Mosaics vs. Fractals in Music

The Backstory

We often hear or use the phrase, "the medium is the message," when addressing modern music. This may be a valuable heuristic or guide, but it there's a better one I'd like to take credit for inventing: "The Motivation is the Message," or perhaps, "The Methodology is the Message."

In doing so, I assert that certain structural-formal elements in a musical composition can be important signifiers, illuminating the means of production behind its existence, and thus provide their own message. These messages may be separate from or even conflicting with the superficial or obvious elements in a piece, but they are every bit as important.

By way of analogy, I'd like to suggest that traditional sacred Music uses a very different approach to composition that is manifest at a structural or formal level. Visually, we may analogize traditional sacred Music to the fractal; post-modern or modern music to the mosaic. (N. B. I'll gloss over this topic in the interest of time and space. If anyone wants more depth, please contact me and we can flesh this out further.)

Musical Meaning: Multileveled

Meaning, as carried through Music, can exist on multiple levels. For example:

  1. The text of a vocal work will consist of the usual structures in language, and meaning is delivered via the language and its idioms
  2. Certain gestures in the music may highlight or emphasize certain words ("text painting," often consisting of specific directed intervals, volume, etc)
  3. The formal structure of the composition may be based on a specific program or story, or
  4. The formal structure of the composition may be based on concepts "mapped over" from an extra-musical source (i.e., minimalism as related to certain Eastern religions)

For us, the fourth category will hold the most interest in today's discussion. Most of us would agree that the text of a Bach Cantata (#1) attempts to express, amplify, or illuminate truths from God's Word--perhaps the appointed reading from the Lectionary for that day. In fact, you could read the lyrics to a cantata (without the music) and learn quite a bit.

Most of us would be surprised, however, that there are deeper Musical structures and strategies (see #4) that strive to express those truths just as earnestly as the text being sung. Perhaps even purely instrumental compositions have the ability to convey these truths! It's difficult to grasp how the beauty of God's creation and saving work through Christ can be manifest in pure Music--at a level far deeper than what may be expressed in the lyrics of a particular piece.

Musical Fractals?

In Music there are developmental techniques

In Music we have a word for this approach: Fortspinnung (a vestigal definition here, a "spinning forth" of an idea that provides the "motor" for a composition. Another analogy used is that of a cell. A cell contains all of the DNA necessary to generate a complete, sophisticated organism, and so also does a tiny motivic fragment contain "musical DNA" from which an entire composition can be derived. I routinely take "Analysis Breaks" on this blog, where I try to expose how this ideal is expressed through motivic and structural consistency. These brief excursions only hint at the deeper structures, but hopefully whets your appetite.

The presence of a tiny musical idea (motive) and its transformations, serving as a the basis for the entire work, resonates strongly with the notion of the fractal ( In a fractal diagram, we see how a self-referential mathematical function can be "worked out" through many levels--providing a graphic that shows a consistency between the larger structures and the smaller ones. The curious thing about an image (or graph) drawn using a fractal method is that it tends to look the same whether you've "zoomed in on it" or not. Certain characteristics of the structure look the same whether you're looking at the picture from a distance, or through a microscope.

Such an approach is undertaken as a conscious imitation of the self-same intra-referential (or self-similar?) nature of Holy Scripture--the very Lutheran idea that "Scripture interprets Scripture" resonates with the self-validating ideas of type/antitype, of prophecy/fulfillment. The beauty in sacred Music is in how the deeper structures are used to testify or reflect God's Glory in creation, and His saving work through Christ's death and resurrection. There are elements of this compositional philosophy that touch upon eschatological ideals as well--it's really quite an interesting avenue of approach.

I personally find great comfort and hope in hearing even turbulent passages in a Bach Fugue; for I know that any "threatening" dissonances or gestures are still bound by the deeper logic that guides the passage--and the composition as a whole. As Christians, how can we not cherish this message?

Musical Mosaics

A very different compositional aesthetic may be found by listening to Stravinsky's The Rite Of Spring, which was famous and controversial for many reasons.

Plenty of information (and recordings) concerning this piece abound, but I'd like to direct you to the following summary:

Note particularly how the form of the piece represented a departure from convention:

  • People hearing The Rite of Spring for the first time notice that several sections break off suddenly instead of coming to a traditional close: a musical convention that allows us to sense the conclusion of a segment or work. Instead, Stravinsky slashes the fabric of the music at an unexpected moment, suddenly replacing one broken off section with a completely different one. This technique is a radical departure from typical classical or romantic compositions, where explicit transitions between contrasting sections are the norm.

Stravinsky's approach to large-scale formal structure was to 'bolt together' different sections to create jarring contrasts. This "additive technique" rejects the earlier notion that compositions need to be unified by motivic development or a large-scale architectonic ideal (in other words, "goodbye fractals.") Perhaps Stravinsky may be understood as a "postmodernist" composer, one who turned away from the earlier ideals by replacing them with a pastiche, or a montage.

What Does a Mosaic Mean?

The Wikipedia article on 'mosaic' ( contains some great images of how the mosaic technique is used to create a larger image.

Aurally, a composition built in the 'mosaic' style will be heard as having regular sections that, to some degree, aurally cross-cut with one another. They may or may not form any kind of cohesive "picture," but are releated to one another only by proximity. Imagine such a piece built with fifteen four-bar sections. It might be "heard" the way this "looks:"

Individual segements do not necessarily connect or relate with one another, they are meant to be understood as a whole (a Gestalt if you prefer). There is no narrative in the sense that one section develops or changes logically into the next; the organizational strategy is that they simply exist and lo! A larger picture emerges. An abstract mosaic (or collage) wouldn't necessarily provide any direct representational picture at all, but instead provide a kaleidescopic splash of colors and textures.

Now, there's nothing wrong with a good mosaic, but it's important to know and understand that the idea of a developmental/motivic (fractal) composition is going to communicate a different aesthetic or philosophy than a mosaic/pastiche. Additive compositions, that is to say, works that move through time simply by adding on different sections, do not portray the same type of developmental transformations, and thus communicate something different musically. Many compositions in this style were written as conscious rejections of the prevailing "motivic" (or "fractal") styles, advocating an aesthetic (and world view) that denies an over-arching narrative, but instead, a pastiche of unrelated and random events. There is no Fortspinnung, but instead a hodgepodge of ideas.

It's instructive and provocative to consider modern popular music as being largely "additive" in its construction, with its clearly demarcated sections (verse, chorus, bridge) and additive structures (verse, chorus, repeat, verse, repeat, repeat and fade).