Embodied Transformations in Piano Music
James Bungert, University of Wisconsin – Madison
The Transformational Attitude
Early twentieth-century American music critic James Huneker (1900) writes that:
The [Chopin] Berceuse, op. 57, published June, 1845 … is the very sophistication of the art of musical ornamentation. It is built on a tonic and dominant bass – the triad of the tonic and the chord of the dominant seventh. A rocking theme is set over this basso ostinato and the most enchanting effects are produced. The rhythm never alters in the bass, and against this background, the monotone of a dark gray sky, the composer arranges an astonishing variety of fireworks, some florid, some subdued, but all delicate in tracery and design. Modulations from pigeon egg blue to Nile green, most misty and subtle modulations, dissolve before one’s eyes, and for a moment the sky is peppered with tiny stars in doubles, each independently tinted. Within a small segment of the chromatic bow Chopin has imprisoned new, strangely dissonant colors. It is a miracle; and after the drawn-out chord of the dominant seventh and the rain of silvery fire ceases one realizes that the whole piece is a delicious illusion, but an ululation in the key of Db, the apotheosis of pyrotechnical colorature. (269–70)
By this lovely, colorful account, Chopin’s Berceuse is almost exclusively visual: “dark gray sky,” “tiny stars in doubles,” “rain of silvery fire,” etc. Like real fireworks, the “pyrotechnics” in the right hand happen up there, against “the monotone of a dark gray sky,” away from us here, the passive spectators sprawled out on the grass. Such imagery, by its very definition, is passively observed from some distance, so it naturally resists active participation. In other words, Huneker leaves no room for a discussion of the sound of the Berceuse, nor the act and/or feeling of performing it. Considering its author, this brief description is therefore somewhat ironic: here we cannot tell that Huneker spent a great deal of time playing piano throughout his career, writing extensively not only about Chopin’s complete works, but Brahms’s too – which would demand a first-hand familiarity with the chosen repertoire.
Nevertheless, Huneker is remembered today primarily as a critic and essayist and less as a pianist. And based on his description of the Berceuse, we cannot help but imagine Huneker hurriedly writing at his typewriter, perhaps under some publication deadline, away from the piano – using only the Berceuse’s score. In fact, despite his well-known acquaintance with the instrument and its practitioners, nothing about this description indicates that he has even heard the Berceuse before, let alone played it – although realistically, we assume he’s done both. Perhaps the most curious word, among many, in Huneker’s description is imprisoned. “Within a small segment of the chromatic bow Chopin has imprisoned new, strangely dissonant colors.” What could this mean? Maybe the “colors” are actually note heads bearing accidentals in the score, which just by glancing one finds peppered throughout the piece – a flurry of chromaticism. A score certainly has plenty of space in its staff and barlines in which to detain notes. But more to the point, perhaps “imprisoned” denotes how musical actions – actions that Huneker implements and experiences gracefully, fluidly, ephemerally, physically – sit dead on the page, frozen into note heads. Huneker’s passage holds more evidence of Huneker’s discursive distance from the Berceuse, although we won’t fully dissect it here. [1] In spite of his broad knowledge and experience of the piano and its repertoire, Huneker’s Berceuse comes across as a Berceuse in which nothing actually happens. In fact, he says so himself: it’s only a “delicious illusion.”
While the visuality and passivity of Huneker’s description are a bit extreme, we could take them to represent a great deal of music-theoretical literature whose analyses proceed from the score in disregard of the actual act of making music; and we know of many, many examples. Such “score-based” analyses often conceive music as a thing constructed out of atomic, individual, static, abstract objects – e.g. what are called “notes.” Score-based analyses also tend to focus on some “quantified,” or “measured” “distances” within abstract space between these so-called objects, or even between them both vertically and horizontally on the printed page – an approach we might call “intervallic.” A score-based conception therefore commonly separates music from our physically performing bodies – like the paper on which scores are printed – maybe up in the dark gray sky, in order that we might see it better, and to ensure that we sit far enough away, at a safe distance, so it won’t somehow contaminate our thinking about it.
