Luce, Steingrimsson, and Narens (Psychological Review, 117, 1247–1258, 2010) postulated that if ratio magnitude productions involving two perceptual dimensions exhibit “cross-dimensional commutativity,” they may be represented on a single internal scale of subjective intensity. Commutativity here refers to the order independence of successive magnitude productions (e.g., adjusting the subjective intensity of a stimulus successively by factors of 2 and 3 should produce the same result regardless of which factor comes first [×2×3 = ×3×2]). In the present experiment, these operations were performed (1) within the same modality (here: loudness or brightness), and (2) across modalities—that is, making productions from light to sound (e.g., “make the sound twice as loud as the light is bright”) and back, or vice versa. In individual, within-subjects experiments involving repeated loudness and brightness productions, 13 participants made adjustments to evaluate both kinds of commutativity. In line with previous findings (Ellermeier, Kattner, & Raum, Attention, Perception, & Psychophysics, 83[7], 2955–2967, 2021), both intra-modal and cross-modal commutativity held for most participants, but the final results of corresponding sequences of cross-modal and intra-modal adjustments (e.g., of the type ×2×3) typically did not coincide. That inconsistency is interpreted as participants choosing different internal reference points when making cross-modal versus intra-modal magnitude productions, but it does not preclude their using a common internal yardstick. The aggregated and raw data of all participants are available in an OSF repository (https://osf.io/5avbw/?view_only=687aef266f174648863f86b4982e35b9). The study has not been preregistered.
