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:D
['F D>FAB (B/A/)G/F/ A2 D>FA>F GEE>F D>FA>B{B}', 'F DF d>f (e/f/)d/c/ d2 DA d>f', '(3DEF (3FEF', 'DA df']  
X:1
L:1/8
M:4/4
K:D
 F | D>FAB (B/A/)G/F/ A2 | D>FA>F GEE>F | D>FA>B{B} AG/F/ A>c |{c} d>B AF GEE :: F | 
 DF d>f (e/f/)d/c/ d2 | DA d>f e>d e<f | (DF) dg (f/e/)d/c/ d2 | d>B AF GEE :: F | 
 (3DEF (3FEF (3FEF (3FEF | (3DEF (3FEF GEEF | (3DEF (3FEF FABc |{Bc} d>B AF GEE :: F/D/ | 
 DA df (f/e/d/)c/ d2 | DA df (f/e/d/)c/ d2 | DA df gee>f | DA df f/e/d/c/{c} (d2 | d>)B AF GEE :|  