Musical Aspects of a Ballet Class

In classes where a pianist is present, teacher and musician work together in a semi-improvisational way to create exercises for a group of ballet dancers or students. Classes to recorded music, or where the music has been prescribed in advance—such as for an examination or assessment—are a different matter altogether, and not my concern here, since in these classes, there is no burden on the teacher to communicate about music. Most teachers outside the vocational training and professional dance sectors use recorded music for classes, but learning to work with musicians usually forms part of the training of ballet teachers regardless of whether they will do so later, so some grounding in the rudiments of music is provided, often by one of the musicians already employed to accompany classes.

In full-time vocational training or at professional level, a class lasts on average an hour and a half, during which a teacher devises a series of about 20 exercises of perhaps 32 or 64 bars in length, that comprise ballet steps and movements appropriate to the skill-level of participants. She may have prepared these in advance and memorized them, or created them during the class. The nearest equivalent in musical practice is the vocal warm-ups given to singers before a choir rehearsal, though ballet exercises are longer and more complex. The teacher first "marks" the exercise, that is, she announces its content and structure to the dancers in an abbreviated form. In a professional-level class, two minutes of real-time exercise might be reduced to just a few seconds of ballet terminology and physical demonstration, with quick hand gestures signifying larger, slower movements, and "counts" indicating what should happen when and for how long. By convention, exercises and their music in ballet classes are almost invariably constructed in multiples of eight-count phrases. An experienced ballet accompanist can pick up from this minimal description what is required musically, especially if they have worked with the same teacher many times.1 With less experienced musicians, it is vital for teachers to be able to describe what kind of music they want in terms of meter and tempo. Specifying length is less critical, since the teacher can always just warn the musician to stop playing when the exercise is about to end.

The Problem with Time Signature: Meter, Subdivision, and Movement

Many ballet teachers get by very well without referring to time signatures by using their voice to convey the rhythm and meter of an exercise, but they cannot avoid the topic altogether. Musicians and other teachers refer to them, and they are used in dance examination syllabi and class outlines, as well as in notation systems such as Labanotation or Benesh Movement Notation. Track listings on specialist albums of music for ballet classes often include a classification by time signature, for example "Battements glissés: 6/8" or "Pirouettes: 3/4." Those who train ballet teachers in formal or informal settings will pass on terminology and conventions from their own training, saying for example that they prefer 3/4 for this kind of movement, or 4/4 for that. Pianists may ask the teacher to describe the kind of music they need, and their first question might be: "What time signature do you want?" Thus in ballet training and education, time signatures exist "in the wild," alienated from their notational context, and picking up new and sometimes misleading or irrational meanings as a result. For example, some teachers will insist on students being able to recognize the "difference between 6/8 and 3/4," even though there are many cases where they are indistinguishable. If nothing else, natural curiosity leads teachers and dancers to want to know why this is called a 3/4, and that is a 6/8, and what the difference is between a 2/4 and a 4/4, and so on.

Such questions prove difficult to answer except in a way that would confuse the student even further. For someone moving, a change of time signature from 2/4 to 4/4 or 12/8, or from 3/4 to 6/8 might make little noticeable difference, since under many conditions, all that has changed is the subdivision of the same underlying beat. Some ballet exercises consist of long, slow movements of legs and arms that take several bars, and from the dancer's perspective, it is only the number of counts that is important. Whether the movement is accompanied by two bars of 4/4, of 12/8, or eight bars of 3/4 is almost irrelevant. Similarly, for someone marching or making movements in a march-like rhythm, if the music changes from a march in 4/4 such as the Radetzky March to one in 12/8 such as Sousa's Liberty Bell, the music may have a different feel (that is, the sense of motion in the music changes), but they are still moving at the same speed, with the same number of steps and the same (binary) number of limbs.2 Dancers commonly move in hypermetrical 3 relationship with the notated time signature (Jordan, 2000), and so if anything, what is difficult for them to grasp is the opposite: the existence of levels of subdivision below a reference beat level. This illuminates London's observation that there is no "essential distinction to be made between meter and so-called hypermeter," because "having several levels of metric structure present above the perceived beat is no more extraordinary than having several levels of subdivision below it" (2012, pp. 17-18).

