[See the handout for the first three transcriptions; the video transcription is available here, on Vimeo.]
To begin this proposal defense, I would like to share four transcriptions of Euler’s eleventh harmonic species, each with its unique realization in sound. The first transcription, on the left of the handout, is my own, and it consists of three parts. Table A shows every possible way to multiply together the species’ six generating prime numbers, to produce twenty-seven values between one and nine hundred. Table B transforms arithmetic into musical notation, by interpreting each of the above table’s values as the partial of a very low F. In this lower table, we can see musical patterns emerge from mathematical ones. Scanning from left to right, we find that each row contains the same note in three different octaves: three F’s in the top row, three C’s in the row below that, and so on. Meanwhile, each column contains three clumps of twelfths: look, for example, at the central clump of A2, E4, and B5, or the upper-right clump of F1, C3, and G4. Finally, as we skip from a note in one of these clumps to the corresponding note of the clump below it—from, say, the F1 in the upper-right corner to the A3 a bit further down—the pitch leaps up two octaves plus a third. To the right of the tables, I have arranged these twenty-seven notes in staff notation. Taken all together, they span the range of human hearing. Leaving out the lowest two notes and the highest two notes, which exceed the piano’s range, I will play as much of the species as I can, first as a grand arpeggio, then as ascending block chords: [play]
The second transcription is by Euler himself, and appears in his Attempt at a New Theory of Music, in a table among various other harmonic species. Rather than displaying the species as a single massive chord, as I have, Euler slices it into more manageable chunks, and transposes these chunks to fit on the grand staff. The powers of two below each chord show where each slice fits into the species as a whole—a correspondence I indicate in my more vertical transcription. Euler’s compression of his species’ range, of course, creates a sonic effect different from the first: [play]
The third transcription, also by Euler, appears a bit later on in his Attempt. In this variation, notes become numbers once again: not as frequency relations now, but rather as the intervals of a figured bass. If we take this notation seriously, the species’ sound changes again, becoming even more compact: [play]
The fourth and final transcription is a five-minute video I made to illuminate the harmonic relationships of Euler’s species in a new way. [play]
In my proposal, I emphasize why this project is important to me as a teacher. But, in one way or another, you have each asked me what on earth my adventure into eighteenth-century Europe has to do me as a composer. This introduction gives me an opportunity to explain what my historical work shares with my creative work. It is something I have thought a lot about, but never really taken the time to articulate. Let me try to explain it now.
It should be clear that in my compositions, I am not borrowing Baroque sounds or techniques in the traditional sense. Broadly speaking, I am interested in harmony and counterpoint. I enjoy thinking about chords, and I’m happy to imagine my music as a fabric of interwoven lines. The weights, densities, and patterns of this fabric, however, have nothing to do with the surface textures of Baroque music, or even, really, with the concepts that are essential to Baroque musical thought. Cadences, voice leading, consonance and dissonance—these ideas are not for me. The Baroque aesthetic I am trying to capture, through both my historical work and composition, is not this.
What is it, then? First, it is the drama of literacy, a game of signs and representations that strikes me (and not just me) as a quintessential aspect of Baroque style. I make this point briefly in the proposal, but it is worth reiterating and developing. At some point over the last several years, I lost interest in sonority as such—which is a dangerous thing for a composer to admit! Fortunately, as my enchantment with sound by itself faded, a fascination with sound’s relationship to its inscription grew in its place. I became wary of those who closed their eyes to listen without distraction. The distractions themselves, and our habits of ignoring them, became more interesting to me than the pure experience of sound such habits are meant to produce. This is why I find Tristan Murail’s philosophy of composition so distasteful; this is why I create video scores and other musical visualizations. I want to celebrate music literacy as the play of correspondences, not to hide it as an embarrassing by-product of the sonic. Therefore, I stage my compositions to bring out this drama, which, for me, is the drama of musical interpretation in its rawest and most lively form.
My compositions and historical research, then, share a concern with the presentation of writing. Beyond this, they share something more delicate and elusive. In his work on a Baroque aesthetic, Deleuze writes, “The Baroque refers not to an essence but rather to an operative function, to a trait.” For Deleuze, this trait “twists and turns its folds, pushing them to infinity, fold over fold, one upon the other. ” This trait of folding, however, is not the Baroque aesthetic I have in mind for my own work. There is another function of the Baroque—what I would like to call an aesthetic of transcription. It involves a sensitivity to equivalences and transformations, not only across media and senses, but also between the so-called complete work and the example or fragment. It creates ecstasies of knowledge through the juxtaposition of representations, using improbable correlations to hint at meanings that exceed perception. I find it in the Cartesian analysis that exposes the overlap between algebra and geometry; in the spoken language of tabla bols that mimics so perfectly the movement of the hands; in the grammar of computer languages that is not simply correctness for its own sake; and, of course, in the Baroque chord tables that reveal to us the rules of sound. Adapting a phrase from Nietzsche: “Even the wisest of us occasionally becomes a fool for transcription, if only insofar as he feels a thought to be truer when it presents itself multiply.” The is this truth I foolishly pursue through my compositions and magnify through my research, with the hope that it is enriched by its own multiplicity.