>> I wonder... how is it possible
>> to simulate resonation? It should be possible to do so, but I can't
>>think for the life of me how it might be done. Any
>>ideas/suggestions?
 LB> I can think of several methods.  One of the simplest would be to
 LB> sample some examples of various resonations and then derive the
 LB> formulas from them.  
  Hmm... sometimes, trying to derive a formula from a set of values can be 
easier said than done. 
 LB> This would also take into account all the
 LB> various frequency dependent reflections.  A rough(very)
 LB> approximation that could be played with and modified to yield
 LB> interesting experimental results would be to take the parameters for
 LB> the normal sounding of the particular object, that is the ratios
 LB> corresponding to the amplitudes of its fundamental and overtones, --
 LB> then write an algorithm that takes the frequencies present in the
 LB> samples being processed and compares them to those of the
 LB> partials of the object being resonated, and (probabaly on a natural
 LB> log scale) multiplies to find the corresponding amplitudes of the
 LB> resonated partials.
  Okay, I've read this through several times and I'm not completely sure I 
follow you. I know the meaning of overtone and fundamental, but I'm not sure 
I'm up to speed on what a partial is or how a natural log scale would apply 
here. I think what you're suggesting is to write an algorithm that:
1.      Finds the frequencies that make up a particular sample
        and computes the amplitude of each. In particular, it would
        try to find the strongest frequency and any multiples
        thereof (corresponding to overtones of that frequency).
2.      Given a sample and a set of data either generated in 1
        or given by the user, mixes that sample with itself at
        different frequencies.
  This is very close to the algorithm I was planning to use to generate the 
base sample, to simulate the vibration of strings or air within a tube, etc. 
I didn't know that resonation within a chamber behaved the same as, say, 
thevibration of a string. Perhaps one way to measure the behaviour of 
different instruments would be to generate a pure sine wave (starting low and 
with increasing frequency) through a speaker located roughly where the 
strings would be in a stringed instrument, then record the resulting sound. 
By comparing the frequencies in the final sound with the frequency of the 
sine wave, one could perhaps get some idea of what was going on.
  ...but how would one take the shape of the instrument and type of material 
it was made of into account?
 LB> Once the algorithm was created we could start playing with the
 LB> parameters like the partials and their amplitudes of resonation to
 LB> synthesize new sounds.  It's be like creating materials which may or
 LB> may not exist to resonate.  Lots of fun.  Especially if we take into
 LB> account multiple objects to be resonated.  Entire synthetic
 LB> environments could be created and played in!
  Yes, that would be wonderful. But I think we need to first explore the 
algorithms and formulae in more detail.
 LB> Ring modulation traditionally was a method for multiplying the sums
 LB> and differences of the frequencies present in the original waveform.
  I'd be interested in learning more details about this. Where can I find out 
more information?
 LB> originaly produced the sound.  I used to mix in an extra sine wave to
 LB> account for the strong minor third partial present in classical bells.
  Really? Where can you find information such as this out? If I'm actually 
going to write a sinthesis algorithm, I'm going to need to learn everything I 
can about this type of thing.
  - Cyclone
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