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
['cAA eAA', 'ecA dcd']  
X:1
L:1/8
M:6/8
K:A
|: ed | c/d/cA BAA | aga e3 | cAA eAA | Bcd Bed | cAA eAA | aga e2 d | c/d/ec BAB |1 cAG A :|2 
 cAG A3 |: cBc ecA | dcd daa | cBc ecA | dcd B3 | c2 c ecA | dcd daa | c/d/ec BAB |1 cAG A3 :|2 
 cAG A ||  