Processing musical information is a task many of us perform effortlessly, and often, unconsciously. In order to gain a better understanding of this basic human cognitive ability, we propose a mathematical model for tonality, the underlying principles for tonal music. The model simultaneously incorporates pitch, interval, chord and key relations. It generates

Computer models for determining key boundaries are important tools for computer analysis of music, computational modeling of music cognition, content-based categorization and retrieval of music information and automatic generating of expressive performance. This paper proposes a Boundary Search Algorithm (BSA) for determining points of modulation in a piece of music using a geometric model for tonality called the Spiral Array.For a given number of key changes, the computational complexity of the algorithm is polynomial in the number of pitchevents. We present and discuss computational results for two selections from J.S. Bach's "A Little Notebook for Anna Magdalena". Comparisons between the choices of an expert listener and the algorithm indicates that in human cognition, a dynamic interplay exists between memory and presentknowledge, thus maximizing the opportunity for the information to coalesce into meaningful patterns. 1

Music today is more ubiquitous, accessible, and democratized than ever. Thanks to technologies such as high-end home studios, audio compression, and digital distribution, music now surrounds us in everyday life, almost every piece of music is a few minutes of download away, and almost any western musician, novice or expert, can compose, perform and distribute their music directly to their listeners from their home studios. But at the same time these technologies lead to some concerning social effects on the culture of consuming and creating music. Although music is available for more people, in more locations, and for longer periods of time, most listeners experience it in an incidental, unengaged, or utilitarian manner. On the creation side, home studios promote private and isolated practice of music making where hardly any musical instruments or even musicians are needed, and where the value of live

This article describes the development of an application for generating tonal melodies. The goal of the project is to ascertain our current understanding of tonal music by means of algorithmic music generation. The method followed consists of four stages: 1) selection of music-theoretical insights, 2) translation of these insights into a set of principles, 3) conversion of the principles into a computational model having the form of an algorithm for music generation, 4) testing the “music ” generated by the algorithm to evaluate the adequacy of the model. As an example, the method is implemented in Melody Generator, an algorithm for generating tonal melodies. The program has a structure suited for generating, displaying, playing and storing melodies, functions which are all accessible via a dedicated interface. The actual generation of melodies, is based in part on constraints imposed by the tonal context, i.e. by meter and key, the settings of which are controlled by means of parameters on the interface. For another part, it is based upon a set of construction principles including the notion of a hierarchical organization, and the idea that melodies consist of a skeleton that may be elaborated in various ways. After these aspects were implemented as specific sub-algorithms, the device produces simple but well-structured tonal melodies.