....I also like 12 fret necks. I like to imagine that letting the body touch the neck at the point of harmonics disrupts the sound waves less. Wave reflections should stack in phase.
Doubtful it means anything, but it's all in fun!
Yes, it means nothing (with respect to harmonics). The second harmonic is only over the 12th fret when playing an open string, so even if it did matter, it would only matter for those 6 notes.
What it does mean is that the bridge is in a slightly different place than it would be on a 14 fret neck, which has to be accounted for in the bracing, which effects the way the top moves, but it's pretty subtle.
I apologize for not making my thinking clearer, I was just touching on my ideas, which are not so much ideas like words, but mental images/visualization. I'm more intuitive than mathematical. Don't confuse me with the facts!
Anyway, here is an attempt to change the ideas into words.
First a disclaimer, I'm vaguely aware that guitars, like sailboats, have compromises made to make them playable. So my discussion here is merely the thought flow I've had while playing with my guitars, it's not meant to be exact, I don't have any urge to argue (this is sailnet after all) about any of it. I'm sure I'm glossing over the fine points.
I do know for sure that the idea of wave forms moving through the guitar had nothing to do with why I own several 12 fret neck guitars, and play them more than the 14 fret guitars I own. It's just an idea that occurred to me while playing them. You are probably right that the construction is more important, perhaps the proportionally larger "chest" on the box allows more resonance, I don't build guitars, just enjoy them. I think Martin claims there vintage guitars move the X bracing up an inch, so that may be a factor, creating a more flexible "belly".
The following is stuff I've thought about, not anything that is proven or backed up or taught anywhere.
I probably should not have mentioned the harmonics in the previous post, I was using them to define the location as being at a major nodal (non-moving) point on the string. I didn't mean that the harmonics were the wave forms that interested me. I think harmonics are too easy to achieve. Thinking back to my high school physics class, I was visualizing the wave tank. When the wave cycles per second were adjusted so outgoing waves were in sync with waves reflected off the end wall we got perfect standing waves, with nodes that held still while standing waves moved up and down.
Those standing waves are what we like in music. Many perfect fractions of the wave cycles will also match up (sync) with the standing waves. The frets on the guitar automatically make those fractions (with some compromises of course), but with a fretless instrument it's easy to hear/feel them.
The 12th fret is unique in that if fingered you get an octave above the open string. If you play the harmonic there you also get an octave. There is nowhere else like it. I suppose it more or less cuts the string in half.
I visualize the sound waves resonating by bouncing (reflecting) back and forth, on the sting and through the guitar body and neck, the sustain coming from the trapped standing waves reinforcing each other with nowhere to go.
As a side note, I also visualize that as strings get older and suffer corrosion, metal fatigue, and crimps at the frets and ends they develop stiff spots, where sound waves are disrupted and scattered a bit, sending out random waves that are not in sync. This of course kills the purity of the sound and makes fritzy dissonance. You still get the standing waves, but they are covered with tiny random waves.
(Back to sailing for a second.) Imagine a smooth wave train from the wake of a powerboat at a distance on a calm surface of water, and then imagine the same wake with a gusty irregular wind blowing over it, and hitting dock pilings etc. The choppy one is the sound wave on the old corroded string. To me that helps me understand why I like brand new strings, the waves keep a purer form for a longer time. I always wipe down (polish) the strings when done playing, to at least reduce the corrosion from my dirty sweaty fingers and skin acid. The other stuff can't be helped.
Anyway, side "note" over with. Waves reflect off any fixed object that interferes with their free motion. Since (again, I visualize, no proof) the waves are traveling up and down the length of the guitar, it's probable that the vertical rise of the sound box (body) of the guitar acts like a "strong back" in carpentry, at right angles to the length of the guitar, and causes a stiff spot. Since this change in flex should make reflections, it is important that it lands on a non moving nodal point.
The 14th fret is a nodal point, so no problem. But, the 12th fret is the ultimate nodal point, just play harmonics at various points and see if anywhere is as easy as the 12th fret. And since it is also the open string octave point, it seems (to me) to be the ultimate point for a stiff spot in the flow. Any note played on the guitar will have a node at this point (and the 14th fret also). When playing open chords at the nut the open strings should have some reflections that are octaves. Octave reflections are longer than harmonics, they seem to last longer and can be felt more easily and, for an old fart like me, heard more easily. Generally turning your sound energy into high frequencies reduces its effectiveness, we feel bass easier, it carries further. A stiff, poorly resonating guitar turns a lot of the sound energy into harmonics, sounds bright and detailed, but is not as thick and rich sounding. The octave reflection seems like a small point, but if waves are moving a hundred times a second you can see where bleeding off energy into harmonics can have an almost immediate effect.
I own an old large black(gun)powder horn from the southwest that has carved and inked on it a guitar - among other things like senoritas, and wine bottles and glasses, and a lizard. It's not in front of me, but I believe the guitar has a 12 fret neck. I'll bet for a century or more they were normally built with 12 fret necks, and the 14 fret neck is a modern compromise to allow playing further up. For all I know it started after amplification when good acoustics became less important. Personally, I now own a 12 fret neck with a cutaway to reach the higher frets, I know I often want to go to a high D chord which I can't get cleanly without the cutaway. I'm sure the cutaway detracts from the sound - compromise again!