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I just learned that Milhaud wrote two string quartets which can be played separately or can be combined into a single octet performance. Would this count as an example of polyphony, or is music like this in its own special category?

Perhaps it's more common in vocal pieces, e.g. "A Little Night Music" when "Soon," "Later," and "Now" are sung simultaneously, or various competing duets in opera.

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    Are the two halves in the same keys at the same times? – Tim Oct 15 '19 at 14:07
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    Without knowing Milhaud's work: a string quartet qualifies as polyphony on its own,combining it with another won't change anything here.I suspect, there is another term, since Quodlibet is close but not fully matching. – guidot Oct 15 '19 at 14:15
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    why polyphony only when played together? one single quartet would be also polyphony ... ups, guidot ... and quodlibet was also my association :) I also thought this must be called chamber music, especially the quartet no. 8 by Shostakovitch ! I'd like to poste this link as it contains some great examples, en.wikipedia.org/wiki/Chamber_music – Albrecht Hügli Oct 15 '19 at 14:36
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I found this source "Virgil Thomson: Music Chronicles 1940-1954" which refers to the Milhaud pieces as a "double-barreled work" or "double piece."

And every other mention of this technique I can find also refers to the Milhaud composition, so maybe it's simply not common enough to merit its own jargon!

It is technically polyphony and counterpoint as well, but that doesn't address the real idiosyncrasy of the subject, that it's two separate pieces that work both in isolation and when combined.

This seems like a blue ocean opportunity for inventing your own name for the concept, I do like "double-barreled" but how about something like "combinatorial composition" or "modular music?" (We already have the "mashup" genre for unintended combinations, but I assume that's outside the scope here.)

EDIT: Apparently "modular music" is already a term of art and it seems applicable to Milhaud's work: https://en.wikipedia.org/wiki/Modular_music

Modular music is music that originates from the combination and overlapping of different compositions one over the other. The compositions —also called modules— are written by one or many different composers in different moments. New modules can be added or removed to create a totally new work, a new composition, different from the original one.

It's even cited as the "technique" behind the invention of counterpoint in the Medieval era

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