Fourier-Analysis and FM-synthesis

[johns at oei.com]

     I never tried to make any composite patches using additive synthesis 
     using an analog synth because it takes so many darned VCOs. But, I do 
     own a Kawai K1 (bought 1989) that seems to provide plenty of of the 
     basic raw materials to start to experiment along this line.  It offers 
     many wavetable sine waves at many octaves in many voices.  You could 
     build a sound based on more sine waves than you would need, I'm sure.  
     And you can detune each "oscillator".
     
     Here's what I learned from my limited trials about simulating complex 
     waveforms:
     
     1. There's more to sound than just sine wave amplitude relationships. 
     There is also phase and amplitude relationships that change over time 
     in a predictable and unpredictable way.  This can be very hard to 
     characterize and duplicate in most peoples homes or studios 
     (especially if you want to use many components in your composite 
     waveform).
     
     2. Sound transients can be simulated also using fourier components and 
     these are even more random than the steady state signal components 
     mentioned above.
     
     3. I found that for best results, you should do all the math on paper 
     ahead of time.  You must know what you want before you do it.  There 
     is no seat-of-the-pants synth programming here.  A good starting point 
     that will give you some good starting insight is to first characterize 
     a sawtooth using a fourier expression then go ahead and program it in. 
     (Like I said, K1 is great for this kind of stuff; maybe others too.)
     
     JJS