Mark,
> but this begs the question of what "the
> desired acoustic impedances" are.
To my mind, you've nailed the heart of the dilemma--which, in a general
sense, is the question of what should a shakuhachi sound like? This flute
(as are most flutes) is frustratingly exclusionary. Which is to say, it
doesn't seem like you can have everything in one flute. Everybody wants that
dark romantic mellow sound along with the ability to play the high notes
with brilliant musicality. The trouble is that to accentuate one
necessitates the exclusion of the other--kind of like trying to be tall and
short at the same time. Picking a middle ground doesn't do justice to
either. So until somebody comes up with something very clever, the old 'bag
full of flutes' seems about the only way to go.
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.
So what are "the desired acoustic impedances"? I don't know, pick what you
like and then make up a story to support it. That you've recovered the Lost
Watazumi Flute. That it's based on the Music of the Spheres. That it mirrors
the DNA molecule. That these impedances make the flute most efficient.
Whatever.
Nelson
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