If Beethoven had written:
That would be unintelligible, because it belongs to no known genre of music from Beethoven's time.
Instead, Beethoven's music could never be mistaken for Danny & the Juniors, and indeed, we're convinced that both Beethoven and Tchaikovsky rolled over under the onslaught of such "noise". ;-)
So in this case, "unintelligible" simply means unrecognizable as a certain category of music, in this case, Beethoven quartets.
Beethoven was a scandalously original innovator in his day. “What is that horrible noise?!?” they said.