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Figure 3. The transformation of the bowed string input waveform into the radiated sound by the bridge and body shell resonances for one selected note. Vertical dashed lines: Frequencies of the bowed string partials.
bowed notes on the double bass is vitally important; other- wise, the note is over before it has even started! The ability to achieve a clean start to a bowed note is one of the skills of a really good player on any bowed instrument (Guettler and Askenfelt, 1997). This involves controlling the acceleration of the bow following contact with the string as well its veloc- ity, position, and downward force. This is one of the most important factors differentiating the skills of a top soloist from those of a good amateur player, let alone a beginner.
The short audio extract (Audio 1, http://goo.gl/UtNOI4) of the sound produced by the piezoelectrically measured bowed string force acting on the bridge (Woodhouse, 2014) illustrates both the already violin-like sound of the driving force and the skill of an expert performer in controlling its subtle inflections of both amplitude and pitch.
Excitation of Body Shell Modes
The radiated sound of the violin is therefore determined by the overlap of the comb of harmonic partials excited by the Helmholtz wave on the bowed string and the multiplicity of resonant radiating body shell modes, with the bridge acting as an acoustic filter between, as illustrated schematically in Figure 3.
The isolated bridge resting on a rigid platform has two im- portant in-plane resonances at around 3 kHz and 6 kHz, ro- tation of its upper half about its waist and bouncing up and down on its two feet. When mounted on the island area of
the top plate, such resonances are strongly damped by their coupling to the body shell modes.
As many as 40 harmonic partials can be observed in the sound of the lowest bowed open string on a cello! The time- varying strengths of each of these partials, modified in am- plitude by the player and the multiresonant acoustic filter re- sponse of the instrument, will then be processed within the cochlea of the ear and the highly sophisticated audio pro- cesses that take place in the brain. The resulting complex- ity of the signals reaching the brain ultimately determines the listener’s perception of the quality of an instrument as played by a particular player.
Because of the multiresonant response of the violin, the waveform and spectrum of the radiated sound is very differ- ent from that of the input Helmholtz sawtooth force at the bridge, as illustrated by the computer simulation in Figure 3. It also varies wildly from note to note, and even within an individual note, when played with vibrato. Yet the sound of the violin perceived by the player and listener remains re- markably uniform, other than slight changes when bowing on different strings. This paradox suggests that the quality of an instrument cannot be determined simply by the frequen- cies and strengths of the individual resonances excited. This has encouraged the view that the frequency-averaged formant structure is perhaps the most important generic feature, with both the overall intensity and balance of sound radiated in the upper and lower frequency ranges being important.
However, if a single period of the recorded waveform of the recorded sound of a violin is selected and repeated indefi- nitely, the sound is like that of any crude Fourier synthesizer and nothing like a violin (Audio 2, http://goo.gl/UtNOI4). This suggests that the fluctuations in frequency, amplitude, and timbre, even within a single bowed note, strongly affect the perceived quality of a violin’s sound. The “complexity” of the sound arises from the strongly frequency- and direc- tional-dependent fluctuations in spectral content or timbre, the use of vibrato, noise associated with the finite width of the bow hair in contact with the string, frictional forces, and the superposition of reflections from the surrounding walls (Meyer, 1992). All such factors provide a continuously changing input to the ear. This allows the brain to focus on the instrument being played, which may be just as important as the overall intensity of the perceived sound in determin- ing an instrument’s “projection.” Averaging the frequency response would clearly reduce the complexity of the radiated sound, hence interest to the listener.
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