The brain encodes information in the spiking dynamics of recurrently connected inhibitory (I) and excitatory (E) neurons. Recurrent Spiking Neural Networks (RSNNs) have the potential to illuminate mechanisms of neurobiological computation. While inhibition and excitation underlie cortical dynamics, the roles of individual E and I neurons, as well as distinct I neuron subclasses, remain unclear. To elucidate these roles, we created biologically plausible RSNNs with leaky integrate and fire neurons and trained the networks on variations of a temporal task. We find that distinct interneuron subclasses create varied timescales of behavior, resulting in improved temporal task performance. For biological realism, we implemented a refractory period, sparse connectivity, and a 4:1 E:I ratio (1). To explore the role of diverse inhibition, we created a second model with three types of interneurons: PValb, SST, and 5Htr3a (1,2). We first trained our single-I-class model and our three-I-class model on two temporal tasks. The three-I-class model displayed better excitation regulation, smoother phase transitions, and performed better on both tasks, suggesting that diverse inhibition facilitates computation. To understand the roles of E and I neurons, we trained our two models on a temporal sine wave generation task with inputs of amplitude, period and a clock-like signal. With continually varied period and amplitude, we found that specific I and E neurons drove the production of positive or negative sine wave phases by activating during specific phases. Some phase-tuned I neurons drove phase transitions through inhibition or disinhibition of E neurons. Phase-tuned neurons temporally scaled their firing patterns to account for period variation, with more pronounced scaling in the model with three I neuron classes (3). We further investigated E and I neuron roles by training models on tasks with varying target amplitude or period. Higher inhibitory activity in the varying amplitude task suggested I neurons regulate excitation for amplitude determination. Next, we trained our networks on a short-term memory task by providing the amplitude and period inputs for a limited time. Without continuous input, the relative importance of excitatory activity increased to support self-sustained network dynamics. Our results demonstrate that the diversity of I neurons, along with the unique functional roles of individual E and I neurons, support computation over time in neocortex.