In a soft, sweet, and melodious manner; with pleasant smoothness.
From Latin 'dulcis' via Old French 'doulcet,' with the adverbial suffix '-ly.' This was a preferred form in English during the Renaissance and medieval periods.
Musicians in the 1500s would have used 'dulcetly' to describe how to sing sweetly—it's basically the ancestor of how we now say 'melodiously' or 'with feeling'!
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