#1
got a quick question for you music theorist...i've been on a huge radiohead kick lately, and i've come across Karma Police...the song appears to be out of A Aeolian, but there is a bass walk to G major that has an F# in it, and the D major chord is used...so basically it is A Aeolian with an F# in there. The presence of D major is what throws me for a loop...if it was a D minor i would feel more comfortable calling it A Aeolian, but it's a major. it also uses a B minor instead of B diminished, which is also "outside" of A Aeolian.

my question is not whether or not the song is A Aeolian...it is obviously not, but what scales should i use to improv or write some lead lines? obviously following the chords is one option, but are there any "tricks" to finding scales that fit? basically, are there non-diatonic scales i need to learn, or just piece together different scales at different times in the song?

my apologies if this is worded in a confusing way...not sure how else to put it.
#2
either piece together stuff you know or play it with whatever you feel like doing, which is what I recommend don't rely on theory to tell you how to play. this song sounds pretty much atonal anyways.
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#3
Sounds just like Amin to me...but I haven't listened to Karma Police so I'm not sure - That F# is probably part of a D7 chord not Dmaj. D7 is diatonic to Gdominant. So you're shifting tonality but not really moving out of Amin. Also...F# is commonly used to walk a bass line. And bass lines in general contain a lot of chromatic approach tones that are not invasive to the guitar lead. Unless you really want to approach it modally I'd keep it in Amin. Hope it helps a little.

But, if it's Dmajor and Gmajor...something else could be happenin'.

EDIT: I meant "D7 is diatonic to Gmaj" sorry
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#4
It's very common to borrow a chord from one of the parallel scales and modes. In this case, D comes from the A Dorian scale. What you'll want to do is play F# rather than F over that part of the song, or just avoid those notes entirely. I suggest trying both and mixing it up.