Indeed, in my experience, it is the difference between duple and triple subdivision, so simple and basic to a musician, that persistently causes confusion in teaching about meter and time signature to dance teachers.4 Even the waltz, or rather especially the waltz, that archetypical example of 3/4, and the dance form that permeates the 19^th-century ballet repertoire and the ballet class, causes problems. This is why: watch people in a room where waltz music is playing, and you probably see them tilt their head or sway from side to side. You will probably do it yourself. Germans call this schunkeln, and have a category of waltz for pieces in 3/4 time that make you want to sway from side to side, the Schunkelwalzer. If you are counting at all, swaying from one side to the other is a binary motion—so where is the 3, or the 4 of the so-called 3/4 time?

I am not saying anything new here. Bengtsson (1987) drew attention to this and other anomalies in movement, hearing and notation in relation to the waltz. Nobody, he says, hears "fourths" in a 3/4, and although it is so readily taken for granted that waltzes are in 3/4, three beats in a bar, we cannot know that "everybody feels (or conceptualizes) waltz rhythm movement in such a way" (p. 73). Notation and dance movement do not correspond directly: one complete movement in the waltz comprises six steps rather than three, and are often grouped together to become twelve. At a fast tempo, dancers and listeners, if they are counting at all, may well (and justifiably) count to four, "perceiving movement-carrying groups of four 'triplets', mostly without knowing anything about triplets at all" (p. 73). Although the time signature 3/4 is regarded as synonymous with the waltz, bars of 3/4 in a waltz occur in hypermetric pairs, or pairs of pairs, (McKee, 2012, p. 94; van der Merwe, 2004, pp. 250-251), and indeed, some 19^th-century waltzes or waltz-like pieces were notated in 6/8.5

Similarly, Zuckerkandl (1956) describes the mistake a "naïve listener" might make while listening to Johann Strauss's Emperor Waltz (see Figure 1). His example demonstrates exactly what often confuses dance teachers:

A naïve listener, asked to count along in time, will almost certainly count 1-2-3-4-1- etc. If he is then told that this is a waltz, and that a waltz is notoriously in three-four time, not in four-four, he will be perplexed to explain his supposed mistake. Strictly speaking, however, he did not count wrong; he merely did not count with the basic beat, as the accompaniment gives it: He counted with the melody. (p. 177)

It is to explain such confusions that I prefer to teach student teachers about meter and hypermeter before introducing time signatures. My hope is that an understanding of meter will help to dispel such the belief, that for example, a 6/8 is necessarily faster than 3/4, or that a 2/4 will always sound different to a 4/4. Just as Zuckerkandl recruited the naïve listener's "mistaken" response in order to expose its eventual rationality when viewed as part of a theory of metrical hierarchy or hypermeter (without using those terms), so I use the same approach to introduce the concept of hypermeter.

I ask students to arrange themselves in rows to represent different metrical levels: one at the back who represents a sub-phrase of four bars, two in front of them represent two-bar units, then four representing bar-level, then three at beat level. A further row can be added at the front for as many eighth notes as the class size will allow, in groups of six. I encourage them to think of themselves as part of a managerial hierarchy, level 1 representing a chief executive, level 2 senior managers and so on. I play a waltz that is familiar to them such as Tchaikovsky's "Waltz of the Flowers" from The Nutcracker, and ask members of each row to make a movement or sound that marks the pulse at each respective level. I usually suggest that students toward the back (higher level) make slow arcs of the arms, and those nearer the front (middle and lower levels) make sways or claps. This enables them to experience immediately several things about meter: that it consists of multiple levels of periodicity; that the same metrical pattern can be thought of in several ways, according to which level you choose as your main beat; that a time signature such as 3/4 or 6/8 represents a hierarchy of beats, which may be triple at one level but duple at another.

