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
['', 'A{dBA} B2 B{dcB} c2', 'g2 a bag']  
X:1
L:1/8
M:6/8
K:G
 dc || A{dBA} B2 B{dcB} c2 | ded cAG | E{GFE} F2 DED | DGG FGA | A{dBA} B2 B{dcB} c2 | dcA d2 e |1 
{a} fed cAF | AGF G2 A :|2 f2 d cAF | AGF GBd || f{agf} g2 def |{agf} g2 a bag | e{afe} f2 dfa | 
{b} afd cAG | f{agf} g2 def |{agf} g2 a bag | fed cAF | AGF GBd | f{agf} g2 d{edc} d2 | g2 a bag | 
 e{afe} f2 daa |{b} afd cAG | f{agf} g2 def |{agf} g2 a bag | f2 d cAF | AGF G3 ||  