I'm listening to Rachmaninoff's Etude-tableau, Op. 33, No. 1. The first section of this piece made me think of a question to pose.
This piece has a definite opening melody, and it's really REALLY slow. Like, cantus firmus slow. It's played over a rhythmic underpinning that, if removed, would result in most listeners unable to tell for sure (just listening to the remaining melody) where the beat is supposed to be, what the time signature is (and with all that slow syncopation, does that even matter, without the rhythmic part?) Most of the measures have a long note, starting on a weak beat, tied well into the next measure. You can't even tell without the sheet music where beat 1 of a measure is, or where the time signature changes.
I guess what I'm asking is -- once a melody becomes so slow as to lose its sense of structure to the listener (you can't just sing along with it, unless you really, really know it) -- does it cease to function as a melody at all?