All epilepsies are defined by a propensity for recurrent seizures, characterized by hypersynchronous electrographic activity. Understanding this overarching property would be advanced by a thorough quantification of how the global synchrony of the epileptic brain responds to small perturbations that do not trigger seizures. Here, we leverage analysis of transient focal bursts of epileptiform activity, termed interictal epileptiform discharges (IEDs), to characterize this response. Specifically, we use a group of 145 participants implanted with intracranial EEG (iEEG) electrodes to quantify changes in 5 functional connectivity measures associated with three properties of IEDs: their presence, spread, and number. We perform this analysis in 5 frequency bands in order to contextualize our findings in relation to ongoing neural processes at different spatial and temporal scales. We find that, across frequency bands, both the presence and spread of IEDs tend to lead to independent increases of functional connectivity, but only in functional connectivity measures influenced by the amplitude, rather than the phase, of a signal. We find that these increases are not explained by simple subgroups of connections, such as the weakest connections in the brain, or only connections within the seizure onset zone. Evaluating patterns of similarity across different bands and measure combinations, we find that the presence of IEDs impacts high frequencies (gamma and high gamma)and low frequencies (theta, alpha, and beta) differently, although responses within each group are similar. Using grouped LASSO regression, we identify which individual-level features explain differences in functional connectivity changes associated with IEDs. While no single feature robustly explains observed differences, the most consistently included predictor across bands and measures is the anatomical locus of IEDs. Overall, this work provides compelling evidence for increases in global synchrony associated with IEDs, and delivers a thorough exploration of different functional connectivity measures, frequency bands, and IED properties. These observations show a disruption of several types of ongoing neural dynamics associated with IEDs. Additionally, we provide a starting point for future models of how small perturbations affect neural systems and how those systems support the hypersynchrony seen in epilepsy.