ROUND AND ROUND THIS GREEN SUGAR TREE. AKA and see “Kate Lay Sleeping,” “Kate’s Laid in the Hay,” “Whitewashed Kate.”American, Song Tune and Reel. USA, southwestern Pa. A Dorian. Standard tuning. AB. The tune is familiar from playparty and sea shanty traditions, and seems to Bayard to have been better known as a vocal than an instrumental air..