So where Huneker apparently began with the score, representing an enormous discrepancy between musical discourse and the act of music making, here we begin with musical performance, with the hope of beginning to address this discrepancy. At the very least, music comprises both aural and physical action. That is, musical performances occur temporally; they are impermanent, ephemeral. In order to reproduce any particular performance, therefore, we need a practical way to preserve and transmit them across geographical distances and through historical time, perhaps some kind of “code.” The code with which traditional Western scores notate musical performances has a proven track record of practicality, but it almost invariably represents performances metaphorically, even allegorically. It comprises two kinds of notation that appear adjacent to one another on the same page: diastematic and phonetic. (Rastall 1982, 1–11.) Diastematic notation exploits the “pictorial” characteristics of a two-dimensional space – a Cartesian “score plane” – and in so doing, functions iconically. It represents frequency vertically on the page, and it represents their changes horizontally on the same page. Pitch and time thus each accrue some actual measureable physical distance on the surface of the score’s paper. Further, diastematic notation comprises the staff and the note heads, not necessarily in the familiar Cartesian-ordered-pair format (x, y), but which are nonetheless “plotted” in the form of note heads on the staff. The “x-axis” represents time, and the “y-axis” represents pitch, and together (time, pitch) they piggyback the assumption that music can be meaningfully quantified in the abstract. Phonetic notation, on the other hand, is symbolic, comprising literally written-out instructions: “p” means “softly,” “dolce” means “sweetly,” “as loudly as possible” means “as loudly as possible,” etc. (I suppose articulations could fall on either side of the diastematic/phonetic fence, but never on it: slurs are more iconic because they encompass multiple note heads “through time,” along the x-axis of the staff. Conversely, staccato and marcato markings, for example, apply to individual note heads; they’re not iconic, they’re learned, symbolic.)
When music is preserved in this fashion, it’s assumed that at some point “in the future,” on the “other side” of the transmission, a specially trained performer will decode the score back into musical performance. Put another way, the printed page of awkward, lopsided instructions will be converted back into the enormously complex and graceful actions we call musical performance. Ideally, the whole process boils down to this: the composer performs or imagines a performance of a piece based on past experience performing or watching performance (which might be called “improvisation”), writes the piece down (“composing”), and then a performer who is (usually) not the composer performs it using only the score. [2] This whole creative process begins and ends with performance, rendering the score a highly circumscribed medium that connects historically/geographically separated musical performances. Unfortunately, the notation itself presents an enormous reduction of the many aural and physical actions involved in the musical performance it attempts to represent. But whatever is “reduced out” or even “lost” in any notation is the very same set of skills and training the performer is assumed to posses, which will complete the process. As a reduction of performance, then, scores assume a form different in kind from the performances they are meant to represent; and unfortunately, many score-based analyses take this difference as evidence that scores are not only a set of coded performance instructions, but that they represent something else that is not the performance, something somehow purely conceptual, abstract, mysterious, even alien – something whose analytical translation will facilitate a proper understanding. In this sense, score-based analyses “place the cart before the horse,” as they say.
This project hopes to urge us to finally face the music: without the physical actions that make music, many of which the score appears to omit, we wouldn’t have music in the first place, let alone scores. Too few musicologists have tackled this issue, and even then only in the last twenty-five years, with the topic generating little or no momentum. Suzanne Cusick (1994) describes a gap between musicological disciplines and her own sense of musicality, a gap that she finds severely troubling:
Contemplating (sometimes in my own work) what has felt to me like a profoundly unmusical quality to some music criticism led me to reconsider the “situation” that is the central core of my own sense of musicality. The central core of my musicality is performance, an identity so strong that I can barely imagine what other musical identities people (especially critics) might have. As I began to think from the performer in myself, and not from the musicologist in her, I felt acutely that I was not supposed to be thinking that way. I began, further, to suspect that there were reasons related to gender that my musicological self had been professionally formed to be different from my performing self. As a performer, I act on and with what we ordinarily call music with my body; as a musicologist I have been formed to act on (and with?) what we ordinarily call music with my mind, and only with my mind. Thus, my musicological habitus inclines me to think about music’s fixed, textlike qualities, an inclination that is perpetually at odds with the way my performing self inclines to think about and respond to music. And when I turn to music theory as a tool to help me understand a piece I need to know about, I find that its habitus, too, inclines to focus on music’s fixed, textlike qualities. (9–10)
For some reason, our musicological/music-theoretical selves are professionally formed to be different from our performing selves. Cusick continues half-sarcastically: “A performer’s composer-identification is never as complete as a listener’s; what impedes it is the sense that the work temporarily becomes not-the-work, but instead something you do.” [3] (18) But she feels that “a theory of musical bodies would most helpfully theorize, I think, from a performer-centered subject position, because it is performers who are most ignored and dismissed by a mind-mind conception of music.” (18) In other words, discourse on music typically treats it as a series of “signals” somehow transmitted from the composer’s mind to the listener/analyst’s mind, and to embrace the performer, let alone their physical body, would undoubtedly breach the fragile boundaries circumscribing this elite, conceptual dominion. As Cusick suggests, rather than reflecting how things are, or how things may be, this familiar situation reflects the almost ideological position that the “mind” holds in our academic activities. To fully reconcile musical discourse and the act of music making is far beyond the scope of this article. Rather, this approach forms a point of departure: we’ll simply focus more intently on our performance, and hopefully we’ll begin to learn something new about that very weird thing we call “music” along the way.
