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Musicology as an Object for HPS? An Exploration
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Dean Rickles

Whither Philosophy of Musicology?

A large part of philosophy involves work falling within ‘Philosophy of X’ studies (where X = some specific field or subject matter: physics, mind, art, and so on). Though philosophy of music is one such area that receives considerable attention, musicology (not music, but rather the study thereof) has yet to be given the full ‘Philosophy of X’ treatment (at least not in any systematic way). Of course, within philosophy of music, philosophers often discuss elements that involve musicology in some way, but musicology itself is rarely the direct object of investigation and there tends to be a curious disconnect between discussions of philosophy of music and musicology. It has long been a lingering ambition of mine to establish ‘philosophy of musicology’ within the philosophy of science, in much the same vein as physics, biology, economics, and other sciences (in this case, it would be, uniquely so far as I can see, the philosophy of science of a study of an art).

In this brief note I present a snapshot of the form this might take by pointing to some potential issues and themes, borrowing from standard research avenues in history and philosophy of science (HPS). The main lesson will be that there is a fundamental problem of musicology that has a strong philosophy of science flavor and that unifies many apparently distinct issues: there is a question mark over whether musicology is/should be an analysis of ‘given’ subjective experience of a musical work, or an analysis of the objective sonic structure of the work (or some other such non-subjective aspect). I would argue that examining this problem has the potential to add some clarity and focus to many old debates in philosophy of music (some of which will be touched upon below). (This note is based on a talk that covered a far greater range of issues. Here, I select a small subset.)

Very roughly, I take musicology to be the analysis of musical structure--what it is and how it works (i.e., how it generates its effects)--both particular and general: that is, for specific musical works and families of works or all musical works. My own attention was drawn to the possibility of studying musicology from an HPS-oriented perspective after reading Milton Babbitt’s work. Babbitt himself explicitly linked his ideas to those coming from HPS, in particular the logical positivism of the Vienna Circle (see McCreless 1997 for a discussion). A particular remark triggered my interest: “[E]very musical composition justifiably may be regarded as an experiment, the embodiment of hypotheses as to certain specific conditions of musical coherence” (1962: 49). Babbitt’s central concern was the way electronic music lifted the limits of music from instrumental capabilities to the “perceptual and conceptual capacities of the human auditor”--though while electronic music opens up infinite acoustic possibilities, he argued that “realistic musical needs .. are satisfied by a discrete, finite collection of values” (1964: 92).

Babbitt also draws attention, albeit in an indirect way, to what I called “the fundamental problem.” In a famous passage, castigated for its elitism, he writes:

Why should the layman be other than bored and puzzled by what he is unable to understand, music or anything else? It is only the translation of this boredom and puzzlement into resentment and denunciation that seems to me indefensible. After all, the public does have its own music, its ubiquitous music: music to eat by, to read by, to dance by, and to be impressed by. Why refuse to recognize the possibility that contemporary music has reached a stage long since attained by other forms of activity? The time has passed when the normally well-educated man without special preparation could understand the most advanced work in, for example, mathematics, philosophy, and physics. Advanced music, to the extent that it reflects the knowledge and originality of the informed composer, scarcely can be expected to appear more intelligible than these arts and sciences to the person whose musical education usually has been even less extensive than his background in other fields. (1958: 39)
What interests me here are the reasons behind this disparity of treatment. I would argue that the situation is analogous to the study of time: there too, the layman is happy to engage in discussions about the flow of time, the end of time, and any number of issues that strictly speaking demand some technical expertise (in the psychology and neuroscience of time or the physics and philosophy of time). In both cases, time and music, there seems to be a sense of immediacy or directness in our access that is absent in the perusal of a mathematical proof. One has the sense that no skill or training is needed to hear music or experience time, and that the scientific study of both builds on some basic phenomena shared by all (perhaps even shared by some non-human animals). With respect to time, Poincaré wrote that “psychologic time is given to us and must needs create scientific and physical time” (1913: 27). Yet, in both cases, time and music, there is an apparently external, objective component too. We have a split, and there is a question mark over what we intend by time and music in both cases too: inner sense or outer structure?

