(The Pythagorean Comma is an artifact of one of the more common systems for building musical scales. Shepard tones are not related to the Pythagorean Comma; the paradoxical pitch judgements can be experienced regardless of the scale being used.) The Shepard phenomenon is a paradox of pitch judgement. We have a set of tones, say W, X, Y, and Z, and everyone who hears them will agree that X is higher than W, Y than X, Z than Y, and ... W than Z! This circular pitch judgement can be observed with as few as three tones, but grows more reliable and compelling when there are more tones in the circle. A continuous version also exists, and nothing can be eerier than hearing a glissando tone wailing eternally higher and higher ... but never getting any higher! The central idea is that a rich musical tone with weak odd harmonics has two possible perceived frequencies, one twice the other. To see this, imagine that the weak odd harmonics vanish entirely. The even harmonics alone form the harmonics of a note one octave higher. When the odd harmonics are present but weak, the listener can choose to hear either the fundamental pitch or the octave; the phenomenon is similar to the Necker cube, a visual figure which can be perceived in two different ways at will. When two such ambiguous tones are presented, the listener will unconsciously choose to perceive them as close together in pitch, and will select the fundamental or the octave of each tone accordingly. Using this principle it is possible to prepare a circle of tones, with the even harmonics weakening as the fundamental pitch rises. Additional refinements make the harmonic intensities resemble a ruler function, smoothing out the transitions and eliminating any sense of "turning a corner" when the fundamental and its odd harmonics finally vanish entirely. -A