An arpeggio playing apparatus comprises a musical tone signal generating device including a plurality of arpeggio playing parts, or an automatic music playing device and at least one arpeggio playing part. The arpeggio playing part is capable of playing an automatic arpeggio with an arpeggio pattern at a progression tempo. Under the condition that one of the arpeggio playing parts or the automatic music playing device has started playing an automatic arpeggio or an automatic music performance at the progression tempo which defines a synchronization timing consisting of periodically aligned synchronization grids, when a start instruction for a new arpeggio playing part is received, the new arpeggio playing part starts the operation in synchronism with the defined synchronization timing. If the start instruction comes at a time point within a delay margin, the arpeggio playing is started immediately and the first span of the arpeggio pattern is played in a shortened time length between the start instruction and the first coming synchronization grid. If the start instruction comes at a time point outside the delay margin, the start of the arpeggio playing is suspended until the first coming synchronization grid.