Atonal oder tonal?

I recently followed a thread online somewhere about one of those monstrously dense total chromatic pieces associated with the New Complexers* and the question came up of whether or not segments or fragments found here or there which could be articulated and heard as resolving onto conventional tonal templates — triads, seventh chords, alterations of these, sequences or progressions of these, etc. — could then, and if so, ought to be heard as 'tonal' although the prevailing atmosphere of the piece was — for better or worse (and yes, some participants in thread wished to jetison the term altogether with some argument (and a reasonable one, though I disagree) about its impossibility) — 'atonal.'  

I happen to think that it's possible to have a stretch of music that is atonal in the sense of its not being parseable as belonging to a particular key-centered tonality.  To get there would require an even distribution of the possible pitches such that samples of any reasonably large size would tend to have the same net content.  James Tenney's ergodic concept is spot on, here, and the classical Princetonian 12-tone technique could come very close, but there is an inevitable rub and that's the fact that (a) our auditory nervous system doesn't take in every collection of pitches thrown at them with indifference as to the qualities of the relationships between tones and (b) most of experiences with music are with music that privileges particular tonal relationships and/or gives otherwise constrains their use.  The phenomenon of sensory consonance is a real physiological one (evolutionarily piggybacked with some likelihood on speech perception), and configurations of pitches which fall into sensorially consonant relationships will be distinguished from those which don't.  The strictures among the early adaptors of Schoenbergian 12-tone technique included an avoidance of octaves and major/minor triads, possibly from the insight (inhearing?) that these would assert themselves acoustically from other configurations, defeating the atonal ideal. 

There is a story about John Cage, then an editor of New Music Edition, meeting Milton Babbitt with great enthusiasm to talk about how Babbitt had "broken the rules" and used major and minor triads in his Three Compositions for Piano (1947) which Cage had then recommended for publication.  Cage's enthusiasm for a neutral approach to the natural affects of musical intervals can be understood in the context of his own early works in which had used a 25-tone collection, thus rejecting the principle of octave equivalency found in the more orthodox 12-tone techniques of the time.  Babbitt reported being amused at Cage's enthusiasm, for it appeared to be emphasizing an aspect of his musich which he had heard as incidental, as his work with 12-tone technique was as much an auditional practice as a compositional one, and that auditional practice was predicated on treating intervallic and chordal arrangements as distinct but with equal structural compentency. (This would lighten up considerably in Babbitt's later music, as a more playful approach to the nature and nurture of pitch relations appears allowing at times even the prominent foregrounding of local materials that evoked tonal music.)  I don't think that we have come very much further from this standoff between Cage and Babbitt, the first with a form of music-acoustical realism, the second a species of idealism or platonism, but I do expect that there's still considerable charge to be found and heard in the very distance between these positions.

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* I believe that the work in question was by Michael Finnissy, but I won't bet the house on it and the following notes don't ride on it.