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This observation suggests that by exagerating the aspect of chroma,
"one might be able to bring about a breakdown of transitivity in judgements
of relative pitch" (R. Shepard, "Circularity in Judgements of Relative
Pitch", Journal of the Acoustical Society of America, 36(12), pp.
2346-2353). Specifically, if the aspect of tonal height could be
altogether suppressed, then the helix would become a circle, with jugdements
of pitch becoming similarly circular.
The effect of such an illusion can be compared to the endless staircase of the visual artist M. C. Esher. For one who is ascending the staircase, each step is indeed moving up: there is the sensation, locally, of movement with respect to height. However, globally, the sensation of upward movement begins to break down. Hence, the principle of height is localized: as you move from step to step you know that you are going up. Globally, however, you are not moving up (or down) at all.
The following example is an endless ascending sequence of Shepard tones. As you listen, you will notice that at first each succesive tone seems indeed to be ascending. However, after awhile the sensation of ascending tone begins to weaken until you perceive that indeed the tone has not risen at all. The longer you listen, the stronger the effect becomes.
Notice that while each ascending Shepard tone seems to be higher than the previous one, it seems that, over the long run, the quality of ascent is ambiguous at best.