A key step in sensory information processing involves modulation and integration of neuronal oscillations in disparate frequency bands, a poorly understood process. Here, we investigate how top-down input causes frequency changes in slow oscillations during sensory processing and, in turn, how the slow oscillations are combined with fast oscillations (which encode sensory input). Using experimental connectivity patterns and strengths of interneurons, we develop a system-level model of a neuronal circuit controlling these oscillatory behaviors, allowing us to understand the mechanisms responsible for the observed oscillatory behaviors. Our analysis discovers a circuit capable of producing the observed oscillatory behaviors and finds that a detailed balance in the strength of synaptic connections is the critical determinant to produce such oscillatory behaviors. We not only uncover how disparate frequency bands are modulated and combined but also give insights into the causes of abnormal neuronal activities present in brain disorders.