Cross-modal commutativity of magnitude productions of loudness and brightness

In their fundamental paper, Luce, Steingrimsson, and Narens (2010, Psychological Review, 117, 1247-1258) proposed that ratio productions constituting a generalization of cross-modality matching may be represented on a single scale of subjective intensity, if they meet "cross-dimensional commutativity." The present experiment is the first to test this axiom by making truly cross-modal adjustments of the type: "Make the sound three times as loud as the light appears bright!" Twenty participants repeatedly adjusted the level of a burst of noise to result in the desired sensation ratio (e.g., to be three times as intense) compared to the brightness emanating from a grayscale square, and vice versa. Cross-modal commutativity was tested by comparing a set of successive ×2×3 productions with a set of ×3×2 productions. When this property was individually evaluated for each of 20 participants and for two possible directions, i.e., starting out with a noise burst or a luminous patch, only seven of the 40 tests indicated a statistically significant violation of cross-modal commutativity. Cross-modal monotonicity, i.e. checking whether ×1, ×2, and ×3 adjustments are strictly ordered, was evaluated on the same data set and found to hold. Multiplicativity, by contrast, i.e., comparing the outcome of a ×1×6 adjustment with ×2×3 sequences, irrespective of order, was violated in 17 of 40 tests, or at least once for all but six participants. This suggests that both loudness and brightness sensations may be measured on a common ratio scale of subjective intensity, but cautions against interpreting the numbers involved at face value.