Ken Cashion wrote:
"The need is simple...make the top of the box amplify the sound from
the strings. How to do this can be complex. "
I'd put that a bit differently: I don't consider the guitar to be in
any sense an 'amplifier', since it only works with the energy that's
in the strings, unlike the usual amplifier, that uses a small input
signal to modulate an outside energy source. You're absolutely right
about the complexity part, though!
One of the problems we have is that, as usual, we're setting up
conflicting constraints. On the one hand, we want the strings to be
'ideal' ones, producing as close to a harmonic series of overtones as
possible. To do that, we'd have to have the string ends fixed;
absolutely immobile. If that were the case, the guitar would not make
any sound, since the top could not move. On the other hand, if we were
to make a top that moved as freely as the strings it would, in effect,
be a continuation of the strings, and they ould not 'know' how long
they were, or what pitch to produce. So, as usual, we end up settling
on some sort of compromise that is 'good enough', and good enough is a
matter of opinion.
You tell the string how long it is by providing an impedance mismatch
at the end. The impedance of the string established by it's density
and tension and length. Hooking it on to something that is either
stiffer or floppier, or lighter or heavier, will provide the mismatch.
Since strings are themselves fairly light and flexible a heavy stiff
bridge works well.
There are a few ways to see to it that the string stops vibrating at a
particular point on the bridge. You can pinch it in a slot, as they do
on resos, pass it between pins that bend it sideways, as on a piano,
or 'break' it over a saddle, as we usually do. In theory, you should
only need enough break angle to keep the string from hopping off the
saddle as it vibrates upward, and normally 12-15 degrees will do.
If you break the string downward toward the top to stop it, you have
to have some way of providing that downward force, and a structure
that can withstand it over the long term. On the usual type of flat
tiop or classical bridge, which we could call a 'stop' bridge, some
means is used to tie the string down behind the saddle. This causes
the back edge of the bridge to pull upward, and we have to provide the
structure to resist that torque. The tailpiece ties the strings
indirectly to the end block, eliminating the need for a glue line
between the bridge and the top. However, for this to work the geometry
of the instrument must allow in one way or other for that 12 degrees
or so of break angle. Normally this calles for a tall bridge, althogh
there are mechanical ways of making the tailpiece presss downward on
the strings, which call, in turn, for a strong tailpiece. Either way,
the strings are pressing downward on the top, and it has to be strong
enough to resist that load over the long term. Archtop guitars
normally have fairly thick tops, and even then I've seen a lot of them
that have sunk over the years because the geometry was not up to the
task.
Usually to increase the break angle you have to raise the strings
further off the top, so it's hard isolate the effects of the two.
Raising the strings off the top does give more leverage to the tension
change part of the signal, which, happens at twice the fundamental
pitch of the string and multiples of that. In a recent experiment I
noted a rise in the even-order partials of a string when I raised them
further off the top of the guitar, which is what one would expect if
leverage were of primary importance. It is difficult to see why break
angle alone would have that outcome; one would expect it to 'raise all
the boats'. As further confirmation, there was also a large increase
in the high frequency 'longitudinal' wave signal from the string in
the output of the guitar, and that would also only make sense if
increased leverage was in effect. I will note that I did not hold the
break angle constant in this experiment, and need to do that as well,
but so far the results seem to favor a larger role for leverage than
break angle.
In short, there's a lot we need to sort out yet, and we'll get there
eventually.