The Problem of Metrical Accent

There is still a problem, however. To understand hypermeter, one first has to have a concept of metrical accent, and this model still does not help with that. The metrical grouping 6 is an emergent property of the coincidence of the two pulse levels. Dancers in each line represent single, accentless pulse-events in a stream that are only organized into metrical groups by the slower pulse events represented in the line behind, out of sight and out of mind. It is an interesting framework to place over music, but it does not help novice teachers with their immediate problem, which is to be able to recognize and confidently express duple and triple meter (or subdivision) as salient features of music when teaching. By "confidently express," I mean use the voice to convey a secure and accurate tempo, and indicate meter by with a sense of weight on the first beat and lightness on unaccented beats. Some teachers can do this instinctively, whether they have previous musical training or not. In trying to find ways to teach this to those who cannot, I wondered whether the upright, well-held upper body posture, stretched legs and courteous formality that are characteristic of ballet training might be inimical to the kind of bouncing, bobbing, foot-tapping and swaying that contribute to a felt sense of meter.

This was not just guesswork: there is compelling evidence to suggest that the vestibular system plays an important role in meter perception (Phillips-Silver & Trainor, 2005, 2007, 2008; Trainor, Gao, Lei, Lehtovaara, & Harris, 2009; Trainor, 2007). Movements such as nodding the head, bending the knees or swaying from side to side not only help listeners to entrain to a beat in music, but are also crucial for parsing or construing meter. For example, a listener will hear a stream of accentless pulses as "in two" or "in three" if she sways from side to side every two or three beats. Once the meter has been established this way, she will continue to hear it this way even if she stops swaying, similar to the phenomenon of "subjective rhythmization," or more appropriately, as Large (2008, p. 197) points out, subjective meter, whereby metrical grouping is heard in a stream of unaccented pulses—hearing the ticking of a clock as "tick tock," even though the sound comprises only a series of identical ticks, for example.

Equally compelling was Robert Hatten's theory of musical gesture as energetic shaping through time, in which he states that for Western music at least, "meter functions like a gravitational field that conditions our embodied sense of up versus down" (2004, p. 115). If we perceive motion in music, then that virtual motion (or rather, our perception of an agent in music that moves) is subject to virtual forces such as gravity:

If meter and tonality each afford analogies to gravitation, or more broadly, vectoral space, together they enhance an experience of embodied motion, in that they provide the listener with dynamics and constraints comparable to those the body experiences in a natural environment, including its orientation as up or down. (2004, p. 117)

His work seemed to bring to life—literally, through the suggestion of human motion in the music—classical compositions that I can find cerebral and disembodied at times. In his interpretation, the two-note slur, for example, can been seen as:

[the] musical analogue to such ritualized social gestures as bows, nods, inflections of the wrist and hand, and other aristocratic social graces…the weak-beat galant cadence captures the qualitative character of all gracious social gesturing in the eighteenth century, male and female alike. (2004, p.140)

I found the theory convincing because it resonated immediately with my own embodied experience of music, and identified for me the essence of what I would consider "unmusical" marking, that is, the absence of a connection between metrical accent and weight.

With these two aspects of meter in mind—the role of the vestibular system, and Hatten's theory of meter as a virtual gravitational field—I set out to see if I could use these ideas with students to try to learn to make connections between weight, gesture, meter, and voice. In the next section I describe a class where I tried this out. Although I call this "experimenting," I should emphasize that this was not a formally designed experiment, but an ad hoc strategy in an everyday teaching episode that turned out to raise more questions than it answered.

Meter and the Trained Body

However, while such a contradiction is just a footnote in Hatten's discussion, "conventionalized dance steps" are what my students have specialized in since childhood. Hatten's assertions about meter and gravity seem instinctively correct to me, but they may not seem so to dancers who have spent many years training their bodies to move to music in highly skilled, but not necessarily simple or obvious ways, until they become second nature through continual practice. They have learned to dance the baroque minuet, the polonaise, the waltz, and other dances where downward movements do not necessarily coincide with metrical accents.

