Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/2
K:F
['f3 c fcd>_e c3 F G3 A', 'F2 A>B c>d(Bc) f3 d (cd)(cA) G3']  
X:1
L:1/8
M:2/2
K:F
|: f3 c fcd>_e | c3 F G3 A | (cA)(GA) (cd)(cA) | e2 g2 g2 f>e | f3 a (_ba)(gf) | (dc)(d/e/)f G3 B | 
 (cf)(dB) (cA)(fc) | A2 F2 F2 :: A>B | c>d(Bc) f3 d | (cd)(cA) G3 F | (Bd)(cA) (fd)(ec) | 
 G2 c2 c2 d>e | f3 a (b/a/)(g/f/) g>a | f>F (G/A/)B A2 (GF) | d3 c f3 g | a2 f2 f2 |]  