Some Korean traditional music is interesting if you're into that sort of thing. Sinawi is this kind of improvisational ensemble shamanic drone jazz music. Bubble Pop it aint.
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San ul lim is one the first names to get mentioned by those looking for interesting records with a western rockish feel to them. His first few lps are worth a listen but I ultimately find them a little bogus.
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As for other more modern forms, S.Koreans love their folk ssw stuff and pretty middle of the road rock, but unfortunately, unlike the Japanese they're mostly too conservative to reach into the the more interesting extremities of any musical style.
Most Trot I find pretty unbearable, but it's hugely popular in Korea. It's like the easy listening crooner music of Korea and in a similar way to what you'd find over here, it bleeds into other musical forms to occasionally give you something listenable, but on the whole I pass.
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North Korea is too oppressed to have pop music as far as I'm aware. I know that on occasion the S.Korean military have been know to blast Girls Generation across the border using ridiculously powerful military sound systems and I don't doubt there is a black market for kpop in N.Korea, but I don't think you'd be allowed to do anything creative in N.Korea that doesn't praise their dear leader, so I duno about home grown popmusic.
These little kids shred tho
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(gets good about halfway in)