If
you are well acquainted with electronic music, be it as a practitioner or as an amateur,
maybe you have some knowledge of the today's basic sound synthesis techniques: FM, AM,
Additive, Subtractive, and wavetable. The latter is mostly used in "high
quality" expanders and synthesisers, and is based upon digitally sampled sound
textures of the musical instrument you want imitate. You must then add some trick for
pitch shifting, some envelope generators to control the attack of sounds, and some LFO
(low Frequency Oscillator) to obtain tremolo and vibrato, but in this way you can get a
sound, sometimes and in given circumstances, quite similar to the original one, and in any
case better than the sound obtained, f.i., using FM - at least from the mimic point of
view.
Original
instruments are better than their copies - as anyone can agree. Electronic sound are also
generally considered not as much "interesting", mainly because of its
"stiffness". This "stiffness" is due IMHO to the circumstance that
these synthesis techniques are based upon signal models, giving thus little control
capability to the performer. What makes "interesting" (or beautiful, or
pleasant, or expressive) the sound of an acoustic instrument is the gesture of the player.
Anyone can note the difference between the same instrument and the same excerpt, as played
by the favourite soloist or by a beginner. In these cases you can find, among so many
differences, even a different sound.
Synthesis
by physical modelling represents an alternative approach to electronic sound generation:
you simulate the motion of a vibrating object (excited in some simple or complex way by
the performer) letting this simulation generate the sound. For this purpose, you must
first build a mathematical model of the vibrating object (the musical instrument, lato
sensu), from the point of view of its motion (i.e. the physical model), then you have to
provide the means to numerically calculate such a motion - in real time, if possible. This
means, shortly, that you are involved in PDEs (partial derivative Differential Equations)
and in the various numerical integration techniques, taking into account excitations and
bonds.
Any
"musical instrument" can be considered, generally speaking, as composed by a
non-linear exciter, and a (near to) linear resonator. The PDEs governing the resonator are
substantially wave equations, which admit, as a general solution, the superimposition of
opposite travelling waves. For this reason, the most frequent approach to the problem is
the use of delay lines or waveguides, in which you let suitable waveshapes travel back and
forth
This
is not the method we used: the PDE is instead solved by means of some original
methods. More details here.
With
our approach, the performer can control many parameters in real time (more than with
the usual physical instruments, including parameters that are not "variable" in
the real world). Each parameter has a straightforward physical meaning, giving an
intuitive support to the player.
