Computer Sound Synthesis 2

MUS_TECH 335 Selected Topics

Physical Modeling Synthesis

WaveguidesWhen 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.

Excitation

Resonances

Output

Energy Source and Its Application

Physical Body of Instrument

WaveguidesThe 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).

Non-linear Excitation

Linear Resonator

Output

Energy Source

Its Application

Physical Body of Instrument

FeedbackEnergy Source

WaveguidesA 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.

LP

Nut String Bow String Bridge Body

resonances

WaveguidesAmong 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 velocityBow forceBow position

WaveguidesThe 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 velocity Bow Table

Bow force

WaveguidesDepending 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.

WaveguidesThis 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.

WaveguidesThe 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).

Simple ClarinetWaveguides

z-m

z-m

p-

HP

LP-

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.

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Simple ClarinetWaveguides

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.

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Simple ClarinetWaveguides

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

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Simple ClarinetWaveguides

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

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