Created on 21 July 1997.
Last modified on 5 August 2000.



A paradoxical two-tone pattern is explored, which is heard as ascending when played in one key but as descending when played in a different key. The pattern thus provides a striking counterexample to the principle of invariance under transposition. In addition, the pattern in any one key is heard as ascending by some listeners and descending by others. This study examines the effects of spectral variables on how the pattern is perceived.


Certain series of tones appear to ascend or descend infinitely in pitch. Other patterns change when shifted in key and indicate an influence of speech on the perception of music.







A special set of computer-generated complex tones is shown to lead to a complete breakdown of transitivity in judgments of relative pitch. Indeed, the tones can be represented as equally spaced points around a circle in such a way that the clockwise neighbor of each tone is judged higher in pitch while the counterclockwise neighbor is judged lower in pitch. Diametrically opposed tones -- though clearly different in pitch -- are quite ambiguous as to the direction of the difference. The results demonstrate the operation of a ``proximity principle'' for the continuum of frequency and suggest that perceived pitch cannot be adequately represented by a purely rectilinear scale.


We describe five demonstration programs for displaying variants of effects reported in the vision literature. The demonstrations use a windowed workstation environment, the X Window System Version 11. The performance of the window system is analyzed in terms of our implementation experience and suggestions are made for future window system architectures based on that experience. The visual effects are then discussed in terms of what they teach us about the display of information within a windowed environment and the tools that the visual effects themselves provide for improving that environment.

Scott Flinn (