Philip,
You wrote::
John's post about Helmholtz resonators seems to
suggest that a long narrow neck would cause more (or at least
different)
resonance problems than a bag where the neck opens out broadly from
the
narrowest point at the stock, "
I did the sum earlier this evening - a bag with a conical neck has the
same fundamental frequency (ish) as a bag of the same volume, but a
cylindrical neck of the same length, with the same cross-section as
halfway along the cone.
So the advantage is mainly that you avoid sharp corners. It doesn't
move the frequency much.
The higher harmonics of the bag resonance will typically be way higher,
whatever its shape - experimentally you can check this by blowing the
harmonics of a beer bottle. A Newcastle Brown bottle is a good
Helmholtz shape, and the 2nd harmonic is a lot higher than the
fundamental, while the 3rd and 4th are far higher again --
ear-splitting! Good embouchure practice, and excellent for getting
yourself thrown out of places.
John
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