This is sort of an extension of the conversation @Ken320 and I were having on the chat.
I was basically saying that, in my experiences reading/discussing Allen Forte:
1. Forte wanting to have it both ways (saying that it doesn't matter what the composer did, since we can never fully know anyway, and also claiming that Schoenberg/Webern/etc. strongly cared about PC sets in his music), essentially begging the question
2. There is no evidence of Schoenberg using PC sets in his music, despite us having ample evidence that he thought very deeply about how to formulate tone rows
3. the interlocutor theorists being unable to hear any of the relationships that Forte describes with PC sets
4. claiming Forte is attempting to take over the composer's authority with Forte's own as a theorist.
I can definitely see where they come from, especially with No. 3.
Quick rundown on PC sets:
1. convert pitch classes to numbers [C G A] -> [0 7 9]
2. transpose to 0 [0 7 9]
3. find the shortest distance between any consecutive ascending form of the set [7 9 0]
4. transpose to 0 (025). The set class is (025). Any transposition of (025), forwards or backwards is part of set (025).
Forte would use these set classes in millions of ways; inverting them, finding every instance of it and its 12-tone aggregate complement in any atonal piece (segmentation), finding interval class vectors, using those vectors to construct genera of potential subsets and supersets, the list goes on. Many Forte followers have introduced many additional concepts to his theories like set multiplication, maximally related sets, etc.
These arguments don't stop with atonal analysis; Schenkerian analysis for tonal music gets a lot of heat for being so reductionist that the music isn't really even being analyzed anymore. Some people even think the way we analyze chords with Roman numerals is reductionist.
Even though I think analysis is inherently reductionist, I'm curious as to what anyone thinks about this kind of stuff and would be willing to go through any strange concepts (though I'm not an expert in any way). I feel like as composers we have a different take on this kind of thing.