[sdiy] additive synthesis parameters

[ASSI]

On Samstag, 8. April 2006 19:09, ASSI wrote:
> While we're on the subject of stretched harmonics - does anybody have
> a reference handy for how large the typical stretch is for various
> instruments and exactly how the partials are stretched?

Thanks for the responses so far, I think I should explain myself a bit 
better. Sorry, this is going to be long.

I had made a cue-sheet for the harmonic series and some Pythagorean 
tunings. From tuning my own piano I know that it stretches about a 
third of a semitone from middle to highest C. What I don't really know 
is the harmonic structure of that stretch, you tune the strings 
relative to two harmonics after setting two base octaves in the middle. 
Out of that one "Physics of Musical Instruments" lecture (in german) I 
took the formula for the spectrum of a string with stiffness (but 
without mass) and meddled with the parameters until it matched the 
33cent stretch. A real string has mass however, but a) I have no 
information of how important the two contributions are in relation to 
each other and b) the combination of both is quite unwieldy. The 
cue-sheet is here (I don't know how useful this is to other people, but 
if you want to look at it anyway...):
http://Stromeko.Synth.net/diy/tuning.pdf

How does this relate to synthesis? I have found that all synths using 
strictly periodic waveforms (wavetable and a few others) sound the same 
at some very basic level. I can't explain any better, but they do have 
a certain character to their sound that I attribute to the resulting 
perfect harmonic series. I've done a few sounds where I tried to 
deliberately introduce stretch, which is surprisingly difficult. My 
best idea so far has been to use two sines for 1st and 2nd harmonic, 
stack a wavetable based complex waveform on top and stretch these three 
slightly - this has resulted in some very useable sound that sound very 
nice in some range of the stretch parameter.

The theory for the stretch is based on the shortening of the apparent 
string length due to stiffness at the clamped ends or alternatively by 
viewing the string as transmission line with dispersion (higher 
frequencies travel faster than lower ones). So one would think that 
filters with dispersion could be used, but I didn't find much or 
anything about such filters, let alone how to design them for audio 
frequencies.

So here I am looking for an efficient way to synthesize sounds with 
stretched (and compressed, as some combinations of mass and stiffness 
allow) harmonics and so far found - nothing. There seem to be no 
spectra for comparison purposes, either. Analyzing something like a 
piano is difficult as there is a lot of mode-coupling going on and I 
don't have any good long samples of the sustain phase of single bass 
strings yet. I'm also not sure whether the resolution from the 
frequency analysis will be good enough, as I expect quite some 
development in the harmonic structure over time.


Achim.
-- 
+<[Q+ Matrix-12 WAVE#46 Neuron microQkb Andromeda XTk sonic heaven]>+

SD adaptations for KORG EX-800 and Poly-800MkII V0.9:
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