Alternative theories of harmony

Question

Do you know of any alternative (to functional) descriptive theories of harmony or attempts at creating them?

By that I mean attempts to explain both functional and non-functional harmonies in a single and coherent way, focusing for example on voice leading and not function or any other approach.

To try to explain better as it indeed might sound confusing: in today's music we come across progressions that are not easy to explain using functional harmony so we invented this term non-functional harmony that seems to be just a way of saying: the established theory doesn't really handle this case very well. Hence the question: is there any research or attempts to create more unified theory of why certain chord progressions sound good and others don't.

And I don't really mean microtonal or serial theories but attempts at describing all existing practice of western harmony based on 12-tone scale in a different way.

Answer 1

Dmitri Tymoczko's books on geometric harmony are one attempt. They are an extension of neo-Riemannian harmony based on the Tonnetz. (Editorial: I found these more useful for laying out accordion buttons than for explaining tonal or other relations.) Older (pre-1800) works on figured bass try to explain things from a non-functional viewpoint; they suffer from not being updated for the last 200 years or so.

The Jazz Harmony stuff does try to explain jazz practice although much of jazz can be explained with ordinary harmony.

Much of Common Practice Period harmony is a taxonomy of Bach, Beethoven, Mozart, Vivaldi, etc. The neo-Riemannians try to incorporate later practice (Wagner, Richard Strauss, Debussy, Ravel etc.) in an expanded taxonomy. Harmony is taxonomy, not biochemistry and explains what people did, not what they should have done or should do in the future.

Modern books on harmony (from Frank Shepard to Robert Gauldin) do explain much more than just functional harmony. Voice leading is probably more important than function in most cases anyway.Felix Salzer's Counterpoint in Composition covers voice leading rather well.