Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/8=180
M:6/8
K:D
['A dfA d2', 'f3 gfg']  
X:1
L:1/8
Q:1/8=180
M:6/8
K:D
|: A | dfA d2 A | dfA d2 f | a2 f d2 f | fee e2 A | dfA d2 A | dfA d2 e | f2 f ede | d3 d2 :: e | 
 f3 gfg | a3 f2 a | agg gff | fee efg | f3 gfg | a2 f d2 f | efg fge | edd d2 :|  