This paper studies the construction of symbolic abstractions for periodic event-triggered systems. To construct symbolic abstractions, the original event-triggered mechanism is over- and under-approximated, and thus the abstract event-triggered mechanisms are different from the original one, which leads to the asynchronous phenomenon between the original system and the constructed symbolic abstractions. To deal with this issue, an interface is proposed to guarantee the synchronization between the original and abstract event-triggering mechanisms and the equivalence relations between the original system and the constructed symbolic model. Furthermore, we study the controller refinement based on these two constructed symbolic models. Finally, the obtained results are illustrated via a numerical example.