We have studied short-term variations of the blazar OJ 287, suspected to host a supermassive black hole binary. In this study, we use a two-season optical R-band data set from 2004 to 2006 which consists of 3991 data points from the OJ 287 observation campaign. It has sections of dense time coverage, and is largely independent from previously published data. We find that these data confirm the existence of a ∼50 d periodic component, presumably related to the half-period of the innermost stable circular orbit (ISCO) of the primary black hole. In addition, we find several pseudo-periodic components in the 1-7 d range, most prominently at 3.5 d, which are likely Lorentz contracted jet re-emission of the 50 d component. The typical 50-d cycle exhibits a slow rise of brightness and a rapid dimming before the start of the new cycle. We explain this as being due to a spiral wave in the accretion disc which feeds the central black hole in this manner.