I would say that the direction of the plucking should be almost irrelevant.
The bridge represents a node of the wave while the antinodes (where the mass
of the string moves) is in the middle of the string (if you are not playing
harmonics otherwise there are more nodes and antinodes but always a node at
the bridge and one at the nut). So there shouldn't be a relevant effect due
to the orientation of the plan in which the strings vibrates because at the
bridge there is no transversal string movement, in the ideal case.
So, what does actually make the sound? The way the pull of the
string on the bridge changes when the string vibrates and the way the top
and the bridge react to it. When vibrating, in the instant when the string
is stressed (in a curved shape to say so) there is the maximum pull on the
bridge, in the instant when it's straight it's again in the equilibrium
position and the pull is the same pull of the string at rest. Of course the
picture is much more complicated as the string envelope is not a simple
sinusoid but the sum of the many sinusoids, which are the harmonics, that
produces the timbre of the instrument. As anyone knows one can control the
power spectrum of the harmonics plucking the strings in different positions
with respect to the bridge.
If the top was perfectly rigid you wouldn't hear any relevant sound,
just the sound produced by the turbulence produced in the air by the moving
string. On the contrary the whole which consists of the bridge, the top and
the chains is a complex system of springs and masses. Simplifying, one can
consider the top as a foil of some uniform and elastic material. At some
height from the top there is the bridge hole where the string is tied. In
rest conditions the string pulls the top of the bridge which tends to rotate
toward the nut to ease the pull. This is very important. If the hole was
done just over the top the bridge would not rotate. There wouldn't be a
significant torque but only a pull parallel to the top which couldn't create
any oscillation in the top itself. The higher the holes over the top the
higher is the torque which the strings apply to the bridge. To counteract
this torque the top bends because it's solidly glued to the bridge. You can
easily see on your lutes that the part of the top which is in front of the
bridge is a little bit curved inside the lute and the contrary is for the
part of the top behind the bridge. When you remove the strings the top tends
to go back in a plane shape. This is one of the reason for which is
advisable to change one string at once, that is to maintain the top under a
constant tension.
Well, you have got the picture: when the strings vibrate, the torque
it applies to the bridge changes periodically and so the top curves more or
less to counteract the extra torque. The weight of the bridge is important
too as it's a moving mass which interacts with the oscillations of the top.
Also the rotation of the bridge interacts with the string itself being a
movable point instead of a fixed one as the nut is. The pull of the string
is very important. If one uses strings too heavy for the thickness of the
top, the bend of the top is so strong that the amplitude of the oscillation
is smaller: the bridge has not enough freedom to oscillate. The sound decays
soon and it's percussive. If the strings are too light on the contrary there
is not enough strength involved and you get a too weak even if resonating
sound. Of course there is a quite ample range between the two extremes.
The chains are very important not only to avoid the collapse of the
top but mostly to modulate the way the top oscillates. In fact to make the
top more rigid against the torque applied by the bridge the chains should be
parallel to the strings but they are on the contrary almost all
perpendicular to the strings and perpendicular to the oscillations mode of
the top. Just a few chains near the bridge are shaped differently. The other
chains are weights which makes more difficult to the top to oscillate where
they are, so they let the oscillation modes which have the nodes in
correspondence of their position to resonate freely and dump the modes which
have the antinodes there. Also they add mass to the top and so probably
prolongs the oscillation which otherwise would be dumped soon.
When I went to collect the new marvelous 6c that Martin Shepherd
built me, he showed me that the two main chains under a Renaissance top
where not parallel but slightly angled. I think that this was done to
counterbalance the effect of reinforcement of the oscillating modes which
have the nodes where the bars are, making different part of the top
responding better to different frequencies.
Said this (I hope it isn't just a mountain of baloney 8^))), I think there
is actually a difference if one plucks inside the lute or semi parallel to
the top, but I think it has more to do with the attack of the finger to the
strings, the strength the finger transmits and the way the string is
released. With a pluck inside perhaps, in the lute case, is easier to have
both strings to sound at full volume.
Francesco
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