Sorry, I think I just created the most ridiculous bass possible.
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Bahaha! That's awesome.
What exactly is your reason for wanting extra stiffness? I'm confused about your goals here, and the problem(s) you are trying to solve or avoid.
Yes, same here.
What do you mean by your statement that most of the instruments we play these days are over-engineered? You want to build a better bass by doing a sloppier job designing it?
Ah, okay. But to clarify, they are under-engineering their basses, playing it safe by making everything into rigid beams. Stability, sustain, pingy sound, etc are the usual excuses. The result is a solid, beautiful looking, plank of wood with pickups. The sound is all in the pickups. Or maybe a really cool preamp. Low risk, cool looking, yawn, everybody does that.
You, on the other hand, are looking to use superior and excessive engineering to make the frame of the bass participate in the sound, bringing in rich tonal qualities that you can't get from rigid planks of wood with pickups. You are crossing over into the other side of bass building, where only the brave Luthiers venture.
My take: take a large enough but thin piece of wood (say 3/4") and shape it into a body. Bolt the neck on its surface. It's essentially as if the entire bass was routed to the depth of the neck pocket, hence no neck pocket (though there's no routing necessary, because it was thin to begin with). But it's also very thin, thus its structure is compromised, giving it more acoustic sound.
The bridge would need to be tall (I'm thinking sort of like on an upright), or placed on a block of wood. Between the neck and the bridge, you could place your pickup anywhere, and no routing required.
If the solidbody design is essentially about taking away wood that is not needed (e.g. neck pocket and pickup routs), this approach adds wood where needed (e.g. pillars). I'm not sure if it's a viable design, but I presume it's not used by large manufacturers because it would take more work and be less reliable than routing, and luthiers wouldn't do it because it's of lesser quality than a properly built bass.
Michihiro Matsuda with Rick Toone are the top of that tree...
I'm hoping to push beyond that.
What you're refering to is pretty close to Jens Ritter's Princess guitars...
Ritter Princess Isabella Benson Tribute