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:C
['A4 z']  
X:1
L:1/8
M:6/8
K:C
 A | A2 E E2 F | G2 A3 B | (cB) A ^G2 B | A4 z A | A2 B c2 d | ee c3 d | (cBA) ^G2 B | A4 z A | 
 G2 F E2 ^D | cc B3 B | e2 d c2 A | B4 z c | d2 e A2 B | d2 c G2 A | (dc) B ^G2 E | A4 z x |]  