Motivation

The goal of this research is to develop a model that enables a computer to symbolically examine a piece of classical music which is never exposed to it, and tell who is the composer. As a classical music fan myself, I observed that when we listen to unknown music, we almost always like to classify the style of the music. Actually, we even make guesses on who is the composer, and a person with higher accuracy is often considered as a better listener. While in this research, it is avoided to address on the controversy of quantifying how well a person listens to music, I am still curious if music appreciation, and composer identification in particular, can be statistically learned by a computer.

I claim that music can be dealt with as random processes. The claim is based on the fact that music consists of time-sequences of musical events, such as notes, chords, dynamics, rhythmic patterns, etc. It is already known that other types of time-sequences, such as stock prices, are quite successfully modeled by random processes. Therefore, I claim that the process of musical composition can be modeled as a realization of an underlying random process, and the underlying random process is what we fuzzily call ``musical styles''. If we further hypothesize that each composer has his/her unique style, then the composer identification problem becomes what is known by engineers as a ``system identification'' problem.

Among the many system identification techniques that already exist, this research explores the Markov chain model due to its simplicity. Due to the simple assumption that the future is conditionally independent to the past given the present, a Markov chain can be characterized by its state-transition probability matrix. However, we have to point out that the assumption is ignorant of macroscopic musical structures, and it is therefore valid to question the validity of Markov modeling of music in general.

Although, in this research, I am awared of the general validity issue, I remain optimistic that Markov models may be sufficiently sophisticated to teach a computer to appreciate music, as far as composer identification is concerned. The rest of the paper is organized as follows. Section 2 describes the general methods. Section 3 documents the experiments that have been done so far. Results are discussed in Section 4, and possible future directions are pointed out in Section 5.