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echo: music_comp_101
to: STEFAN XENOS
from: LAWRENCE BENZMILLER
date: 1996-06-05 15:38:00
subject: Synthesis Algorithm

;-)Hi again, greek "stranger"!
 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.
 SX>>  Hmm... sometimes, trying to derive a formula from a set of values can 
be
SX>> easier said than done.
_Ain't it the truth...
     ...and isn't that the understament of the decade.
The entire method of physical modeling synthesis would not exist without such 
efforts to find and simplify just such formuli however.
SX>> I know the meaning of overtone and fundamental, but I'm not sure
I'm up to speed on what a partial is...
A partial is an overtone in relation to a specific timbre, eg. the 
fourth,partial of a violin waveform is the third overtone, and the first 
partial is the fundamental.  Usually it is used to speak of the amplitude of 
each partial, each of which would be a sine wave with an envelope function 
representing it's amplitude over time.  Very common to Fourier resynthesis 
algorithms, ie simple additive synthesis using individual sine waves.  This 
method creates very acurate reproductions of sounds but uses an ungodly 
number of oscillators.  However, this is not a problem in non-real-time 
software based synthesis algorithms.
SX>>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. 

didn't know that resonation within a chamber behaved the same as, say,
thevibration of a string. 
Not exactly, but resonation of an object conforms to the form of vibration 
common to the object.  Resonance of a chamber, no matter how large or small, 
conforms to the same formulas in a general sense, wether simulating a pipe or 
a room.  As do strings and coils go together, etc.  It's just a matter of
incorporating the physical properties of the objects you wish to stimulate. 
SX>> ...but how would one take the shape of the instrument and type of 
material
it was made of into account?
The recent stuff I have been reading states that to do so incorporates the 
mathematics of waveguides.  I do not yet understand this math fully, and if 
you have anything to teach or explain in this area, I would be eternally 
greatfull.
***Ring modulation formuli***
I haven't looked at that stuff in years, so it will do me good to check out 
some sources, Stefan.  I promise to pass along anything in the way of 
references I can find to you, my friend.  Please do the same if you can.
Pax tibi,
Lawrence
--- Maximus 2.02
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