Haskore Music Notation - An Algebra of Music

We have developed a simple algebraic approach to music description and composition called Haskore In this framework musical objects consist of primitive notions such as notes and rests operations to transform musical objects such as transpose and tempo scaling and operations to combine musical objects to form more complex ones such as concurrent and sequential composition When these simple notions are embedded into a functional language such as Haskell rather complex musical relationships can be expressed clearly and succinctly Exploiting the algebraic properties of Haskore we have furthermore de ned a notion of literal performance devoid of articulation through which observationally equivalent musical objects can be determined With this basis many useful properties can be proved such as commutative associative and distributive properties of various operators An algebra of music thus surfaces Introduction Traditional music notation often called common practice notation has many well known limitations From our perspective the following are particularly acute Traditional notation is unable to adequately capture a composer s intentions in par ticular structural aspects of a composition Traditional notation is biased towards music that is humanly performable This is not surprising of course but is an obstacle when trying to notate music intended for computer performance where the notation is often found to be de cient inconsistent and redundant Many well known not just contemporary ideas in music theory are di cult if not impossible to express in traditional notation The basic concepts of atonal music theory For for example are impossible to express without the use of a meta logic more preferable would be a common notation that could be used to express musical objects and the interrelationships between them Modern notions of algorithmic composition are also impossible to express in traditional notation there is simply no notion of algorithm at all These shortcomings along with our experience in computer music and algorithmic com position have led us to seek alternatives to traditional music notation Our background in the theory design and implementation of high level programming languages in particu lar functional languages has led us to a rather satisfying solution based on the functional language Haskell HPJWe In fact we did not design a new language at all our system