Constructing a Piano: A Key is Provided by Leonhard Euler

Year: 2001 Authors: Robert L. Bailey

Core claim

Choosing how many notes belong in an octave is a mathematical and musical design problem, and Euler’s ideas provide a key historical framework for it.

Topics

octave division, keyboard scales, harmonic structure, Leonhard Euler

Domains

number theory, harmonic analysis, ratio-based tuning, music theory, instrument design, keyboard construction

Methods

historical overview, comparative discussion, theoretical framing

Media

piano, keyboard instrument, musical scale

Paper text

The text below is the locally extracted OCR/Markdown version of the paper. Raw PDF files remain local and are not published here.

BRIDGES Mathematical Connections in Art, Music, and Science

Constructing a Piano

A Key is Provided by Leonhard Euler

Robert L. Bailey Department of Mathematics Niagara University Niagara University, NY 14109

Developing a scale for a keyboard instrument involves a certain set of criteria. “Dividing the octave” is a general problem in which one must decide how many notes should be in an octave in order to preserve a certain harmonic structure. The background of this problem and the contributions of Leonhard Euler, history’s most prolific mathematician, will be presented. Other schemes for structuring the octave will be briefly considered.