[Intro/Verse]
E|----------|
B|----------| I don't know how many times it actually plays but you get
G|3---------| the idea; it's Gm for the whole verse.
D|5---------|
A|5-(x120)--|
E|5---------|

If that's not exciting enough for you there's always the backing vocal melody

E|----------------| |-------------------|
B|----------------| |-------------------|
G|----------------| Or an octave  |-----7-10-8-7------|
D|----------------| higher        |---8----------10---|
A|----5-8-6-5-3---| |10-----------------|
E|5-8-------------| |-------------------|

There are some extra harmonies on top of this through the second verse

[Chorus]
E|--------------------------------|
B|--------------------------------|
G|3-3-3-3-7-7-7-7-0-0-0-0-0-0-0-0-|  
D|5-5-5-5-8-8-8-8-1-1-1-1-1-1-1-1-|  
A|5-5-5-5-8-8-8-8-1-1-1-1-1-1-1-1-|
D|5-5-5-5-8-8-8-8-1-1-1-1-1-1-1-1-|

Gm - Bb - Eb in other words


[Bridge]

E|------------------|
B|------------------| This is a weird bit. Sounds like Russell's sliding back and forth
G|------------------| between these two notes while tremolo picking, and catching the chromatic
D|5/8/5/8/5/8/5/8---| notes in between. Knowing him it could well be a pitch shifting pedal though.
A|------------------| Play around with it a bit I'm sure you'll get something that's roughly correct.
E|------------------|

That bit also turns up quite low in the mix in the final bit

E|------------------------------------------------10-11-12-13-14-15-15-15-15-|
B|--------------------------------9-10-11-12-13-14---------------------------|
G|-------------------8-9-10-11-12--------------------------------------------|
D|5-6-7-8-9-10-11-12---------------------------------------------------------|
A|---------------------------------------------------------------------------|
E|---------------------------------------------------------------------------|

More tremolo picking. The timing you can pick up from the song and you might find 
it easier to change on which string you play some notes. I'd say Russell's definitely 
using some pitch effects here because there's certainly a fifth above that last note
but the fretboard on a telecaster isn't that long. Curse him and his fancy technology. 

E|-------------------------------------------------|
B|---------------------------------------------6---|
G|----3--------7---------------3-------7-----------|
D|---------------------8---------------------------|
A|-----------------6-----------------------6-------|
E|5-------8----------------5-------8---------------|