Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/4
M:4/4
K:Edor
['E E B B A G F', 'G A', 'G A']  
X:1
L:1/4
M:4/4
K:Edor
 E | E B B A | G F E D | E F G A | B3 :| B/c/ | d3/2 F/ F G | A A G A | d d F G | A2 G A | 
 B d c/B/ A | B A G F |"^(a)" E F G E | A2 G A | B d c/B/ A | B A G F | E3 |] 
"^(a) What she actually sang was" E F G E | G2 F G | A =c B/A/ G | A G F E | D3 |]  