This idea, of some brute non-conceptual content that forms the raw materials of musicology, is explicit in many musicological studies. Rameau, for example, claimed to have based his own harmonic research (setting the standard for well over a century) on the idea of the ‘blank slate’: forgetting all that one knows about music and rebuilding from untainted elements of consciousness--he claimed to have employed Descartes’ skeptical method to reach this state (see Christensen 2004). Schoenberg too, most likely borrowing from early positivist ideas, expressed a similar belief in basic phenomena: “again and again, to begin at the beginning; again and again to examine anew for ourselves and attempt to organize anew for ourselves. Regarding nothing as given but the phenomena” (1911/1983: 8).

Here we see the origins of a tension between the subjective experience of music and the objective structure as the ‘proper object’ of musicology. Ultimately, an integration of the two is most likely required, since the ‘objective’ (external) structure, while not quite dependent on observers in a deep sense, will bear many of its properties (e.g., the range of pitches and durations used) as a result of aspects of the construction of observers and the limits of their experience.

Let us now focus on some specific applications that an HPS might have within musicology. We see this fundamental problem arise again and again in these applications. Rather than pursuing these in detail, I simply point towards some potential research topics, and discuss some of the interpretive options.

Musical Paradigms?

With respect to the “H” part of HPS, we can include the study of musical paradigms (in terms of both musical style and performance style), the issue of authenticity, and ‘historical performance.’ On the subject of musical paradigms, there has in fact been some work carried out already, by Ed Slowik (2007), though using an analogy between musical style and Kuhn’s notion of a paradigm primarily as a means of making sense of the latter rather than the former. However, the analogy can be used in the other direction. Slowik’s example of sonata form is indeed amenable to a paradigm interpretation. As he notes, eighteenth-century sonata form gave composers a “solid framework in which to construct and arrange their musical ideas” (providing the pattern: introduction; exposition; development; recapitulation; coda). Sonata form accounted for a huge proportion of classical composition and given the constraints it imposes, “a musical paradigm thereby largely determines and controls the musical thoughts and experiences of the composer” (p. 10).

The analogy is not perfect, however: what counts as “competition,” “crisis” or “anomaly?” Otavio Bueno suggested to me that the lack of novel phenomena might itself function as a generator of crisis, demanding new forms of composition or variations to the existing sonata form. This lack of development (in the case of Western pop music) has in fact been modeled recently, using statistical techniques (Serra et al., 2012), where the authors use the terminology of “blockage” to describe the dearth of new musical ideas. What they show, more precisely, is that frequency distributions for pitch, timbre, and loudness fit a relatively stationary pattern--especially so for pitch, which obeys a power law distribution (with simple pitch sequences possessing significantly larger probability mass in the distribution). One can, given this, make fairly good (successful) predictions about the likelihood of hearing some chord given an initial chord (within Western music). Moreover, there is a strong tendency to prefer simpler chords and keys (C major, and its relative minor A minor, with no sharps or flats) are far more prevalent.

Repertoire selection paradigms (governing allowable program choices) also submit to quantitative, statistical analysis. So far as I know, the first attempt was conducted by statistician John Mueller (1951), using paybills, programs, diaries, and reviews as data. What he showed was that the repertoire was dominated by a handful of composers leading to a skewed performance distribution he labelled a “popularity pyramid.” This has some resemblance to Robert Merton’s notion of the Matthew effect, whereby cumulative advantage accrues to those that have some initial edge. There have been similar studies in HPS (e.g. Bettencourt et al., 2006) whereby epidemiological techniques have been applied to model the spread of ideas (including theories and theoretical tools, such as Feynman diagrams). Zanette (2006) has studied Zipf’s law (governing word usage frequency) in the context of note usage frequency in music, showing how the law can be related to the creation of musical context (that is, a background within which musical coherence and incoherence can be established). One can envisage a very useful cross-fertilisation of ideas here whereby just as musical styles and revolutions can be statistically modelled and detected, so can scientific revolutions. I might also add that such automated classification of styles, performance, and genre can be interpreted as pointing to underlying regularities, whether ultimately conventional or not.

Authenticity or Incommensurability?

