Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:3/4
K:Dmin
['a>f df/d/ ^ce/c/ d^c/d/ ed/e/ fg a>f', 'D2 d/e/f/g/ aa ff g/f/g/a/ b2 g2']  
X:1
L:1/8
M:3/4
K:Dmin
 a>f df/d/ ^ce/c/ | d^c/d/ ed/e/ fg | a>f dd ^cc | A=B/^c/ d2 D2 :: d/e/f/g/ aa ff | 
 g/f/g/a/ b2 g2 | e>f g/f/g/a/ ge | f/e/f/g/ a2 f2 | a>f df/d/ ^ce/c/ | d^c/d/ ed/e/ fg | 
 a>f dd ^cc | A=B/^c/ d2 D2 :|  