Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:6/8
K:D
['A FDF Adc Bcd efg', "D2 (d'/4c'/4b/4c'/4 d/)a fdf ad'a fdf abc'"]  
X:1
L:1/8
M:6/8
K:D
 (A/4B/4c/ | d2) A FDF | Adc Bcd | efg Bcd | cec ABc | d2 A FDF | Adc Bcd | efg ABc | d3 D2 :: 
 (d'/4c'/4b/4c'/4 | d/)a fdf | ad'a fdf | abc' be'd' | Tc'3 a2 d' | f'd'b d'f'b | e'c'a bd'f | 
 ge'g ed'c' | d'3 d2 :|  