Bowing as Periodic Plucking

The ``leaning sawtooth'' waveforms observed by Helmholtz for steady state bowed strings can be obtained by periodically ``plucking'' the string in only one direction along the string [437]. In principle, a traveling impulsive excitation is introduced into the string in the right-going direction for a ``down bow'' and in the left-going direction for an ``up bow.'' This simplified bowing simulation works best for smooth bowing styles in which the notes have slow attacks. More varied types of attack can be achieved using the more physically accurate McIntyre-Woodhouse theory [314,440].

Commuting the string and resonator means that the string is now plucked by a periodically repeated resonator impulse response. A nice simplified vibrato implementation is available by varying the impulse-response retriggering period, i.e., the vibrato is implemented in the excitation oscillator and not in the delay loop. The string loop delay need not be modulated at all. While this departs from being a physical model, the vibrato quality is satisfying and qualitatively similar to that obtained by a rigorous physical model. Figure 7.5 illustrates the overall block diagram of the simplified bowed string and its commuted and response-excited versions.

Figure 7.5: a) The simplified bowed string, including amplitude, pitch, and vibrato controls. The frequency control is also used by the string. b) Equivalent diagram with resonator and string commuted. c) Equivalent diagram in which the resonator impulse response is played into the string each pitch period.

In current technology, it is reasonable to store one recording of the resonator impulse response in digital memory as one of many possible string excitation tables. The excitation can contribute to many aspects of the tone to be synthesized, such as whether it is a violin or a cello, the force of the bow, and where the bow is playing on the string. Also, graphical