Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:3/8=110
M:6/8
K:G
['BcB d2 d cBA B2 A GFG', 'ABA AFd Afd']  
X:1
L:1/8
Q:3/8=110
M:6/8
K:G
 c | BcB d2 d | cBA B2 A | GFG BAG | BAG F2 D | BcB d2 d | cBA B2 A | GFG BAG |"^1" AEF G2 :: z | 
 ABA AFd | Afd eaf | gec dAF | AGE E2 A | ABA AFd | Afd Aaf | ge"^2" c dAF | GE^C D2 ::  