Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/2
K:E
['F E2 EF ECA,E F2 FG FECB,', 'e/e/e (ge)']  
X:1
L:1/8
M:2/2
K:E
 F | E2 EF ECA,E | F2 FG FECB, | E2 EG Bcef | gbfa gee :| f | e/e/e (ge) fege | begf eccf | 
 e/e/e (ge) bege | ceBc GEEf | e/e/e (ge) fege | begf eccB | ceBc GBFa | gbfa gee ||  