I'm not convinced about any of this 'air in the pocket' or the analogies to a fair bit, though I could be wrong. Sum's point about there being a discernable difference is important to keep in mind also.
Why, because most of us, or those that have worked on making good set ups, have shims andtherefor 'air' as a natural consequence. The analogy of john's...
In this analogy we ahve a weight bearing load directly down and so, the bigger the surface area the better, but in teh gutiar neck, it is acting more as a lever, pulling up under string pressure to the rear of teh pocket....
nevertheless...a good fitting pocket is advantageous from a structural point of view and adds to the rigidity. Not at all sure about the use of that kind of compound as there are lots of perfectly adequate alternatives that would also work...plastic wood for instance, in cobination with strong non compressive shims, or a shim made to fit...lets face it, shims need only be fractions of a mm in most cases anyway. I've used all kinds of materials and found that they or the wood around it under the significant pressure of the screws compress well to conformity.
Fitting tothe side can be a problem, especially with soemthing like a strat which has little 'side' support with the double cutaways compared to say a telecaster or an LP and the like. Again, one can use a material like plastic wood (or stronger epoxy based things) to build this up to make things fit 'perfectly'.
The above pictures are of the 'jazz strat' project hich required a complete neck pocket reconstruction to mate the odd neck to the odd body. The bottom of the neck pocket required a big wedge to get the required height and angle to it, but the sides also needed to be built up around the neck itself. I used wooden 'tounge depressors or icecream sticks'in the most partand finished off with plastic wood aroung the neck. Once dry, removed the neck and back filled to that level and a little beyound then carefully sanded it back till if fitted 'perectly. One benefit of the 'plastic wood' is it is water based and will not really 'stick' to the varnished neck. Similarly, the base was treated such and not sure, but suspect I did shim it as well in the end just a little as this is an important 'adjustment'...
In relation to 'sustin' shiming a neck often improves things by raising teh bridge and so improving the breakover angle on the bridge and providing morepressure, far more than a little 'ait' in teh pocket. From a 'forces and pressures' pont of view, the forces are mostly to the back of the pocket pushing down, to the front pulling up against the screws. So the loads are very different to those described in john's 'straight down compression' construction example where all the load is down and the bigger the area taking the load is advantageous.
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On my acoustic Godin seagull, it is interesting that they use a special mirror router device to perectly fit a particular neck to a particular body. On an acoustic, rigidiy is very important as you want all that energy to be transmitted to the top. Although it is not obvious, these necks are joined through a big neck join and bolts and with the neck going through to the end of the fretboard along with the truss rod and no percivable 'gaps'...so it is possible to make 'perfect fits' as good, possibly more so than a glued in 'set neck'...
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Honestly though, on most electric guitars and the way they are set up and played, a little 'air' in an otherwise 'tight' join will have little if any disernable efect and the resutls may well be skewed. I obviously could be 'wrong' but really, on practically all my guitars I ahve added shims and so 'air' and all that has occured that is disernable, is an
improvement due to the angle in regards to the bridge and the break over and pressure there. This was particularly evident in my tele which I beleive has a brass shim and quite a bit of a 'gap' under it (though tight all around) as the khalers are particularly prone to having to shallow a break over those roller saddles.
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As for the actual thread, the scalloping will by necessity result in a decrease in 'rigidity' even if the truss rod provides adequate 'spring' to counteract the string pressure and remain straight...far, far more of an effect than a 0.5mm of partial air under the neck that is not carrying any kind of compressive load (that is all in the rear of the neck pocket).
After hearing a clean example of the problem GD has been having finally, the resuts are very poor. Is it noticable under heavy distorion, well, possibly but then, doing that provides extreme compression to the signal and hard to discern. That is is 'acoustically louder' is related to the conservation of energy I suspect. If you can hear it, like if there is heat in a circuit, then there is energy lost as something is vibrating enough to move the air so that we hear it more, which apparently the case.
WIKI
So, by picking a string you are introducing energy, how that is expended detirmine how the speed at which the energy is lost and so the 'sustian'. The ideal structure would be extremely ridgid and resistant to vibration. The guitar neck is a long thin structure and obviously a 'weak link' that requires careful consideration. Something like carbon fibre necks is going to have fairly extreme qualities in this regard, certainly in relation to the energy in a string to move it and compared to wood. The forces are also 'up' in relation tothe strings, so adding a very hard ridgid materail like hard maple, rosewood and ebony will have a bit of an effect on the structure, as wil this 'lamination' which provides more ridgid strength. By shaving away this critical fretboard and hard material and creating thinner 'lamination' all these aspects are adversely affected...and so the neck might well 'move' and it is not just the movement of the strings in air that youcan 'hear' but the neck itself perhaps.