What of the thorny topic of ‘historical performance’? The issue is easily expressed: Suppose we could give a perfect sonic replication of Bach’s music as played in his own period: would we hear it as they did? One influential school of musicology argues that we do an injustice to the music if we fail to recreate it as closely as possible to how it would have originally sounded. Roger Scruton argues that the idea of historical performance “cocoon[s] the past in a wad of phoney scholarship, to elevate musicology over music, and to confine Bach and his contemporaries to an acoustic time-warp” (1997, 448). I tend to agree with Scruton. Lawson and Stowell in their study The Historical Performance of Music (1999) object offering the reconstruction of “dead languages” as an “effective” counterexample to Scruton’s claim, yet they admit, that we can’t tell “what they really sounded like” (158). This surely defeats their argument since the ‘phenomenological’ aspect is exactly at the root of this issue! It’s no counterexample at all.

Here one can also introduce the Kuhnian notion of incommensurability, for doesn’t the ability to reproduce “as Bach’s contemporaries would have heard” involve the idea that listening is simple, unfettered by concepts (as described above)? Certainly, Malcom Budd (1985) has argued that one can understand the core experience of music as given in this way, as has DeBellis (2008) more recently (though with subtle differences), arguing that musical understanding is constructed from ‘phenomenological feel’. But as Goodman and Elgin point out:
A particular auditory event might be heard as a noise, as a piercing noise, as the sound of a trumpet, as a B flat, as the first note of a fanfare, or in any of indefinitely many other ways. To characterise what is heard as the sound of a trumpet or as the first note of a fanfare requires a good deal of background knowledge. But every characterisation relies on background knowledge of one sort or another. Even to recognise something as a sound requires knowing how to differentiate sounds from other sources of sensory stimulation, and how to segment auditory input into separate events. Sensation is sometimes supposed to be primarily given. Doesn’t a sound present a certain quality or set of qualities even to a person ignorant of its source or musical context? The trouble with saying this is that neither a sensation nor anything else comes already labelled. (1988: 9-10)
If we accept this analysis, as I think we should, then at best our experiments with historical performance can indicate what it would be like if we transplanted ourselves (replete with all of our modern concepts) into some other period.

This way of looking at authenticity and historical performance can be related back to the fundamental problem alluded to earlier, since if the object of music is the subjective experience of a listener, then recreating the sonic structure alone (however accurate) will never be enough to achieve parity between a period listener and a present day listener. If the sonic structure is our focus, however, then playing in the right style, on the right instruments, would bring us towards parity. Even here, however, without recordings, I fail to see how historical performers could claim to match older ways of actually performing--one only has to look at the variations in rubato and portamento in early recordings to see that a written description such as “played with heavy portamento” could pick out many violinists that sound utterly distinct. Hence, simply playing on period instruments, with some basic qualiative descriptions about how they were played, will not pin down how the instruments were played. In fact, the example of dead languages from above applies very well here: one can use such languages, but working out how they were actually spoken will always be guesswork.

Observer Selection in Musicology?

With respect to the concept of tonality, Brian Hyer notes that there is a “recurrent tension” in music theory over “whether the term [tonality] refers to the objective properties of the music--its fixed internal structure--or the cognitive experience of listeners, whether tonality is inherent in the music or constitutes what one author [R. Norton] describes as ‘a form of consciousness’” (2002: 727). This is, of course, just a restricted version of our fundamental problem.

It is clear that there will be some kind of ‘observer selection’ process involved in basic musicological concepts such as tonality, since music lies within a limited pitch range as a consequence of the frequency sensitivity of the human auditory system, having nothing to do specifically with music--aliens with entirely different auditory capabilities might well have very different music that we would be incapable of experiencing! That is, at least part of the way (our) music is has to do with the way we are put together. One can probe deeper in the case of tonality, in fact, and bring in empirical studies. For example, there is something distinctly structural about tonal music. As Carol Krumhansl notes, “tones acquire meaning through their relationships to other tones” (1979, p. 370). In other words, musical context affects the perception and representation of pitch. Tonic tones are perceived as “closest,” then diatonic, then non-tonic (this generates a tonal hierarchy). It is precisely the interplay of tonal stability and instability that generates musical tension (produced by motions away from the tonal center) and release (produced by motion back to tonal center).

