The Use of Ratios in the Player Piano Studies of Conlon Nancarrow

Julie Scrivener
Bridges: Mathematical Connections in Art, Music, and Science (2001)
Pages 159–166


The forty-nine Studies for player piano by Conlon Nancarrow are pervaded by the use of mathematical ratios, particularly ratios based on intervals found in the justly-tuned scale. Nancarrow found a remarkable variety of ways in which to deploy ratios in his Studies. The most obvious and Pervasive use is in the establishment of different simultaneous tempos related by ratios as simple as 3:4 to as complex as e/pi. Ratios were also used to establish relationships between pitch materials and other details, and in certain structural features. This paper is an introductory survey of the use of ratios in these Studies.