This is a great questions, originally posted by David Smooke of NewMusicBox. David discusses the process of writing a piece over a year ago, getting it performed, revised, performed again and eventually recorded (there is a YouTube video of the piece in his post). Reading through his process I thought of my own concept of when does a composition become a composition.
In some respects there is a realization of the piece at conception. I have a notebook that I keep with me and jot down ideas for pieces. Some of these are fully formed, while others are only basic concepts. Of these ideas, only 20-30% ever get moved beyond this stage (or at least that's the current rate). This is because I get too many ideas to realize them all. Even though I don't work on an idea, I keep it because I never know when I might come back to it or envelope it into another idea.
If I start to take a piece beyond the notebook stage, this is generally because I have someone interested in performing it. There is no guarantee of a performance, just the interest. This means I need to create something on paper (with little black notes) that the performer can see and consider. Should this get enough interest (in either them or me), the piece continues. However, I often find the initial idea didn't evolve the way I thought it should and the concept dies - or rather is laid to rest for potential future resurrection.
When a piece has moved beyond the first draft (which generally isn't even a complete working of the piece or even a rough piano reduction) I get energized to the point I feel I have to complete it. It is at this point a composition becomes real (for me). This point where I have to see a piece to the end is when I feel it has a life of its own - worthy of a title (whether it already had one or not) - and when I move it from "compositions in progress" to a folder all its own.
However, even when I'm finished with a piece, it's been handed over to the performers (and performed), I still ponder it. Should I do this or that, change this note, add (or subtract) this section??? The symphony I wrote three years ago is still undergoing this process, because I am still learning new things, techniques and ideas. This doesn't mean I feel the piece is incomplete or somehow not finished. I don't let a piece get performed unless I feel it the best it can be (for where I'm at at the moment). But, just because it's performed doesn't mean it can't still be improved. How many great composers edited their works after the initial performance???
So, when does a composition become a composition? For me, this is when I feel it has to be completed, which is long before it is performed (or even finished being composed). However, when is a composition completed? For me none of them will be truly completed until I'm dead and can no longer ponder potential changes.