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:F
['fe dc']  
X:1
L:1/8
M:4/4
K:F
 f2 c2 fe dc | d2 c_B B4 | gf fe dc c2 | c_B BA GF FG | AF AF _BG BG | cB cA dc dA | _BA GF EG DF | 
 C2 CB, C2 GE | FE FD _B,C DB, | GF GE CD EC | AF AF DE FD | _BA BG EF GE | F2 A_B c2 de | 
 f2 ef gf ed | c2 A_B cB AG | F2 f2 F2 D2 | C2 F2 FE FG | FE FG F2 C2 | A2 A2 A_B AG | 
 FG A_B c2 BA | _B2 f2 ef ge | fe dc c'2 c2 | a2 fa _ba gf | eg df ce ag | fe fd _Bc dB | 
 gf ge cd ec | ag af de fd | _ba bg ef ge | a2 f2 f4 | e2 c2 c2 Ac | fe dc _BA GA | F2 FE F2 D2 |]  