Written In Rhythm, Hearing It Without?

Something has been bugging me for a while now. When a composer writes a piece, and lets say there is an introducton to this piece, played in a free kind of way by the performer. How is this music then heard in the rhytm in which it is written?

For example how do you possibly hear written triplets when they are played not as such because of the free interpretation? Did the composer just write the triplets to give the performer an idea of what he wants to convey? ..

It is an odd thing to me and I hope someone can enlighten me.

Just because it's not in tempo, doesn't mean the rhythms aren't felt. They may be ambiguous, pushed, pulled, stretched - but the relationships from one note to another will still convey some sense of rhythm and time.

It's the relationship of the notes - spatially, in time - that a composer is dictating. This one longer than that one, these go by quicker than those; while the actual durations are freely interpreted, it should still have a sense of rhythm and time.

Thnx for your reply. I will check this next time I listen. I was just thinking about it because im trying to transcribe some music which is not written down, and is played without a steady pulse. and Its really hard for me deciding what note values to use and where the beats are.