Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:6/8
K:E
['E2 A']  
X:1
L:1/8
M:6/8
K:E
 =C | =GGGAAA | =GGF E2 A | =G2 F E2 A | =G2 F E2 A | =G2 F E2 A | =G3 E2 A | =G2 F E2 A | 
 =G3 E2 A | =G2 F E2 A | =G2 F E2 A | =G2 F E2 A | =G2 F E2 =C | =GGGAAA | =GGF E2 |]  