Rob Sturman

Applied Project --- The Mathematics of Musical Tuning

Tuning a musical scale is far from simple. Despite the fact that in the modern (Western) world a solution to this problem is now firmly established, for centuries alternative solutions have been proposed, implemented, and used with great success. One of the first musical theorists was Pythagoras, whose understanding of ratios and fractions formulated the ideas of musical intervals. Such intervals can be used to construct musical scales. Unfortunately, simple properties of numbers mean that these scales have terrible internal inconsistencies. At the other end of the spectrum, modern music uses equal temperament, which irons out these inconsistencies, but at the expense of purity of Pythagorean intervals. Lying in between are a host of fascinating tunings, such as Meantone, Just, Well-Temperament and Werckmeister.

One of the drawbacks of the literature on the history of musical tuning is the huge amount of jargon and unwieldy terminology. One aim of this project would be to use the mathematics intrinsic to all the scales described above to describe their characteristics in a concise way.

Some knowledge of the theory of music would be advantageous, but not essential, for this project. Interested candidates should contact Dr Rob Sturman.