Across many species, a major function of vocal communication is to convey formidability, with low voice frequencies traditionally considered the main vehicle for projecting large size and aggression. Vocal loudness is often ignored, yet it might explain some puzzling exceptions to this frequency code. Here we demonstrate, through acoustic analyses of over 3,000 human vocalizations and four perceptual experiments, that vocalizers produce low frequencies when attempting to sound large, but loudness is prioritized for displays of strength and aggression. Our results show that, although being loud is effective for signaling strength and aggression, it poses a physiological trade-off with low frequencies because a loud voice is achieved by elevating pitch and opening the mouth wide into a-like vowels. This may explain why aggressive vocalizations are often high-pitched and why open vowels are considered "large" in sound symbolism despite their high first formant. Callers often compensate by adding vocal harshness (nonlinear vocal phenomena) to undesirably high-pitched loud vocalizations, but a combination of low and loud remains an honest predictor of both perceived and actual physical formidability. The proposed notion of a loudness-frequency trade-off thus adds a new dimension to the widely accepted frequency code and requires a fundamental rethinking of the evolutionary forces shaping the form of acoustic signals. (PsycInfo Database Record (c) 2024 APA, all rights reserved).