Since the Goddess has turned into stone a year ago, the Sprites have been trying to find the notes needed for the unfreezing song. They haven't had any luck and Jamie hasn't been very successful either. When you arrive on the farm the Sprites ask for your assistance to find the tones.
Finding music notes requires that you accomplish certain tasks in the game. It could be as simple as putting an item into the shipping bin, or as challenging as reaching the 100th floor of a mine. When you receive a music note your character will hold it above his/her head and you'll be told what you did to get the note.
You can find all the notes you've discovered so far by going into your summary menus and rotating to the Notes page.
Every time you find 5 notes, head back to the Goddess Spring. The notes will turn into a piece of the orchestra needed to play the song for the Goddess.
05 Notes: Marimba
10 Notes: Timpani
15 Notes: Harp
20 Notes: Piano
25 Notes: Violin
30 Notes: Cello
35 Notes: Flute
40 Notes: Acoustic Guitar
45 Notes: Trumpet
50 Notes: The orchestra plays
You only need 50 notes to awaken the Goddess and/or marry Jamie.