Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:4/4
K:C
['c2 ec (eg)ec', 'c A GFEF GABc (Bd)dc (Bd)de GEF']  
X:1
L:1/8
M:4/4
K:C
 G | c2 ec (eg)ec | (Bd)dc (Bd)de | c2 ec (eg)ec | BagB c2 c :| A | GFEF GABc | (Bd)dc (Bd)de | 
 GEF GABc | AagB c2 cA | (GF)EF GABc | Bddc Bdde | cedf egfa | gefd c2 c ||  