Hatten implies that the most obvious way for steps and music to relate is that that downward steps should go with downbeats, but it is not clear how this association should have come about. Why is it the obvious way? Although the construction of the theory of gesture is robust and convincing, we nonetheless have to take for granted as a premise that "the dynamic environment in which we experience our bodies and their gestures has its virtual counterpart in music" (p. 115). This virtual field is just "there" as an entailment of the theory of motion in music, and with it, unexplained, as far as I can see, the idea that it is natural to associate downward motion (or resting) with metrical accents. A similar premise is evident in Steve Larson's theory of rhythmic gravity: "the terms 'downbeat' and 'upbeat' reflect the simplest ways in which dance-like motions associate downward physical motions with musical motions towards metrically stable points….In the domain of meter, 'down' beats are moments of greater metric stability" (Larson, 2012, pp. 148-149).8

Musicians might find it strange to associate downbeats with upward motion, but then their bodies do not always move in natural or obvious ways either. Given that my students and I have both taken part in rigorous, long-term physical training of different types, is there any reason why I should regard my embodied sense of motion in music as any more real, instinctive, spontaneous, or "musical" than theirs?9 The body that I bring to music has undergone years of physical training, learning to sit at a piano and associate downbeats with downward motions of the arms that are no more natural than a dancer's arabesque, insofar as they have to be learned and practiced until they become automatic. If I nod my head or tap my foot to music, can I ever tell conclusively whether this is something that I "naturally" do, or if it as a result of my experience as a musician and the kind of movements that I have made while playing and learning to play?

So while I am convinced that our understanding of music is in some way grounded in bodily experience (indeed, what else could it be grounded in?), I am also persuaded from experience of working with dancers that different bodies, different regimes of physical training, different bodily stances while listening (whether sitting, walking, dancing), even different clothing, can lead to different hearings of the same music (see Maes, Leman, Palmer, & Wanderley, 2014, for a recent summary of research in this field). Larson (2012) allows for such differences in his discussion of how listeners parse pulses into meter: the fact that people group beats in different ways "underscores the point that it is our minds, not just the stimuli, that shape the meaning that is created" (p. 137). He is clear that the "hearing as" of different listeners will vary according to their experience and context. He also warns that although sensations of flow, motion, and forces are not inherent in the music, even though they tend to be experienced as such: they are "created in the mind of the listener, who then attributes them to the music" (p. 137). In a footnote, he says further that whenever he speaks of musical forces, the reader "should understand that I am speaking not of tendencies literally present in the music as stimulus, but of tendencies attributed by the minds of experienced listeners (who experience the music as if it were literally subject to such forces" (Larson, 2012, pp. 337-338).

This is similar, though not entirely equivalent, to the point that Green makes about the difficulty of distinguishing, except theoretically, between two types of musical meaning that she categorizes as either "inherent" (or "inter-sonic") or "delineated" (Green 2005, 2008, pp. 87-91). Inherent or inter-sonic meanings are those that are proper to the conventions of a musical style, and are only construed as meaningful if the listener is competent in that style through enculturation or learning. Delineated meanings are those that are strongly associated with the music, but point to things external to the musical sounds and structures. DeNora draws on this distinction to develop a theory of how music affords and enables action: "Music comes to afford things when it is perceived as incorporating into itself and/or its performance some property of the extra-musical, so as to be perceived as 'doing' the thing to which it points" (DeNora, 2003, p. 57). As an example, a piece of music in 3/4 time can only be heard as "a waltz" by someone who is familiar with that dance form. If they have danced the waltz, they may attribute motional qualities to the music that they feel make them want to waltz, but at least some of these qualities have been inferred by the listener by association with things outside the musical sound.

