Elizabeth Cronin (1879-1956) who was born in West Cork, sang this song in 1951 to Alan Lomax. Cronin was a musician and songwriter who sang traditional Irish music. you can hear her sing it in the video below.

Dance to Your Daddy - Irish Children's Songs - Ireland - Mama Lisa's World: Children's Songs and Rhymes from Around the World  - Intro Image
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You can hear Elizabeth Cronin sing "Dance to Your Daddy" in the video below. It's the first song you'll hear…

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