What did Winnie, her grandmother, and the stranger hear in the distance in "Tuck Everlasting"?

As Winnie, her grandmother, and the stranger stand in front of her grandmother's cottage, they hear "a faint, surprising wisp of music...a tinkling little melody", come floating to them through "the sounds of crickets and sighing trees".  Winnie's grandmother is excited, saying that it's been years since she has heard the sound.  She calls it "elf music", and wants to hurry away at once to tell Winnie's father.  Winnie, who has never heard the strain before, thinks "it sounds like a music box".

The three listeners hear the music twice; the second time "it tinkle(s) its way faintly through the little melody three times before it fade(s)".  Taking Winnie firmly by the hand, Winnie's grandmother marches purposefully up the path back into the cottage, while the stranger, with an ominous "expression...of intense satisfaction...turn(s) and disappear(s) down the shadowy road", whistling "the tinkling little melody" softly to himself (Chapter 4).

The song comes from a little music box belonging to Mae Tuck.  After she and her sons have "kidnapped" Winnie, Mae brings it out distractedly to soothe the child, who is understandably upset.  Winnie recognizes the tune from when she heard it before with her grandmother and the stranger.  The music box seems to have the capacity to "relax them all", and Winnie decides that "no one who owned a thing like this could be too disagreeable" (Chapter 6).