How do I improve on this, like per-say, I'm listening to a piece of music and at one specific part, its too fast to hear, so I slow it down with a program like Transcribe! or Amazing Slow Downer (programs that keep pitch) and its slowed down but dissonant or blurry to the ears (not clear).

Does music theory come into play in these situations? (i.e) picking up sweep picking in songs, (try slowing it down and listen to what it sounds like)

Thanks in advance!
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Theory plays a big part. If you know what key it is, and what scale(s) are being used, just play around with them a bit until you get it. Or just improvise something in that key.
Quote by Geldin
Junior's usually at least a little terse, but he knows his stuff. I've always read his posts in a grouchy grandfather voice, a grouchy grandfather with a huge stiffy for alternate picking.
Besides that, he's right this time. As usual.
Definitely theory plays a part in it. If someone is playing in Cminor or F major...there are major and minor sweeps and variations in between. Youtube has some good tutorials about sweeping...and some really shitty ones... The best videos break down left and right hand technique. Kristopher Dahl I always find to be helpful. I find Paul Gilbert to be the masterclass of teaching lessons. I just get his teaching style and methodology. Matt Heafy from Trivium is also a decent source of info.

I know this wasnt exactly particular to playing solos by ear... but these videos and people should help your practice...which should train your ear to recognize more easily.