In a harsh, discordant, or unpleasant manner; in a way that produces clashing or grating sounds.
From 'cacophonic' + the adverbial suffix '-ally'; standard English adverb formation that transforms adjectives into manner adverbs.
Adding '-ally' to adjectives is so automatic in English that we don't think about it—but it's a relatively modern feature; older English often just used the adjective form as both adjective and adverb, making texts from before 1700 sound odd to modern ears.
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