Musical Transformation

One Dimension of the Musical Story

Today I will introduce the idea of "musical transformation," which is a metaphor for describing how musical ideas are altered through the course of a composition through transformative functions. Indeed, some might call this "the development" of a musical idea. I'll contrast the application of transformations (argumentation) with the act of exposition, identify some transformative techniques, and present an example piece.

Reasons:

1. From a formal/analytical standpoint, it's useful to identify transformations used in Music. In an empirical sense, through the analysis of a large body of works, we can name and discuss common techniques.

2. Perhaps more importantly, the listener, by being aware that the potential for these transformations exist, may begin to approach the act of listening in a way that allow him or her to understand the progression of a composition.

3. Finally, the idea of "transformation-as-narrative" becomes a Musical Strategy (caps intentional) that connects directly to (or at the very least, forces us to consider) the central nervous system of aesthetics (Music and otherwise), and thus potentially the transcendental/metaphysical.

The philosophies (or if you prefer, meta-meanings) that inform a composer's work are often most obvious when regarded in light of the presence or absence of a transformative style of composition. (Unlike pseudo-gnoistic organizational structures or kabbalistic encodings that resist/deny reception or perception, the ability to project and receive transformative events in music is certainly possible.) Consider the perennial fascination of popular musicians with Eastern philosophy, which consciously rejects the idea of a transcendental, transformative narrative--a rejection I would argue results in a static, minimalist perspective in art, music, and philosophy.

Exposition vs. Argumentation: Two Functions

First, music has an expository function. When someone picks up a guitar and begins playing a piece, they are "exposing" a musical idea. In a fugue, the initial measures could be an exposition of an idea (or "subject,") and later measures provide an exposition of a different idea ("countersubject") and so on. The purpose of an expository passage is to introduce an idea; an idea that is presumably later expanded upon.

Second, music can exhibit an argumentative function. A musical idea, once introduced (exposed), may then be used in a myriad of ways to proceed from the original idea to other. Much like the application of mathematical axioms to construct proofs, certain "musical functions" are applied (perhaps in succesion) to musical ideas. Whether the final act of a composition represents the "Q.E.D." is another matter entirely!

Argumentation is accomplished by transforming musical ideas in time. Like proceeding "from the known to the unknown," musical transformations proceed from the familiar to the unfamiliar--through specific, identifiable, mechanisms or functions. The workings of these functions are discrete (they may be categorized) and may even be intelligible (this is debatable, but certainly possibly true in many situations). Much like a mathematical function, a thematic transformation has an input and an output; for us, obviously, both the inputs and the outputs are "music."

Can we derive any meaning from these transformations? It would be prescriptive and naive to associate a particular transformative activity with a specific extra-musical meaning. For example, a melodic idea that is "sped up" from its original (by halving its rhythmic values) may strike a listener as being stated "in a more urgent way." Another listener may hear it as representing "a joyful proclamation," and so on.

These questions go far deeper than we'll discuss here, but we should marvel at the fact that the transformation has been applied at all.

Some Examples

Here are two common argumentative, or transformational musical stratiges:

1. Augmentation: For any given musical idea, we can extend (augment) it in time by lengthening some of the rhythmic note-values, or we can extend it in the pitch space by increasing the intervals between successive pitches.

  1. Diminution: We can compress (diminish) a musical idea in time by decreasing one (or all) pitch durations, thereby "speeding up" an idea.

An example follows. The idea is exposed/presented in the first measure, followed by the results of an augmentation (#1) strategy where the rhythmic values are doubled, another augmentation (#1) strategy where the intervals between successive pitches are increased, and an example of diminution (#2) strategy, where the rhythmic values are halved, but the composer has also freely added ('filled in') the figure with some pitches that aren't necessarily distinguishable to the original idea:

It's not difficult to imagine that there exist many additional strategies, nor is it difficult to believe there are strategies that are either so subtle that they may be hard to hear, or ones so transformative that their result is unintelligible.

Some Common Strategies

Here's a brief list of possible transformation strategies. Where possible, I've identified where they are employed our example music, below.

