Hi Arle-
I don't remember Daniel Wolverson's discussion - I'm glad to see it now...
The flattening of the pitch when the chien starts to vibrate is probably an
effect which is known in violins when bowed hard. Probably, the chien
continues to be the end node of the vibrating string as normal. The effect
arises because the string has a finite stiffness and doesn't execute a
perfect Helmholtz motion; instead of sharp triangular displacements
travelling up and down the string, the corners are rounded (N. H.
Fletcher & T. D. Rossing, Physics of Musical Instruments, Springer 1998).
The
amount by which the bow modifies the shape of the displacements leads to a
connection between the bow force and the shape of the displacement (and the
frequency). I don't have details of a quantitative model. This explanation
of the
effect should be testable; if people who observe it fix the chien so it
can't buzz and then play as hard as if using the chien, the trompette
should still
detune [anyone care to try this?]. If the effect annoys them, a different
make of string (lower stiffness) might reduce it.
I feel as if I've tested this idea - I "fixed" the chien by simply holding
it down to keep it from buzzing and continuing to crank as if I was
attempting to buzz... no drop in pitch. Anyway, doesn't his test condition
describe the permanent condition of all the other non-buzzing strings?
I expect that your calculation is right [the one indicating that a pitch
drop of ~150 cents would be expected if the tirant to the top of the string
were vibrating], that it's not that the string beyond the chien suddenly
becomes added to the string length. However, there might be a related
explanation, which is the other possibility. It's also known from violins
that when two strings pass over the same bridge, there is a coupling between
their separate resonances that modifies the frequencies of both (this is
also the effect that harmonica players use to bend the pitch down; Johnston
1987, cited in the same reference as above). It's likely that the degree of
coupling between the back and front halves of the trompette string increases
once the chien vibrates, causing the detuning to increase. The test is that
the detuning would presumably be prevented if the chien was fixed so it
can't move (unlike in the first case). The cure for the detuning might then
be to increase the mass of the string behind the chien in order to push the
separate resonances further apart and decrease their interaction.
This is more interesting! It's true, this is an effect that harmonica
players use (I've never been able to bent pitch *up* on a harmonica!). But
in this case we're not talking about two similarly tuned reeds vibrating
simultaneously, nor are we talking about two separate bowed strings resting
on the same bridge. Do you suppose the same effect applies with only one
string on the bridge, and that being bowed on only one side of the bridge?
~ Matt
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Matthew Szostak - Hurdy-Gurdies
7 Grove Street
Camden, Maine 04843
phone: 207-236-9576
email: [EMAIL PROTECTED]
website: http://www.midcoast.com/~beechhil/vielle
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