Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/16
M:3/4
K:Amin
['A2>B2 c2BG E4 c2c2 d2cd e2e2 efed', 'g2ga g2fe gfed']  
X:1
L:1/16
M:3/4
K:Amin
 A2>B2 c2BG E4 | c2c2 d2cd e2e2 | efed cdcB A2AB | cBA^G A4 A,4 :: e2ef g2ga g2fe | gfed d2cB c4 | 
 cdef g2ga g2fe | gfed d4 e4 | c2cd B2Bc A2A2 | c2cd B2Bc A4 | e2e2 gfed c2B2 | cBA^G A4 A,4 :|  