I asked an engineer today at work, whose specialty is vibration analysis, about some guitar related stuff. I found out some interesting info. Just some conclusions I drew:
1) More dense = more inertia for a string or vibrating object to overcome, but more sustain once set in motion. I sat there for a while analyzing the engineering formula for inertia as applied to a vibrating string between two points. More mass means more inertia, so while it may be more resistant to being set into motion initially, once set into motion it will take more for it to be dampened.
2) Ways to get more sustain: hit the string harder (more initial force), pluck it more towards the center of the string (force in the equation is modified by where it impacts the string), and make the two points between which the string is suspended more resistant to being moved (one way: making them more dense, since more mass means, again, harder to set it into motion, but then also harder to dampen the motion).
3) All other things being equal, thicker strings require more tension to tune them to pitch. This could both cause strings to not vibrate as long compared to their thinner cousins, but also mean that they vibrate longer due to mass in the form of inertia. The jury's still out: I'd need to calculate the dampening effect of the string due to tension and then the amount of inerta the string would have, since those two factors will be combating each other.
4) It's nice that electric guitars are electric, but ultimately, this means that the wood will have a small effect on overall tone. True, it will have an effect, but the wood is more of a damper that has other resonant frequencies, so it will color the tone, but sucky wood will have sucky tone. Case in point: maple is more dense than swamp ash, which gives it higher sustain (since it resists motion being transfered to it more, thus sort of reduces the dampening of string motion by the body), but you may not like the overtones it has due to its internal resonant frequencies.
5) More mass means more inertia applies to floating tremolos. For example, an aluminum tremolo block and such will be less dense than nickel or steel, meaning that you will get less sustain, or should, all other things being equal. Callaham's tremolo blocks should, then, be better for sustain. Also, a six-point tremolo block bolt pattern should get less lost sustain to the dampening of other factors, but the jury is still out.
The most I got to was the "how much vibration will you get based on string and force". Bottom line, however: more sustain should come from having end fulcrums (i.e. string nut and bridge) that are more resistant to vibration (i.e. their larger mass / resonant frequency tends to reflect energy back to the string rather than dampen it). Also, the last thing we found together was that if you have strings and a bridge / nut that are the same material, you should get better sustain, all things being equal. If you can afford a nickel steel string nut and saddles that are the same alloy as "pure nickel" strings, you should get nice sustain, all other things being equal.
Lastly, yes, when I told the engineer how pickups were made, he agreed that they could be essentially acting as magnetic dampeners if too powerful, so more sustain should come from weaker magnets and/or magnets farther from the strings, but again, there's no one "magic bullet" for getting huge sustain: too many factors.
I'll start digging into more math monday
), people thought that 12 lb Les Pauls with brass nuts and heavy hardware was the route to tonal nirvana. Ultimately, a lot of those instruments were deemed more useful as firewood than as musical instruments. Perhaps things are coming full-circle.