This approach, then, loosely adopts David Lewin’s transformational attitude. This attitude focuses not on quantified intervals between objects, like a more score-based or intervallic approach might, but rather the qualitative activity of moving through space between them. That is to say, the transformational attitude conceives of music as something we do. Lewin describes this attitude in Generalized Musical Intervals and Transformations (1987):
Given locations s and t in our space this attitude does not ask for some observed measure of extension between reified “points”; rather it asks: “If I am at s and wish to get to t, what characteristic gesture … should I perform in order to arrive there?” … This attitude is by and large the attitude of someone inside the music, as idealized dancer and/or singer. No external observer (analyst, listener) is needed. (159)
The transformational attitude, that is, models various actions that occur through musical space, in contrast to measuring intervals between static points on some version of a Cartesian grid. Lewin and others have used the transformational attitude to conceptualize relations between harmonies, the mutations of a motive, etc. But because this attitude conceives of music as something we do, we might also include the performer’s physical actions. We’re concerned here with actions through both aural space and physical space, spaces whose phenomenological profiles operate within our own single performance space in rather fascinating ways, as we’ll discover. As Cusick urges, here we’ll “theorize from a performer-oriented subject position, because it is performers who are most ignored and dismissed by a mind-mind conception of music.” Let us now return to the Berceuse. For in spite of Huneker’s description, we’ll come to know the Berceuse not as an “illusion,” but rather as a musical performance whose essence comprises aural and physical actions.
The Chopin Berceuse: Two Musical Cycles, Watershed
As the brackets in Example 1 suggest, two distinct, coincident musical cycles arise when we perform the serene accompanimental ostinato of the Berceuse.
Example 1. Chopin’s Berceuse in Db Major, Op. 57 (1844), ms. 1-2.
The first cycle, which I’ll call the “duple cycle,” involves a compound duple meter that both arises from and gently cradles the accompaniment’s tonic-dominant oscillation. Tonic begins each oscillation on the downbeat, but yields to the dominant on beat four: the major third Db–F on beat three expands outward to the diminished fifth C–Gb, and Gb tops the figure’s contour, in a strong metrical position. In a way, this dominant has greater “amplitude” than the tonic, but as much as it “dominates” the oscillation, dominant does not resolve back to tonic on the next downbeat. The quarter note Ab on beat five creates a rhythmic grouping boundary between each oscillation and the next – beat six lacks an “attack.” Thus, tonic only begins the next cycle on the following downbeat rather than continuing the previous one. As performers, we stress the dominant by giving beat four added dynamic emphasis, and by holding onto beats four through six a little longer, creating a gently ebbing and flowing rubato. Physically, our left wrist remains in line with the forearm through beat three, allowing the thumb to rest comfortably on the wide, white, outer portion of the F key. On beat four, the thumb moves up and in toward the piano to play the black Gb key. In so doing, the thumb “abducts”; it extends outward away from the palm. Simultaneously, the hand pivots on the fifth finger causing what is known as “ulnar deviation,” in which the wrist twists laterally toward the left little finger. The hand also “supinates” – rotates slightly to the left. The tension of this complex hand/wrist motion matches the stress we add to beat four, but it contrasts the legato slur marking and the ostinato’s otherwise peaceful attitude. In addition to this oscillation, the right foot lightly flutters the damper pedal just after beats one and four to prevent the texture from becoming too thick. As performers, we thus engage both aurally and physically with this cycle’s duple-meter oscillations in harmony, melodic contour, rubato, dynamic emphasis, hand and wrist position, and pedaling.
