Music theory is stuff that people learn about music when they study music. Like scales, chords, chord sequences, meter, rhythm, melody, counterpoint etc. It's called "theory", because when you study it, you are not actually doing music.
A Theory of Music
A theory of music, on the other hand, would be something that explains what music is. It would be a scientific theory.
There is some overlap between the two, because music theory depends on observation of the patterns that occur in music, and any theory of music has to explain those patterns, and any attempt to develop such a theory will likely use the known patterns of music as a guide.
But in the end, there is still a gap between the descriptive nature of traditional music theory, and the explanatory nature of a hypothetical scientific theory of music.
The Idea of a Scientific Theory of Music is Controversial
Many people react strongly to the idea that it might be possible to find some mathematical formula that completely defines how musical any item of music is.
But that is what a scientific theory of music promises to do. Any supposed theory of music which does not predict which musical items are the most musical is not a complete and satisfactory theory of music.
For most people, the failure of music theory to be predictive in this sense is just a general fact about life, i.e. music cannot be understood scientifically.
There are other reasons why music is often considered to be beyond the reach of mathematical or scientific understanding. For example:
- Music is art, whereas mathematics and science are science.
- Music is about emotions, whereas science is rational.
- You can't specify what is musical, because different people like different music.
For those of us used to the idea that the universe is scientifically comprehensible, these reasons are just confused thinking:
- The failure of one formula to completely predict the musicality of musical items does not rule out the possibility of discovering some other formula which does predict it with 100% accuracy.
- Music may be art, but art, and the effect that it has on us, can be studied scientifically. (Of course the scientific study of music might reveal that music is not really a form of art, or at least that it is distinct from all other forms of art.)
- Music has something to do with emotion, but emotions can be studied scientifically just as much as anything else, and ultimately they are the result of physical processes happening in the brain.
- If different people like different music, this doesn't rule out the possibility of scientific explanation, it just means that any predictive theory has to take account of the factors that cause variation in musical taste.
What Makes a Theory Scientific?
There are two major characteristics of a scientific theory:
- It makes predictions which can be verified
- It is consistent with existing scientific knowledge (or if it isn't, there has to be a very good reason why not)
If your theory is about fundamental physics, you can dispense with the second requirement, but only because it is effectively subsumed within the first requirement, i.e. all observed facts about everything in the Universe have to be predictable in principle by your theory.
For all other scientific theories about anything else, including theories about music, the consistency requirement is absolutely important.
In the case of music, the most important consistency requirement has to do with the fact that music is an aspect of human behaviour, and human beings are living organisms belonging to a species, which, like all other species, has evolved.
You might read sometimes that maybe music can be "explained" by evolution. But this misses the point. Within our existing scientific understanding of what life is and how it got here, evolution is a given. Any scientific theory of music has to be consistent with evolution, whether it wants to be or not.
This is not quite the same thing as requiring that music itself be an adaptation, and there is plenty of room for developing theories which explain behaviours not themselves adaptations but which are indirect side-effects of other behaviours or tendencies which are adaptations. Nevertheless, we must be very suspicious of any supposed theory of music which is too disconnected from consideration of the adaptedness of whatever it is that makes music happen that makes people enjoy music.
The Need to "Define" Music is Somewhat Overrated
Those attempting or professing to study music are often concerned to properly define music. So, for example, Wikipedia's Music page links to a Definition of music, and music is one of the few topics to have such a separate "Definition" page.
One result of the apparently pressing need to define music exactly is the endless silly discussions of John Cage's infamous 4'33" (which is 4 minutes and 33 seconds of silence, just in case you didn't know).
However, the history of science shows us that completely satisfactory definitions usually only appear after the concept being defined has been explained by scientific study.
To give a simple example, prior to the development of modern astronomy, we might have attempted to define what the word "star" means. We might have come up with the following definition:
- A point of light appearing in the night sky
We could then have debated as to whether other non-point-like lights in the night sky should be included (like the Milky Way), and what about special cases, like shooting stars, and wandering stars, and "new" stars (i.e. novae and supernovae). It probably wouldn't even occur to us to consider the Sun, after all it is obviously not a point of light, and it never appears at night.
But our scientific understanding of what a star is has developed, and we now know that there is a certain category of astronomical object, which includes non-wandering stars, novae, supernovae and the Sun, but which does not include "wandering" stars or shooting stars.
With the wisdom of hindsight, we can see that our ability to determine a better definition for the word "star" could only happen after we learnt what each of those different astronomical objects actually is. Attempting to find the perfect definition of "star" before developing a scientific understanding of the phenomenon would have been a waste of time, time which would have been better spent just studying said phenomenon, rather than attempting to define in advance what is or isn't included within it.