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What kind of questions does theory of music try to answer?

I wonder whether there are formal theories of music which define axioms and rules of inference. There must be plenty possible small theories. For example, a (quite useless) theory for all diatonic pieces in any major key would prove that every note is from mode in some key or prove otherwise. A slightly more complex theory might add dominant cadences and so on.

Are there formal, consistent theories that would would not reject successful music but reject almost all randomly generated notes?

I know there is some work in this field, take Emily for example, a software that can generate music. If generated music is lacking or not interesting, I imagine that a simpler goal would be to not reject good music.

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There aren't any approaches to music theory as you described it. Fundamentally, physics and math are objective, but music is subjective. –  Kevin Mar 17 at 3:26
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The music theory is more like a physical theory than a mathematical theory. It primarily tries to explain phenomena that are out there, rather than build a self-sufficient formal system. –  n.m. Mar 17 at 8:26
    
I think you might also be asking about algorithmic composition. Google it. There are commercial and open-source music applications that employ heuristic routines to facilitate composing music. –  Wheat Williams Mar 17 at 23:34

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up vote 10 down vote accepted

You've asked a very broad question that is difficult to answer succinctly.

The maxim "Theory follows practice" is apt here.

For centuries, musicians have simply been composing music. From time to time, academic musicians have examined the way that music has been written in order to elucidate principles and rules about how the most enduringly popular and influential music is created. They have written down these principles, which are effectively applied mathematics and physics related to pitches and rhythms and the overall structure of whole pieces of music.

Musicians writing music may or may not be aware of the underlying mathematics and physics, to varying degrees. But many people who learn to be musicians find it very helpful to study music theory so that they can better understand how to compose their own music, or how to better read and interpret the music that other people have written which they wish to perform.

For all students who pursue a bachelor's degree in music performance, music theory is a two-year curriculum. Students who pursue a degree in what is called "theory and composition" study the subject of music theory for much longer than that.

It is not necessary to learn the subject of music theory thoroughly in order to be a successful performing musician, or a successful songwriter. However, all musicians, whether they read music or have formal training or not, pick up some music theory along the way, whether they are very aware of it or not.

Get a college textbook on the subject of music theory, and read through its table of contents. You will see the various range of topics that are taught. If you are curious, you can read a great deal on the subject.

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Wait. Is this common misconception that math-spoiled folks have when being introduced to the subject? I have never thought about that. Since it also applies to so called 'serious' music I thought it would be like what is 'formal' in math. –  Rumca Mar 17 at 19:06
    
+1 for the penultimate paragraph, at least ! –  Tim Mar 18 at 8:55

Yes, this kind of axiomatic theorizing is the domain of PhDs in Music Theory. Check out the articles in academic journals like: The Journal of Music Theory, Music Theory Online, and Perspectives of New Music.

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What kind of questions does theory of music try to answer?

It is simple Music Theory investigates the phenomena of what makes good music. It really is that simple. Music Theorist realized in some point in the past that certain chord progressions worked well together and eventually this realization became widespread and it became a rule.

The thing is that the rules of music theory are just ways in which musicians of the past have used to make good music. It is not arbitrary rules meant to stifle creativity but more like guidelines to help the creation of beautiful music.

I was amazed when I first started doing harmony at the fact that as I learned more about the tradition and rules of music the writing of my harmony exercises actually became music. Eventually it actually became pretty. Almost something that you could call music.

This was a real eye opener. I was not just doing leg work for a diploma anymore I was actually learning how to make music. Needless to say I looked differently at the proposition of learning theory and realised why it was such an important part of doing music.

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