Varieties of Music Theory

Choosing that title, I'm reminded of a wonderful book by William Empson, published in 1930 called Seven Types of Ambiguity. Or maybe Varieties of Religious Experience by William James. But never mind! The thing is that we normally think of music theory as being a single thing. At the very rudimentary level that seems reasonable, but as soon as you get into the details you should start noticing that "music theory" as we find it in most books only applies to a part of music. Theorists get around this embarrassing fact by saying that music theory applies to the "common practice" period in music, that stretch of time from about 1600 to around 1900. The implication is that the rest of music history is uncommon or something.

The truth is that each epoch in music history, which at its maximum extent begins with the earliest written music and discussion thereof by the Greeks in the 4th century BC, has its own characteristic theory of music. With the Greeks about all we have left is the theory as the music itself has either disappeared or is only sketchily represented in notation. But beginning in the so-called Dark Ages, around 600 AD, we find the earliest chants of the Catholic Church, later called "Gregorian Chant" after Pope Gregory who was traditionally credited with many of the chants (through divine inspiration, of course). Here is an early offertory, Iubilate deo universa terra:

The kind of music theory used to talk about this kind of music is quite different from other kinds. You run across terms like authentic and plagal modes, reciting tones, ambitus and the mysterious process known as "centonization". The reason you need a different kind of music theory for chant is that the musical structures are completely different from what we find in music from other times and places.

By the high Middle Ages, music was composed in entirely different ways using an entirely different kind of notation and we need a different kind of music theory to talk about it. Characteristic terms for this period are isorhythm, Franconian notation, rhythmic modes and the formes fixes. Here is some of the notation:

And here is a little of the music:

As each variety of music theory has its characteristic terms, just hearing them tells us what time and place we are talking about. The terms "RO", "interval vector" and "combinatoriality" are associated with serial music of the Second Viennese School. The "RO" means that the tone row is being heard in retrograde at the original transposition. Interval vector is a concept borrowed from mathematical set theory and combinatoriality refers to the way part of the row can mirror another part of the row. I think! Here is an example of serial music; a piano piece by Arnold Schoenberg:

Sometimes a single word or term can bring to mind a certain kind of music. For example, if you use the word "phasing" in talking about music, you can really only be talking about the music of Steve Reich. Phasing is a technique he used in some earlier works where two instruments playing the same rhythmic pattern slowly diverge with one slightly speeding up. Here is what that sounds like:

You see why you need completely different kinds of theory? Then there are musics that probably have no theoretical discussion, perhaps because no-one has really figured out what is going on:

So we might need a lot more theories of music. Or maybe we give up on theory entirely and just let the music wash over us as we drift into a sonic stupor.