Synchronization of neural activity in the gamma frequency band is associated with various cognitive phenomena. Abnormalities of gamma synchronization may underlie symptoms of several neurological and psychiatric disorders such as schizophrenia and autism spectrum disorder. Properties of neural oscillations in the gamma band depend critically on the synaptic properties of the underlying circuits. This study explores how synaptic properties in pyramidal-interneuronal circuits affect not only the average synchronization strength but also the fine temporal patterning of neural synchrony. If two signals show only moderate synchrony strength, it may be possible to consider these dynamics as alternating between synchronized and desynchronized states. We use a model of connected circuits that produces pyramidal-interneuronal gamma (PING) oscillations to explore the temporal patterning of synchronized and desynchronized intervals. Changes in synaptic strength may alter the temporal patterning of synchronized dynamics (even if the average synchrony strength is not changed). Larger values of local synaptic connections promote longer desynchronization durations, while larger values of long-range synaptic connections promote shorter desynchronization durations. Furthermore, we show that circuits with different temporal patterning of synchronization may have different sensitivity to synaptic input. Thus, the alterations of synaptic strength may mediate physiological properties of neural circuits not only through change in the average synchrony level of gamma oscillations, but also through change in how synchrony is patterned in time over very short time scales.