1
general::
Phrase(s): *for a song
Fig. cheaply. (As if the singing of a song were payment. *Typically: buy something ~; get something ~; pick up someone ~.) • No one else wanted it, so I picked it up for a song. • I could buy this house for a song, because it’s so ugly.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Very cheaply, for little money, especially for less than something is worth. For example, "I know a man . . . sold a goodly manor for a song" (Shakespeare, All's Well That Ends Well, 3:2). This idiom alludes to the pennies given to street singers or to the small cost of sheet music. [Late 1500s]
American Heritage Idioms