LEDGE - END OF THE FIDDLER by Nick Apollonio.

Now the fiddler and Jim Brown set out on the thirty-first of May   
To play the dance at Rockland thirteen miles across the bay
With the wind southeast on the sunlit sea their pinky skipped along
Their hearts were full as the rising moon and the air was full of song.

[Also, the last stanza mentions June.]

Recording by Gordon Bok.