sdsollod asked:
"- Is it possible to design a back somewhere in the middle between live and reflective to attempt to achieve an overall versatile instrument or will this effort simply render the design neither live or reflective?"
Im starting with this one because it's really the central question. As far as I've been able to figure out from testing a lot of guitars, the only truely pure 'reflective' back is on an Ovation, although some of the Renaissence 'chittarras battante' might qualify. Any normal guitar you're likely to run into has a back that both 'reacts' and 'reflects'. It's really a matter of degree.
If you think about it, when the back vibrates it has to be getting the energy from someplace, and the only place it can come from is the strings. Since the back is heavier than the top, facing in the wrong direction, and is usually up against somebody's pudgy avoirdopois, it's not going to be nearly as effective a sound producer as the top. This suggests that making the back as 'dead' and 'relfective' as possible might be the way to go. I think that's probably pretty close to right, but not totally.
There is one range where the back can actually help the output power of the guitar, and that's in the 'bass reflex' range down at the low end. The top and back get into a sort of complicated dance as you go up in pitch from the lowest notes to about the open G pitch, and a back that can move even a little in that range will pump some air through the sound hole. It's complicated in part because the back is responding to two forces from the top that are out of phase with each orther: the air pressure in the box rises as the top moves 'in' and pushes the back away, but, at the same time the edge of the top pulls the side up, and pulls the back along with it. These things don't exactly cancel out because the lowest resonance of each plate is at a different pitch. If the top were the only thing working the bellows the air moving through the hole would be pretty much cancelled out by air moving off the top in the opposite direction ,and thus not much sound would be produced in that range as you move away from the guitar. With the dance the back is doing you can end up with significantly more power output, and an 'interesting' spectrum too.
Above roughly the open G string pitch back movement does pretty much 'steal' power, but mostly at fairly specific pitches. In other words, the back is mostly reflective anyway, except when it's not. The resulting 'dips' in the output of the guitar account for a lot of the 'tone color' that allows the player to 'shape' the sound. What probably counts here is how deep and narrow the dips in the spectrum caused by back motion are: if they're shallow and/or narrow they won't coost much power, but can still contribute to 'color'. A heavy and/or stiff back will tend to be harder to move, and keep the dips shallow. A back with low losses makes narrower dips. Note that we're describing woods like Brazilian rosewood, that is dense, stiff, and rings a long time when you tap it because it has such low losses.
"- Does a live back limit the head room and projection? ...or does a reflective back limit overtones?"
Let's see: given the above we'd expect a mahogany back to be 'live' and an IRW one to be 'reflective'. Does a D-18 have more or less 'projection' than a D-28? Overtones?
In my experience as a maker, 'headroom' comes from the top more than the back. It's mostly a matter of top density and stiffness (which go together), the top bracing profiles, and bridge mass, in order of importance, IMO.
"- Perhaps the reason players gravitate to a particular shape or style of guitar reflects the style they play. For instance, bluegrass players prefer dreadnaughts, rag players like L-00s, many country players like jumbos, and fingerstylists like OMs and OOOs. It appears that generally, the various styles of guitars are designed with either a live or reflective back depending on their style of play."
Again, it seems to me that it's not so much the 'live' or 'reflective' back that comes in here, as a combination of other design elements. Dreads have a particular timbre, in part because of the shallow waist, that suits the rythm style called for in Blugrass playing. Small bodies, like the L-00, are more 'treble balanced' than bigger ones, and can also actually produce more power, so they have a tendency to 'cut' and 'project' more, as well as the kind of 'clarity' that helps bring out the ragtime structure. OMs, and 000s have a 'warmer' sound than the smaller boxes, and the waisted shape gives them more mid-range clarity than the Dreads, which suits the usages of fingerstyle playing. And so on.
So, yes, a maker can and does mess with the proportions of 'active' and 'reflective' in the back as part of the way they shape the tone. There's no 'purity' though, and the proportions that will work depend on each maker's methods of work, design philosophy, and choice of wood for a particular guitar, as well as the desired outcome, of course.
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I've read over your comments several times. As expected, its quite complicated and there are no easy answers. It appears from your comments, that the back wood species plays a large roll... "we'd expect a mahogany back to be 'live' and an IRW one to be 'reflective'". I would assume that bracing also contributes to a large degree. As you said, " a sort of complicated dance". Which I assume has to do with size and dimension of the bracing. It stands to reason that you could make a mahogany back more reflective with stuffer bracing and a IRW back more live with less stuff bracing...