In machining processes, regenerative chatter is an unstable vibration which adversely affects surface finish, cutting tools, and spindle bearings. Under some cutting conditions, the beat effect, an interference pattern between two periodical vibrations of slightly different frequencies, has been a common phenomenon where the amplitude of chatter vibration tends to increase and decrease periodically. Until now, few studies have been conducted to analyze the beat effect in machining chatter. On the other hand, researchers have developed various chatter detection methods with the objective to timely avoid detrimental effects induced by chatter. However, none of the existing chatter detection methods in the literature has ever considered the beat effect. The neglect of the beat effect will adversely affect the effectiveness of these methods and even result in false alarms. In this paper, the significance level and the mechanism of the beat effect in turning chatter are analyzed by time domain simulation. Afterward, a multiscale wavelet packet entropy (MWPE) method is proposed to detect machining chatter regardless of the occurrence of the beat effect. The determination strategy of the scale factor in the MWPE is presented based on the beat period, whose relationship with the damping ratio and spindle speed is derived analytically in orthogonal turning scenarios. Finally, machining tests are conducted to verify the feasibility and effectiveness of the proposed chatter detection method with respect to the presence and absence of the beat effect.