title: Are psychophysical scales of intensities the same or different when stimuli vary on other dimensions? Theory with experiments varying loudness and pitch.
abstract: Most studies concerning psychological measurement scales of intensive attributes have concluded that these scales are of ratio type and that the psychophysical function is closely approximated by a power function. Experiments show, for such cases, that a commutativity property must hold under either successive increases or successive decreases provided, e.g., all other independent dimensions are fixed. A good deal of data support this conclusion. However, little or no attention has been paid to whether or not such subjective intensity scales differ when an independent dimension such as frequency (pitch in audition, color in vision, etc.) is varied. Using a simple and favorably tested theoretical model for global psychophysics, the authors arrive at a necessary and sufficient cross-dimension, commutativity condition for a common intensity ratio scale to exist. For example, the data show that the loudness of a tone at frequency f and another tone at frequency g can each be viewed as arising from a common property of loudness over intensity/frequency pairs. Comparing one version of cross-dimensional commutativity with the corresponding 1-dimensional commutativity property discriminates between a general representation of the ratio scale property and a special case of it.
  
  
  CONCLUSIONS
  Does the theory extend to other intensive continua (prothetic attributes)? If so, which ones? And does it extend to cross-modal matching?
authors.affiliation: Institute for Mathematical Behavioral Science, University of California, Irvine, Irvine, CA 92697-5100, USA.
authors.forename: R Duncan
authors.initials: RD
authors.lastname: Luce
authors.forename: Ragnar
authors.initials: R
authors.lastname: Steingrimsson
authors.forename: Louis
authors.initials: L
authors.lastname: Narens
mesh_terms: D000161:Acoustic Stimulation / Q000523:psychology*; D001307:Auditory Perception / Q000502:physiology*; D001309:Auditory Threshold / Q000502:physiology; D006801:Humans; D008144:Loudness Perception / Q000502:physiology*; D008960:Models, Psychological; D010897:Pitch Discrimination / Q000502:physiology; D010898:Pitch Perception / Q000502:physiology*