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:C
['', 'eAA BAA eAA Bcd', 'A2 A a2']  
X:1
L:1/8
M:4/4
K:C
[M:6/8][K:A] g_b[Q:1/8=320](3Bcd |: eAA BAA | eAA Bcd | eAA fed | BGG Bcd | eAA BAA | eAA Bcd | 
 faf gfe |1 dBG Bcd :|2 dBG BdB || A3 a3 | ged e2 A | A2 A a2 B | BAG BdB | A2 A a2 a | gef g2 f | 
 gba g2 e | dBG BdB :|  