Try reading some poetry. Poetry is language distilled and focused, and is much more intent on rhythmic/musical sounds than prose. I am firmly of the belief that at least some grounding in poetry and poetic techniques makes anyone a better writer.
Like a lot of things, TV taught me about this.
No wait, come back.
Look at Aaron Sorkin's stuff, at the way he structures lines and dialogue. Sorkin does this fascinating thing with conversations where both characters basically build the information so it goes something like:
JOSH:So the thing.
CJ:The thing with the Defence secretary? That thing.
JOSH:Yes, the thing with the defence secretary. We need to talk to him.
CJ:About what? The fact he's just spoken out against abortion, something he is biologically INCAPABLE of experiencing or the fact that he called a female reporter 'darlin'' whilst doing it.
JOSH:...The first one.
CJ:So sexism's okay now?
JOSH:Toby's working on the memo.
CJ:Joshua!
Back and forth, build and rebuild. 'Celestial Navigation' from season 1 features the best example of this ever.
Then take a look at David Mamet, who does the same thing through entirely minimal dialogue. Mamet works like Pinter, using the empty spaces to pass on the actual information. Witness this exchange from Redbelt, which I'm pretty sure I'm slightly misquoting.
'Did you tell her you fought in the war?'
'Yes.'
'Did you tell her what you did?'
Then there's Shane Black, who writes with the pace of a classical pianist. Witness this exchange from Kiss Kiss Bang Bang, one of the finest films of the last twenty years:
Perry: My $2000 ceramic Vektor my mother got me as a special gift. You threw in the lake next to the car. What happens when they drag the lake? You think they'll find my pistol. Jesus. Look up "idiot" in the dictionary. You know what you'll find?
Harry: A picture of me?
Perry: No! The definition of the word idiot, which you fucking are!
and:
Harry: What is it out here with these women?
Harmony: Oh please, Harry, they're no different from anywhere else.
Harry: Yes, they are. These are damaged goods, every one of them, from way back. I'm telling you, you take a guy who sleeps with 100 women a year, go into his childhood - dollars to doughnuts, it's relatively unspectacular. Now, you take one of these... gals, who sleeps with 100 guys a year, and I *bet* you if you look in their childhood, there's something rotten in Denver.
Harmony: Denmark.
Harry: That too! But it's abandonment, it's abuse, it's, "My uncle put his ping-ping in my papa!"... and then they all come out here! I mean, it's literally like someone took America by the East Coast and shook it, and all the normal girls managed to hang on.
Harmony: OK, everyone who hates Harry raise your hand!
[All the girls in the club raise their hands.]
Perry: See that? Obedient little bitches too.
Girl: Fuck you! [Throws a glass at Perry, which he ducks.]
In print there's the repetition of phrase and motif that people like Cormac Mcarthy play with, specifically the use of a man carrying a torch as the embodiment of life and hope ('We're carrying the fire' being repeated throughout The Road which also in 'Each the other's world entire' has one of the best summations of parental love ever written) or Douglas Coupland's fondness for emphasising the distance and disconnection his characters feel with life by communicating at a distance and through their internet presence or other characters' views of them as shown in Generation A.
Basically rhythm is the point at which you stop being good and start being great, harnessing your influences and past experience in a way that makes something new. Or at least that's my theory:)