I've been working on a lot of alternate and sweep picking, and as a result I believe I have fairly strong muting technique. One thing that's becoming a bit of a hangup is when I lift my finger off a fret (particularly the 7th or 12th) before immediately changing to another string, the note on the next string sounds terrible because the harmonic is still ringing out. I can prevent this with my picking hand thumb when the next string is higher, but when descending to a lower string, I can't think of a good way to prevent the harmonic from ringing. Any suggestions?
Sounds like you are playing a bit sloppy. Slow it down, make it smooth so every note rigs out clearly and you don't get an overtones.
Quote by strat0blaster
This is terrible advice. Even worse than the useless dry, sarcastic comment I made.

Quote by Cathbard
I'm too old for the Jim Morrison look now. When I was gigging I had a fine arse.
I actually practice everything very slowly and strive for accuracy and consistency. The problem is that I can't seem to find the proper way to release a string when I'm playing over a fret prone to harmonics without actually causing one to ring for at least a moment, even outside the context of a phrase.
what I do is either slightly lift my finger to make the note 'dead', or I keep my finger closer to the last fret (finger on 12th fret is closer to 11th but without creating fret buzz), however, I only have a small practice amp so my guitar doesnt create as many harmonics as yours probably does.