Perception of a regular beat in music is inferred from different types of accents. For example, increases in loudness cause intensity accents, and the grouping of time intervals in a rhythm creates temporal accents. Accents are expected to occur on the beat: when accents are “missing” on the beat, the beat is more difficult to find. However, it is unclear whether accents occurring off the beat alter beat perception similarly to missing accents on the beat. Moreover, no one has examined whether intensity accents influence beat perception more or less strongly than temporal accents, nor how musical expertise affects sensitivity to each type of accent. In two experiments, we obtained ratings of difficulty in finding the beat in rhythms with either temporal or intensity accents, and which varied in the number of accents on the beat as well as the number of accents off the beat. In both experiments, the occurrence of accents on the beat facilitated beat detection more in musical experts than in musical novices. In addition, the number of accents on the beat affected beat finding more in rhythms with temporal accents than in rhythms with intensity accents. The effect of accents off the beat was much weaker than the effect of accents on the beat and appeared to depend on musical expertise, as well as on the number of accents on the beat: when many accents on the beat are missing, beat perception is quite difficult, and adding accents off the beat may not reduce beat perception further. Overall, the different types of accents were processed qualitatively differently, depending on musical expertise. Therefore, these findings indicate the importance of designing ecologically valid stimuli when testing beat perception in musical novices, who may need different types of accent information than musical experts to be able to find a beat. Furthermore, our findings stress the importance of carefully designing rhythms for social and clinical applications of beat perception, as not all listeners treat all rhythms alike.