Weakly electric "wave" fish make highly regular electric organ discharges (EODs) for precise electrolocation. Yet, they modulate the ongoing rhythmicity of their EOD during social interactions. These modulations may last from a few milliseconds to tens of minutes. In this paper we describe the different types of EOD modulations, what they may signal to recipient fish, and how they are generated on a neural level. Our main conclusions, based on a species called the brown ghost (Apteronotus leptorhynchus) are that fish: (1) show sexual dimorphism in the signals that they generate; (2) make different signals depending on Whether they are interacting with a fish of the opposite sex or, within their own sex, to a fish of that which is dominant or subordinate to it; (3) are able to assess relative dominance from electrical cues; (4) have a type of plasticity in the pacemaker nucleus, the control center for the EOD, that occurs after stimulation of NMDA receptors that causes a long-lasting (tens of minutes to hours) change in EOD frequency; (5) that this NMDA receptor-dependent change may occur in reflexive responses, like the jamming avoidance response (JAR), as well as after certain long-lasting social signals. We propose that NMDA-receptor dependent increases in EOD frequency during the JAR adaptively shift the EOD frequency to a new value to avoid jamming by another fish and that such increases in EOD frequency during social encounters may be advantageous since social dominance seems to be positively correlated with EOD frequency in both sexes.