Computer Sound Synthesis 2 MUS_TECH 335 Selected Topics Computer Sound Synthesis 2

Physical Modeling Synthesis

Waveguides Energy Source and Its Application Excitation When we discussed physical modeling with resonant filters, we separated the excitation from the resonances of the body with no implication that there was any direct interaction between the two. In simulating a plucked string we in fact made the same assumption. Energy Source and Its Application Excitation Physical Body of Instrument Resonances Output

Waveguides Energy Source Feedback Energy Source Its Application The method by which energy is imparted to most musical instruments involves some form of on-going control and feedback, even for the sound to be produced. This is a model first proposed by McIntyre, Schumacher and Woodhouse (1983). Energy Source Feedback Energy Source Its Application Non-linear Excitation Physical Body of Instrument Linear Resonator Output

Waveguides Nut String Bow String Bridge Body LP A good example is the bowing of a string instrument. The action of the bow on the string is influenced by the motion of the string itself. There is an interaction between the two. resonances LP Nut String Bow String Bridge Body

Waveguides Bow velocity Bow force Bow position Among the physical factors affecting the action of the bow with the string are the bow velocity, the bow force and the bow position. These interact with the instantaneous velocity of the string to create the characteristic bowed string motion. Bow velocity Bow force Bow position

Waveguides The easiest way to approach the motion of the string is with velocity waves and to simulate the bow action in terms of velocity. The actual physical interaction of these variables is handled in a look-up table. Bow force Bow Table Bow velocity

Waveguides Depending on the bow velocity, bow force, bow position and the instantaneous velocity of the string, the bow alternately sticks to the string or slips as the string moves.

Waveguides This causes the velocity wave to largely alternate between two values. The integral of the motion yields the displacement wave of the string which resembles a sawtooth wave.

Waveguides The bow position influences which harmonics will be produced. If the bow sits on the string at a position that is not a simple integer division of the string length, then it will excite all harmonics. If it sits at the node of vibration for a particular harmonic, then that harmonic can not occur and it is suppressed. In the computational model, this behavior drops out of the waveguide simulated automatically.

Waveguides The sound of the violin is also strongly shaped by the resonant structure of the violin’s body. This response is very frequency-dependent and complex. The individual harmonics of notes with different frequencies will each have different amplitudes. Vibrato of a string is very complex because the amplitude of the harmonics goes up and down with the changes of frequency.

Waveguides This complexity in frequency response is created by the complexity in the design of the body of the instrument where every feature has a special effect on the sound.

Waveguides The various individual resonances that combine to create the overall response of the body can be related to individual features in the motion of the surface of the body.

Waveguides The simulation of the violin body can be accomplished by direct high-order modeling in the frequency domain. Alternative, it can be accomplished by time domain modeling (usually with the main air resonance handled by a filter).

Waveguides Simple Clarinet z-m HP LP z-m - p - Mouth Reed Bore Bell The clarinet is a popular instrument to simulate by waveguide. At a first approximation, the fingering changes with the tone-holes can be simulated simply by changing the length of the bore. The pressure wave at the bell reflects back with opposite sign, but the pressure wave at the mouthpiece does not. z-m HP - p LP - z-m Mouth Reed Bore Bell

Waveguides Simple Clarinet At the open end of the pipe, the pressure must be the same as outside the pipe. At the mouthpiece the pressure can have maximum variation.

Waveguides Simple Clarinet Because one end of the pipe has pressure fixed at zero, the frequencies supported by the pipe are odd multiples of a fundamental frequency.

Waveguides Simple Clarinet The amount of air pressure produces different dynamics and differences in timbre.