Are you mathematical?

Let me put that another way: Do you like music? Because, inescapably, they are the same question, and the 'why' of that riddle has perplexed natural philosophers and musicians for at least 3 millenia. Of course our mathematics cannot really describe nature, but it is tantalizingly curious that nature should be even approximately describable by our humble equations, and for those curious about that "unknowing exercise of our mathematical faculties" we call 'music', Seed offers an intro article by Dmitri Tymoczko, discoverer of the bold new math of music, a short article one might call A Young Person's Guide to the Orbifold Quotient Space Theory of Music.

Read carefully, there will be an exam later ...

how do we combine harmony and melody to make music? In other words, what makes music sound good?

To answer these questions, we need mathematics, just as Pythagoras supposed. But as I and other music theorists have recently shown, we need a kind of mathematics that Pythagoras could not have imagined: the geometry and topology of what mathematicians call "quotient spaces" or "orbifolds." These exotic spaces contain singularities-- "unusual" points that are analogous to the black holes of Einstein's general relativity--that can be described using only very recent mathematics. Western music can ultimately be represented as a series of points and line segments on abstract shapes in higher dimensions. If we can understand their structure, then the deep principles underlying Western music will finally be revealed.
[ Seed: The Shape of Music ]

Which ontologically means also "the deep principles underlying the human conscious experience of that music", a trifling semantic detail, but important if we want to talk of final revelations: Nicolai Tesla observed "Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality." and this became true (or was always true) under the old regime of the music descended from Pythagorean/Ptolomaic Rational Harmony and the even the rhythmic pulse-charts of Schillinger. Finally be revealled? I seriously doubt that, but I do think we've learned something important about ourselves.

Despite his very intricate and mathematical theory, at least Schillinger was humble enough to admit to limitations of the model in describing the real nature. He said something about writing music from theory on one side, but then having to write for the human being as the final authority on 'good'. From physics, here's Einstein's caveat on the limits of Theory:

"It may well be true that this system of equations is reasonable from a logical standpoint. But this does not prove that it corresponds to nature ... Pure logical thinking cannot yield us any knowledge of the empirical world: all knowledge of reality starts from experience and ends in it"

In other words, we may have a new description for music, but any prescription has to be considered, at best, tentative. Musically, the ultimate judge is still not the yardsticks of the logical theoretical, but in actual responses by actual listeners, but nonetheless, given that caveat, a good theory that finds a useful correspondence in Nature is still a star-chart we can use to plot new courses that may get us Someplace Else.

"you might say, 'Wow, I didn't realize the Safeway was close to the disco.' We can now go back and look at hundreds of years of this intuitive musical pathmaking and realize that there are some very simple principles that describe the process."
[ The Geometry of Music - TIME ]

But it could also mean there are some very good reasons why the high concrete brick wall kept the disco crowd from an easy path to their groceries :)