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:Dmix
['e2 ^cA eAAA GEDE G2 EG AGAB', 'dcBc dggg dgbg eaaa eaag']  
X:1
L:1/8
M:4/4
K:Dmix
 e2 ^cA eAAA | GEDE G2 EG | AGAB cBcd | efge d2 gf | e2 ^cA eAAA | GEDE G2 EG | AGAB cBcd | 
 efge dcBc || dggg dgbg | eaaa eaag | efge defg | afge dcBc | dggg dgbg | eaaa eaag | e2 ge defg | 
 afge defg |]  