Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/4
Q:1/4=120
M:2/4
K:G
['G G A/>G/ F3/2 G/ A B', 'e e']  
X:1
L:1/4
Q:1/4=120
M:2/4
K:G
 G G A/>G/ | F3/2 G/ A | B B c | B3/2 A/ G | A{BcA} G F | G3{DEFG} || e e e |{fgaf} e d c | d d d | 
 d3/2 c/ B | c d/c/B/A/ |]  