Andrew M. Cavallo

Multiplicity in Unity: A Hallmark of Great Music

Bach, of course, excels at deriving musical variety from highly economical means, i.e., at unfolding, as it were, a simple musical idea into a complete work often filled with surprising turns and great complexity.

However, no matter how surprising or complex Bach's music becomes, each passage bears a genetic resemblance to the passages from which it emerged: there is thus a principle in each Bach piece that reveals multiplicity in unity.

Soon the listener may be extraordinarily far from the apparent simplicity of the beginning; and yet one seldom has the impression that Bach has simply abandoned one idea and glued another onto it.

The music unfolds in such a way that new material is not discontinuous with what came before; it may be surprising or even jarring, but it should remain genetically related to the material from which it emerged.

Much pivots on this point. A composer can produce variety simply by introducing another idea whenever the previous idea has exhausted its immediate usefulness. A new riff follows the old riff. A new meter follows the old meter. A new harmonic idea follows the previous one. Another section arrives because something different has to happen.

But such an approach, though capable of producing inexpensive complexity, nevertheless results in, at best, a piece that is artificial and, at worst, a great big unintelligible mess.

Bach demonstrates something far more difficult. He can travel enormous distances while maintaining an intelligible relationship between the destination and the point of departure. Indeed, the farther he travels while preserving that relationship, the more remarkable the achievement becomes.

In other words, the music of Bach, like the music of all great composers, reveals multiplicity in unity.

This can be understood as a kind of optimization problem. Suppose an engineer is designing a car and cares about two things: speed and safety. One can maximize speed by minimizing safety. Similarly, one could maximize safety by minimizing speed. Both approaches are rooted in straightforward maximization, but neither produces an optimal car if the goal is to make it as fast as possible while simultaneously as safe as possible. In other words, speed and safety are competing value factors.

Something analogous occurs in great music. Economy of means and musical variety are likewise competing value factors. Purely maximize economy and one arrives at musical poverty; purely maximize variety and one approaches chaos. The compositional problem is therefore not one of pure maximization but of optimization: to derive the greatest musical variety from the most economical adequate means.

Bach's genius is exemplary precisely in this respect. The extraordinary variety of his music does not require an equally extraordinary proliferation of independent musical ideas. Instead, astonishing multiplicity unfolds from remarkably economical material while remaining unified with the material from which it emerged.

Fertile Musical Ideas Are Pregnant With Entire Scores

To say that a musical idea is “pregnant” with a piece requires some qualification.

A motive does not logically entail one and only one composition. Four notes do not contain a completed fugue in miniature. Two accomplished composers might begin with the same motive and produce quite different compositions.

A fertile musical idea is pregnant not with one inevitable future but with a field of possibilities.

I explore the idea that a simple yet fertile musical idea is pregnant with great musical possibilities in my recent article Anatomy of a Vivaldi-Inspired Neoclassical Rock Guitar Solo, wherein I offer a measure-by-measure analysis of a Vivaldi-inspired solo from my song Teutonic Knights.

Composition and Deduction: An Analogy

What is accordingly at issue is an analogy with deduction.

In a deductive argument, conclusions are not simply attached to premises because one happens to find them interesting; rather, each new sentence follows from those that precede it by rules of inference.

Something analogous occurs in a well-constructed musical composition.

The originating motive functions somewhat like a premise, establishing a musical identity and a field of possibilities. This field of possibilities is not, however, arbitrary; rather, it is structured by musical relationships rooted in the diatonic scale—and the diatonic scale is, in turn, rooted in objective mathematical relationships that correspond to axio-metaphysical principles of truth, beauty, and goodness. Moreover, a composer navigates this field of possibilities not in an arbitrary way but rather by established rules and modes of musical composition.

However, by its very nature, an analogy must not be pressed too far. A musical motive does not entail its continuation in the manner that premises may entail a conclusion in formal logic. There is no algorithm by which one feeds a Bach subject into a machine and obtains the Well-Tempered Clavier. Creativity is, by definition, non-algorithmic. Once an algorithm is known for producing a result, the process becomes mechanical. Mechanical processes famously produce terrible music, as evidenced by the recent proliferation of AI-generated music. Therefore, the analogy with deduction is illuminating—yet it is only an analogy.

A Musical Accessibility Relation Within a Field of Possibilities

If a fertile musical idea establishes a field of possibilities, then the possibilities within that field differ in their accessibility to one another. By definition, possibilities outside that field are inaccessible and thus lead to some musical absurdity or contradiction.

This suggests another way of understanding musical creativity. Musical creativity does not consist merely in moving to an unexpected musical location, which is easily accomplished by introducing something unrelated. Rather, true musical creativity consists, at least in part, in discovering an unexpected but intelligible path from one musical possibility to another.

There are therefore two easy extremes. A composer may remain confined to the most immediately accessible possibilities, producing music that is perfectly coherent but predictable. Or he may leap arbitrarily from one unrelated idea to another, producing surprise at the expense of unity. The more difficult achievement lies between these extremes: to travel to remote and unexpected regions of the possibility-space while preserving an intelligible relation to the material from which the journey began.

Bach again provides the obvious model. He can arrive at a musical location that one might never have predicted from the opening idea; yet, when the path is retraced, the transformations that carried the music there are intelligible. The destination is surprising without being arbitrary.

We might therefore characterize one aspect of compositional genius as the ability to perceive relations of accessibility that less creative composers fail to perceive. The fertile musical idea provides the possibilities; established musical principles structure relations among them; creativity discovers unexpected pathways through that structure.

This brings us again to multiplicity in unity. The greater the composer's ability to travel through this field without breaking its underlying relations of accessibility, the greater the multiplicity that can emerge without sacrificing unity.

Private Online Guitar and Composition Lessons

If this approach interests you, I offer private online instruction for guitarists working in rock, hard rock, melodic heavy metal, and neoclassical guitar.

Students may pursue a Performer Track, a Composer Track, or a combined Performer–Composer Track. Depending on the student's goals, lessons may include guitar technique, improvisation, composition, arrangement, recording, mixing, mastering, and the development of complete musical works.

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