Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/4=120
M:6/8
K:D
['A d2 (e/d/) cde f>gf e2 A', 'A2 A d>ed cde fgf e2 A', 'F (F/G/) (A/B/)', 'f2 E F (F/G/) (A/B/) cAc dgf{f}']  
X:1
L:1/8
Q:1/4=120
M:6/8
K:D
"^Tenderly" A | d2 (e/d/) cde | f>gf e2 A | .B.A.G .F.G.A | (c>de/c/) A2 || A | d>ed cde | 
 fgf e2 A | .A.F.A .G.F.E | (D3 D2) |] | E | F (F/G/) (A/B/) .c.A.A | .B.G.G .c.A.A | 
 F (F/G/) (A/B/) cAc | dec f2 || E | F (F/G/) (A/B/) cAc | dgf{f} e2 d | .c.A.F{A} .G.F.E | 
 (D3 D2) |]  