Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/8=320
M:6/8
K:G
['d BGG BGG BcB BAG dBB gdB', 'bgg agf ege dcB', 'dGG BGG BAG ece dBG FAA A2', 'dcB ceg dBG FAA A2 g bgg']  
X:1
L:1/8
Q:1/8=320
M:6/8
K:G
 d | BGG BGG | BcB BAG | dBB gdB | ABA A2 d | BGG BGG | BcB BAG | dBB gdB | ABA G2 :|"^2" g | 
 bgg agf | ege dcB | GBd gfg | efg a3 | bgg agf | ege dcB | def gdB | GAG G2 :|"^3" d | BGG dGG | 
 BGG BAG | ece dBG | FAA A2 c | BGG dGG | BcB BAG | def gdB | GAG G2 :|"^4" d | gbg faf | ege dcB | 
 ceg dBG | FAA A2 g | bgg agf | ege dcB | def gdB | GAG G2 :|  