Perceiving Slope and Acceleration: Evidence for Variable Tempo Sampling in Pitch-Based Sonification of Functions

Sonification offers a non-visual way to understand data, with pitch-based encodings being the most common. Yet, how well people perceive slope and acceleration-key features of data trends-remains poorly understood. Drawing on people's natural abilities to perceive tempo, we introduce a novel sampling method for pitch-based sonification to enhance the perception of slope and acceleration in univariate functions. While traditional sonification methods often sample data at uniform x-spacing, yielding notes played at a fixed tempo with variable pitch intervals (Variable Pitch Interval), our approach samples at uniform y-spacing, producing notes with consistent pitch intervals but variable tempo (Variable Tempo). We conducted psychoacoustic experiments to understand slope and acceleration perception across three sampling methods: Variable Pitch Interval, Variable Tempo, and a Continuous (no sampling) baseline. In slope comparison tasks, Variable Tempo was more accurate than the other methods when modulated by the magnitude ratio between slopes. For acceleration perception, just-noticeable differences under Variable Tempo were over 13 times finer than with other methods. Participants also commonly reported higher confidence, lower mental effort, and a stronger preference for Variable Tempo compared to other methods. This work contributes models of slope and acceleration perception across pitch-based sonification techniques, introduces Variable Tempo as a novel and preferred sampling method, and provides promising initial evidence that leveraging timing can lead to more sensitive, accurate, and precise interpretation of derivative-based data features.