Kent Kennan’s Counterpoint book begins with the single line. Not all counterpoint books do this, but I think it is critical – funnily enough Schoenberg’s Preliminary exercises in counterpoint does not begin with the single line in any serious way, but his notes on counterpoint collected in Coherence, counterpoint, instrumentation, instruction in form raise the critical question of the single line.
The main thing about constructing the single line (at least in any ‘traditional’ style) is that it has to be capable of maintaining independence and coherence within a polyphonic setting, as well as capable of being open to (or even implying or necessitating) the the existence of other lines.
Thus the relationship between lines in traditional counterpoint is an internal relationship at the heart of each line. Unlike some modern forms of counterpoint where the independence of lines is taken to an extreme limit – the sheer juxtaposition of pre-existing lines – traditional counterpoint conceives of its individual lines as always already in relation, even if the line that the original is relating to has not yet been written. Counterpoint is not an external system imposed upon melodies from the outside, nor is it as simple as writing a ‘cantus firmus’ type melody, complete in itself, to which the other melodies must relate and subordinate themselves. Counterpoint lives in all of its lines.
The totality imprints its stamp on all the lines of force within it, and there is no single line that ‘represents’ absolutely the totality. Perhaps this is even the case in more ‘concertante’ type of writing which has stricter hierarchies between the lines, although much less obviously than, say, in a fugue.