L is for Line

I don't teach composition often, but when I do I usually start with some exercises in counterpoint, and counterpoint, as far as I'm concerned, starts with the notion of line.  Origin, end, range or extremity, contour, balance, gravity, straight, broken, crooked, meandering, leaps and step, gaps and fills: the language we use when we speak of line is rich and metaphorical.  The precision of the (point,) line (, plane) in mathematics is useful, but only within limits when applied to music.  I usually make sure the student knows Paul Klee's Pedagogical Sketchbook, that marvelous Bauhaus primer beginning with a line taking a walk, distinguishing active,medial and passive lines, introducing complementarity of lines, structures, arrows etc. (someday I'll write a "G is for Garden" just about Klee's gardens!)  Line is also intimate with melody and contrapuntal lines aspire to the melodic: Christian Wolff's early insights about successions of events becoming melodic can be usefully placed alongside Ezra Pound's idiosyncratic theory of harmony — in which there is a function so that any two events, however alike or different in character — may define a line provided sufficient time passes between them. A good story told well also follows a line.  I like to recite the story of Jarl van Hoother and the Prankqueen from Finnegans Wake as a more-or-less classical folktale; it put my kids straight to sleep for years.  Finally, David Antin has a wonderful talk on line music counterpoint disjunction and the measure of mind (on this page, please listen to both parts of the recording!) with a fine example of a life as a line.