Using Mathematica to Compose Music and Analyze Music with Information Theory

In this paper we present two case studies for the application of the technical computing software

Mathematica

in the domain of music creation and music research. The first section describes an experimental interface for the usage of random points, parametric curves and other mathematical objects in the role of three-dimensional musical scores. Similar to the technology of the old-fashioned player piano roles which encode any arbitrary piece for mechanical player piano in three basic dimensions (onset, pitch, duration) we provide an interface where a 3-dimensional score is created, visualized and played. With this software the scores can be created with the assistance of a rich arsenal of mathematical functions and also the sound of each single note can be controlled in terms of mathematical functions. The aim of this software is the creation of experimental musical pieces which explore the musical potential of certain mathematical functions. In this paper we restrict ourselves to sketch the interface. The more interesting aspects, namely the ‘musicality’ of concrete sonifications of certain mathematical objects, are subject to our live demonstrations in Berlin.

In the second section we show how information theory may be used in the analysis of musical scores and how specialized packages of the software Mathematica may assist such investigations. As a particularly interesting topic we describe the calculation of the transfer entropy between selected instrumental parts in Beethoven symphonies.