Wendy Carlos’s Xenharmonic Keyboard
Jordan Schettler · Mathematics Magazine · 2019
Summary.Wendy Carlos is an American composer and electronic musician who constructed three closely related musical scales she called α, β, and γ. These scales are xenharmonic, i.e., unrelated to the familiar 12-tone scale. However, the 5 black and 7 white keys contained in one octave on a standard keyboard have a strong analogy with representations of the α and β scales contained in one perfect fifth on the γ scale. We explore this analogy using idea from algebra and number theory, and find that Carlos’s three scales arise naturally from the theory of continued fractions. Moreover, an infinite family of similarly “nice” musical scales arises from the same construction.