I'm now, as of about an hour ago, the proud owner of a Mesa Boogie Triple Rectifier, which I'm running through a Marshall 1960A quad, which makes for quite a nice pairing.

I'm playing an Epiphone guitar which is nice to play but I want to replace the stock pickups because they're not all that great. The problem is, I know nothing about pickups so I was hoping that you guys might be able to help me out.

The kind of sounds I'm after are similar to acts like A Perfect Circle, Oceansize, (Neon Ballroom era) Silverchair, Mogwai (more for their clean) and Cog (particularly their distortion sound, and I know these guys use Mesa) - to me their sounds are all smooth, low end heavy, have a real thick, clear distortion and a smooth, clear clean sound.

Any help would be awesome!
get some seymour duncan JB's, those are popular, or a pearly gates also from duncan. go to seymour duncan's website and see what they got. they make great pickups and they are pretty affordable too.

Traynor YCV50 Blue
epi les paul w/ SD Alnico II pros
Dunlop Slash Wah
EH Deluxe Memory Boy
Moen Jimi Vibe
Danelectro Cool Cat Fuzz
Zvex Vexter Fuzz Factory
VHT 2x12 w/ V30's
The low end heavy and thick nature of their sound comes from the amp and compression. In addition to the Mesa Boogie amps a couple of the bands you listed use alesis 3630 compressor. The clear distortion is a combo of the amp and the pickups. The smooth cleans, and clear cleans are more down to the pickups than anything.

You need medium to low output pickups with alnico magnets. Alnico 5 will be brighter, more defined, and more clear. Alnico 2 will me warmer and smoother. I'd stay away from anything over about 14K and would probably lean more to the reagion of 8.5 to 12K. This will compress your tone enough to give you nice controll over the distortion but not so much that you sound dull or nasel when clean. Stay away from ceramic magnet pickups because don't sound smooth. Stay away from high output alnico pickups don't sound clear for cleans or for distortion.

You can't go wrong with one of the many types of slightly overwound PAF's like the ones from DiMarzio or Seymour Duncan. The bands you listed to not use true vintage style PAF's so I don't think that is what you want. If you wanted more smooth tone (particularly from the neck) there are always the alnico 2 pickups like the Seth lover model, pearly gates, or the anlico 2 pro.

Or you could always have me whip up a good set of hand wound pickups for you.
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