Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/4
K:G
['B,2 B,2', 'G,E, [M:6/8] G,G,E, G,G,D, ||[M:2/4]', '', 'D,2 D, z', 'G,,2 G,,2']  
X:1
L:1/8
M:2/4
K:G
 z2 G,G, | B,2 B,2 | B,2 G,G, | A,2 A,2 | A,2 B,A, ||[M:3/4] G,2 G,2 G,E, || 
[M:6/8] G,G,E, G,G,D, ||[M:2/4] E,2 G,E, | D,2 D,2 | D, z G,G, ||[M:3/4] G,2 G,2 D,D, | 
 E,2 E, z G,E, ||[M:5/8] D,2 D, z D, | D,B,,B,,G,,G,, ||[M:2/4] G,,2 G,, z | G,,2 G,,2 | G,,2 z2 |]  