A 78-page paper entitled Discrete-time modeling of musical instruments, written by Vesa VÃ¤limÃ¤ki et al., has been published in Reports on Progress in Physics It’s a great place to start if you want to get into digital modeling of musical instruments. You would also do well to check out Julius Smith’s online publications.
4. Instrument modeling
One of my interests is in the synthesis of musical sound. This page has sound samples of a guitar
that I synthesized from using a technique called digital waveguide
modelling. Note how the sound improves as the model progresses.
- This is the sound of a very basic waveguide. AU WAV
- This is the sound of the waveguide with frequency dependent
decay on the string. Note how the high frequencies die away quicker. AU WAV
(waveguide + frequency dependent decay)
- This is the waveguide with a filter to simulate the
acoustic response of the guitar body. AU WAV
(waveguide + frequency dependent decay + filter to simulate the body)
- This is the final sound. In this case, a better filter is
used to simulate the acoustic response of the body. AU WAV
(waveguide + frequency dependent decay + better filter to simulate the body)
I found a very cool sound synthesis package called Tao. To use it you draw strings and other objects on the screen and make ways to excite them. Then you can visually animate them and hear how they sound. I haven’t used it but they have a number of examples and animations at the website. Now if they only had something like that for air columns and voices!