Effects of nonlinear sound propagation on the characteristic timbres of brass instruments

Abstract

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.

Nonlinear forced vibrations of thin structures with tuned eigenfrequencies: the cases of 1:2:4 and 1:2:2 internal resonances

“…The string is obviously the most common case for string instruments sharing the two properties of nonlinear vibrations together with commensurable eigenfrequencies; see, e.g., [12,17,18,32]. Nonlinearities are also encountered in reed instruments such as saxophone and clarinette; see, e.g., [27] and brass instruments (see, e.g., [20]) and references therein. For percussion instruments, gongs, cymbals, and steelpans (or steeldrums) are also known for displaying geometric nonlinearity due to the large amplitude vibrations of the main shell structure.…”

Is Nonlinear Propagation Responsible for the Brassiness of Elephant Trumpet Calls?

“…Rumbles are characterised by an extremely lowfundamental frequency(approx. [16][17][18])which directly reflects the extraordinary size of the elephant vocal folds [4]. Additionally,i nvestigations of the resonance frequencies of rumbles indicate that the trunk is involved in addition to the oral cavity in shaping the spectral envelope of most, butnot all, calls [3,6].…”

“…Akey parameter for predicting the severity of this nonlinear steepening is the critical shock length distance [15] associated with the profile of the initial source signal (F0, amplitude and wave shape). When the length of the bore approaches this critical value, as is the case in brass instruments played at fortissimo level, the strong distortion of wavesd uring their propagation inside the bore affects the spectral content of the radiated signal, conferring its distinctive brassy quality [17]. The exceptional length of the elephant'strunk opens up the possibility that the nonlinear steepening effect might be significant during elephant trumpeting, as in brass instruments.…”

Vibration modes and sound characteristic analysis for different sizes of singing bowls

“…Myers et al [8] showed the sound generation mechanism for brass instrument. Different geometry variation and effects on radiated sound frequencies were investigated.…”