Notes as means to express tempo relationship

Counterpoint conceived as relation of distinct temporal layers. On the one hand this is the ‘harmony of the spheres’ expressing time as proportion, and hence classical and static; on the other hand it allows for the most extreme temporal dissonance. The latter is of course contained in the former: Discordia concors

This abstract temporal dimension doesn’t actually legislate on the content used to fill it. In fact it is simply a formal plotting – this is an aspect of Elliott Carter’s music too, of course.

How to resolve this?

Conlon Nancarrow chooses not to resolve it, but embrace the disjunction. The material is completely expendable:

When you use canon, you are repeating the same thing melodically, so you don’t have to think about it, and you can concern yourself more with temporal aspects. You simplify the melodic elements, and you can follow more the temporal material. (p. 5, in ‘Interviews in Mexico City and San Fransisco’, Roger Reynolds, American Music, 2(2), 1984)

And more emphatically:

I don’t think of a line, but of a collection of temporal relationships and, in fact, the melodic line is simply a crutch in order to realize certain temporal ideas. (p. 6)

Well, that’s one way of thinking about it…