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<P>Marko, thanks for doing this. My inbox was filling up with all of the physics discussions that I am only mildly interested in hearing about but not on a daily basis. Setting up a separate home was great!<BR><BR></P></DIV><BR><BR><BR>
<DIV><EM><FONT color=#0000cc><STRONG>Lynne Nicholson</STRONG></FONT></EM></DIV>
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<DIV><EM><FONT color=#0000cc><STRONG> </DIV></STRONG></FONT></EM>
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<DIV></DIV>>From: Mark Millonas <MILLONAS@EMAIL.ARC.NASA.GOV>
<DIV></DIV>>Reply-To: Shakuhachi@communication.ucsd.edu
<DIV></DIV>>To: Shakuhachi@communication.ucsd.edu
<DIV></DIV>>Subject: advert for new group, and last ever physics related post
<DIV></DIV>>Date: Tue, 23 Sep 2003 13:45:04 -0700
<DIV></DIV>>
<DIV></DIV>>Hi:
<DIV></DIV>>
<DIV></DIV>>Some of us have decided to move the physics discussion of bores in
<DIV></DIV>>relation to the shak elsewhere.
<DIV></DIV>>If it isn't too annoying I will just relate here my first posting
<DIV></DIV>>*there* so in case there
<DIV></DIV>>is anyone on this list that likes the topic and flavor (at least as
<DIV></DIV>>exemplified by this
<DIV></DIV>>one posting) they can join us or listen in. I also do this with the
<DIV></DIV>>hopes that some of the musician
<DIV></DIV>>and shak makers might help us out on some things if it look like
<DIV></DIV>>anything they might be interested in.
<DIV></DIV>>I promise not to post anymore acoustics related (but perhaps
<DIV></DIV>>culturally charged) stuff here anymore.
<DIV></DIV>>
<DIV></DIV>>Anyway, first post at ShakuhachiDesign@yahoogroups.com, last post
<DIV></DIV>>here.
<DIV></DIV>>
<DIV></DIV>>-------------------------------------------------------
<DIV></DIV>>
<DIV></DIV>>A possible place to start a discussion might be the following paper:
<DIV></DIV>>A. H. Benade. On woodwind instrument bores, J. Acoust. Soc. Am.
<DIV></DIV>>31(2):137-146 (1959).
<DIV></DIV>>Unfortunately it is BPDF (before pdf) so the only way to get a copy
<DIV></DIV>>is to go to a university library,
<DIV></DIV>>or I could scan it if anyone can tell me how to post it here.
<DIV></DIV>>
<DIV></DIV>>I think this might be a good place to start both because the results
<DIV></DIV>>in the paper are particularly simple and because it methodology is a
<DIV></DIV>>simple
<DIV></DIV>>example of the one I originally proposed: define the required
<DIV></DIV>>acoustic features then infer the bores that fit those features.
<DIV></DIV>>His results are for close-ended woodwinds, but I can go home and see
<DIV></DIV>>if I can re-do all the proofs for open ended bores. That
<DIV></DIV>>is, unless someone can point me to a place where this has already
<DIV></DIV>>been done.
<DIV></DIV>>
<DIV></DIV>>There are two acoustic features that Benade uses and will be
<DIV></DIV>>immediately recognizable to the musician with
<DIV></DIV>>no mathematical training whatsoever: (1) The first and second
<DIV></DIV>>resonance of a bore (lower and second register) should have
<DIV></DIV>>frequencies in the ration of 1:2 (play at exactly one octave apart)
<DIV></DIV>>and (2) that (1) should hold if you "chop" the bore down to
<DIV></DIV>>any length (that is, for any fingering where all the holes are
<DIV></DIV>>closed up to a certain point). So the criteria are that the flute
<DIV></DIV>>play in tune
<DIV></DIV>>in the first and second registers for all the basic notes.
<DIV></DIV>>
<DIV></DIV>>Criteria (1) requires that the bore have the shape where the
<DIV></DIV>>cross-sectional area depend exponentially
<DIV></DIV>>on the length S(x) ~ x^a (a Bessel horn), where a is called the
<DIV></DIV>>flare constant.
<DIV></DIV>>If we add (2) this then a = 0 and a = 2 are the *only* shapes that
<DIV></DIV>>*exactly* satisfy these two requirements.
<DIV></DIV>>These are cylinders and cones. The shak doesn't fit either of these
<DIV></DIV>>two categories, but
<DIV></DIV>>(generally speaking) is a cylinder connected to a reverse cone,
<DIV></DIV>>connected to something that looks along like a Bessel flair
<DIV></DIV>>with a>2.
<DIV></DIV>>
<DIV></DIV>>It is possible that there are some major compromises going on here
<DIV></DIV>>in terms of playing, but
<DIV></DIV>>there are also several ways of relaxing the criteria that could also
<DIV></DIV>>explain the shape.
<DIV></DIV>>For example, in the shak we don't need the registers to be in tune
<DIV></DIV>>for arbitrary lengths
<DIV></DIV>>of bore, but only for specified lengths corresponding to the notes
<DIV></DIV>>of the scale: that is for
<DIV></DIV>>5 lengths of corresponding to the pentatonic scale. Because of this
<DIV></DIV>>the
<DIV></DIV>>shape (based just on these most simple criteria) could be morphed.
<DIV></DIV>>So within this "wiggle room"
<DIV></DIV>>what kind of shapes would be allowed, and are there any that come
<DIV></DIV>>close to the traditional shak shape.
<DIV></DIV>>This is something that could be explored mathematically is anyone is
<DIV></DIV>>clever enough, but could also
<DIV></DIV>>be explore via the computer. Furthermore, more experience shak
<DIV></DIV>>makers my already have a "feel" for this
<DIV></DIV>>wiggle room, and perhaps they could comment on this, if they are
<DIV></DIV>>willing.
<DIV></DIV>>
<DIV></DIV>>
<DIV></DIV>>By the way, hopefully nobody remembers but I said something stupid a
<DIV></DIV>>while back. It *IS* the peaks
<DIV></DIV>>of the input impedance (not the minima) that correspond to the
<DIV></DIV>>resonance because that's
<DIV></DIV>>where the wave bound around and build up rather than pass right
<DIV></DIV>>through.
<DIV></DIV>>Sorry about that.
<DIV></DIV>>
<DIV></DIV>>Marko
<DIV></DIV>>
<DIV></DIV>>
<DIV></DIV>>_____________________________________________
<DIV></DIV>>
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