Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/2
K:D
['f2 e/f/g f2 e2 dfed', 'BA d2 c/d/e d2 e/f/g']  
X:1
L:1/8
M:2/2
K:D
 f2 e/f/g f2 e2 | dfed Tc2 BA | d2 c/d/e d2 (e/f/g) | fagf e4 | f2 e/f/g f2 e2 | dfed c2 TBA | 
 d2 c/d/e d2 e/f/g | fdAc d4 :: a2 g/a/b adfg | ab/a/ g/f/e/d/ Tc2 BA | d2 c/d/e d2 e/f/g | 
 fagf{f} e4 | f2 d/e/f/g/ f2 e2 | dfed c2 BA | d2 c/d/e d2 e/f/g | fdAc d4 :|  