This is work compiled from http://strategywiki.org/wiki/Eternal_Sonata/Score_Pieces
and Xobx360achievements.org and tweaked by my own work throughout the game. There are potential spoilers in this guide.
You can only acquire ALL the score pieces through Encore mode. Also, Eternal Sonata does not number your score pieces when you acquire them. Chances are that your score pieces are out of order. Strategywiki.org has pictures of each piece to match up with the following numbering.
1. Inside the stall/shrine next to March's house in Agogo Village
2. In a chest at the end of Fort Fermata, after you defeat the boss.
3. In a boat outside Cantabile Inn, located near the save point.
4. In a chest in Woodblock Groves, this is near the middle save point (North Center region).
5. Once you've entered Andante City proper, it is in the third room you pass, a store room, on the shelves to your right.
6. Hidden near a rock pillar in the entrance of Andante City proper (you must first find a note in some boxes next to the house that triggers the event to go to the graveyard).
7. On a bookshelf on the Baroque Ship's east deck, guest room to the right
8. On the bow of the Baroque Ship, in a barrel, after you trigger a scene with Fredrick.
9. Pirate Ship Dolce, on basement level 4, halfway along the corridor there is a room to your right with a chest in containing this piece.
10. In a record player in Baroque Castle, on the ground floor level, 2nd room in the east corridor.
11. In a clock in Baroque Castle, on the 2nd floor, far east room
12. On a desk in the Baroque City Inn’s first floor west room.
13. The left snowman at Baroque City Entrance.
14. In the cave on the right from the second point in Sharp Mountains.
15. In the fireplace in the Sharp Mountain Lodge.
16. In a treasure chest in Wah Lava Cave, shortly after entering (North Side 2).
17. In the back right corner of the Ritardando Bakery (inside).
18. On the left side of the Ritardando Bakery (inside).
19. In a treasure chest in Mandolin Church Catacombs.
20. In Baroque Tavern, in the wine cellar after completing the Pirate Sidequest. You must have both Pirate Papers from defeating Dolce in the pirate ship (compulsory to the story) as well as Wah Lava Caves (optional), and have examined the six pillars in the Mandolin Church Catacombs in Ritardando (past the waterfall section). After obtaining these, speaking to the employee in the Wine Cellar and selecting the third option will result in a third fight against Dolce, after which this Score Piece can be found in one of the barrels.
21. From a merchant at the Celesta Forest entrance, after obtaining the Aria Temple Key.
22. Attached to the Cello Tree at Cowbell Heights.
** The following pieces require you to have the Hero’s Crest and entering the secret dungeon, Mysterious Unison. The Hero’s Crest is found in the Double Reed Tower.
23. Mysterious Unison Floor 4
24. Mysterious Unison Floor 9
25. Mysterious Unison Floor 12
2nd Playthrough (Encore Mode)
Chapter 1 through 5
26. Play Score Piece 24 with Easygoing Flat in the entrance of Tenuto Village, near the save point.
27. In Heaven’s Mirror Forest head to where you defeated the Big Boar (boss) and find a giant green mushroom with a squirrel on it. Talk to the squirrel.
28. In the Forte City Tavern, upstairs on the second table.
29. Examine the sewer grating near the door to the Inn of Forte City.
30. Talking to the man with chest pains at Forte City Castle Gate (after acquiring the Teleport Room Key). You *must* have spoken to the grandma in Baroque City Inn in Chapter 4 to be able to get this Score Piece, as she falls to sleep in later chapters.
31. Some players report that you can get this score piece early in Chapter 6. A gift from the couple in the house south of the merchant in Baroque City after saving the man from Sharp Mountains. This requires climbing Sharp Mountains once more and battling a reasonably easy mini-boss.
-- As soon as Chapter 7 begins you must immediately backtrack to collect these final pieces.
31. If you were unable to get Score Piece 31 in chapter 6 here are the same directions: a gift from the couple in the house south of the merchant in Baroque City after saving the man from Sharp Mountains. This requires climbing Sharp Mountains once more and battling a reasonably easy mini-boss.
32. Play Score Piece 19 with Disappointed Note on the Fort Fermata side of Cabasa Bridge (North Side).