There is the decades old and by now well-entrenched tradition of seeing Stockhausen and Boulez of the late 1950s as refugees from the austere perceptual chaos of total serialism, who found creative haven in the shimmering, slowly undulating, and temporally undirected sound surfaces inspired by Debussy. The earliest source of this tradition that I’ve come across was the great pianist and Debussy interpreter Paul Jacobs, who described Debussy as an inspiration for Stockhausen and Boulez in his 1970 article on that composer. (Whether or not Jacobs was the first to claim this connection – I do not know. The article was written for the first edition of The Dictionary of Contemporary Music.)
This is certainly true of Boulez, whose obsessive fixation on the exaggeratedly ‘orientalist’ surface elements in his music - ‘exotic’ Javanese, Balinese or Japanese timbres and sonorities, ritualistic phrasing, a ‘Buddhist’ embrace of undirected perspective on time - made the surface-focused sound world of Le Marteau and (the inner movements of) Pli selon pli feel as dated today as the exaggerated tail fins on American cars of that period. At some level of formal abstraction the “Debussy connection” also applies to Stockhausen. Yet this background similarity strikes me as being far less telling about the music of these two composers than some of their background differences. As I hear it, their music has been much more deeply affected (and differentiated) by their respective metaphysics: the grandiose, ‘deep’, transcendental German metaphysics lurking in the Weltanschauung of a German intellectual, and the slim, rationalist, "of this world" metaphysics typical of the French after Descartes. (The French had many distinguished philosophers since Descartes, but their philosophical concerns were far better moored to this world than those of the grand-transcendental relay team of Kant, Hegel, Schopenhauer, Fichte and Heidegger.)
It takes only a few of Stockhausen's general (philosophical) pronouncements on the "nature" of time, space, mind, etc., to hear an echo of German metaphysics, albeit metaphysics whose vocabulary has been updated by 20th century physics (and later by the jargon of "new age-ish" spiritualism). And Stockhausen’s music from the late 1950s and early 1960s reveals these metaphysical allegiances by oozing metaphysical grandeur underneath whatever formal devices he employs at the moment, whether in the slender pointillist Kontra-Punkte or in the massive tectonic shifts of Gruppen, Carre, and Punkte. In the latter three works, the orchestral palette alone – in which Stockhausen’s highly declamatory, massive brass outbursts and growling basses contrast so sharply with the bass-shy, silvery, sparkling palette employed by Boulez – takes my mind to those “cathedrals in sound” so characteristic of the late 19th century Austro-German orchestral music. If refined, reserved, inwardly sensuous Debussy is Stockhausen’s ancestor, he is an uncle at best, and a rather distant one at that. To my ear, the DNA of Stockhausen’s music is far closer to that of Bruckner and Mahler – the two composers whose gargantuan compositions were driven by loudly proclaimed and equally grandiose metaphysical commitments. To ignore (or de-emphasize) this connection is to misrepresent the foundations of Stockhausen’s musical aesthetics. After all, Stockhausen did want to write a Mass - something that neither Debussy nor Boulez would even consider as a hypothetical possibility (but which Bruckner actually did write, and which Mahler approached indirectly with Veni Creator Spiritus).
With Boulez, on the other hand, the metaphysical grandeur is avoided in the typically French manner, which aims at avoiding excesses of any kind (including metaphysical). To be sure, Boulez's light, glittering, sparkling soundscapes are rich with formal complexity, but this complexity seems to be in the service of elegance and sophistication unburdened by the heavy weight of (a typically Germanic) ponderousness. (Just as the cool, refined and reserved piano playing of the so-called French school, however sophisticated, always sounds ‘light’ when contrasted with the "deep in the keys", grandly phrased Germanic interpretations.) And this pervasive, airy lightness of Boulez’s music strikes me as entirely natural, coming from a creative mind which sees the world (and the human condition therein) as complex, but not because it is bolted down to some complex 'metaphysical foundation'.