[komponisto]

>This is one reason that the music of the 2nd Viennese School (Schoenberg, Webern, Berg) is so impossible to look at: the structure of the music is obfuscated by the structure of the notation

Wrong. First of all, it's not "impossible" to look at by any means; I think it's beautiful to look at (as great music usually is).

There is a good reason why Schoenberg abandoned his (briefly-held) ideas about new forms of notation (and went on to produce another three decades' worth of music in traditional notation). He, and his disciples Berg and Webern, were steeped in the Western art music tradition, of which they believed their work to be a natural continuation. They didn't have a very good theoretical understanding of the new music they were creating -- because, apparently, music theory is hard. But they could sense its intimate relationship to its historical predecessors; indeed, they specifically, cultivated that relationship, baking it into the music. This, in my view, is why they were never going to break away from the visual representation of that relationship, of that continuity -- namely, traditional notation.

The idea that their music is not in a key is widespread, but incorrect. Inferential distance (https://wiki.lesswrong.com/wiki/Inferential_distance) precludes me from being able to explain this concisely in a non-misleading way, unfortunately.

[theOnliest]

I was being a bit hyperbolic; certainly it's not impossible to look at, and I quite like a lot of it. My experiences showing it to students is that people often find it foreboding on first glance, and part of that has to do with all of the accidentals used. It doesn't look like music they're familiar with, even though, as you point out, it comes from the same tradition.

> The idea that their music is not in a key is widespread, but incorrect. Inferential distance (https://wiki.lesswrong.com/wiki/Inferential_distance) precludes me from being able to explain this concisely in a non-misleading way, unfortunately.

I'd be interested to hear your thoughts on this. (I have a PhD in music theory, so the distance may not be as great as you'd imagined.)

[komponisto]

>My experiences showing it to students is that people often find it foreboding on first glance, and part of that has to do with all of the accidentals used

But, of course, other late-Romantic and early-modern music has almost as many accidentals. (Try the music of Max Reger, to take my favorite example du jour.)

I personally think accidentals ought to be retrospectively regarded as implicitly or explicitly attached to every note, with a convention of omitting them for brevity in passages that stay in a single diatonic area for long stretches. This 'retconning' of notational convention makes them seem much less forbidding to me.

>I have a PhD in music theory, so the distance may not be as great as you'd imagined

(Indeed, I wasn't expecting that!) That does cut down on it significantly, though it still needs more exposition than can be given in a comment.

Very briefly, the idea is that if (following Schenker and Westergaard, and for that matter the implications of staff notation itself) you take a line-based view rather than a chord-based view, tonality doesn't depend on "classified chords". And if, furthermore, you discard the peculiar non-Bayesian notion of tonality characteristic of German theory at turn of the twentieth century (where a key must be "established" or "confirmed" by a cadential ritual in order to be said to exist), you find that you can always read local keys if you zoom in enough; and out of these local keys grow the global ones.

There's a pernicious confusion that persists in music theory between tonal function and the chord-based view (to the point where the former is most commonly referred to as "harmonic function", as if the two were conceptually inseparable). But a tone has a scale-degree value independently of its participation in vertical "chords". This should have been clear ever since Schenker ; yet it is so poorly understood that, for example, Daniel Harrison could write a whole book advocating this view, all the while under the impression that he is doing something new and non-Schenkerian, when in fact this is part of the core of Schenkerian theory (as the origin of the circumflex notation testifies).