There are, of course, a variety of elements, beyond tonality, that go into music, forming the structure of a musical work (though it is possible to carve this structure in different ways, depending on the method of analysis). This includes pitch, meter, and loundness as important elements. Pitch is simply the brain’s representation of the periodicity (frequency) of sound waves. It is not frequency itself, but is linked to perception, thus demanding a subject: frequency does not. Relative pitch is central to music perception: we can change absolute pitch leaving relative pitches invariant and ‘preserve the musical structure.’ In fact, relative pitch recognition appears to be rather a basic feature of the human mind: infants can recognize transposed melodies as the same melody. But general melodic contour information is easier to assess than interval information. For example, untrained listeners can barely distinguish a major from a minor third (octaves are the exception here, which untrained listeners, and infants, can easily recognize). Notes possess basic frequencies (cycles per second), e.g., A = 440hz. It is the ratio between frequencies that is essential: one experiences ‘consonance’ when the frequency ratio is a ratio of small integers, e.g. 1:1 = unison; 2:1 = octave (440 Hz: 880 Hz); 3:1 = perfect fifth. Consonance has an obvious psychological element: it is pleasing to us. The octave is the foundation for musical scales: it is divided in such a way precisely so as to preserve consonance! Hence, we see clearly how aspects of human cognitive architecture filter in to the nature of music and musicology--this is what I meant by my phrase “observer selection” above.

Meter is also part of the structural representation of a piece. However, it too is grounded in aspects of human cognitive architecture. It is a form of entrainment: i.e., a synchronization of internal biological features with external aspects of environment. This is what causes bodily movements to become coordinated with music in dance and foot tapping. However: crucially, there’s a small threshold of time-scales within which temporal groupings will trigger our rhythmic responses (and this responsiveness is distinctly human, it seems--cf. Tecumseh Fitch, 2011). Mari Riess Jones (1989) argues that people utilize invariant structure abstracted from the “temporal rhythmicities” of some event to attentionally prepare for ‘when’ forthcoming events will happen (= “expectancies”). Meter relates, then, to an “attentional stance” an observer has towards sounds, such that a pattern or grouping is imposed by the observer: one and the same set of sounds could be carved up like this in multiple ways--London (2012) gives a detailed analysis and defense of the idea that meter functions in this way. It is, again, an act of observer selection.

In fact, the observer selectivity involved in tonality has an identified neural basis, revealed by localized activation patterns in the cortex mapping to relationships among tonal keys. Janata et al. claim to have found evidence, in fMRI experiments, of “an area in rostromedial prefrontal cortex that tracks activation in tonal space” mapping on the “formal geometric structure that determines distance relationships within a harmonic or tonal space” in the context of Western tonal music. They found that “[d]ifferent voxels [3D pixels] in this area exhibited selectivity for different keys” (2002, p. 2167). There is a psychological analogue of the “formal geometric structure” highlighted by Janata et al. too that can be seen in a paper of Mary Riess Jones, on the selectivity involved in music, where she argues that that “world patterns [musical patterns] are subjectively represented as nested relations within a multidimensional space defined by pitch, loudness, and time” (1976, p. 523). (See Raffman, 2011, pp. 595-6 for more on the neural basis of tonality.)

This notion of a “tonal space” forms the basis of an influential approach to musical analysis due to David Lewin (1987), which models and analyses musical structure using the idea that intervals are tantamount to transformations on such a space (i.e., functions that take some point in the space and spit out another). Dmitri Tymoczko (2011) has recently built this basic idea up into a detailed geometrical framework. He aims to chart the ‘shape’ of musical spaces and does so using fairly advanced topological notions producing a kind of translation manual between musicological ideas and (highly non-trivial) abstract spaces. Firstly, rather than thinking in terms of pitch space (simply a space whose points are different pitches, ordered in the traditional linear way, such that a musical work traces a path through it), Tymoczko, following standard practice, identifies the same pitches (e.g., middle C, C above, C below, and all other Cs), producing “pitch-class” spaces. This is rooted in simple octave-equivalence which generates a cyclic pattern. Tymoczko notes that now the corresponding space is an example of an “orbifold” (an orbit manifold, where the manifold has been “quotiented” by octave equivalence, thus identifying certain points). Tymoczko generalizes this to all intervals. For example, one could go from middle C to E flat by going up or down (and then jump any number of octaves up or down) to get the same interval. Hence, these motions are identified. What this means is that Lewin’s intervals are here transformed into equivalence classes of motions (orbits). Again one can apply this to chords of any type: the same chord will simply be playable in many different ways, and these are to be identified. There are five musical transformations for quotienting out redundant structure, according to Tymoczko, which generate various equivalence classes of musical entity (e.g., chords, chord types, chord progressions, pitch class, …).

