The first of the observations concerned a question of the foundations for thinking about the music itself. Fleisher invoked the old chestnut about an affinity between music and mathematics and then suggested that a more valid affinity could be found in physics. His argument was that music is all about motion and thus should be considered in light of those fundamental laws of motion through which we understand so much about the physical world. This opens the door to some interesting pedagogical methods. Thus, one might benefit from converting the literal terminology of physics (mass, velocity, momentum, energy, impulse, and so forth) into a metaphorical terminology for how music is performed (and perhaps also perceived). One may even adopt literal interpretations of concepts of both time and space in ways that are meaningful in musical practice. (Consider the spatial perspective I took in writing about last week's Chamber Music Masters performance at the Conservatory.) On the other hand both the literal and the metaphoric can easily come under strain when one starts considering the rules that are stated in terms of physical terminology. Would it really make sense to talk about Newtonian conservation of energy, let alone the relativistic impact of near-light-speed velocities? In other words invoking physics may get your head in the right place for certain perspectives, as long as you remember that, whatever the positivists may try to tell you, musical phenomena cannot be reduced to physical phenomena.
Taking the positivists to task also raises another problem with trying to form too great an affinity with physics. This concerns the extent to which the performance of the music that occupied Fleisher in his Master Class is fundamentally a matter of interpreting a text, even if the lexical primitives of that text involve the symbols of music notation, rather than words in the English language. From this point of view, I need to emphasize, once again, the precept that the interpretation of any text in a "natural" language (and we may regard any instance of music notation as such a text) needs to be informed by not only the laws of the objective world (which is the only legitimate domain of physics) but also the principles through which we understand behavioral patterns in the subjective and social worlds. Within this expanded scope what may simply be called "events" in the physical world need to be sorted out (drawing upon the terminology of narratology) into "actions" and "happenings," the distinction being that actions are performed by (usually motivated) agents, while agents are not directly involved in the occurrence of happenings. Of particularly importance is that adjective "motivated" (even if I chose to parenthesize it): Music "moves" as much through the motives of composers and performers as it does through the "physical specifications" of tempo. In the analysis of literary texts, Kenneth Burke attached so much importance to motive that he tried to approach it structurally (through a "grammar"), functionally (through a "rhetoric"), and interpretatively (through a "symbolic"). Looking back on Burke's accomplishments, it is hard to tell how successful he ultimately was; but I suspect it was from Burke that I first started trying to apply the trivium of logic, grammar, and rhetoric to the systematic study of performance practice.
Thus, in some way or another, I feel it is important to approach performance within the framework of the interpretation of texts; and this brings me to the second of Fleisher's observations. He talked with his final student about approaching music on both a "micro-level" and a "macro-level." The micro-level is the level of notation primitives and how those primitives are "translated" into those actions from which performance emerges. The macro-level, on the other hand, is the level from which the performer can perceive what it being performed in its entirety and then understand where every instance of performance is situated within that broader view.
In order to clarify what he meant by the macro-level, Fleisher asked the student to imagine that the wall on the side of the performing space was covered with all the pages of the sheet music (suggesting that a larger wall would be needed if a Wagner opera were being performed). This is, again, valuable as a metaphor; but the metaphor only goes so far. After all, as is the case in most semiotic systems, the relationship between the signifiers of music notation and what they signify is a purely arbitrary one. Fleisher might do better to acquaint himself with the research of Robert Cogan, who has spent much of his professional life analyzing music on the basis of visual traces of the physical vibrations that produce the auditory signals we hear. The equipment Cogan used for his first studies is hopelessly primitive by today's standards; but the good news is that anyone not afraid of computer software can now easily reproduce his results with far higher-quality displays. Furthermore, most of that software supports a "zooming" feature, through which any duration of time, from that of a Chopin ballade to the entirety of Siegfried, can be expanded or contracted to fit the extent of any horizontal time line.
By way of demonstration, one of the examples that Cogan considered in his book, New Images of Musical Sound, was the first movement of Beethoven's Opus 109 E major piano sonata. Here is a version of Cogan's image, which originally required about twelve inches, reduced to a seven-inch printout (subsequently reduced for display in this post) with software I was running on a Macintosh in Singapore back in 1995:
I offer this illustration to make two points:
- If we really want to visualize a composition in its entirety, we should do so in terms of its actual physical features (even if they are the features of a specific performance), rather than the notational abstraction of a performance.
- Computer software has matured to a point that we can visualize an entire musical performance on any display scale, no matter how large or small.
I do not always agree with the analyses that Cogan extracted from his data; but I agree with Fleisher about the need to think at the macro-level. Technology is now available to support such thinking, and it may be time for us to address more seriously how that technology can be put to good use. By way of a personal disclaimer, I should note that I served as advisor to a Master's student at the National Institute of Education at Nanyang Technological University in Singapore, who submitted her thesis based on the use of this technology in June of 1997. My only regret is of how little has been done to continue this work in the ensuing ten years!