Syntax Of Music

The rhythmic structure of music is by and large not taught in the schools. This is due in part to the fact that 19th and 20th century concert music represents one of history's most significant experiments in breaking down and circumventing the principles of musical structure. Other prominent experiments include Indian classical music, and progressive and free Jazz.

Most of the rest of the world's music is built on a framework I call a MatrixOfRelatedFrequencies.

Rhythm serves to subdivide time in a number of ways simultaneously. A time period X could for example be viewed as 128 beats, 32 measures, four eight-measure phrases, or one four-phrase piece. Unlike a gallon of water, which could be viewed either as four quarts, or as 128 ounces, music builds reference to its many levels of subdivision into its fabric.

Let's take an interval of time x, and subdivide it. The simplest type of subdivision is by powers of two. This is the subdivision from which the durations of musical notes are derived. The graph of this pattern looks like so:

 1======O===============================O

 1/2====O===============O===============O

 1/4====O=======O=======O=======O=======O

 1/8====O===O===O===O===O===O===O===O===O

 1/16===O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O

 1/32===OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

     0x             1/2x               2x

A variant of this, which I discovered while analyzing Reggae music, comes when we look at every second member of the above set:

 1======================================O

 1/2====================O================

 1/4============O===============O========

 1/8========O=======O=======O=======O====

 1/16=====O===O===O===O===O===O===O===O==

 1/32===O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O=O

            0x          1/2x            2x

The simplest case example of musical structure maps to a binary tree. (Is this too obvious?)

When I was in math class in high school, I remember discussing the orders of magnitude of infinities. I was really fascinated by the proof showing that the rational numbers were of the same order of infinity as the integers. The proof involved laying out all the rational numbers onto a plane. This is possible because any rational number can be expressed as a fraction, which is a function of two integers.

 1|1/11/21/31/41/5.....

 2|2/12/22/32/42/5.....

 3|3/13/23/33/43/5.....

Although the plane is infinitely long and infinitely wide, there is a single thread that can wind around in such a way as to connect all the points in the plane. It was this thread that fascinated me. I was convinced that it had something to do with music, although it was many years before I figured out what it was.

Many years later, I was reading about fractals, and the musical traversal of a plane occurred to me. Here are the first 32 integers mapped onto a plane according to musical structure:

0102050617182122

0304070819202324

0910131425262930

1112151627283132

What's interesting about this mapping is that the first 4^n integers always occupy a square. Also, if we look at the traversal of every 4^nth integer we see the exact same pattern at a different scale. I'll call this pattern NestedZeds.

I figured out a type of music notation paper where each of the first 16 integers is represented with one measure of traditional musical notation. I can then score a LeadSheet to virtually any pop song or jazz standard using one sheet of paper, without ever writing out the same measure twice. The quadrants of the page are labeled ABCD, and a line at the top of the page shows the pattern of the song as a function of ABC and D. A typically maps to verses, B to choruses, C to the bridge, and D to any additional new material. Each of the quadrants is treated the same way, with the labels wxyz. A typical pop song might have the form:

A[wxwz]A["]B[wxyz]A[wxwz]B[wxwxwxyz]C[wxwy]C[wxwz]A[wz]B[wxwxwx.....]

In my work as a professional musician, I've written out dozens of songs using this method. I like it because there is always a clear relationship between the parts of a song and their position on the page.

--eric moon

As a footnote, I finally got to put this notational method to use, as keyboardist with german-punk icon Nina Hagen on her fall tour last year. I was able to write out the songs almost as fast as the band played them for me, did the first show with virtually no rehearsal, and never got more than slightly lost. (at least she never noticed.)

--eric moon

It would be very nice, if we could deepen the dialogue. What about a pointer to a site with your music. -- FridemarPache

And how about a tutorial to study this notation system?

CategoryMusic