Todd Rose wrote: "Just to clarify, when you said, "If you make two tops of different density wood, but make them to the same thickness, you'll find that the one with the lower density will be a bit lighter in weight" ...you meant stiffness, not thickness, right?"
Right, missed that mistake, it's two tops of different DENSITY and the same STIFFNESS.
Also, I didn't say you should look for FLOPPY tops, I said look for LIGHT (low density) ones. I, too, try to avoid tops with too much cross grain flex, if only because they're harder to tune.
Back weight:
In general, you would not expect the back to be as good a sound producer as the top. After all, it's usually heavier than the top, it's not being driven directly by the strings, and it's facing into your soft pudgy belly, where the sound can't go very far anyway.
As far as I can tell, the back only contributes to power output in the 'bass reflex' range, where air is being pumped through the sound hole most actively. If the 'main back' tap tone is low enough for it to couple with the 'main top' tap tone, it will help the top pump air through the hole, and also act as another added mass (along with the top) that will drop the 'main air' pitch. Usualy this works best if the back is about a semitone above the top pitch.
A light back seems to be more effective at working with the top in the bass reflex range. Surprisingly, in some ways, since the 'bass reflex' is the low range, this often seems to make for a 'bright' sound. I suspect that this has something to do with the faster 'attack' of a light back: the sound is more 'edgy'. It's also likely that another mechanism that was noticed by Wright in his 1996 PhD modeling study of guitar acoustics comes into play.
We all know that any guitar top or back will have a number of resonant pitches, where it is easy to drive to a high amplitude. These are analogous to the 'overtones' of a string, but not at 'harmonic' pitches, because of the complicated structure. It turns out that the 'main top' and 'main back' modes are much more effective at producing sound than any of the other modes. This is simply because all of the others consist of a number of areas that are out of phase with each other, and thus cancel out, more or less. Wright noticed that the 'main top' mode is so much better at producing sound that it dominates the output of the guitar all the way from the 'mair air' pitch, an octave or so below it's own natural frequency, all the way up to about 1000 Hz; the fundamental of the highest note you can play. Thus, making the 'main top' mode stronger can actually improve the output of the high frequencies. This seems weird, but remember, resos pretty much only have a 'main top' type of motion, and they've got lots of high end.
Above the 'main back' frequency any energy that is fed into the back is energy that can't be driving the more effective top. Thus it seems that limiting the amount the back moves at higher frequencies would probably be helpful. There are a couple of ways to do that.
One is to give it a high 'impedance'. That's just a measurement of how hard it is to drive something at a particular frequency; physically it's the Force/Velocity at that frequency. Since (again, acording to what I can find out so far) most of the energy that moves the back comes from the air in the box, and air has a low impedance. If you make the back heavy or stiff most of the energy of the air just bounces off, and doesn't cause the back to move.
Another is to limit the 'damping' of the back: decrease the amount of energy dissipated as it moves. Not only does this cost less power per cycle, but it also limits the range of frequiecies over which the back can be easily driven. This is because low damping oscillators have a narrow 'band width' (or 'high Q values'): they can only be easily driven near the resonant pitch. A familiar example is a kid on a swing; you can only get them going high if you match your pushes to the natural rythm of the swing. On the guitar you could think of the top as the person doing the pushing, and the back as the swing. If you look at the output spectrum of a guitar, it will often be the case that the back resonances will be seen as dips in the output. A high Q back will tend to have narrower dips. You don't always want to _eliminate_ these: they seem to add to 'tone color', but you want to minmise the amount of energy you lose.
There's another aspect to low daming/high Q that's interesting. One thing that Q value means is the proportion of energy that's being lost per cycle. A piece of rosewood with a Q value of 100 is losing 1% of the energy of vibration for every round trip. It's also hard to feed energy into the system much faster than that. Again, you don't usually try to get the kid on the swing up to full height with one push. It takes a while to get a high-Q back going, and this, too, probably limits the losses to it.
In light of this it's probably no coincidence that we like rosewoods, which are dense and have low damping. It's also no surprise that either light or heavy backs can work well, although they do tend to sound different, of course.
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