The other cycle, which I’ll call the “manual cycle,” arises from the physical actions necessitated by the accompanimental figure. Although the perfect twelfth from the bass Db to the “tenor” Ab lies outside the normal span of one hand, it wouldn’t normally require any unusual exertions on our part to cover the distance between them. However, in order to play beats two through five using the same hand position, we must play both Db and Ab with the fifth finger. Thus we must move the hand quickly to the right as the pedal sustains the bass, shifting the spine and center of gravity slightly to the right as well. Interestingly, even though the damper pedal aurally connects Db and Ab, Db is marked staccato, perhaps reflecting the physical rapidity with which we move the left hand after beat one. Before covering the span, we look at the keyboard in order to see Ab as a place that lies a certain distance from Db, the same distance our little finger will cover. José Luiz Bermúdez (2005, 306) calls such a process object-relative spatial coding, which uses a “frame of reference whose origin is some body part.” Here, we calculate the distance to Ab in terms of the “left hand’s position on Db.” After completing this procedure, beats two through five rely on what Bermúdez calls body-internal spatial coding, which automatically makes spatial calculations within interior body space without conscious reference to quantified distances between points in (Cartesian) space. Body-internal calculations are largely sufficient after beat two because the rest of the figure lies more or less “within the hand” – that is, until just before the next downbeat. The little finger’s position on Ab defines a single “hand space,” shown by the longest brackets in Example 1, whose onset is syncopated against beats one and four of the duple cycle. Without this syncopation, we’d only have one musical cycle. In this sense, Ab forms a tactile frame of reference for the duration of the figure with which the necessary body-internal calculations can occur.
For the most part, the duple cycle involves bodily motions – changes in hand and wrist position, pedaling, etc. – that occur “away” from the head and torso, in places peripheral to the center of our performing body. The manual cycle, on the other hand, occurs within the whole left arm and trunk, places more central to our performing body. From a performer’s perspective, both the duple and manual cycles are necessary for a good performance: the duple cycle rocks the cradle and the manual cycle ensures the smoothest possible legato connection as we play F-to-Gb with only the thumb. Ironically, from a listener’s perspective, a good performer would sublimate the manual cycle into the duple cycle, leaving only the duple cycle aurally available to the listener. That is, if the manual cycle is doing its job, listeners can’t hear it. Figure 1 attempts to model the actions of the duple and manual cycles.
Figure 1. Transformational graph of the Berceuse’s accompanimental ostinato.
We don’t read Figure 1 as we might read a score, but rather, we read it as a transformational graph: the left side of the diagram represents the downbeat of each measure, and the right side represents beat four, not beat six. The horizontal bidirectional arrow between the “Db” node and the oblong “Ab —— T” node (“T” stands for tonic) represents the back-and-forth motion of our left hand between Db and Ab. “OR(11)” pertains to the nature of the action: Ab lies eleven diatonic scale steps away from Db, and “OR” stands for object-relative spatial coding. The oblong “Ab —— T” node in the center of the graph shows the “hand space” created by placing the little finger on the tenor Ab: there are no harmonic changes and no motions of the arm through physical space. “BI(D)” (“D” stands for “dominant”) pertains to the changes that use only body-internal spatial coding during beats two through five. The parallel solid arrows leading rightward from both F and T to Gb and D attempt to reinforce this unidirectionality. The F–Gb motion at the top-right of the graph represents the left thumb motion, which is a part of the overall motion from T to D. The small unidirectional horizontal arrow at the top of the graph represents our left thumb’s motion: from the wide, outer portion of the white F key (open arrowhead) to the black Gb (closed arrowhead), our thumb moves up and in toward the piano (small diagonal arrow). The long curved arrow near the bottom of the graph shows the one-way orientation of the duple cycle: the tonic begins with Db in the bass, and yields to the dominant, not to return. The arrow’s broad curvature represents how the duple cycle comprises motion from one “pole” to the other, thus circumventing much of the manual cycle’s activity in between, shown by the curly bracket at the very bottom.
On the downbeat of ms. 3, the right hand begins the descant shown in Example 2, whose melodic profile is much less consistent than the accompaniment’s cyclic organization.
Example 2. Berceuse, ms. 3-6.