It is in this problematic space where it is difficult to determine whether we are simply "hearing" or "hearing as," that meter is located. London (2012, p. 18) describes the nature and origin of metrical accent as a "perennial bugbear of music-theoretical accounts of meter." His own theory of meter as a form of entrainment places "the accentual burden on the entrained listener rather than on the music" (p. 18). This is not to say that there are no accents phenomenally present in the music, but that metric patterns do not depend on metric accent (in the sounding music) in order to be perceived as such and continued in the mind of the listener. Iyer (1998) likewise states that the best understanding of meter is "as a cognitive/perceptual phenomenon, not as an objective reality of the acoustic signal. However, this distinction is often elided, so we might speak of the meter of a piece of music." In a particularly remarkable example, Agawu (2006, pp. 23-24) explains how a knowledge of the way that the feet move in Southern Ewe dances can fundamentally alter the way that the "Standard Pattern" of West African rhythm is understood and transcribed, changing what has often been notated and theorized as an additive meter, to a divisive one. Meter is established for dancers and musicians alike by the physical or imagined presence of the dancing body. It "cannot (always) be inferred from the sounding forms alone. One brings a metric attitude—perhaps even a metric prejudice—to the performance" (2006, p. 23). This metric attitude, Agawu continues, is no different to the conventional understandings that an enculturated listener brings to tonal music, in which harmonic changes are heard as tensions and resolutions, for example. What listeners hear "in" the music are not all immanent properties of the works, "some are perspectives formed from certain ways of world-making" (2006, p. 24).

In the kind of basic music theory that is taught to dance teachers, however, meter is often presented as if it were a property of the music, that is, that there is, or should be, a pattern of weak and strong beats objectively observable in the musical signal that will enable the student to calculate and deliver up the correct time signature to the teacher in a test. Musical examples used for such tests have to be metrically unambiguous either by design or performance to make the task possible.10

Alternatives to Meter: Vitality Forms and the Digital and Analogue in Music And Dance

When I originally began this article as a paper for the student day at the SEMPRE conference on Music and Empathy in 2013, I concluded that Daniel Stern's (2010) concept of vitality forms was a much more appropriate starting place to consider relations between music and dance than meter, given the problems I have outlined above. Stern uses the term "dynamic forms of vitality" to describe the supramodal or amodal "how" of an action rather than its content. These vitality forms, which combine ideas of "force, movement, space, directionality and aliveness" as well as time and intensity (2010, p. 17) are crucial, in his view, to affect attunement, one of the processes involved in empathy. For example, a mother might match an infant's excited facial expression with an expression of excitement in another modality such as sound. It differs from imitation, where the content of an action is mirrored or copied, but reflects instead "the mother's attempt to share the infant's subjective experience." By choosing her own modality and content, the mother "assures the baby that she understood, within herself, what it felt like to do what he did" (p. 114). This capacity for attunement in different modalities is what makes vitality forms, in Stern's view, the "Esperanto" (p. 21) that enables communication and collaboration between art forms.

This highlights the affective, gestural aspects of music, dance, and communication that are not captured by meter, counting, or time signature. Without vitality forms, Stern says, human interactions would be "digital rather than analogic" (p. 4), which seems to echo Lefebvre's criticism of a tendency to attribute mechanical overtones to rhythms, ignoring the "organic aspect of rhythmed movements." Musicians, as producers of rhythms, "often reduce them to the counting of beats [des mesures]: 'One-two-three-one-two-three'"(Lefebvre, 2004, p. 6). This describes well the common situation where ballet teachers tell accompanists that they want "a 3/4" or "a 2/4," or mark an exercise with deadpan counts, without communicating anything about the dynamic qualities of the movement, or what it feels like to do it.11 As a result, novice accompanists often fail to understand the intention of the exercise, or the effort involved, and choose inappropriate music as a result. Guest (1983, pp. 8-9) identifies another analog-digital distinction between music and dance: in contrast to music where pitches can "jump" in intervals, all movement is "chromatic," that is, it is impossible for parts of a body to move from one position to another without traversing the space in between, even if fast, jerkily performed movements appear to do so to a spectator.12 What attracted me to Stern's theory was that vitality forms seemed to offer an immediate, intuitive way to see connections and commonalities between music and dance that are obscured, misrepresented, or left out altogether by meter and time signature.

