Laputa, Jonathan Swift's floating island in the clouds, was populated by mathematicians, astronomers, and music theorists whose "heads," Gulliver describes, "were all reclined to the right or to the left" with "one of their eyes turned inward, and the other directly up to the zenith."1 Swift's cutting satire on the insularity of the theoreticians amongst us, and our perceived disconnection from practice and reality, is echoed at many levels today. From reactionary political agendas to discredit university research to the persistent undergraduate's complaint about the irrelevance of the forbidden and dreaded parallel fifths to her flute playing, a rejection of theoretical abstraction is heard.
Johann Mattheson's Der vollkommene Kapellmeister, with its wonderful subtitle "A thorough survey of all things with which one must be familiar . . . to conduct a chapel honorably," attacks Laputanism with zeal. This is an example of Mattheson's searing pen: "Heinrich Loris, the learned pickled-herring of Glaris, was more skilled at riding a jackass into a public oratorium and playing other audacious tricks than at writing something substantive on music. His Dodecachordon cost him ten years. It is a book in which nothing is more estimable than the time spent on it."
After lambasting other theorists, including Guido and Gafurius, Mattheson concludes: "These men tormented themselves terribly to bring the consonances into mathematical formthey considered all to be musical heretics who made use of anything other than the diatonic scale. What they wrote was harmful, and we see the effects today in a thousand places."
Mattheson's concern for theory based on practicality is stated with greater positivism by Noam Chomsky. "No discipline," he writes, "can concern itself in a productive way with acquisition or utilization of a form of knowledge without being concerned with the nature of that system of knowledge."
Modeling musical practices demands that theorists face musical issues without hiding behind abstractions. I believe that the perceived disconnectedness of music theory today is due, in part, to a lack of tools with which to model various aspects of the musical experience. In order to understand the Laputan mind set, consider for a moment Johannes Kepler. At first glance, Kepler appears to be the consummate Laputan. An astronomer, mathematician, and music theorist all rolled into one. Kepler concerned himself with the harmony of the spheres rather than with the mundane workings of earthly music. However, a critical reading of Kepler reveals the role of music theory in his work to be anything but disconnected. Kepler"s harmony of the worlds uses music to model a situation whose complexity demanded analogy. Specifically, he wanted to experience planetary motion as seen from the impossible vantage point of the sun. By thinking of each planet as a voice in a motet, he was able to reveal that planetary motion is not circular but elliptical. The physical laws and relationships between motion, distance, and mass that are followed by a planet reacting to the eccentricities of an ellipse remain at the core of space exploration today. Had Kepler not modeled physical motion with music, he never could have realized these fundamental laws of physics and astronomical facts. In fact, music not only unlocked the mysteries of planetary motion for Kepler, but also served to justify his realizations that his refutation of previous beliefs did not threaten the requisite demand for divine perfectionit simply altered the understanding of what that perfection was.
The most beautiful punch line I ever ran across in a theoretical treatise is in Kepler's conclusionhe understatedly tosses out the idea that since planetary motion and alignment are harmonically related in a way that can be actually modeled musically, the logical way to discover the true moment of cosmic creation is to consider the universe as a score, the planets as voices, and work one's way backwards through the cosmic motet to find the logical beginning point.
Viewing Kepler's use of music theory as a method of modeling transforms the abstraction and seeming disconnectedness of his work into a practical and terrifically creative endeavor. Kepler's use of music is a precursor to the enormous role of visualization tools in today's sciences, and suggests that perhaps building models with music can be a robust and rewarding task for the theorist. And so, in the spirit of Kepler, I propose that building theoretical models returns an awareness of relevance and practicality to theory. Furthermore, modeling not only facilitates connections, it demands that we make the connections between theory and practice that seem to so many to be sorely lacking.
Recent research in modeling cognitive processes in music, musical performance practices, and composition, in addition to timbral and musical instrument modeling, is providing a powerful arsenal of tools for research, production, and pedagogy. After decades of attempting to synthesize individual sounds from analytical models, recent attempts to model the physical attributes of the instruments, rather than the sounds, have opened up vast new areas of sound production and interpretation. Even minute details, such as Chris Chafe's recent studies of the vortex created by a flautist blowing into her instrument, have not only contributed to greater understanding of sound and sound production, but to greater understanding of the physics of the vortex in general.
Performance is the black box of music theory. This, unfortunately, will remain the case until effective tools with which we can transcribe, isolate, and quantify performance attributes are developed, for building models requires flexible tools. Recent developments in applied mathematics have created an arsenal of tools that, although they are still in their infancy, suggest powerful implications for music research and production. According to Fourier analysis . . . a musical signal could be described in the time domain, but without frequency, or in the frequency domain but without time resolution. Recent developments and applications of adaptive local trigonometric transforms allow for a synthesis of these domainsthus opening up the black box and unleashing a wealth of research to be done by theorists.
Our research in adaptive trigonometric transforms in music analysis also has applications in data compression, restorations of historical recordings, denoising, automated transcription, composition, and sound synthesis. For example, in our denoising of the 1889 Edison cylinder recording of Brahms at the piano, we succeeded in peeling off layers of noise to reveal and transcribe the highly improvisatory and stylized performance of Brahms's first Hungarian Dance. Since these analytical/transcription methods are adaptive to musical detail, the classic dichotomy of description and analysis do not hold. In fact, the entire concept of reductive analysis demands redefinition in consideration of the implications of such tools.
Unlike the other models that I have presented today, compositional modeling has been done by theorists for centuries. Remarkably, as early as 1843, Ada Lovelace imagined the use of compositional modeling using Sir Charles Babbage's Analytical Engine. The mechanism, she conjectured, might be applicable to "the fundamental relations of pitched sounds in the science of harmony and of musical composition . . . were objects found whose fundamental relations could be expressed by those of the abstract science of operations."2 Understanding and codifying transformational functions have not only been a personal compositional tool but have also provided a theoretical groundwork for analysis of developmental composition techniques and have been enormously beneficial as a pedagogical tool.
And so we return to the floating island of Laputa. "And although they are dextrous enough on a piece of paper . . . " writes Swift, "I have not seen a more clumsy, awkward, and unhandy people, . . . Imagination, fancy, and invention, they are wholly strangers to, nor have [they] any words in their language by which those ideas can be expressed; . . ."3
The black boxes of music theorythe domains that have always played the disconnected counterpartsintuition, imagination, fancy, inventionsuddenly seem less strange. Our awkward inability to deal with these mysterious terms is finding refreshing new solutions as we seek out already existing connections.
1Jonathan Swift, Gulliver's Travels (NY: Rinehart & Co., 1948), p. 148.
2Ada A. Lovelace, "Notes upon the memoir 'Sketch of the Analytical Engine Invented by Charles Babbage,'" in Philip and Emily Morricon, Charles Babbage and His Calculating Engines (New York: Dover Publications, Inc., 1961), 247.
3Swift, op. cit., p. 153.