Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:4/4
K:Ador
['dBGB ABGB', 'e2 dg e2']  
X:1
L:1/8
M:4/4
K:Ador
 B | dBGB ABGB | dBGB A3 B | dBGB ABGB | c2 Bc A2 Bc | dBGB ABGB | dBGB A3 B | dBGB ABGB | 
 c2 Bc A3 || B/d/ | e2 dg e2 dg | e2 dB A2 Bd | e2 de gedB | c2 Bc A2 Bd | e2 dg e2 dg | 
 e2 dB A2 (3Bcd | eaaf gedB | c2 Bc A3 ||  