page said:
...How do you ignore key without sounding like ****?
Good answers so far. In my opinion, the actual 'tone row' concept was developed by Schoenberg as a compositional tool, and he's known for it, as well as his student Webern (one of my favorites).
But Tone Rows don't necessarily equal Atonal music. It was Schoenberg's answer to composing with the concept of the least amount of tonal center as possible.
Nor does Atonal music equal Tone Rows - see what I mean? It was one guy's solution to the problem.
It almost looks as though you, Page, are in a small way running from the problem of not hearing 'key' by delving into atonal music. A couple of things on that: when you're stepping out of key (or a central tonality) you almost have to 'hear' better than normal because you have almost nothing else to rely on. That's why Schoenberg did his thing with the rules of the Tone Row. You have to, at some point, create a set of rules and stick to them if you're not using your ear. Tone Rows are fun to work with and in the hands of a master composer like Schoenberg or Webern, it's a highly organized mathematical sort of music that works - esp in the case of Schoenberg, in my opinion. Some of his stuff, even without tonal center, is SCARY-emotion stuff!
So if you want to delve into it, go for it - it's really fun stuff.
BUT if you want to go totally atonal, you'd have to throw even his rules out the window and just go...well, atonal. And THAT's the part where your ear is the only thing you can rely on at all. It's a pretty rarified atmosphere you get into there. It's good to go there even if you wind up not using it and going back to more tonal stuff. It's like you're in space and there's nothing to grasp onto except your intuition about things - and that's the beauty.
It's also the lesson, in a way, because when you're into it, you might tend, as I did, to 'crave' tonality. You start hearing tonal concepts and ideas in your head and have to decide whether you're going to have to throw them out simply on the basis that they 'do' sound tonal. You might come up with some pretty tasty stuff, but do you toss it or keep it?
That's an interesting position to be in and you might, at some point, realize that you 'are' actually hearing the stuff in your head - which I think is what you were orginally getting at.
--Which might be a case where more practice 'listening' to the inner music, and less time practicing 'music' will help.
That said, the part of your original post I quoted: 'without sounding like..."
See, if you're going to do this, you have to throw out even that part of things. Sounding like "". I mean, examine the reason you'd worry about something like that. It sounds bad because...why? Because you already have a preconcept of what music 'should' sound like, and everything and anything that doesn't sound that way, sounds 'bad.'
It's a prejudice of sorts to think that way, because by saying that, it shows that your worries are in no way connected to what you're trying to do. They don't go together. 'Good' music; 'bad' music. Where you say you wish to head - you have to throw all that aside if you really want to get into it. To have 'no rules' so to speak, means you have to throw out even the rules that say you can't have any rules, and that includes your own personal disposition and attitude toward what is valuable in music.
And for most of us having grown up in Western music cultures, that means any subconscious disposition toward 'tonal' music.
Lose that, and you'd be on your way, pretty much.
Then, perhaps, take a walk out in a forest somewhere, or go down to a river or stream or the ocean. Listen to the true 'atonal' music that surrounds you. Noise. Pure, simple, never repeating sounds that mix and harmonize in ways, I think perhaps Schoenberg would have envied. It's all there already, it's just...well us humans tend to want things to be 'repeatable'; to be able to put things in little boxes and have them close at hand to be recalled and replayed and renewed whenever we wish. But the true atonal stuff, it's not like that. It never repeats.
Sometimes I sit listening to the water fountain near a place where I work, and space out on it and appreciate it. The sounds never repeat; the patterns of water never are quite exactly the same - ever. The way the water splashes is never the same and it goes on and on hour by hour, day by day, and I sit and have to laugh when my mind starts to try and find some pattern, some balancing to the equation.
Because it's perfectly balanced, and there's also no pattern!
And so I tell myself, "Man, if you were a hot**** composer, you'd be able to transcribe that...."
--But what part of it, since it never ends? And to what purpose.
So that, to me, is the true 'atonal' stuff. I think maybe Arnold and Anton heard the real stuff and tried to find a way to write it down so others could hear it too. But...everyone can hear that stuff by themselves when you think about it.
So it still comes back to YOU hearing it.
Best regards and good luck!
If you choose not to define a conventional tone center then you are free to distribute pitches as you like, or not at all. 
