Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:3/4
K:G
['c (TBA AB) G3 (G FG) A(D', '(g2 Tgf) (fg) d4 (cB) A(G', 'd/c/B) c3 d ec d(g fg) dG']  
X:1
L:1/8
M:3/4
K:G
|: d3 c (TBA | AB) G3 (G | FG) A(D F)G | (AB){c} (BA) FA | (c d2) c (TBA | AB) G3 (G | 
 FG) A(D F)A | (F G2) A{c} Bc :: (cd) (g2 Tgf) | (fg) d4 | (cB) A(G F)E | (DE) (FG) AB | 
 d2 (g2 Tgf) | (fg) d4 | (cB) A(G F)D |1 G3 A{c} Bc :|2 G6 |: A3 (B c/B/A) | B3 (c d/c/B) | 
 c3 d ec | d(g fg) dG | F3 G AF | G3 A{c} (Bd) | c2 B3 G | (FG) AF G2 :|  