For many different reasons, we generally position the thumb on the wide, outer portion of the white keys, exploiting the thumb’s natural aptitude to fold inward toward and under the palm, what’s known as “adduction.” Here, the thumb comfortably plays F at the end of ms. 3 before the fourth finger crosses over – “vaults” – the thumb to play Eb on the downbeat of ms. 4. Similarly, the thumb tucks under the index finger from Bb to C in the second half of ms. 4. Then, in ms. 5, in order to quickly span the major ninth between Ab and Bb, we must swap the thumb for the ring finger while holding down Db, resulting in ulnar deviation. Similar to what we experienced in the left hand, this swap pulls the rest of the arm in toward the piano, but the overall motion is naturally reversed toward the right pinky. Given the tactile topography of the key of Db major, the hands/arms are prone to shift between a comfortable terrain dappled with thumb-friendly white keys where the thumb can sink further into the keyboard to more easily anchor the hand and a more precarious environment in which the hand is perched on the raised black keys, which resist the thumb’s innate proclivity to drop down below the palm.
The transformational graph in Figure 2 models the actions of the right hand during the opening variation of the Berceuse.
Figure 2. Topographical transformational graph of Db major.
It spans Ab4–Bb5, the same range spanned by the first four measures of melody in the Berceuse shown back in Example 2. If we momentarily ignore the arrows, the nodes in Figure 2 appear to be arranged within an “empty” two-dimensional space, without any “scaffolding” to organize them like the graph in Figure 1. They are arranged proximally in order to represent the keyboard topography of Db major: Ab4, Bb4, Db5, Eb5, Gb5, Ab5 and Bb5 (black keys) are set above C5 and F5 (white keys) representing how the black keys are raised with respect to the white keys. C5 is closer to Db5 than Bb4, and F5 is closer to Gb5 than Eb5, reflecting the location of the two semitones within the Db major diatonic scale. Instead of literally mapping all of the many possible “moves” within this section of the piano keyboard with hundreds of arrows, their proximal arrangement in “empty” two-dimensional space allows us to imagine the possible moves. This kind of topographical profile in two-dimensional space might work for any piece in Db major. The arrows in Figure 2 represent some of the concrete actions of the right-hand melody through ms. 3-6 in the Berceuse: we begin on the white F5, move to the left, in, and up to the black Eb5, then rightward to Ab5, and so forth. Open arrowheads point to white keys; closed, black arrowheads point to black keys.
Example 3 proceeds to a much later passage in the Berceuse.
Example 3. Berceuse, ms. 55-60.
Up until ms. 55, both the duple and manual cycles are fully and continuously operative. But on beat four, the accompanimental figure changes for the first time in the piece: the left thumb no longer moves up and into Gb, the foot briefly stops fluttering the damper pedal, and rather than yielding to dominant, we abide with tonic. At the same time, our right thumb affixes to the outer portion of the Cb key, recalling previous chromatic alterations in the melody. Then in ms. 55–57, Cb becomes a fulcrum on which the right hand crosses over and back between two contrasting sixteenth-note melodic “waves.” With these right-hand melodic waves, the duple cycle’s characteristic slow duple oscillation seems to have transferred from a harmonic domain in the left hand, across the body, and into a melodic domain in the right hand. However, the lack of harmonic change allows the duple cycle to fade into the background. Even so, all of the characteristics of the manual cycle remain intact in the left hand: the registral gap between Db and Ab, both kinds of spatial coding, the hand space set on Ab, etc. The manual cycle, which is more central to the core of our performing body, comes increasingly to the fore.
On the downbeat of ms. 59, Cb moves to Bb, initiating an apparent shift to the subdominant above a stationary 1,ˆ in the bass. It may seem inconsequential, but this event articulates a remarkable watershed, a moment of breakthrough in the Berceuse within and between aural and physical musical spaces. As a subdominant, this move balances the tonic-dominant cradle-rocking oscillation that has characterized the duple cycle thus far by lying “on the other side” of the tonic from the dominant. But Db in the bass complicates the situation. Db pulls the ground out from under the subdominant and – literally – suspends it in second inversion. The subdominant is thus groundless; it just hangs there. Simultaneously, the Gb pentatonic collection permeates the musical texture. Our hands are drawn up onto the black keys, above and away from the craggy topographical profile of Db major, and we encounter a tactile “ether” – an absence – between the black keys.
