274
6 Shocks and Surprises: Refining the Elementary Model
movement of Shéhérazade by Rimsky-Korsakov, reproduced in Fig. 6.2b, does not
have a specific dynamic marking, but the instruction con forza is a strong hint that a
brassy sound is appropriate. A touch of brassiness can add salience to an otherwise
fairly quiet accented note; in the excerpt from Claude Debussy’s Prélude à l’aprèsmidi d’un faun shown in Fig. 6.2c, the first horn is specifically asked to play such
a note cuivré, before hand-stopping the instrument to play the following passage
pianissimo (Del Mar 1983).
The French term ‘cuivré’, like the English ‘brassy’, suggests that the effect is
due to forced vibrations in the metal bell. It is clear, however, from a variety of
experimental and theoretical studies, that the amplitudes of bell vibrations are much
too small to explain the phenomenon (see Sect. 6.6). It has also been suggested that
the open area of the aperture between the player’s lips, which has an approximately
sinusoidal variation at low dynamic levels and medium to high pitches, might
saturate for very loud playing, resulting in a clipped waveform and the generation
of additional upper harmonics. Experiments involving high-speed filming of the lips
of players (Bromage et al. 2006) have shown no evidence of such saturation during
brassy playing (see Sect. 3.1).
It is now generally accepted that the explanation for the transition to brassy
timbre is that proposed by Hirschberg et al. (1996b), following an earlier suggestion
by Beauchamp (1969, 1980). In very loud playing, the linear acoustic approximation
is no longer valid, and nonlinear propagation in the instrument air column leads to
a gradually increasing distortion of the sound wave as it travels down the tube. In
trumpets, trombones and french horns, which have a high proportion of cylindrical
tubing, the distortion can result in the sudden pressure jump described as a shock
wave. The resulting radiated time signal is the periodic sequence of very sharp peaks
illustrated in Sect. 4.6.5. The common description of this group of instruments as
‘bright’ (French ‘cuivres clairs’) reflects the extreme brightness of their timbre at
high dynamic levels. In flugelhorns, euphoniums and tubas, most of the tubing with
no valves activated is either conical or flaring, and the distortion is not sufficiently
strong to allow the full development of a shock wave within the tube. This group of
instruments is sometimes described as ‘mellow’ (French ‘cuivres doux’), since the
spectral enrichment at high dynamic levels is less marked.
6.1.2 Experimental Evidence for Shock Waves in Brass
Instruments
The effects of nonlinear propagation can be seen in pressure measurements made
by Gilbert and Petiot (1997) at different points along the bore of a trombone
(Fig. 6.3). In this case, the trombone was blown by a human player. A microphone
in the mouthpiece shows that, for quiet playing (musical dynamic p), the pressure
variation is almost sinusoidal. In contrast, for very loud playing (musical dynamic
ff ), the point in the vibration cycle at which the lips open is marked by a rapid
6 Shocks and Surprises: Refining the Elementary Model
movement of Shéhérazade by Rimsky-Korsakov, reproduced in Fig. 6.2b, does not
have a specific dynamic marking, but the instruction con forza is a strong hint that a
brassy sound is appropriate. A touch of brassiness can add salience to an otherwise
fairly quiet accented note; in the excerpt from Claude Debussy’s Prélude à l’aprèsmidi d’un faun shown in Fig. 6.2c, the first horn is specifically asked to play such
a note cuivré, before hand-stopping the instrument to play the following passage
pianissimo (Del Mar 1983).
The French term ‘cuivré’, like the English ‘brassy’, suggests that the effect is
due to forced vibrations in the metal bell. It is clear, however, from a variety of
experimental and theoretical studies, that the amplitudes of bell vibrations are much
too small to explain the phenomenon (see Sect. 6.6). It has also been suggested that
the open area of the aperture between the player’s lips, which has an approximately
sinusoidal variation at low dynamic levels and medium to high pitches, might
saturate for very loud playing, resulting in a clipped waveform and the generation
of additional upper harmonics. Experiments involving high-speed filming of the lips
of players (Bromage et al. 2006) have shown no evidence of such saturation during
brassy playing (see Sect. 3.1).
It is now generally accepted that the explanation for the transition to brassy
timbre is that proposed by Hirschberg et al. (1996b), following an earlier suggestion
by Beauchamp (1969, 1980). In very loud playing, the linear acoustic approximation
is no longer valid, and nonlinear propagation in the instrument air column leads to
a gradually increasing distortion of the sound wave as it travels down the tube. In
trumpets, trombones and french horns, which have a high proportion of cylindrical
tubing, the distortion can result in the sudden pressure jump described as a shock
wave. The resulting radiated time signal is the periodic sequence of very sharp peaks
illustrated in Sect. 4.6.5. The common description of this group of instruments as
‘bright’ (French ‘cuivres clairs’) reflects the extreme brightness of their timbre at
high dynamic levels. In flugelhorns, euphoniums and tubas, most of the tubing with
no valves activated is either conical or flaring, and the distortion is not sufficiently
strong to allow the full development of a shock wave within the tube. This group of
instruments is sometimes described as ‘mellow’ (French ‘cuivres doux’), since the
spectral enrichment at high dynamic levels is less marked.
6.1.2 Experimental Evidence for Shock Waves in Brass
Instruments
The effects of nonlinear propagation can be seen in pressure measurements made
by Gilbert and Petiot (1997) at different points along the bore of a trombone
(Fig. 6.3). In this case, the trombone was blown by a human player. A microphone
in the mouthpiece shows that, for quiet playing (musical dynamic p), the pressure
variation is almost sinusoidal. In contrast, for very loud playing (musical dynamic
ff ), the point in the vibration cycle at which the lips open is marked by a rapid