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:A
['A2 ABAB cAB cecBAB']  
X:1
L:1/8
M:6/8
K:A
 E | A2 ABAB | cAB | cecBAB | A2 E | A2 ABAB | cAB | cecBAB | A2 c | e2 ccBc | dBB/c/ | d2 dcBA | 
 Bed/B/ | A2 ABAB | cAB | cecBAB | A2 |]  