Michel Paul Guy de Chabanon, a French 18th century musician, musicologist and man of letters "...had an interest in spiders and played the violin for them to see what music they liked..." (quote sourced form Claude Lévi-Strauss's "Look, listen, read").
Alas, Lévi-Strauss's book does not tell us what music spiders did like.
For Georges Bataille, the spider was an almost formless creature, an invertebrate that is not like anything: "To declare (...) that the universe is not like anything, and is simply formless, is tantamount to saying that the universe is something like a spider or spittle" (Documents 7, 1929).
Certainly, Bataille's perspective on the spider is anthropocentric. Nonetheless, though highly sensitive to vibration, spiders have no ears. For that reason alone, the music spiders like would sound formless to us, unlike any music hitherto made by man, the audio equivalent of spittle.
Translating the music spiders like to human music is impossible. As Lévi-Strauss notes, translation "... is impossible in music, for lacking words it possesses as many languages as composers, and, ultimately, as compositions. Musical languages are, relative to each other, untranslatable, though conceivably they could be transformable - even if this has not, or has hardly been attempted".
In my imagination, if the music spiders like could be transformed to human terms, it might sound something like Tasmanian Black Metal band Striborg's latest album, the predatory and poisonous "Ghostwoodlands".