Here are some tips for summoning Sprites.

At the perilous precipice: Play the Song of Sworcery and interact with the two rainbows in the sky.
At the stolid log bridge: Play the Song of Sworcery and interact with the four pairs of trees on either side of the river.
At the sheep's meadow: Play the Song of Sworcery and interact with the sky just above the "oddly shaped stick overlooking the meadow".