Rather than proposing a new theory, the goal here is to introduce and explore some of the foundational ideas that are commonly shared across different music schools. Before we delve into functional music theory, we need to establish some basic concepts in general terms.
The Nature of Music Theory
Music theory inevitable emerges as soon as you ask the question, "What is music?". It’s an abstract concept, it resists absolute definition, but we can extract core ideas from the diverse interpretations. At a basic level, music belongs to the arts and is deeply tied to subjectivity, culture, and human expression.
The Transference of Information Through Sound
Music, in essence, is communication—an abstract form through which ideas, emotions, and concepts are transferred from one mind to another. This transfer occurs through various media: sound, symbol, and thought. Primarily, it is known to humans through the medium of sound, though secondary forms, such as symbols or memory, retain an operational presence.
If we are to delve deeper, we find that sound itself is a carrier of information, operating within the physical realm, yet touching the cognitive. Information exists before sound; sound encodes it. Music, in turn, is a higher-level abstraction, an arrangement of sound—an information matrix, if you will.
Sound and Human Responses
Many abstract sounds provoke responses—biological, emotional, and psychological—without conscious arrangement.
A soft rainfall may invoke tranquility in some, while a thunderstorm might provoke anxiety.
Sounds like laughter can elicit joy, while gagging sounds may trigger a reflex response.
Herein lies a crucial question: Are these sounds, which clearly communicate and evoke response, music? They are not traditionally recognized as such, but they exist within the same structure of information and response that music operates within.
Sound, Order, and the Illusion of Predictability
What, then, of music’s relationship to order? We speak of the "arrangement of sound." To arrange, one must introduce a semblance of order. However, order is a concept which, when examined, fractures into multiple interpretations. To the human mind, order suggests predictability, structure, a system of relationships. Yet, order can also be chaotic—an arrangement need not be symmetrical, nor need it follow a discernible pattern, to be ordered.
Thus, even an arrangement of random, chaotic sounds retains the capacity to provoke emotional responses. Music, while often regarded as the embodiment of order and harmony, can collapse into noise—and yet, it is still perceived as music by some.
This ambiguity is significant. To define music is, therefore, to draw a line in the sand, a line that is ultimately subjective. It is a construct, one that shifts depending on the observer.
Traditional Core Elements of Music: Rhythm, Harmony, and Melody
In the realm of music theory, certain elements have achieved universal recognition—rhythm, harmony, and melody. Though they are typically considered distinct, these elements are, in fact, temporal manifestations of the same underlying phenomenon.
One could posit that rhythm is harmony extended through time, just as harmony is an instantaneous rhythm. In this sense, these elements are malleable, capable of transforming into either noise or structured sound. This convergence of philosophical concepts is common among schools of thought in music theory, revealing the unity between these seemingly distinct categories.
Thus, when we study music theory, we often refer to this phenomenon simply as 'harmony,' a term that encompasses the multidimensional spectrum of sound—including rhythm, melody, and even noise. Harmony becomes a representative of this shared information, a framework that binds these different expressions of sound into a cohesive whole. It is through this lens that we can explore not only music’s more structured elements but also its potential for transformation and abstraction.
The Function of Music
Functional music theory explores the function of sound within music. In well-defined music, broader concepts like song function have been studied, suggesting universal characteristics. For example, research has shown that even people from isolated cultures can recognize common types of songs (like lullabies or dance music) from other cultures.
Functional music theory, as it stands, concerns itself with the relationships between sounds—specifically, the roles that pitches play within sequences, and how they elicit logical emotional responses in the listener.
At the heart of this theory lies the recognition of octaves as chroma equivalent.
Octaves represent the simplest integer ratio, 1:2, a pattern of zero entropy in information terms. This ratio is both mathematically and physically significant, as it is both the second harmonic and the second subharmonic of the fundamental. Its prevalence is no coincidence; it is a natural consequence of how sound is produced and perceived. It is, in effect, the final reduction of integer space, the last refuge of harmony.
From there, functional theory spirals outward, it seeks to understand the pull between tones, the gravity that holds music and emotion together, is a study of relationships. In this framework, cadences—the resolution points in music—are not arbitrary but are structured to evoke a predictable, logical response in the human mind.
Music as a Universal Language
But are these cadences universal? Are they independent of the mind, existing as objective truths in the same way as mathematical laws? The answer is elusive. While most musical traditions acknowledge a hierarchy of pitches—melodies, cadences, and symmetries that revolve around a central note—this hierarchy is as much a reflection of the human mind as it is of the natural world.
Functional music theory presents compelling evidence for the universality of certain musical structures, yet cultural differences beg the question: how much of music is learned, and how much is inherent?
The pentatonic scale—so often cited as a universal structure—presents an intriguing case. Is it a natural construct, born of the universe itself, or is it merely a human invention? Some argue that the scale, like the twelve-tone equal temperament system, is a tool—technology devised by humans to impose order on sound.
From the first person to construct a scale based on the harmonic series, we have continuously reinforced this learning, repeating it in our music, our instruments, our art. Yet, does this repetition prove that it is a natural truth, or merely that we have taught ourselves to hear it that way?
The Nature of Music as Information
Claude Debussy once suggested that music travels through the very fabric of space, with the artist merely acting as an antenna, receiving signals from beyond the veil of consciousness. While poetic, this idea holds a kernel of truth. Music, as information, is remarkably simple in its symbolic and physical structure. It is compressible, reducible to patterns and ratios, even in its most intricate forms. Without delving too deeply into signal processing, music is unique among other forms of information in that it exists already in its optimal format for communication. Music is the wave itself.
Throughout history, music has been used to soothe, inspire, manipulate, and control—its functions as varied as the societies that produce it. The universe, though governed by fixed laws, is far from static. Music, like all things, evolves.
In this discussion of functional music theory, I have aimed to collapse the spectrum of interpretations without extending the influence of any particular school. I’ve deliberately avoided overemphasizing terms like 'tonic' and 'octave'—I haven’t even mentioned 'dominant.' As we progress through the study of pitch function, schools of thought inevitably diverge. Nevertheless, there is solid ground beneath many theories. For instance, just intonation systems have evolved impressively, retaining backward compatibility with Western tradition. Similarly, the xenharmonic school has extended the study of interval functions in fascinating ways. Yet, I argue that some of these approaches neglect fundamental concepts, such as the use of interval and chroma matrices, revealing a weakness in their grasp of tuning systems and their intervals’ functional roles. (and don't even mention timbre!)
From functional theory, I accept the significance of the tonic (the baptism) and the octave (the crucifixion). As for the rest of the music-bible, it may well be apocryphal. And without exaggeration, musicians can thrive without any theory at all. For some, theory is merely an extra layer of fun.
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