Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:4/4
K:Ador
['A2 eA AAeA', 'eaaa eaaf']  
X:1
L:1/8
M:4/4
K:Ador
 A2 eA AAeA | G2 dG AGGE | A2 eA AAeA | GABd eBdB | A2 eA AAeA | G2 dG AGGA | GEDE GABd |1 
 eBdB A3 G :|2 eBdB A3 B |: eaaa eaaf | g2 bg dgb^g | eaaa eaaf | gedB GABd | eaaa eaaf | 
 g2 bg dgb^g | edef gbaf |1 gedB A2 Bd :|2 gedB A3 G ||  