Alfredo's father, Carlo, was also a professional cellist, as were Carlo's brothers Cesare and Gioacchino; his mother was a pianist, who gave the boy his first music lessons.
Alfredův otec Carlo byl také profesionální violoncellista, stejně jako Carlovi bratři Cesare a Gioacchino; jeho matka byla klavíristka a dávala chlapci první hudební lekce.