Here's the much-discussed 1954 definiion:
"Folk music is the product of a musical tradition that has been evolved through the process of oral transmission. The factors that shape the tradition are:

      (i) continuity which links the present with the past;
      (ii) variation which springs from the creative impulse of the individual or the group;
      (iii) selection by the community, which determines the form or forms in which the music survives.

The term can be applied to music that has been evolved from rudimentary beginnings by a community uninfluenced by popular and art music and it can likewise be applied to music which has originated with an individual composer and has subsequently been absorbed into the unwritten living tradition of a community.
The term does not cover composed popular music that has been taken over ready-made by a community and remains unchanged, for it is the re-fashioning and re-creation of the music by the community that gives it its folk character."

PLease note that it makes no reference to the function of folksong in a society, nor to the style in which the music is played. It would also appear to exclude the performance-oriented arrangements of people like Carthy and Seeger.