Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/2=50
M:4/4
K:Bb
['BGGG DGGG BG G/A/B/c/ d2 d/e/d/c/ BGGG', 'd/c/B/A/ B>cdd gddd B>cdd']  
X:1
L:1/8
Q:1/2=50
M:4/4
K:Bb
|: BGGG DGGG | BG G/A/B/c/ d2 d/e/d/c/ | BGGG DG Gc/B/ | AF F/G/A/B/ c2 d/c/B/A/ :| B>cdd gddd | 
 B>cdd ga{ga} b2 | B>cdd fccB | AF F/G/A/B/ c2 d/c/B/A/ | B>cdd gddd | B>cdd gfga | 
 b<g a<f g<d fc/B/ | AF F/G/A/B/ c2 d/c/B/A/ |]  