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Now let's listen to sequence of octaves. The applet (labeled "sines") plays a sequence of sine tones each one octave apart.

The shepard tone octaves don't sound like octaves -- they sound like unisons:

This is because all of the tones have identical spectra:

In this picture, the red arrow is pointing to the "fundamental" of the first of these tones, while the
green arrow is pointing to the "fundamental" of the second.  As can be seen (and heard),
the notion of fundamental, and ultimately of the very principle of height is called into question when dealing with these kinds of tones.