I am quite sure that the paper Using the Logistic Map to Generate Scratching Sounds, with the amusing abstract

This article presents a mathematical model for generating annoying scratching sounds. Such sounds are generated by frictional motion and have been attributed to the chaotic nature of the frequency spectrum thereby produced. The proposed model is based on the logistic map and is modified to have the stick-slip property of a frictional vibration. The resulting sound is similar to that generated by scratching a chalkboard or glass plate with the fingernails.

used some sort of computer experiments to figure out what types of mathematical functions sound annoying.