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:G
['eA(3.A.A.A eAgA eA(3.A.A.A eAdA eA(3.A.A.A ea{b}ae |{a}', 'ea a2']  
X:1
L:1/8
M:4/4
K:G
 eA(3.A.A.A eAgA | eA(3.A.A.A eAdA | eA(3.A.A.A ea{b}ae |{a} gedB GABd :| ea a2 ba a2 | 
 ea{b}ae gedg | ea a2 (3babag | eBde gdBd | ea a2 ba{b}ag | ea{b}ae g3 a | bg g2 aged | 
 ea{b}ag edBd ||  