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:A
['A>ag>a e<Ac>A', 'g<ee>f e<cc>e f>df>a |1 (3gfe (3dcB (3Ace']  
X:1
L:1/8
M:4/4
K:A
 A>ag>a e<Ac>A | F>Ad>c B>EG>B | A>ag>a e<Ac>A |1 F>AG>B c<AA>G :|2 F>AG>B c<A (3agf |: 
 e<cc>e f<dd>e | d>B^d>f g<ee>f | e<cc>e f>df>a |1 (3gfe (3dcB (3Ace (3agf :|2 
 (3gbg (3efg a>Ac>B ||  