From www.mutopiaproject.org

"Greensleeves" is a traditional English folk song. A broadside ballad by the name "A Newe Northen Dittye of ye Ladye Greene Sleves" was registered by Richard Jones at the London Stationer's Company in September 1580, and the tune is found in several late-16th-century and early-17th-century sources, such as Ballet's MS Lute Book and Het Luitboek van Thysius, as well as various manuscripts preserved in the Seeley Historical Library in the University of Cambridge.
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