I've avoided being involved in forum controversies for a while, but there are some points I'd like to address before they become "internet fact." Please don't take anything personally here, just distinguishing facts from otherwise.
The main reason to have as stiff a neck as possible is to raise the resonant frequency of the neck up to a point that it is not affected by the fundamentals of the various strings and notes as to cause dead spots, like the dreaded "dead Eb" [give or take a note) on the G-string of Fender and Fender-derived basses with a one-piece neck.
I'll just add that it's not just Fender-types. I had an early Pedulla neck-thru (before he did neck reinforcements) with a tilt-back Gibson-ish headstock with small tuners, and it also had the problem.
The second reason is that for what resonance remains, a good neck will decrease the resonance amplitude
I've never heard of this. It's possible so I wouldn't rule it out, but I haven't seen evidence of it.
so you don't get mud from the fundamentals off a range of notes, usually about a major third in span, that all want to resonate together, causing problems with intonation and the overtones lining up with the fundamental.
I don't understand what you're saying here. If you're talking about the mechanical resonance profile of the neck forcing the vibrations of the string, whether fundamental or overtone, to actually shift in frequency, I don't believe that will happen. Put another way, Idon't see the mechanism for increasing the natural inharmonicity of the string.
The best way to make the neck stiffer is to laminate it: 3 or 5 pieces, with contrasting stringers to the main neck wood. For example, a walnut or purpleheart stringer on a maple neck; or maple, bubinga or other "super-maple-type-wood" on something like a wenge neck is common practice.
Walnut is less stiff than maple, so replacing any amount of maple in the neck with walnut will make it less stiff. Bubinga, purpleheart, wenge, etc. will stiffen a maple neck because they are stiffer woods than maple.
The different density of the stringer, with the grain cut cross-ways to the main neck wood, will help stiffen the neck,
Different density will not increase the stiffness. Woods with higher stiffness will increase the neck's stiffness. Higher stiffness is strongly correlated to
higher density, although it is not one-to-one.
thereby raising the resonant frequency of the neck,
yes
and lower the amplitude of the remaining resonances,
as I said before, not certain. If you are making a case that increased stiffness results in increased damping, this is certainly not the case.
to get rid of the mud.
I don't necessarily like graphite rods in necks. They may promote stability from a truss rod perspective,
the truss rod may make a positive or negative contribution towards stability, but its purpose is not provide stability; its purpose is to provide mechanical compensation by adjustment when the neck is not stable.
but any time you remove wood, you remove stiffness, and the graphite does not always make up for that.
Incorrect. CF/epoxy "graphite" rods have tensile, compressive, and flextural moduli of elasticity of better than 130 GPa. The tensile MOE of rock/hard/sugar maple
Acer saccharum is 12.6 GPa. Assuming that it is bonded on all four long surfaces (as was the wood that was removed), any CF rod will have ten times the stiffness of that maple that was removed. The effect on the overall stiffness of the entire neck will be dependent on the design of the neck, including all materials present and their physical configuration. But it will always be an increase.
And there is nothing new in the world: google "Opharion" for 16th century lutes that had fanned frets.
Definitely! That's what they had to do to get a broad range of low to high notes on one instrument, before there were wound strings.
