An active line on a walk: so begins Paul Klee's Pedagogical Sketchbook. I want to write a counterpoint book that begins the same way. The musicians' convention is that line = melody. Everything becomes melodic: Christian Wolff (see Wolff's Lines). So great is our rage for connecting single sounds into lines that "pointillist" or "punctual" music is inevitably heard a melodic. Connect the dots. Fellini's lines, beginning somewhere unlikely, ending up somewhere else improbably. A line can describe a journey, movement from here to there. Or a thread, a path taken or a map to be followed. La Monte Young: Draw a straight line and follow it. Straight lines, wandering lines. The long line, a center of attention continuing through a large work, can defeat — push into the background — the most animated ensemble polyphony.
Musical lines differ from graphic lines in that they are embedded in time, which moves only one way. (Which is often reflected in local stylistic conventions, for example that of common practice harmony in which I -> IV, V, IV -> I, V, V -> I, but V does not -> IV. ) On a graphic surface, one can move in any direction, but in music you can't go backwards in time; musical reiteration, repetition, and recapitulation are replicative operations, not exact returns, and music benefits from the way in which memory (fragile memory) plays with the substance of those replications.