Rhythmic

  • Slowing down or speeding up a melodic idea (rhythmic augmentation or diminution) (Var. 1 and others)
  • Altering rhythmic proportions (dotting, syncopation) (Var. 3)
  • Tempo (fast vs. slow)

Harmonic, Melodic, Intervallic

  • Adjusting leaps or steps in the melodic line (increasing or decreasing)
  • Sequence (repeating an idea at different pitch levels, usually in successive, stepwise ascents or descents)
  • Inverting ideas (steps up, become steps down, etc)
  • Mode mixture (switching between major and minor keys) (Var. 8)
  • Changing register (moving between high and low pitches)
  • Altering texture (thin or thick) (Vars. 4, 6)
  • Introducing new styles (referring to other genres) (Var. 8,9,10, contrapuntal and toccata styles)
  • Adding figurations (flourishes, accompaniment patterns identifiable to a particular instrument, etc) (Var. 10 etc)
  • "Filling in" intervals with stepwise or triadic motion (Vars. 1, 2, 7, etc)

This is by no means a comprehensive list. New strategies are being created all the time--however, you might find it startling that these bookish, ancient, techniques are also the exact same ones used in Jazz improvisation!

An Example of Musical Transformation--Theme and Variations

The "theme and variations," is a specific vehicle wherein the composer introduces a theme (exposition), and subsequently varies it (argumentation).

There are some generally accepted constraints:

  • Each measure in each variation should correspond strongly (harmonically, for example) with each measure in the original theme.
  • By way of creating a dramatic arc, each variation tends to become less and less clear in terms of its correspondence to the original ideas,
  • Intelligibility (and thus the listener's ability to comprehend what variation technique is in play) is maintained by limited in the number of transformations (possibly to a single one) between variations.

Each variation can 'refer' (either objectively, in the score, or subjectively, in the hearer) not only to the original theme, but also to the preceeding variations. The structural confines of the genre create a very interesting "musical laboratory" for the listener and theorist, for by imposing a rigid structure on the variations, the composer and listener can focus their attention on the technique of variation.

The figure below shows a tiny visual example of how the style works. Note the following:

  • The theme is four measures long (green blocks), so also each variation is four measures long. The dots in between each variation represent the application of a transformational technique.
  • There are two variations. The first variation (red) will introduce a transformation of the original material.
  • The second variation (blue) shows the application of another transformation which may be a transformation of the second variation, or a transformation of the theme.
  • The brackets suggest correspondence between each variation and theme, and between variations themselves. The exclamation point (!) posits that the correspondence between a variation and the original theme tends to be overt, while the correspondences between themes is less so (?).

Much like a repeated chorus/solo in Jazz, each subsequent variation builds on or expands upon what proceeds it, but within the strict confines of the formal layout of the theme. In this way, interest is created (through transformation) but structure is preserved.

An Example in the Wild

Consider Mozart's twelve variations on Ah, vous dirai-je, maman (KV 265), a.k.a. "Twinkle Twinkle, Little Star." Please listen to the piece and try to:

  • Enjoy the performance (subjectivity matters),
  • Follow the score (Augenmusik!), and
  • Observe/understand the application of these transformative functions on the original melody.

Each variation represents the application of one or more transformations. Can you discern what transformations are taking place, visually? Aurally? Can you perceive each measure's relationship to the original musical idea? See the chart above to see some suggestions.

I'm hoping that by using what should be a familiar melody (to most), it can be seen and heard how and that musical transformations occur through the performance. Good luck.

Youtube (with score!): https://www.youtube.com/watch?v=NO-ecxHEPqI

Below I've excerpted the the theme, and the first two measures of each variation, for reference.

Here's a rough tabulation of some of the strategies we find in each variation. This is not intended to be comprehensive, but it should provide some food for thought:

Var. Techniques
1 filling in (scalar), rhythmic diminution (16ths)
2 thickening of texture (RH), rhythmic diminution (LH)
3 rhyhmic alteration
4 rhythmic alteration, thickening of texture
5 rhythmic alteration,
6 thickening of texture, rhythmic diminution
7 filling-in, rhythmic diminution
8 mode mixture (c minor), imitative style (baroque?)
9 thickening of texture, (suspensions)
10 rhythmic diminution, keyboard figuration
11 rhythmic alteration, filling-in (chordal skips)
12 thickening of texture, rhythmic diminution

Summary, Conclusions

In this rather extensive (in the future, I'll break it into two or more pieces) post, we've introduced the concept of musical transformation (also known as "development,") and related it to spoken rhetoric. The idea that musical ideas undergo specific transformations through the course of a work resonates with the traditions of rhetoric and narrative. In a rather fixed format (the theme and variations) we saw and heard examples of how these transformations can be used to generate larger musical ideas.

The suggestion was also made that the presence or absence of these events could be indexical to the location of the composition's place in a larger context, a compelling idea we'll be exploring in later posts.

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