But the thumb’s physical motion from Cb to Bb is no less noteworthy. When comparing the right thumb’s Cb–Bb motion to the left thumb’s repeated F–Gb motion, we find that they are in fact bilaterally symmetrical to one another about the Ab “axis” and about the sagittal plane of our body. Apparently, the physical elements of the F–Gb motion, a characteristic feature of the duple cycle, have crossed the sagittal plane from the left to the right to become the larger-scale Cb–Bb motion. Interestingly, unlike the Db major diatonic collection, the Gb pentatonic collection, which comprises all of the black keys and none of the white, is itself bilaterally symmetrical about Ab. At this climactic moment, the Gb pentatonic collection and our sagittal plane together provide a bilaterally symmetrical physical space in which F–Gb can “reverse” to Cb–Bb. And in keeping with the Berceuse’s somnolent tone, our move up to the Gb pentatonic collection, which is as topographically groundless as the subdominant to which it gives rise, perhaps resembles the apparent dissociation of consciousness that characterizes falling asleep – the daily point at which our consciousness surrenders and joins the docile state of our tired physical body.
But what does it even mean to say that some musical object “reverses?” Let’s begin with the hands themselves. From each individual “hand perspective,” F4–Gb4 in the left hand, and Cb–Bb in the right hand are exactly the same: the thumb moves from the wide, outer portion of a white key, up and in, away from the hand’s center, to the next black key. According to our hands, there is no reversal here. [4] But our unidirectional, centrally located frame of reference intuitively recognizes this movement as a reversal: the F–Gb motion begins “on the left” and moves “from left to right” toward the center of our perspective; similarly, Cb–Bb begins “on the right” and moves “from right to left” toward the same center. Apparently, the notion of reversal is closely associated with the presence of the central, unidirectional frame of reference from which we always already perform, from which we always already regard the world. Likewise recall that the duple cycle favors aural space and our bodily extremities: it surrounds us the way that sound fills entire rooms, auditoriums, etc. The manual cycle, on the other hand, arises from the very center of the body, including our central frame of reference; it is more closely associated with physical space.
But then we realize the sheer significance of ms. 59: F–Gb reverses to Cb–Bb according to our body-centric reference frame, that is, from the more centralized perspective of the manual cycle – we access the duple cycle through the manual cycle. From our perspective as performers, the duple and manual cycles, each of which represents slightly different aspects of the same performance, thus come together into a single holistic aural and physical musical experience with a greater sense of musical depth than either cycle, or musical space, has on its own. [5] Unlike similar climactic events discussed by more score-based analyses whose object lies up in the dark gray sky, the effect of ms. 59 emanates from and envelops our performing bodies. In the twelve remaining measures after the watershed, the duple and manual cycles never return as two distinct, coincident musical cycles. They fuse, rather, into one musical experience felt with the greater part of our musical selves.
Figure 3 incorporates both Figures 1 and 2 into a transformational network that represents the coming together of aural and physical musical spaces over the course of the Berceuse. Along with some new components, Figure 1 forms the bottom of Figure 3 and Figure 2 forms the top of Figure 3. The contents of the dotted boxes show the actions of our right hand, and everything else shows the actions of our left hand. From ms. 1-54, our hands operate separately, so we read the network from the top (RH, ms. 1-54) and bottom (LH, ms. 1-54) toward the middle. As the accompaniment begins to change in ms. 55, the right hand “swoops in” to place the thumb on Cb4, mirroring the left thumb’s placement on F4.
Figure 3. Transformational network for the Berceuse as a whole.
The light dotted line that runs diagonally from bottom center to upper right shows the axis of symmetry about Ab4, and our sagittal plane. “I” is not an action per se, but denotes a particular contextually defined characteristic of our physical space in performance: the apparent symmetry of the keyboard and our roughly bilaterally symmetrical body (I = me?). From the middle tier of the network (LH, ms. 55-58), the right thumb is in place on Cb4, but the tonic-dominant oscillation of the duple cycle has receded. That is, the left hand continues to fill out tonic harmony but no longer yields to D – in a sense, we’ve “disconnected” from the two “poles” of the duple cycle. As we continue upward to the watershed, the rising orthography of the network comes to represent the action of our hands, which move up and into the keyboard onto the black keys. The right thumb slides to Bb4, and our left hand now moves twelve diatonic scale steps to Bb3 via object-relative spatial coding. “S” appears in the corresponding oblong node, denoting the groundless subdominant, far away from Db2. The long vertical arrow points to its left side for the same reason that the horizontal arrow points to the left side of the oblong “Ab3 —— T” node in Figure 1: it represents the gradual “filling-out” of subdominant harmony. We access the duple cycle through the manual cycle, bringing aural and physical space together into a single musical experience, a fact represented by how the hands come closer to one another in Figure 3.
