Orientation selectivity emerges in primary visual cortex of primates and carnivores, but with striking diversity. Some neurons exhibit high selectivity for the orientation of bars and gratings, while others are hardly selective at all. It is not known how this diversity arises, nor what function it serves. In macaque V1, orientation selectivity originates in tuned excitatory geniculate input. It is further sculpted by untuned inhibitory cortical input, and the spike threshold nonlinearity. Here, we seek to determine the relative contribution of excitation, inhibition, and spike threshold to the diversity of orientation selectivity in macaque visual cortex. Conventional stimuli used to probe orientation selectivity -- bars and gratings -- fail to dissociate the effects of these mechanisms. However, considering the responses of cortical cells to additive combinations of gratings enables the separate identification of these mechanisms act. We stimulated cortical neurons in anesthetized macaques with stimuli containing multiple incoherently-drifting sinusoidal gratings whose orientations were spaced at 20 deg intervals and whose orientation-dependent contrasts were chosen to match a circular Gaussian profile (standard deviation 0-55 deg). We fit the data with an LN cascade model in which orientation selectivity arises through filtering, suppression, and a threshold nonlinearity. The model accounts for the various changes in response gain and tuning bandwidth with stimulus spread, and reveals that the primary source of tuning diversity in the population arises from variability in the filtering stage.