In Search of Musicality: Can Fractals Show the Way?

Research on characterization and classification of musical compositions have focused on several mathematical and statistical techniques. In this paper, we take a different approach based on music visualization and fractals to investigate the nature of musicality. A musical composition is defined as a sequence of notes and self-similarity plots(SSPs) are constructed on the basis of certain similarity metric. We observe that SSPs are fractals by nature and can distinguish musical compositions from randomly generated sequence of notes. We define the signature of a composition based on fractal dimensions of SSPs and observe that signature of a tune can help classify and characterize a composition. Thus, we conclude that fractals might provide us with the answer to the age-old question of musicality. I. IN SEARCH OF MUSICALITY What makes a sequence of sounds musical? It is a question that has raised much more philosophical arguments than possible explanations both the so called “scientific” and “non-scientific” ones. We now have sufficiently satisfactory explanations for the basic set of notes used in musical compositions thanks to Pythagoras and Bach [1]. Even then, not any combination of notes are musical. Some compositions are aesthetically more musical than others. What are the properties of a sequence of notes which make it musical or soothing to the ears? Why do we like some type of music more than some other types? Why do some compositions arouse a feeling of melancholy while some other compositions are embodiment of serenity or divinity? How can we associate a composition to Beethoven and another piece to Bach just by listening? In this paper, we take a look at a new approach towards musicality and try to answer some of these questions computationally. A. Components of a Composition A Musical composition is multidimensional piece of work consisting of the basic composition as a sequence of notes, the rhythmic beats, the lyrics and its vocal rendition. Any research on the musicality of a piece should consider the piece as a whole (i.e. as an audio signal) rather than the individual parts. Nevertheless, in this work, we focus only on the sequence of notes, because our aim here is to define musicality on the basis of this parameter. Some of the other components of a composition, that have been completely ignored in this work are • Lyrics: The lyrics pertaining to a composition has its own pragmatics, and hence biases the listener towards a specific mood. Since we do not want to use such explicit linguistic information, we will avoid using this. • Rendition: Vocal quality of the renderer and the specific instruments used in a piece are often sufficient to produce some bias, which might be based on cultural conventions. In the Indian context, Shehnai is associated with festivities and Jaltarang or Santoor have a lively tonal effect. Such prejudices should be avoided. • Rhythm: Rythm or the beat pattern is an integral part of any composition. It is a measure of the pace and the periodicity of the composition, and hence is an important parameter of a composition that governs its musical nature to a large extent. The sequence of notes in a composition plays an important role in imparting the characteristics of that music. Mood, genre, temporal and spatial settings are largely governed by the note sequence. This concept has been the heart of both Western and Indian Classical Music1. Therefore, it seems worthwhile to search for the basic nature of musicality of a composition in its note sequences. B. Brief Sketch of the Work In this paper, we describe an approach to investigate the nature of musicality based on fractal dimensions of self-similarity plots. Section 2 describes the construction of the self-similarity plots and through examples illustrates the patterns of music as compared to random strings. Section 3 begins with a discussion on the fractal nature of the self-similarity plots followed by the description of the method used to measure the fractal dimension of the plots. This section also talks about the signature of a tune based on the fractal dimension, that can be used for clustering and categorization of compositions. The concluding section summarizes our basic findings and outlines future research. II. VISUALIZING MUSIC Acoustic signals such as speech and music are stretched over a period of time. The temporal dimension makes the comprehension of the overall structure of the signal difficult for the human brain. Contrary to this, the human brain can 1Indian Classical Music is based on the Raga paradigm, which are considered as the basic structure of a music [2]. identify patterns in a visual image much faster as the whole structure can be perceived at a single point of time. Therefore, a visual representation of a composition can help us understand its features quite fast and provide us with useful insights about musicality. The idea is not new and considerable effort has gone behind music visualization. The ancient Indian endeavour for anthropomorphic descriptions of the Ragas and modern artistic realizations of images elicited by sounds, for example the Walt Disney film Fantasia, are just some of the attempts towards this direction. In this section, we describe a more formal approach towards music visualization based on the works of Foote and Cooper [3], [4].