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:Amix
['e>A (3cBA', '(3ABA (3Bcd e>aa>g a2 g>e d>BG>A B>GB>d']  
X:1
L:1/8
M:4/4
K:Amix
|: a>f | e>A (3cBA G>A (3Bcd | e>A (3cBA G2 a>f | e>A (3cBA G>A (3Bcd | (3efe d>B (3ABA :: (3Bcd | 
 e>aa>g a2 g>e | d>BG>A B>GB>d | (3efg f>a g>fg>d | (3efe d>B (3ABA :|  