Into this basic formal framework, Tymoczko introduces five “principles” that refer back to subjective (and neural) elements, such as preference for consonance, and also efficiency in progressions. He claims these function as constraints, and when one adds such constraints on the organization of musical structure one can understand how musical structure works in the sense of how it sounds pleasing. One can represent pieces of great classical music in Tymoczko’s space, and can test whether the constraints are satisfied. Indeed, in many cases they are. However, while this sounds like a miracle, it is, in fact, highly unsatisfactory as any kind of explanation of musical structure since the constraints are simply the results of empirical studies (such as those mentioned above) that have been plugged in by hand: they are not emergent features of the mathematical framework. It is not really so surprising, then, that one will have a model of ‘pleasing music.’ However, this way of envisioning musical structure does provide a very neat way of making sense of Babbitt’s claim that “every musical composition … may be regarded as an experiment, the embodiment of hypotheses as to certain specific conditions of musical coherence.” Musical compositions can have their tonal structures modelled in such spaces, and if we accept Tymoczko’s constraints (given that they do have some reasonable psychological and neural foundation), then we can judge the success or failure of compositions relative to them. That is, we have a space of musical possibilities and a means of testing which will ‘work.’ Indeed, Tymoczko refers to his constraints as “quasi-laws of musical coherence.” Of course, there will remain a large question mark over the legitimacy and universality of the constraints. But it remains testable territory.

The broad cognitive patterns mentioned above can also be found in another influential, Schenkerian, approach to music, that of Lehrdahl and Jackendoff (1983). Roughly, Schenkerian theory seeks to find the universal patterns in which music is composed; hence, it is natural to look for the roots of universality in shared cognitive features. Lehrdahl and Jackendoff do just this, abstracting out a set of rules for well-formed formulae [WFF] for musical structure. These appear to implement (some of) the observer selection effects, putting them center-stage. For example, they identify the following elements of musical structure:
Grouping Structure: the brain’s method of grouping together musical events that sound like they belong together, into a linear streamMetrical Structure: beat structure, to which musical events are relatedTime-span reduction: selection of important musical eventsProlongational Reduction: [Schenkerian Principle]
They also supply various “Preference Rules” for each WFF rule, based on the “relatively unchanging cognitive foundations of the musical mind”. The question of just how universal these cognitive foundations are is still a matter for experiment (though a relatively straightforward one to design). If they are found to be universal features, then we would appear to have, in sense, laws of music--an idea that clearly would be in need of close scrutiny from philosophers of science.

So what belongs in musicology? What should a musical theory be about? Should we do as in physics and try to eliminate these human-side components and perform what Eddington calls “an epistemological purge” ridding theory of all subjectivity? What would be left behind here if we did this? Really, it is difficult to see how such a purge could ever be possible in the case of music, so integral is the composition of human cognitive architecture to the kinds of musical structure we are faced with. The observer will always be present, then, in some sense, since the ranges of possible structures are constrained by our ability to process them (they must be audible and playable). Instruments too can clearly constrain the regions of musical space that we can sample (and are themselves related again to human auditory processing capabilities, and other physiological aspects in this case)--though we can easily imagine advances in technology that would enable us to both generate and detect a greater range of the spectrum, sampling more regions.

I think what this brief survey shows is that musicology really demands a deeply interdisciplinary approach. It is therefore perfectly understandable to find the music theorist David Lewin writing that “[a]ctually, I am not really sure what a ‘theory of music’ might be” (1986: 377), for a theory of music might well be a theory of many things! Of course, one need not cover all aspects for all kinds of purpose. I don’t expect musicologists to become neuroscientists. My point is, at the deepest level, if we want to understand why musical structure is the way it is--e.g., rather than simply accepting the structure as basic and performing standard analyses of it--then, it requires an integrated approach. However, the kind of integrated analysis that results (involving observer selection effects) makes this an ideal case study for philosophers of science.


