Evolutionary approaches to culture remain contentious. A source of contention is that cultural mutation may be substantial and, if it drives cultural change, then current evolutionary models are not adequate. But we lack studies quantifying the contribution of mutations to directional cultural change. We estimated the contribution of one type of cultural mutations – modification of memes - to directional cultural change using an amenable study system: learned birdsongs in a species that recently entered an urban habitat. Many songbirds have higher minimum song frequency in cities, to alleviate masking by low-frequency noise. We estimated that the input of meme modifications in an urban songbird population explains about half the extent of the population divergence in song frequency. This contribution of cultural mutations is large, but insufficient to explain the entire population divergence. The remaining divergence is due to selection of memes or creation of new memes. We conclude that the input of cultural mutations can be quantitatively important, unlike in genetic evolution, and that it operates together with other mechanisms of cultural evolution. For this and other traits where the input of cultural mutations might be important, quantitative studies of cultural mutation are necessary to calibrate realistic models of cultural evolution.