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
['', '(3cdc AF', '', 'cbge f2']  
X:1
L:1/8
M:4/4
K:F
 A3 B |: cagf egfd | (3cdc AF CFAc |{Bc} BAGA BcdB | (3cdc AF C2 Ac | cagf egfd | (3cdc AF CFAc | 
{Bc} BAGA Bcde |1 fcag f2 AB :|2 fcag f2 || Ac |: acgc fcAc | fcec d2 ^cd | bgaf gfef | 
 gfed c2 Ac | acgc fcAc | dfbf d2 ^cd | bgaf gfed |1 cbge f2 AB :|2 cbge f2 AB ||  