Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/4
M:3/4
K:C
['E G', 'B A G']  
X:1
L:1/4
M:3/4
K:C
 E/D/ | C E G | c2 c | B/c/ d c | A3 | F A F | E G E | D/E/ F/G/ A/B/ | A G E | C E G | c2 c | 
 B/c/ d c | A3 | F A F | E G E | D/E/ F/G/ A/B/ | c2 :: G | G E/G/ E/G/ | A F/A/ F/A/ | B A G | 
 c B A | G E/G/ E/G/ | A F/A/ F/A/ | B A G | c2 :|  