Theory predicts that allometric constraints on sound production should be stronger for the lower frequencies of vocalizations than for their higher frequencies, which could originate an allometry for sound frequency bandwidth. Using song recordings of ca. 1000 passerine species (from >75% passerine genera), we show a significantly steeper allometry for the lower than the higher song frequencies, resulting in a positive allometry of frequency bandwidth: larger species can use wider bandwidths than smaller species. The bandwidth allometry exists in songbirds (oscines), but not non-oscine passerines, indicating that it emerges from a combination of constraints to sound frequency production or transmission and the evolved behavior of oscines: unlike the narrow bandwidths of most non-oscine songs, the learned songs of oscines often use wide bandwidths that can be limited by both lower and upper constraints to sound frequency. This bandwidth allometry has implications for several research topics in acoustic communication.