I’ve seen this problem with some of my pupils’ guitars. It is often the result of a guitar not being checked or set up correctly before sale. It is often found to be a problem with cheaper instruments.
What’s happening is this: your 12th fret is slightly higher than your 11th fret. For this reason, when you press the string at fret 11, the string also touches fret 12. This is why you hear that note instead. It also explains why the note is buzzy: because you are not pressing near fret 12, even though the string is touching fret 12.
Sometimes this problem can be remedied by doing one or all of the following:
- raising the saddle of the problem string to raise the action.
- tightening the truss rod to raise the action.
- filing down the fret that is too high (also known as fret dressing).
- if the problem is due to the 12th fret having partially come out of its groove in the wood, put a protective piece of leather or cardboard over that fret, and VERY GENTLY, without denting it, hammer it back down flush with the fretboard.
All these jobs are best done by an expert! If you bought your guitar recently, you should be able to get the shop to do this for you.
Before buying any new guitar (or when first tuning and checking a pupil’s new guitar) I always perform a very simple check: I play every string on every fret. It is surprisingly common to find a note or two that sound a semi-tone higher, particularly on strings 1 and 2. If a guitar does this when I check it, I don’t buy it, or I suggest a pupil takes it back to where they bought it (either to be replaced or properly set up).