Tonality revisited, part I

What’s Wrong With the World of Music Theory

In G.K. Chesterton’s What’s Wrong With the World, he spends an entire section lamenting the state of education. One of his complaints, perhaps the most telling of all his observations, is the complaint that in modern education, one is not taught to tell the truth; one is taught not to lie, but one is not taught to tell the truth. He described the modern style of teaching debate as a sports game sort of contest, where one uses the facts of reality and tools of rhetoric to argue for their side, without even considering whether their side is the right side.
Analogously, this is true in music theory as well. The student is taught the language and techniques of tonality and then gradually moves on to more diverse, atonal techniques. As they learn, they are never asked whether or not tonality is more than a pleasant convention or a liked, practical technique, and, in contrast, whether atonality is a liberation from needless convention, a way to construct art without pleasure, another element in the vocabulary of musical expression, or an abuse of music itself.
Unlike normal education, it is difficult to read malicious intent into this lack. For most musicians, the study of theory is difficult enough as it is, even before the addition of complicating semi-philosophical considerations. Also, most musicians consider their art as a form of expression, and thus learning the tools used in the music, which is necessary for reading what the music really means into the notes, is more important than whether the tools themselves are good or bad. But I do not find theory difficult, so I will ask the question, and, in the process, try to teach you about theory.
First things first: Precise definitions and precise goals. So, let us define our key term. Music. Unfortunately, composers do not have a consensus as to what the word means. John Cage considers shooting a piano with a shotgun music. For reasons soon to be explained, we will use the definition that scientists use: music is sounds with a regular wave pattern, what we call pitched sound.

The Metaphysics Behind Music Theory Part 1

Now our goal, of course, is to find good music. A thing is good in itself insofar as it is perfect, and good as an means insofar as it is an effective means to a perfect end. As was mentioned above, music is used as an expressive art, thus, most musicians are familiar with the second type of goodness, for if the music is for expression, it is a means, not an end. Therefore, the theorist must be concerned with the first form of goodness. Perfection is further defined as a thing’s adherence to what it is (its form) and the level of this form on the hierarchy of being (the higher a form is, the more Godlike the being it forms). So when we search for good music, what we are searching for is an arrangement of pitched sounds that adhere to their form(s), and some forms are better than others.
Now there are two forms that are involved music. One is the form of music itself, what music is. The other is the form of the particular piece of music, what arrangement of music the particular piece is.
How does this apply to music practically? We might as well begin with tonality, the starting point of music theory. Tonality is based on the assumption that certain mathematical relationships that are part of what pitched sound is ought to be reflected in the arrangement of notes in the particular piece. Notes with the closest relationship mathematically ought to have the closest relationship actually. Expressed philosophically, this is equivalent to saying that the properties of the non-primary matter must have an analog in the form of the whole.
It would seem that there is no basis for holding this position. For no matter what the particular form is, the mathematical relationships will still exist. The particular form, no matter how it tries, cannot undo the mathematical constants of its larger genus.
But there are two ways in which the relationship can exist, one is in the abstract, as was mentioned. The other is in actual sounded notes. And if the notes are not simultaneous, one will cease to exist before the next starts, thus the two tones in which the relationship is must be simultaneous. This idea is the basis behind what we know as tonality, which I will show more or less presently.
A reminder: this is only possible with pitched sound, so defining music as pitched sound places it firmly within these aesthetic parameters, thus making it a useful definition, as well as a popular one.