Gday Tom and shakuhachi fans
thanks for the plug for the shakuhachi acoustics web site (it's at
http://www.phys.unsw.edu.au/music/shakuhachiresults.html).
You're right about those impedance minima: what if they're not at the right
frequency? The problem is complicated because more than one impedance
minimum is usually involved and, if their ratios are not strictly harmonic
(in the ratio 1:2:3 etc), then they don't 'cooperate' as well as if they
were in harmonic ratios. (follow the links on our site to "How harmonic are
harmonics?")
So how to get the minima (i) at just the right frequencies and (ii) in
harmonic ratios while (iii) not upsetting the other notes and (iv) keeping
that cutoff frequency in the desirable range? You're right, we don't know.
We are working on that problem, but it will take us a while. In the mean
time, your answers to that question are pretty damn good.
There's a standard observation one can make about music acoustics:
musical instruments have 'evolved' over centuries and so, thanks to the
knowledge and skill of makers and players, instruments have become very
good at doing what they need to do. For scientists to have anything really
practically helpful to say to makers, our knowledge has to be rather
precise and to consider many subtle effects. We'll get back to you!
Best wishes
Joe
_______________________________________________________________________
Joe Wolfe School of Physics Ph: 61-2-93854954
University of New South Wales UT+10,+11 oct-mar
J.Wolfe@unsw.edu.au UNSW Sydney 2052 Australia Fax 61-2-93856060
_____________________ http://www.phys.unsw.edu.au/~jw _________________
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