I built an acoustic CBG from a box with an MDF lid using a thru neck design. I put it all together and it sounded fabulous, much better than I expected. Then I did something stupid - I took it apart. I wanted to add 1/8th inch to the distance between the strings and the box cover to make space for a magnetic pickup. So I removed 1/8" from the neck cutout and then reassembled. The clearance is now where I want it to be but I have somehow introduced a weird vibration on the A string that produces a sort of rumble sound. The D and G strings are fine, nice and crisp. Other than the removal of some material nothing else has changed. The string isn't vibrating on a fret. The bridge is a nut and bolt type and is solid. The attack angles are the same as before.

So two thoughts. Is it possible that the additional space between the strings and the cover has introduced some odd feedback vibrations (it's now about 1/4")? Or could the neck itself be vibrating because it's now a bit thinner in the part contained in the box itself? Any other ideas?  

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$5 says something is rattling... pluck that string hard and start squeezing and pushing on things...

Inside the box:  If it has a jack, did you glue down the wire?  That one took me hours to figure out...

something is buzzing...

Nothing changed? obviously something did, and I'll throw a guess at the new cut in the neck is uneven/unflat/untight and the lid is now vibrating against it, your low string (A tuned down to G for GDg) is probably causing Ii because its closer to the natural resonant frequency.

Well, I did a little research this afternoon. I twanged and held and pushed and pulled and squeezed everything I could to no avail. So I then removed everything that could be a problem. All I had left was the neck and a large bolt bridge - no cigar box, no wires, nothing. Still got the rumblyvibration sound. Not as loud because there was no box in which it could resonate, but still there. Desperate, and on a whim, I replaced the ebony nut that was there all along with a bolt. Problem solved. Somehow a weird harmonic was being generated at the nut end. Tomorrow I'll make the fix permanent and hopefully that will be that.

It could be that the nut slot is too wide or not angled slightly. This video explains how to slot the nut. I would always protect the fret and guitar head, but I am a hobby woodworker rather than a master guitar maker :0)

https://crimsonguitars.com/guitar-builders-basics-11-cutting-nut-sl...

Interesting video. Thanks for that. 

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