From Vitality Forms to Perspective Taking

On further reflection, however, I realized that these same tensions are already inherent in the opposition between "time-discrete" and "time-continuous" accounts of meter (London, 2012, pp. 19-20, 79-81), and in the disparity between the discrete nature of music notation compared to the continuities of sound and musical gesture referred to by Hatten (2004, p.113) and Spitzer (2004, p. 89). More broadly, they reflect the difference between what Hamilton (2007, p. 119) calls "abstract and humane conceptions of music," such as the Pythagorean concept of music as number as opposed to a "felt conception of music" (see also McClary, 1995). These tensions could thus be acknowledged in the teaching of music, meter, and notation without needing to import the concept of empathy or vitality forms. Moreover, the idea of vitality forms as immediately recognizable, amodal gestalts is at odds with the observations I have already made with regard to metrical accent and gravity in dance forms, where dialogue and listening to the dancers' perspective was necessary in order to understand why their feelings about meter (if indeed they had any at all), might be different to mine.

I now think that as far as meter is concerned, it might be more productive to explore the ways in which dance and music are not like each other, than to start all over again (with vitality affects) by looking at other respects in which they are. The empathic process is still implied here, but it is the otherness of dance and music that is emphasized, which places a greater focus on perspective taking than on affect attunement. Although it is common to believe that music and dance are genetically related as sister arts, or that dance is an interpretative response to music, or that rhythm is common to both art forms, such views can lead a musician to assume that they know more about dance and dancers than they do.13 There are also limits to how much one can talk about dance using the terminology of music without sacrificing conceptual clarity or the particularity of each art form, as McMains and Thomas (2013) have pointed out. I would go a step further than they do, however, and suggest that meter has too many entailments as a musical concept to be applied to dance as a third-party structural device that fits music and dance equally. Does rhythm really offer "a clear point of translation across the mediums" (p. 202) as they maintain?

For example, perhaps the reason that teachers do not always invest their counts with metrical weight is because dancers' counts are not always the conceptual equivalent of beats in a bar. Firstly, they often function more like bar numbers than beats in a bar or a hypermeasure. Like bar numbers, they are the equivalent of addresses or locations on a map, they do not have to function as part of a metrical script (see Guest, 2005, pp. 37-38). Secondly, some teachers count while music is playing as a means of marking pulses, but they could as easily use any words or sounds to do this: the numbers between 1 and 8 do not have any metrical significance in this context, they are simply "counting along." Thirdly, they can occasionally be a way counting up steps rather than counting beats, rather like the numbers in the lyrics of the children's song "One, two, three, four, five, once I caught a fish alive."

Jeanne Bamberger has discussed a similar phenomenon in her research into children's visual representations of rhythm. Analyzing their drawings, she recognized two persistent categories of hearing and counting, one that she calls metric, the other figural (or motivic), related to the concepts of meter and grouping in Lerdahl and Jackendoff (1983). She elaborates on the distinctions between these two kinds of hearing by inventing imaginary students, Met and Mot (standing for "metric-" and "motivic-" oriented hearers) who use counts in different ways. Met sees counts as something that remain the same, units that can be used to measure; Mot uses counts to "count-up," to gather events into a figure, regardless of their temporal relationship. She concludes that counting—at any age—is not simply a "neutral and 'objective' act," but varies according to what a listener considers an object to be counted in the first place (1991, p. 273). This careful nuancing of counting and numbers coincidentally resonates with an observation by Wittgenstein about negation, and the effect of framing questions: if you are asked: "Do you mean the same by both 'ones'?" in the sentence "1 metre is occupied by 1 soldier, and so 2 metres are occupied by 2 soldiers," your answer will be perhaps: "Of course I mean the same: one!" However, if the question is framed as "has '1' a different meaning when it stands for a measure and when it stands for a number?" your answer will be the opposite: that it does have a different meaning (2009, p. 156). "One," it turns out, is not a singular sensation.