Pitch is usually thought of as a one-dimensional psychological attribute corresponding to the one-dimensional physical variable of frequency. However, complex tones can be continuously varied between pitches along at least three different dimensions: (1) a rectilinear dimension of height, (2) a circular dimension of chroma, and (3) a second circular dimension of musical fifths. Accompanying sound demonstrations illustrate each of these three variations-including illusions in which a tone that is cyclically shifted around the chroma circle seems to go ever higher in pitch, and in which a tone that is simultaneously shifted in opposite directions in height and chroma seems always to be rising in pitch but is clearly lower at the end than at the beginning.
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