Computational Music Theory

One of the goals of the study of music theory is to develop sets of rules to describe different styles of music. By formalising these rules so that their semantics are machine intelligible, it is possible to use computers to reason about and analyse these rules – computational music theory. ANTONis an automatic composition system based on this approach. It formalises the rules of Renaissance Counterpoint using AnsProlog and uses an answer set solver to compose pieces. This paper discusses ANTON, presenting the ideas behind the system and focusing on the challenges of modelling and synthesising rhythm. Introduction Music is an important aspect of all cultures, and forms an significant part of many people’s lives. Despite this, and much effort by musicologists and others (for example, (Thakar 1990; Huron 2006; Leach and Fitch 1995b; 1995a)), it remains in many ways a mystery. This paper describes a computational investigation into the basis of music, applying ideas from logic programming and artificial intelligence, with the aim of developing a computational theory of music. This incorporates a logical representation of some musical components so we can apply computational techniques. Our joint aim is to create a system for autonomous music composition, but the authors have different perspectives and motivations. We include composers, algorithmic composers, computer scientists, logicians, performers and listeners. Underlying aims include learning about music and music theory, demonstrating the simplicity and power of the logic tools, and the fun of building an innovative program. All these attitudes have contributed in some way to the overall project. We should stress that the interest is in composition rather than improvisation, with the ability to consider the whole work without linear time constraints. We are currently only considering styles of music that rely on discrete notes and parts, but fully accept that there are other musical genre to which this does not apply. Following a brief description of the language we use, we describe the development of the Copyright c � 2012, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. basic system and musical style rules. We follow this with a description of the problems associated with rhythm, our current solution and a sketch of a putative improved system. We end with some examples and consideration for future work. Background Our work is predicated on the over-strong axiom that for a sequence of musical notes to be considered as a piece of music it must satisfy certain requirements, regardless of the style of music one considers. These rules often specify the progression of a melody, both at micro level (the choice of the next note) and at the macro level (the overall structure). Others describe the harmony, which arises from the relationship between the various voices, while others describe rhythm and the interaction between the various parts in a composition. A composer will use her/his skill, knowledge and creativity to provide a euphonious or meaningful composition that meets these requirements. We have restricted our work currently to discrete notes with pitch and duration. While these rules were developed to guide and support human composers and to teach generations of aspiring musicians and composers, they can, with the appropriate knowledge representation techniques, turned into a computer system that can reason about and apply these rules. Such a system provides an easy and versatile way for automatically composing music. Furthermore, provided that the underlying representation mechanism is sufficiently flexible to allow changes at the level of the individual musical rules themselves, it will give the human composer or musicologist a tool to understand, explore, extend, experiment with the set of musical rules he is working with. In other words, it creates the opportunity to study computational music theory. In this paper we present ANTON v2.0, an extension of ANTON v1.0 reported in (Boenn et al. 2009). ANTON is an automatic composition system based on the set of compositional rules governing tonal Western music, using Answer Set Programming (ASP) (Gelfond and Lifschitz 1991; Baral 2003). ANTON is Knowledge Representation and Reasoning (KR&R) in the truest sense: using the declarative properties of AnsProlog, the ASP language used in our approach, one just writes down the rules of music theory and reason about them. The order of the rules does not matter unlike some logic systems (e.g. Prolog). Musical Metacreation: Papers from the 2012 AIIDE Workshop AAAI Technical Report WS-12-16