The oscillatory tendency of consumer-resource interactions is a key determinant of food-web persistence. Here, we develop a metric for quantifying oscillatory tendency that scales the positive feedback effects of saturating functional responses with the negative feedback effects of self-limitation. We use this metric to predict the oscillatory tendency of a pairwise interaction, tritrophic chain, and tritrophic web. This framework yields two key predictions. First, the oscillatory tendency of any food web increases with the number of trophic links with long handling times regardless of the magnitude of attack rates. Attack rates influence oscillatory tendency only when handling times are short. Second, the realized oscillatory tendency of a trophic link depends on how the product of the attack rate and handling time scales with the strength of self-limitation. Importantly, our metric allows calculations of the critical self-limitation strength at which a consumer-resource interaction moves from stable to oscillatory dynamics. Our data analysis reveals that the majority (77%) of interactions involve low attack rates and handling times, requiring only a modest level of self-limitation to suppress oscillations. Only 23% of the interactions exhibit a strong oscillatory tendency, consistent with previous findings, based on time-series data, that 30% of consumer-resource interactions in nature exhibit oscillations.