Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:3/4
K:F
['c2 A2 FA c3']  
X:1
L:1/8
M:3/4
K:F
 C2 | F3 GAB | A2 F2 FG | A3 GAB | c4 c2 | d3 cBd | c2 A2 FA | c3 ABc | A2 z2 F2 | d3 dfd | 
 c2 A2 FA | c3 dcB | A2 z2 |]  