Peter Kivy has become convinced that it is impossible for pure, instrumental music to be profound. This is because he takes works of such music to be incapable of meeting what he claims to be two necessary conditions for artistic profundity: that the work denotes something profound, and that the work expresses profound propositions about its profound denotatum. The negative part of this paper argues as follows. Although works of pure, instrumental music do, indeed, fail to meet these conditions, the (...) said conditions are not themselves necessary for artistic profundity. In fact, each is a misinterpretation of a distinct, genuinely necessary condition for a work’s being profound: respectively, that the work has a profound subject matter, and that the work handles its profound subject matter in such a way as to elicit a deeper understanding of it in the suitably situated and prepared appreciator. The positive part of the paper elaborates these genuinely necessary conditions for artistic profundity and then argues that, once they have been disentangled from Kivy’s misconstruals of them, it becomes evident that they can be met by pieces of pure, instrumental music. (shrink)