Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:6/8
K:G
['DEF GAB AEF G2 D GFG DGB', 'FGA d^cd gdB def g3 g2 e', 'ABd g2 e agf gfe dBG EcB', 'dBG EcB AGA |1 BGF G2 c']  
X:1
L:1/8
M:6/8
K:G
|: DEF GAB | AEF G2 D | GFG DGB | dec Bcd | ege dcB | cBA BGE | DcB AGA |1 BGF GFE :|2 BGF G2 B |: 
 d^cd gdB | cAG FGA | d^cd gdB | def g3 | g2 e dcB | cBA BGE | DcB AGA |1 BGF G2 B :|2 BGF GFE |: 
 DGB cde | dge dBG | cde dBG | EFG ABd | g2 e agf | gfe dBG | EcB AGA |1 BGF GFE :|2 BGF G2 c |: 
 BAG AFD | GDB, DB,G, | G,B,D GDB, | A,CE A2 a | bgb afa | gfe dBG | EcB AGA |1 BGF G2 c :|2 
 BGF GFE ||  