Introduction to Fred Lerdahl:
Tonal Space, Text Setting, and Musical Narrative
Schoff Memorial Lecture Series
November 26, 2018
As he mentioned in last week’s Schoff lecture, Fred’s magnum opus, the Generative Theory of Tonal Music (or GTTM) had its roots in Bernstein’s Harvard Norton Lectures of 1973 later published as The Unanswered Question. Bernstein was a celebrity, perhaps the last which classical music was able to produce, so these were major cultural and intellectual events. I attended along with Fred and his eventual collaborator on GTTM Ray Jackendoff and probably several thousand others.
I was 14 at the time and while I didn’t know Fred, I did know Ray who, as an MIT graduate student in my father’s department, assumed the status of something like a cousin, as many did, routinely joining us for meals and celebrating holidays with us. An accomplished clarinetist and active freelancer in and around Boston, Ray’s performances of Stravinsky Three Pieces for solo clarinet were revelatory for me as was his post-performance discussion of the perceptual ambiguities resulting from the shifting meters and how performers can choose to resolve these-or not.
Given that some of my initial exposure to sophisticated ideas about music came from a linguist, it makes sense that my initial understanding of linguistics would be channeled by Bernstein through music. Bernstein’s command of the field was significantly impoverished, as many, including Ray and my father, noted at the time. But it did at least invoke some of the core vocabulary and, most importantly, managed to communicate something which is to this day not well understood: that long standing mysteries about the nature of language were finally being addressed or at least coherently formulated in the hallways of MIT building 20.
With that in mind, and in the spirit of MIT linguistics, I’d like to take minor issue with something which Fred said last week about Bernstein’s attempts to formulate musical analogs to linguistic concepts such as parts of speech, transformation, morphemes and phonemes. Fred characterized these as uninteresting. I would say rather that they were the opposite. That is, they were hugely interesting in the sense that they provoked numerous questions which sent many smart and/or artistically sensitive and/or musically informed people scurrying for answers.
And I’ll go even further in praising Bernstein by suggesting that they weren’t wrong-though praise here needs to be accompanied by the cold water provided by the remark of physicist Wolfgang Pauli: sometimes ideas which aren’t wrong are “not *even* wrong”. That is they are not sufficiently well formulated as concepts to determine whether they are true or false. Yes, they might provoke much heat within what is now known as “discourse” extending from barrooms to graduate seminars, but they ultimately provide little light in the form of knowledge of the world and our nature as one species which inhabits it and of our ability to make sense of our relation to it, including the sense we make of language or music.
It is the great virtue of Fred and Ray’s project that it can be described as right, but that it can–and indeed must–also be described as wrong. And that is because it makes specific, testable predictions about how we hear music: a grouping boundary is or is not correctly located by their system of preference rules. Grouping interacts with-but is crucially independent of-the metrical hierarchy characterized by the metrical grid assigned by the system of metrical preference rules. The perception of tonal stability, consonance and dissonance and musical tension and relaxation is represented by time span reduction and prolongational trees, later reformulated within Fred’s Tonal Pitch space.
Not all of these have been confirmed within the many hundreds if not thousands of papers devoted to one or another aspect of the generative theory by this point. Not should that have been the expectation. The scientific method dictates that some hypotheses will be confirmed, others refuted. What the vast literature devoted to it attests to is GTTM having established a normal relationship between abstract theory and concrete experimental verification of a sort which, if not a holy grail, can and should serve as a model for cognitive science moving forward. And while I could voice certain reservations (an imbalance between the theoretical and empirical direction of research) an academic monolith of this order will not be significantly burnished or tarnished by anything that I or anyone else will have to say about it on one, two or many occasions.
What I’ll turn to in conclusion is a subject often unrecognized by those who have the most familiarity with Fred’s work. The iconic status of GTTM notwithstanding, Fred’s theoretical work was not intended as an end in itself. Rather it was in pursuit no of a scientific but an aesthetic objective which found its most profound expression in Fred’s music as well as that of the best of his contemporaries. This was a generation, as those who experience it will easily recall, defined by their awareness of a “crisis in contemporary music,” the widespread view not only in music but in broader intellectual circles that “contemporary music had lost its way”.
The latter phrase is from Fred’s Cognitive Constraints on Compositional Systems, a classic essay which served as a manifesto and has been cited as such in the definitive history of the period, the sixth volume of Taruskin’s Oxford History which devote a substantial section to Fred’s work both as a theorist and composer. Now some decades in the past, Cognitive Constraints’ fundamental critique of high modernist compositional practice is no longer fashionable. But its broader recognition of the necessity of a connection between how listeners hear (as characterized in GTTM) and how composers compose, is now part of common practice or common sense, assumed by composers who often have little idea of who Fred is or of the foundation on which their assumptions rest.
Fred’s careful formulation of certain necessary requirements pertaining to the basic materials from which music is constructed leads to an “aesthetic claim” that “the best music utilizes the full potential of our cognitive resources” and it is here that Fred’s program might be seen as in conflict with certain tendencies in the academy which have questioned the contents of these sorts of strictures. Given our current understanding of the vast range of our capacity for music, now easily accessed through the internet, many are dubious as to whether the notion of constraints, cognitive or otherwise, is worth discussing at all. But it is a misreading to view Fred’s cognitive perspective as in any way culturally chauvinist or even particularist. Fred identifies a range of musical traditions which can and do produce music which issue the kinds of challenges to the listener which Fred regards as fundamental to the musical experience.
Much like the linguists who find in what were previously denigrated as primitive languages syntactic structures of baffling complexity, so too has musical syntax wherever it occurs been shown to reflect the complexity of innate human capacities. This only becomes apparent when music is viewed not as objective form, as music theory has traditionally construed it, but as a Chomskyan “natural object” embodied in the structure, or, as Fred would insist, the structures, we assign it if not in exactly the way which GTTM requires, than in ways closely analogous to them
There are surely some things wrong in certain details of this picture. But productively wrong in the sense which Pauli evoked, in that the kinds of questions which we can now ask have led us to a far better understanding not only of how pieces of music work but how our brains and minds work than we had before.
I can count myself among many of Fred’s former students, colleagues and friends who regard myself as deeply privileged for having had the opportunity which Fred provided to have made a good part of my life around engaging the questions he posed and the answers he provided.