Stephen Law wrote:
"An interesting experiment on weight distribution - Use a bit masking tape to attach a weight (any small, heavy household item will do) to the end of your neck. Compare the sound with and without."
This might make quite a difference in the sound, and in might not: much depends on the relationship between the 'neck' mode frequency and the 'main air'.
The lowest frequency resonance on the guitar is usually a vibration mode of the entire instrument like the fundamental of a xylophone bar: as the head and tailblock move 'up', the neck block moves 'down'. There are two stationary 'node' lines; around the nut or first fret, and across the wide part of the lower bout. In most cases this 'first corpus' mode is well below the pitch of the 'main air' resonance (the 'Helmholtz' type mode of the box), and so can't radiate sound effectively. However, since the neck bends a lot in this mode, if it's stiff, and the head is light, the mode can be up as high as the 'main air' resonance.
When this happens, the corpus or 'neck' mode can couple with the air mode. As the ends move 'upward' the top of the box is being compressed lengthwise, and since most tops are at least somewhat arched or domed, this forces the top to puff outward, and suck a little air into the sound hole. As the head and tail move 'down' the top is pulled flatter, and the air is expelled. Since this is what the 'main air' mode is doing too, the two will work together and influence each other.
If you do an impulse spectrum on a guitar where this is happening, you'll see that the normal 'main air' peak will be split into two peaks, a few Hz apart, with a dip in between. The resonance that was formerly very active and sharply defined at a single pitch is now spread out over a couple of semitones, and the peak is not so tall. The area under the curve, the 'total available horsepower' as it were, can be somewhat greater.
In subjective terms, guitars with this feature often have a 'darker' bass timbre. They are less prone to the usual guitar 'wolf' note at the 'main air' pitch.
It's easy to hear this vibration mode. Hold the guitar up by pinching the neck between the nut and first fret so that it can move freely, damping the strings with your finger. Put your ear close to the headstock surface near the top, and tap on the back of the head with a finger tip. You should be able to make out the 'first corpus' pitch, often as low as 60 Hz, but sometimes up as high as 100. '
The neck bends a lot in this mode, so it is often called the 'neck mode'. The stiffness of the neck and mass of the headstock, make a big difference. Using light weight tuners, or pegs, will raise the pitch of this mode, but often that's about the only 'after market' way to do so. Making the neck thicker at the body end is a good way to rise the pitch of this mode, and carbon fiber reinforcements in the neck can help, too. Cedar necks tend to be lighter than mahogany, and have higher pitched 'neck modes'. In one case of a short scale guitar I actually ended up adding mass to the headstock to get the 'neck' mode down in pitch: that guitar had a somewhat 'cutting' timbre, and achieving the couple smoothed it out noticeably.
To get back to Stephen's comment; this is one of those things that has to match very closely if it's to have a noticeable effect. The half power bandwidths of these modes are only a few Hz; a semitone or less, and you need to get within that range for effective coupling. A few grams one way or the other can make all the difference if they're close, but have no effect at all if they're not. It's like having 007 tied in a chair with the water rising: it doesn't make much difference until it reaches his nose, but the next few centimeters...