Matt,
The matter you raise was first discussed in September 2002 on the
list. Various suggestions were floated at the time, but the final
conclusion was that the tirant was NOT the issue, because the pitch
difference if the tirant were at fault would be, based on my
calculation, roughly one and half semi-tones (i.e., if the trompette
were tuned to C, the pitch would drop to a very flat B or very sharp
Bb when the bridge started buzzing). There was also some speculation
that the length of the chien was at fault, but if that were the case,
you would expect the problem to effect every HG, and Hungarian ones
(which have a longer bridge) more than others. Since this doesn't
seem to be the case, we have to look elsewhere for the problem.
At the time we asked Daniel Wolverson, at the University of Bath, who
had studied the matter. For convenience, I include his response
below. He has a couple of ideas and ways to test them.
Best,
Arle
Hallo again,
Yes, I'd followed the debate second hand via Frank Vickers in Norwich.
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 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.
I don't know if Peter will be pursuing this further but if we have
students
taking up a similar project this year, I'll pass these ideas on to them.
best regards,
Daniel Wolverson