A transformational network such as Figure 3 is both actual and concerned with abstract possibility. It is actual in that it “proceeds” in one direction following the large-scale trajectory of the piece: our left hand moves up from the bottom, and the tonic-to-dominant cradle-rocking pattern never returns. Conversely, Figure 3 is concerned with abstract possibility in that it denotes possible moves for our left hand throughout the piece, and for our right hand’s variations. Lewin (1993) writes that such a network “shows a certain abstractly structured space of possibilities through which the piece moves, but it also shows how the abstract structuring is suggested and bounded by actual transitions within the progress of the piece itself.” (36) It is provocative to think that our left hand itself is more concerned with possibility and that our right hand is more actual: to model both hands simultaneously is perhaps to treat time malleably. In fact, the “I” operation, which is defined by the symmetrical profile of our body and the piano keyboard, does just this. The left thumb moves from F4 to Gb4 (from T to D) and never “back” to F4, a repeated motion that gets transformed through our body into the right hand’s motion from Cb4 to Bb4, which is chronologically “bound” in that it only moves once from Cb4 to Bb4, and never back. This transformation is reflected by the diagonal configuration of I within Figure 3: the left hand’s more local repeated motion (shown horizontally) transforms into our right hand’s single larger-scale motion (shown vertically).
Notes
- For example Huneker writes that the theme is “set over” the basso ostinato. Visually, this locution is as non-metaphorical as it is metaphorical. Indeed, on the two-dimensional “score plane,” the theme is literally set over – on top of – the accompaniment.
- Great musical performances in the Western tradition are rarely, if ever, sight-read directly from a score; rather, performers spend a great deal of time and effort repeatedly rehearsing the particular physical actions from which certain desired musical effects are expected to arise. We often call it “practice.”
- It’s interesting that Cusick uses the locution “composer-identification” as something the listener has more of than the performer and that this unequal distribution is somehow undesirable. That is, she implies that performance should be less an act of playing music that sounds good, or even fun, but that performance should primarily concern itself with connecting to the personal authority of the composer. Even in an article explicitly questioning such authoritative assumptions, she reveals how deeply engrained they are in our academic language.
- This “hand perspective” apparently shares the perspective of mathematician Hermann Weyl, who sees no intrinsic difference between left and right in nature nor (visual) art, to the extent that they can be considered equal. See Hermann Weyl, Symmetry (Princeton: Princeton University Press, 1952), 16–38.
- A useful analogy might be a 3-D slide viewer, which uses a slide made of two pictures, each taken from a slightly divergent point of view: looking at the double slide apart from the viewing apparatus, we can view either picture with both eyes, but not both images with both eyes at the same time. With the slide in the viewer, each eye focuses on a different picture, and our visual cortex constructs a three-dimensional gestalt from the small differences between the pictures – our experience accrues the third dimension that either picture lacks on their own. When the duple and manual cycles merge in the Berceuse, our newfound sense of musical depth arises from their respective phenomenological disparities.
Select Bibliography
Bermúdez, José Luiz (2005). “The Phenomenology of Bodily Awareness.” Phenomenology and Philosophy of Mind. David Woodruff Smith and Amie L. Thomasson eds. Oxford: Clarendon Press.
Cusick Suzanne (1994). “Feminist Theory, Music Theory, and the Mind/Body Problem.” Perspectives of New Music 32/1, 8–27.
Huneker, James (1900). Chopin: the Man and his Music. New York: Charles Scribner’s Sons.
Klumpenhouwer, Henry (2006). “In Order to Stay Asleep as Observers: The Nature and Origins of Anti Cartesianism in Lewin’s Generalized Musical Intervals and Transformations.” Music Theory Spectrum 28/2, 277–89.
Lewin, David (1987). Generalized Musical Intervals and Transformations. New Haven: Yale University Press.
Lewin, David (1993). Musical Form and Transformations. New Haven: Yale University Press.
Lewin, David (1983). “Transformational Techniques in Atonal and Other Music Theories.” Perspectives of New Music 21/1-2, 312–371.
Rastall, Richard (1982). The Notation of Western Music. New York: St. Martin’s Press.
Rings, Steven (2006). Tonality and Transformation. Ph.D. Dissertation, Yale University.
Weyl, Hermann (1952). Symmetry. Princeton: Princeton University Press.
