Hz and 10 000 Hz, were measured at transpulmonary pressures of 30, 20, 10, and 5 ½m H20. There was a substantial amount of interindividual variability in the impedance. There were, however, generally three well defined impedance peaks and the frequencies of these peaks seemed to be dependent upon body size and lung volume. If the airways are modeled simply as a constant diameter tube one is led to the paradoxical conclusion that substantial airway closure occurs at relatively large lung volumes. However, conditions of open airways are consistent with our results if the airways are modeled as having a more complex geometrical shape. We conclude that the input impedance at these high frequencies is variable among individuals, and between lung volumes in any given individual, and that estimates of pathlength or the alveolar boundary condition cannot be easily obtained by interpretation based on simple geometrical models.
It has long been thought by players and instrument makers that the material from which a brass instrument is made influences the tone quality and playing characteristics of the instrument. For instance, the brochure of a maker of custom trombones describes bells made of three alloys: yellow brass (70% Cu, 30% Zn), having the ‘‘clearest sound, sharpest articulation,’’ gold brass (85% Cu, 15% Zn), with ‘‘warm sound, rounded articulation,’’ and red brass (90% Cu, 10% Zn), with ‘‘warmer sound, covered articulation.’’ The bells are made in three metal thicknesses: light weight, with ‘‘flexible tone, rapid response,’’ standard weight, with ‘‘balanced tone, even response,’’ and heavy weight, with ‘‘firm tone, stable response.’’ Most players agree with these statements. This model of trombone is made so that bell sections can be interchanged while leaving the remainder of the instrument intact. The present paper reports the results of measurements under playing conditions on several different bells. Comparisons of steady-state behavior are made via the transfer function between sound pressure in the mouthpiece cup and an on-axis point outside the bell. An attempt will also be made at the rather more difficult task of characterizing the attack transient.
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