Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/4
K:none
['cF/A/ cF d/c/B/G/ E2 BE/G/ BE']  
X:1
L:1/8
M:2/4
K:none
[K:F]"F" f4 |"C7" e4 |"Bb" d4 |"F" c4 |"Bb" Bc/d/ cB |"F" AB/c/ BA |"C7" GA/B/ AG |1"F" FF Ac :|2 
"F" F2 z2 |:"F" C>F AF |"C7" E>G Bc |"Bb" dc"C7" BG |"F" dc AF | C>F AF |"C7" E>G Bc | 
"Bb" dc"C7" BG |"F" FF F z ::"F" cF/A/ cF |"C7" d/c/B/G/ E2 | BE/G/ BE |"F" d/c/A/F/ C2 | 
 cF/A/ cF |"C7" d/c/B/G/ E2 | BE/G/ BE |"F" FA F z :|  