Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/16
M:2/4
K:G
['z (g2<B2) z (f2<B2) z (e2<B2) d2c2', 'z2 D>EF>A c>ad>c B>gd>B G>BA>G |1 F>ed>e']  
X:1
L:1/16
M:2/4
K:G
 z (g2<B2) z (f2<B2) | z (e2<B2) d2c2 | z (B2<^D2) z (B2<E2) | z (B2<F2) G2E2 | 
 z (g2<B2) z (f2<B2) | z (e2<B2) d2c2 | z (B2<^D2) z (B2<E2) | z BFG E2 z2 |: D>EF>A c>ad>c | 
 B>gd>B G>BA>G |1 F>ed>e d>ec>A | G>bg>d e>dB>G :|2 f<a c>d ^d>ec>A | B2[Bg]2[Bg]2 z2 ||  