Double-stop fret buzz

Pretty common- a lot more common than you might think. Here's what's happening...
When you fret the first and fourth string at the seventh fret, the note on the G string is D. Now while fretting the 4th string at the seventh fret, pluck the string between the nut and the where you are fingering. The string will buzz a bit, but the note you hear is also a D. The D note on the G string is setting up a sympathetic vibration on the E string behind where you are fretting it - which is also a D. Three ways to mitigate this problem.

1. Mute the E string behind the 7th fret. Use your second and fourth finger to fret the notes, and use your first to damp the E string behind your second finger.
2. Add a bit more relief. The additional relief may be enough to keep the string from rattling against the frets when it vibrates sympathetically
3. Shim the E string nut slot (or a new nut with slightly higher slot for the E string).

Even a well-designed and set up bass can run into this problem. Solutions 2 or 3 may not really help much if the bass is resonant enough to set up a strong sympathetic vibration. So really, as much as it is a pain in the butt, the first option is often the best.

 

Option 1 above is the "classical" way to play 10ths (minor or major) - second finger fretting the root on the E string with the first finger behind it, and fourth finger fretting the 10th on the G string, with the third finger behind it. It's a more comfortable position with major 10ths, but you get used to it pretty quickly with minor 10ths if you practice enough.

When you start out playing 10ths, you're likely to get a little rattle beyond sympathetic string vibrations just because it's harder to fret both notes than you're used to, due to both the extra pressure involved in fretting two strings and the unfamiliar (and possibly slightly contorted) position of your fretting hand. You will iron this out over time.

 

I've had this happen too but more commonly with certain tritones.
Sometimes it's as simple as detuning the string and retuning it back up. I've had phantom rattles disappear this way.

 

it's only acoustic, though right?

 

yep, like @Turnaround i knew what it was before even opening the thread!

it’s the dreaded “backbuzz” happening between the fretted E and the nut.

the trick is to lay a finger behind the fretting finger on the E.