In a manner relating to or appropriate for a funeral; in a mournful, solemn, or somber way.
From 'funeral' plus the adverb-forming suffix '-ly.' Standard adverbial form created in the 18th-19th centuries.
Using an adverb like 'funerally' lets you describe an action done with funeral-like solemnity—'he spoke funerally' means with deep, mournful tone.
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