Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/16
M:2/4
K:G
['', 'G2 B>cd2 B>cd2 c>BA>G FED2 B>cd2 Bcde', 'g>fg>f g>ab>g']  
X:1
L:1/16
M:2/4
K:G
 G2 |: B>cd2 B>cd2 | c>BA>G FED2 | B>cd2 Bcde | cBcA G2g2 :: g>fg>f g>ab>g | a>gd>b c'>af>a | 
 g>fg>f g>ab>g | a>fd>f g2G2 :|  