15) "Many post-tonal pieces use their essentially contextual and motivic structure to allude to aspects of tonal practice. When these allusions occur at the deeper structural levels, the result is what might be called a middle-ground pun. Formations which had one meaning in a traditional setting are given a new meaning within a new musical structure. In particular, post-tonal music may mimic the appearance of prolongational spans without using truly prolongational voice leading. In such situations, it is crucial not to be seduced by the tonal reference into applying anachronistic aspects of tonal theory."

- Joseph N. Straus, "The Problem of Prolongation in Post-Tonal Music." Journal of Music Theory, XXXI/1 (1987)

If it flaps its ears like an elephant, it is NOT an elephant, because the composer says it is not. Nor should it remind you of an elephant.

Crucial to what? 

The crackpottery of it was implicit in my subsequent gloss: that is not an elephant, it's just a pun on an elephant. Don't think about elephants!!

Q: What do you get when you cross an elephant and a rhinoceros?

A: Elephino!!

I am not strictly anti-Schenkerian. The idea of prolongation means a great deal to me. But to hear references to tonality and misinterpret them as tonal structures is certainly a very apt way of analysing "post-tonal" music. To pretend those references are misleading rather than a productive contradiction is for me a huge pet peeve of undialectical thinking.

Straus isn't really trying to determine whether post-tonal music can actually be 'tonal' or not (and there are various different definitions of what 'tonality' is, some of the broader of which would include, for example, a lot of non-Western art music organised around a single key centre for extended periods), he's simply talking about how certain analytical tools that are illuminating for earlier music are not the most apt for these more recent developments. I don't see any problem with that.

In terms of the pun issue, is it so wrong to say that certain music may on the surface appear like it belongs to a certain genre/tradition, but when one investigates it (which can mean simply listening to it repeatedly) more deeply, it turns out to be quite different? Straus's claim seems essentially along those lines.

By themselves, they wouldn't, no. But what do you make of the notion of 'incorrect analysis'? Does it not imply incorrect hearing, and is there such a thing as incorrect hearing? To talk about op.19/2 purely in terms of its tonal 'implications' I find far more revealing than the usual pc-analysis techniques that are taught in, for example, Straus's Introduction to Post-Tonal Theory, though a more complete picture would be given by thinking about both perspectives.

It's not a notion that I think much of, but Straus doesn't use that term in the passage you cited. He says it's crucial not to use certain anachronistic analytical tools - presumably because he doesn't think they'll reveal very much? Of course one might argue that in some cases (like the Schoenberg) they do tell quite a bit, though surely many would agree that other tools are needed, including those which are less exclusively focused upon pitch? Whether or not the methods he explains and advocates elsewhere are necessarily any more illuminating is another question.