Whilst to some extent it might be argued that tonality is in the ear of the beholder, what to me constitutes tonality is references to triadic material and melodic writing within the music that have indelible connections with aspects of diatonicism. I simply cannot accept the defintion "post-tonal" - just as I am uncomfortable with those such as "post-modern" - since what really matters is how the material concerned may or may not give rise to the definition at hand rather than whether what's being defined comes before or after anything else; in other words (in the present context), there is - to me, at least - no such thing as "post-tonal", especially as music that most people would likely define as broadly tonal was written by numerous composers all over the world throughout the period in which music that could reasonably be described as "atonal" was also being written - so there is a concurrency rather than a sense of before and after. There doesn't have to be a "tonal centre" to define music as "tonal" (the kind of "progressive tonality" found in Nielsen and others where the principal tonal centre moves from point to point during a particular work does not, for example, define it as "atonal") - and the instance of 12-note serialism does not of itself necessarily eschew a sense of tonality. I realise that I'm not doing too well here to make out my case(!) but I nevertheless hope that what I've written here at least makes some sense and helps to focus what might be argued to constitute "tonality" and "atonality".
Best,
Alistair
So, in short, you would (and I don't mean to be simplistic, but for the moment) classify music as tonal or not (i.e., atonal), that is, music that is dependent on functional tonality or references it, and music that does not.
If I understand you correctly, this would put (as I mentioned before) Schnittke squarely in the realm of tonal music, and Webern in that of atonal music.
Upon further reflection, it seems to me that there are perhaps four overall periods (time periods): pre-tonality, tonality, atonality, and post-tonality. The last two may seem somewhat redundant, but let me attempt to further define the terms as I use them. Pre-tonality involves medieval/renaissance music before functional harmony became the rule; tonality is the bulk of tonal music; atonality is a reactionary movement that is actively anti-tonal (that is, one tone acting as monarch, placing other tones in standard functions such as predominant and dominant); post-tonality is what follows the Schoenbergian emancipation, and is the epoch in which we now live: tonality/tonal references are not verboten (not that it ever totally was), yet composers make use of a wide variety of techniques unimagined until the coming of the Second Viennese School.
Thoughts?
Mike
P.S.
As a side-note, I have to agree with your assessment of the word post-modern as a fairly nebulous term . . . at least in common and non-technical usage.
Topic: The Good Atonal Compositions?