Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/4
K:D
['AB/A/ FA de', 'ed ce']  
X:1
L:1/8
M:2/4
K:D
|: B | AB/A/ FA | de f2 | ga/g/ fe | df A2 | AB/A/ FA | de fe/f/ | ga/g/ fe |1 d2 d :|2 d2 |: cd | 
 e2 ed | ce a2 | e2 ef | ge c/B/A | e2 ed | ce ab/a/ | ga/g/ fe |1 d2 :|2 d2- d ||  