As for the weighted headstocks, this does also make some difference, form my experience, it certainly seems to 'change things'. The headstock is even weaker than the neck itself, more prone to potential vibration and the fixing point of the end of the strings. Now, if one weights the neck, there is going to be some changes in the resonant frequency that the neck vibrates at and make it harder to get momentum trying toi vibrate something 'heavy' or more ridgid and so will effect sustain. This can be evidenced by the changing of cheap light weight tuners with heavier sealed ones or indeed 'weighting' or reinforcing the headstock. In my experience anyway, and an 'experiment' that is done often by anyone swapping out tuners.
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The intention of me, or others, I am sure is not to sound 'snide' or 'pompus' and certainly, maintaining ridgidity and strength and removing causes of vibration and loss of energy are all factors. But, the discernable differences does matter. As for using differnt materials to achieve that, well, heat transfer paste to me, seems notthe best, certainly it might remove the 'air' but I suspect it is not really 'load bearing' but designed to transfer heat..and not quite the material to suggest when there are so many other alternatives. A really useful one that I often use for various things, made by Selleys' is this epoxy putty...
www.selleys.com.au/putty/epoxy/knead-it-multi-purpose/Unlike some fillers, this does not shrink, is epoxy and so way harder than wood, it also comes in a 'metal version' or the plain white type, very easy to sue, though generally requires acetone to clean up, but is not messy really. There is an outer core and an inner core, so you just cut of a little bit that you need, kneed it together to start the reaction, and then you have about 5 minutes till set. It is far stronger and harder than say wood but sands and works well.
SOmething like this is designed to do eactly this kind of thing, unlike 'heat transfer paste' which I suspect, given it's application, might well not be so rigid as it must have to expand and contract with heat and so not be quite so 'solid' anyway, perhaps even ahve a dampening effect that would defeat the pupose somewhat.
But again, what is the discernable difference, the common shim, if well done, shows no disernable effect (regardles of what some may "say") as far as I can tell from actually doing it and is common practice. Anacdoatally, for other factors, shims generally improve things, but that is not because the 'air' introduced is advantageous. There are reasons if you think through the stresses at play in this application, that indicate that this is so, the forces are all down at the reatr of the pocket and up at the front and there is a lot of leverage on the guitar neck from the string pressure to that effect.
The thing that keeps occuring is the consideration of one aspect, such as 'sustain' in the title of this thread, as if it can be viewed in isolation or that 'any losses is a bad thing'...in fact, changing these things can radically alter other aspects of the "tone" of the guitar, much of which relates to the harmonic content and the ASDR aspoects of all of them, and of course 'tone' is much coverted in the guitar world, is it not? A perfectly ridgid structure with the full harmonic spectum undampened with an imperfect system of equal temperament and intonation, might well not be a good thing and lack 'character'. Of course though, with electric gutiar, there are so many other factors, particularly with aspects of distortion that make these aspects a little 'mute' to be honest. Once you put on huge amopunts of high gain and compression and such, that will take out all the subtlties anyway as everything will boosted to, ususally well above, the maximum threashold as long as there is any kind of vibration present at all. Most will hardly tell one guitar from another under such conditions anyway! If played in such a way, is it really worth wringing ones hands over such details, again it is as Sum suggests, about discernability to a great extent...and who you consider to be listening, even if you can 'hear it' can anyone else honestly, tothe detriment of what they are hearing in the music?
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Yeah, I know...word length, sounds pompus...but that is neither here nor there. I may well be 'wrong' or missing something for sure, but the principles explained seem to be evident regardless of percieved 'law'. The thing is with any debate, it is the person making the 'claim' who needs to prove or take into account all these aspects and do the 'experimentation' to prove the claims or bring forward other aspects to consider that have been missedby say me or others here. It's not meant to be offensive but to further knowledge and there is nothing better than to be proven 'wrong' with a correct answer for any honest person who desires to p[rogress and improve.
It's not for instance that I personally don't like 'distortion' or 'scolloping' or any of that at all, it may well be that such aspects disolve much of the isues anyway as everything is 'boosted' to the clipping threashold hard, so many of these aspects are of little concern in real world use if you never play 'clean' or you are playing single lines and find the scolloping advantageous or whatever, but, there are sound structural principles at play that can be thought through and considered and I think should be or at least be mentioned, without people getting all 'messed up' about it. And, amny of these things clearly, cant be explained in a few short 'quips' obviously, because no matter how much or amny these things are alluded to, the fall back position for much of teh guitar world (and elsewhere) is to hold on to these commmon 'lores' and misconceptions and such. That's my feeling about it, and it seems to be borne out in practice...could be wrong, but that is for other sto discuss with reasonable answers and princilples.
Anyway, reading these replies are optional, it's not like there are any bonus points, generally the opposite applies...