Large sounds and loud numbers? Investigating the bidirectionality and automaticity of cross-modal loudness-number interactions

Magnitude dimensions influence the processing of each other resulting in shorter reaction times in classification tasks when the magnitude information in both dimensions matches. These effects are often explained by a shared magnitude representation as proposed by A Theory of Magnitude (ATOM). Interactions between numbers and loudness indicate that loudness may also be represented as a magnitude. Three experiments were conducted to investigate loudness-number interactions with regard to cross-modality, automaticity, bidirectionality, and the influence of processing speed. In Experiment 1, participants classified the numerical value of visually presented numbers relative to a preceding standard number. Tones at different loudness levels were presented simultaneously with the target number. In Experiment 2, participants switched between a numerical classification task and a loudness classification task randomly between trials. Experiment 3 was similar to Experiment 1 but with reduced salience of the auditory dimension. Across all experiments, there was an interaction between loudness and number magnitude, with shorter reaction times for large (small) numbers when they were accompanied by loud (soft) tones compared to soft (loud) tones. In addition, Experiment 2 showed a bidirectional influence as the interaction occurred also in the loudness classification task. The effect of distance on the cross-modal loudness-number interaction only partially occurred, as only the loudness distance had an effect on the interaction, and this effect was mediated by task-relevance. This may reflect an asymmetry in the influence between numbers and loudness. Overall, the findings support the hypothesis that loudness is represented as a magnitude according to ATOM.