DBW wrote:
"I researched dead spots and read that the string frequency and the fretboard frequency in particular spots can cancel each other out. My instructor said the fretboard was dry and needed lemon oil."
All guitars, solid body or acoustic, can vibrate as a whole, and have resonances that resemble those of xylophone bars at a number of frequencies. Since the neck does flex a fair amount at these pitches these are often called 'neck modes', and I'm assuming that's what you're talking about.
On most steel string acoustics the lowest 'neck' mode is quite a bit lower in pitch than the low E fundamental. It has stationary 'nodes' somewhere around the nut or first fret, and on a line across the lower bout near the bridge. It's 'way too low in pitch for the string to drive directly on steel strings; on classicals it can be high enough to matter, but the driving mechanism is not direct from the string, but rather through the air and top. It doesn't get moving unless the 'main air' pitch is a pretty close match with the 'neck', and when it does it can actually help the low-end sound.
It's possible to find a couple of higher pitched such modes on most guitars if you work at it, but in general they're not anything to worry about. For one thing they tend to happen at fairly different pitches on different guitars. Remember, these are whole-body resonances, so things like the stiffness of the sides and the mass of the tail block can come into play. Too many variables... They're also much weaker than the lowest 'neck' mode, so you would not expect them to have any major effect. Not saying it's not possible, mind you...
On a solid body electric the neck is by far the lightest and most flexible part. It's not too hard to find three pretty active resonances of the whole machine it the range of the fundamentals of the strings. Often enough, in the few times I've looked at this, the bridge is on or near a stationary 'node' line for all of the lower modes, so the strings can't drive them by pushing on the bridge.* If there was a moving 'antinode' of the resonance at a fret that sounded that pitch the string could drive it. You'd notice a drop off in either volume or sustain, and possibly a change in pitch of that note, or even a 'buzz' caused by the two polarizations of the string vibration having different pitches, as happened to my customer. It's just (barely) possible that oiling the fingerboard might alter the pitch of the resonance enough to 'fix' the problem, at least for a while, by adding some mass and damping and possibly reducing the stiffness a bit.
I don't have data on this, so take that with a very large helping of salt!
*
Any 'free' vibrating beam, like a xylophone bar or solid body guitar, has a moving 'antinode' at both ends. A string attached to the end can easily drive that. Solid body basses tend to have their bridges close to the bottom end, and I suspect that's one reason they have so much trouble with dead notes.