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:A
['cd efec Acea g2 f2', 'f2 fefg f2 e2']  
X:1
L:1/8
M:4/4
K:A
 cd | efec Acea | g2 f2 f2 Bc | dedc Bcde | f2 e2 c2 cd | efec Acea | g2 f2 b2 ba | gagf edcB | 
 A2 c2 A2 :: e2 | c2 e2 edef | e2 d2 dcBc | d2 f2 fefg | f2 e2 c3 d | e2 f2 g2 a2 | a2 g2 gfga | 
 g2 f2 fefg | f2 e2 e3 d | c2 e2 edef | e2 d2 dcBc | d2 f2 fefg | f2 e2 c3 d | e2 f2 g2 a2 | 
 b2 a2 f3 a | gagf edcB | A2 c2 A2 :|  