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, but this was never tested. 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 physical constraint 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 the lower and upper limits of sound frequency production. This bandwidth allometry has implications for several research topics in acoustic communication.