Abstraction is the fundamental method of any theory. To make sense of something, one must abstract it. Thus, I pose this following question about the nature of abstraction:
Can we describe abstraction as the manipulation of the undefinable into definable, and thus make the unorganized into the organized?
Perhaps we can think of it as categorizing the various pieces of food that one would find in stew. Altogether, it is stew. A cohesive entity that is described and functions (when eaten) as one object. However, upon analysis and thus the abstraction of the stew, one could say that it is comprised of several objects. There are pieces of potato, carrot, peas, meat, the liquid, even the dissolved salt and oil can be contributed as pieces of the whole stew. Thus, there are two ways to enjoy the stew. One can think of and interact with the stew as a whole object, and when ordering it at a restaurant, he would say, “Could I get the stew?”, and when consuming it, eat the individual parts of the stew as a whole. The other way one can think of and interact with the stew is as the constitute pieces. He could say, when ordering it at a restaurant, “Could I get pieces of potato, carrot, peas, meat, meat stock, spices, salt, all simmered together in a pot and served hot?” When presented with the concoction of ingredients (parts of the stew), he could then eat it piece by piece, thinking of the individual parts separately, while only vaguely considering the whole stew.
Leaving the (not very good) analogy behind, let’s just look at the question of abstraction.
The stew is easily definable. We can say that there are pieces to the stew and then look at the stew either as the parts or the whole. However, music is not easily definable. Music theorists have, throughout the centuries, given names to different musical objects that they are hearing. This is the definition of abstraction. Notes, for example, as a prime example of this sort of abstraction. What even is a note? A sound? Or perhaps a notion that sound should exist? Is there time involved in sound? What kind of sound should the unadulterated note represent? We have a vague idea of what a note is, but from situation to situation, the idea of the note changes. Many other musical abstractions function in this way as well. Time in music, meter in music, harmony, form, the idea of voices; I can go on and on. Music theorists present that in any of these cases, music, in its essence, can be abstracted into these basic forms. It might not matter that these forms are different in different situations, but at least in this first level of abstraction, ideas can be named. This is the manipulation of the undefinable into the definable.
Let’s then, give a name to these basic forms of music that all other music theory is supplanted upon. Perhaps we can think about these forms of music as the axioms (to steal something from science) of music theory. They are not mathematical axioms of course, since these are neither perfect laws of music, nor even defined into something that might be able to be proved by perfect, basic laws. They are, in their sense, just basic labels for music. We cannot say that this is music theory yet, it is merely abstraction, labeling pieces of the stew for further analysis.
The second step of abstraction is what people know as music theory. I take the idea of notes, or the idea of harmony, define it as something that would make sense for my application of the theory that I want to do, and then, by combining the basic labels of abstraction, create a theory as the second step.
One example is tonality. Tonality exists in the second step of abstraction. We can hear that, yes, tonality exists and if I asked a group of people (who listen to music that has tonality) they would probably say, “Oh yes, when that V chord goes to the I chord, I feel a sense of release!” or perhaps “When I hear a major scale end on the 7th scale degree, that makes me feel uneasy!” But these are all ideas that exist on the second step of abstraction.
How can this be music theory if we are merely asking people to believe that certain phenomena exist? How can anything be provable if we are merely convincing people to believe in a theory, the workings of which are based on faith?
The issue with the first step of abstraction is that we were wrong in labeling the stew! The objects in the stew don’t exist past our perception; they are not grounded in fact, but instead the opinions of other scholars.
Then you would probably say, well let’s just take tonality apart, let’s find the first step, the basic abstraction, the axioms that exist in tonality. The axioms that can be rooted in fact. What could those be? Is it the fact that voice-leading creates tonality, through the principles of counterpoint? Or could that just be an endogenous fallacy where instead, tonality creates voice-leading? Is the fundamental building block of tonality, harmony? Or is it a collection of non-symmetric pitches when mapped on a 12TET cycle?
How can tonality be considered provable if the basic abstraction is not provable?
I believe that this is a fundamental issue with music theory. What are the pieces in the stew (basic abstraction); and what even constitutes the stew (second step in abstraction)? It might be in the sciences that, coming back to the original question, we can describe abstraction as the manipulation of the undefinable into definable, and thus make the unorganized into the organized. However, in music theory, the undefinable remains the undefinable, since labeling the parts is a fundamental issue. And a further however, we assume that we can label, and with our hubris in believing that our labels are correct, and the undefinable has been defined, we make the unorganized into the organized. But we are merely organizing opinions about music into higher levels of opinions about music, without ever looking down and saying:
“What are we standing on?”