Craft a musical piece that integrates the provided melodic theme and the corresponding alphabetical pattern.
X:1
L:1/8
M:2/2
K:Amix
['AAcA dBcA', 'aeca eacg']  
X:1
L:1/8
M:2/2
K:Amix
 e | AAcA dBcA | BBgd BGGe | AAcA dBcA | BBed cAA :| g | aeca eacg | Bggd BGGg | aeca eacg | 
 Beed cAAg | aeca eacg | Bggd BGGg | afge fdec | dBed cAA ||  