Re: acoustic impedances; what makes a good instrument

From: Mark Millonas (millonas@email.arc.nasa.gov)
Date: Mon Sep 15 2003 - 15:10:34 PDT


Nelson:

>Your question translates to the desirable ratio between even and odd
>harmonics. Which can be further reduced to the most desirable ratio between
>the amplitudes of the second and third harmonics. Once that is specified,
>the rest falls into place. This ratio can be arrived at by ear, by arcane
>math ratios (phi and so on), or by throwing dice or some such.

If that is all there is to it (amplitudes of the primary relative to the
next two higher resonance)
then I would say the calculation part would be more of less easy to
do. For example, if you wanted all the first
and second octave notes to be in the same ratio (you pick the ratio you
personally want) then you effectively have a one
parameter family of bores. That is a playing characteristic, but I'm
guessing there might be
more features that can be heard. Even so, I'm interested in calculating a
bore that corresponds
to the desires of the flutemaker/player and also understanding what kinds
of flexibility there might be
within those constraints, so if you told me the ratio you want I could
tell you exactly which bore would best implement that, or given any
constraints specified by
the maker, how to optimally perturb a given bore to get there.

So the question I would ask the experienced players is: is Nelson
right? Would the
relative resonance strengths be the only thing you would look for? If
those are ok for
your tastes is it your observation that this pretty much pins down the
timbre, or is there something more?

Humm, I was just making the point the Karl that I didn't think it would be
that complicated, and now I'm
playing devil's advocate on the other side.

Marko

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