[sdiy] Stretched harmonic synthesis

cheater cheater cheater00social at gmail.com
Sun Feb 20 19:52:37 CET 2022

Nice essay. Now that everyone's caught themselves up to the difference
between ODEs (you differentiate only over time) vs PDEs (you
differentiate over time and x/y/z and you store the state of the
system at those points in a delay line), let me ask my original
question again.

I was wondering if anyone knows any ODEs which generate a signal with
harmonics which are progressively stretched? Meaning higher partials
are further apart.

Or alternatively progressively contracted - higher partials are closer together.

Are ODEs the only kind of differential equation that can be solved
without a delay line?

On Sun, Feb 20, 2022 at 5:13 PM René Schmitz <synth at schmitzbits.de> wrote:
> Hi Matthew and all,
> On 20.02.2022 15:26, Matthew Skala via Synth-diy wrote:
> >
> > A general pattern I've noticed - and I'm not sure whether this may be
> > already known in acoustics, or whether I could formalize it mathematically
> > - is that the kind of spectrum you get from something resonating depends
> > on the number of dimensions the thing has.
> >
> >
> What you describe here is related to what is called modes or room modes.
> Basically how  n-dimensional (standing) waves fit into a given space.
> The number of possible resonant states depends on the dimensions, and
> also on
> the shape of the resonating medium. A lump of wood will have a different
> response than a violin.
> Best,
>   René
> --
> synth at schmitzbits.de
> http://schmitzbits.de
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