References

Babbitt, M. (1958), “Who Cares if You Listen?” High Fidelity 8: 38-40 and 126-7.
Babbitt, M. (1962), “Twelve Tone Rhythmic Structure and the Electronic Medium.” Perspectives in New Music 1: 49-79.
Babbitt, M. (1964), “The Synthesis, Perception, and Specification of Musical Time.” Journal of International Folk Music Council 16: 92-95.
Beltran del Rio, M., Cocho, G. and Naumis, G. (2008), “Universality in the Tail of Musical Note Rank Distribution.” Physica A 387: 5552-5560.
Bettencourt, L., A. Cintron-Arias, D. Kaiser, and C. Castillo-Chavez (2006), “The Power of a Good Idea: Quantitative Modeled of the Spread of Ideas from Epidemiological Models.” Physica A 364: 512-536.
Budd, M. (1985), Music and the Emotions: The Philosophical Theories. Routledge and Kegan Paul.
Christensen, T. (2004), Rameau and Musical Thought in the Enlightenment. Cambridge University Press.
DeBellis, M. (2008), Music and Conceptualization. Cambridge University Press.
Goodman, N. and C. Elgin (1988), Reconceptions in Philosophy and Other Arts and Sciences. Hackett. Publishing Company.
Janata, P. et al. (2002), “The Cortical Topography of Tonal Structures Underlying Western Music.” Nature 298: 2161-2170.
Krumhansl, C. L. (1979), “The Psychological Representation of Musical Pitch in a Tonal Context.” Cognitive Psychology 11: 346-374.
Lawson, C. and R. Stowell (1999), The Historical Performance of Music. Cambridge University Press.
Lehrdahl, F. and R. Jackendoff (1983), A Generative Theory of Tonal Music. MIT Press.
Lewin, D. (1986), “Music Theory, Phenomenology, and Modes of Perception.” Music Perception 3: 327-392.
Lewin, D. (1987), Generalized Musical Intervals and Transformations. New Haven: Yale University Press.
London, J. (2012), Hearing in Time. Oxford University Press.
Patrick McCreless (1997), “Rethinking Contemporary Music Theory.” In A. Kassabian and D. Schwarz (eds.), Keeping Score: Music, Disciplinarity, Culture (pp. 13-53). Charlottesville, VA: University of Virginia Press.
Mueller, J. (1951), The American Symphony Orchestra: A Social History of Musical Taste. Greenwood Publications Group.
Poincare, H. (1913), The Value of Science. Cosimo Classics, New York.
Jones, M. R. (1976), “Time, Our Lost Dimension: Toward a New Theory of Perception, Attention, and Memory.” Psychological Review 83: 323-355.
Jones, M. R. (1989), “Dynamic Attending and Responses to Time.” Psychological Review 96: 459-491.
Raffman, D. (2011), “Music, Philosophy, and Cognitive Science.” In T. Gracyk and A. Kania and (eds.), The Routledge Companion to Philosophy of Music (p. 592-602). Routledge.
Schoenberg, A. (1911/1983), Theory of Harmony (Translated by R. Carter). University of California Press.
Scruton, R. (1997), The Aesthetics of Music. Oxford University Press.
Serra, J., A. Corral, M. Boguna, M. Haro, and J. L. Arcos (2012), “Measuring the Evolution of Contemporary Western Popular Music.” Scientific Reports 2: 1-5.
Slowik, E. (2007), “The Structure of Musical Revolutions.” Philosophy Now 59: 9-11.
Tecumseh Fitch, W. (2011), “The Biology and Evolution of Rhythm: Unravelling a Paradox.” In P. Rebuschat et al. (eds.), Language and Music as Cognitive Systems (pp. 73-95). Oxford University Press.
Tymoczko, D. (2011), The Geometry of Music. Oxford University Press.
Zanette, D. H. (2006), “Zipf’s Law and the Creation of Musical Context.” Musicae Scientiae 10: 3-18.

2013 © Dean Rickles

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