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:D
['[AD]3 BAF A2 B d2 e', 'ABd B2 A']  
X:1
L:1/8
M:6/8
K:D
 [AD]3 BAF | A2 B d2 e | faa baf | e>fe edB | [AD]3 BAF | A2 B d2 e | faf e2 d | d3- d2 B :: 
 ABd B2 A | ABd B2 A | faa baf | e>fe edB | ABd B2 A | ABd B2 A | faf e2 d | d3- d2 :|  