Optical camera communication (OCC) represents a promising visible light communication technology. Nonetheless, typical OCC systems utilizing frame-based cameras are encumbered by limitations, including low bit rate and high processing load. To address these issues, OCC system utilizing an event-based vision sensor (EVS) as receivers have been proposed. The EVS enables high-speed, low-latency, and robust communication due to its asynchronous operation and high dynamic range. In existing event-based OCC systems, conventional modulation schemes such as on-off keying (OOK) and pulse position modulation have been applied, however, to the best of our knowledge, no modulation method has been proposed that fully exploits the unique characteristics of the EVS. This paper proposes a novel modulation scheme, called the event interval modulation (EIM) scheme, specifically designed for event-based OCC. EIM enables improvement in transmission speed by modulating information using the intervals between events. This paper proposes a theoretical model of EIM and conducts a proof-of-concept experiment. First, the parameters of the EVS are tuned and customized to optimize the frequency response specifically for EIM. Then, the maximum modulation order usable in EIM is determined experimentally. We conduct transmission experiments based on the obtained parameters. Finally, we report successful transmission at 28 kbps over 10 meters and 8.4 kbps over 50 meters in an indoor environment. This sets a new benchmark for bit rate in event-based OCC systems.