We build a model of cultural evolution and study the properties of the process in which new chord progressions are repeatedly generated by referencing and modifying past chord progressions. As an extension of the models for biological molecular evolution, this model represents a stochastic process in which references are selected from an accumulating pool of chord segments and new chord segments are created by mutation including insertion, deletion, and substitution of chord symbols. We used a dataset of Japanese popular music and analyzed this evolutionary process by inferring the model parameters. A number of suggestive results regarding the evolution of the creative culture were obtained, including a strong recency bias, large mutation rates and large dynamic changes in mutation probabilities, and correlations between fluctuations and mutation probabilities and between the diffusedness of mutant chord segments and their mutation probabilities. Model-based predictions of new chord progressions were also made.