Sticking it to Milton Babbitt?

In 1958 the popular magazine High Fidelity published an article by the highly intellectual composer Milton Babbitt. Babbitt had entitled the article "The Composer as Specialist;" and it addressed the mindset gulf between many composers following in the footsteps of Arnold Schoenberg and most audiences. (Schoenberg himself had addressed this topic.) Without Babbitt's knowledge or consent, High Fidelity changed the title to "Who Cares if You Listen?;" and Babbitt has been living with the consequences of that decision ever since. However, even if he found the title "offensively vulgar," there remains that connotation of detachment in his "specialist" stance.

I have no idea if Lou Reed and Laurie Anderson intentionally decided to exploit this stance and twit Babbitt at the same time, but they definitely found an amusing and clever way to do so. Here is the BBC News account of their project:

US rock star Lou Reed and his artist wife Laurie Anderson are to stage a "high-frequency concert" for canines in Australia.

Music for Dogs, to be held outside the Sydney Opera House, is billed as "an inter-species social gathering on a scale never seen before in Australia".

The bizarre recital in June will be largely inaudible to the human ear.

The couple said they have experience making music for at least one dog - their rat terrier, Lollabelle.

"She likes things with a lot of smoothness but with beats in them,'' Ms Anderson told the Sydney Morning Herald.

She said the inspiration for the performance at the Vivid Live festival in Sydney came while she was backstage at an event and thought: "Wouldn't it be great, if you were playing a concert and you look out and you see all dogs?"

The show, created by Ms Anderson, will last for 20 minutes as she says "dogs don't have a giant concentration span".

The sounds will be played at high frequency like a dog whistle, setting dogs' ears twitching but barely audible to their owners.

It is billed in the festival programme as "an absolute must for any dog and their two-legged friends".

The link to Babbitt is delightfully obvious: Now we have "Who cares if you can't listen?" However, even if Babbitt was not the intended target, this is clearly aimed at those who tend to get excessively serious about concert attendance, particularly in an opera house. It takes a certain level of chutzpah to break with such a strongly-held social tradition; and I would say that the level is high enough for Reed and Anderson to share the Chutzpah of the Week award!

“No One is Afraid of Uncle Miltie Any More”

Milton Babbitt was a thorn in my side for the better part of the eight years I spent at the Massachusetts Institute of Technology (MIT), four as an undergraduate major in Mathematics and four leading to my doctoral degree in Applied Mathematics. The sharp tip of that point was an essay he had written entitled “Twelve-Tone Invariants as Compositional Determinants,” first published in The Musical Quarterly in 1962 and subsequently included in the book Problems of Modern Music: The Princeton Seminar in Advanced Musical Studies, edited by Paul Henry Lang. (One day when I was not looking, one of my fellow students pencilled in the title page under the words “Problems of Modern Music” the phrase, “Mainly, it doesn’t sound good.” Such was life during my student days.)

I suppose it would be fair to say that Babbitt wrote his article to make the case that group theory (a discipline of abstract algebra) could be harnessed to analyze twelve-tone compositions. To be fair, Arnold Schoenberg himself had developed a representation in the form of a twelve-by-twelve grid, which, for any given twelve-tone row, provided a compact representation of the 48 statements of the row, accounting for the twelve chromatic transpositions of the row itself, along with the inversion, retrograde, and retrograde-inversion forms. My guess is that, when Babbitt saw one of those grids for the first time, the concept of permutation groups leapt to mind. (Babbitt began his collegiate education as a mathematics major, only later moving over to music.)

MIT had an impressive number of mathematicians on its faculty, and many of them were well-versed in group theory. So, since I was having a lot of trouble getting my head around Babbitt’s Problems in Modern Music essay, I loaned my book to one of the full professors on that faculty. When I came by his office the next morning, he declaimed, “What is this garbage?” (or words to that effect). It did not take me long to finally recognize that, while Babbitt may have known how to talk the talk of a mathematician, he was pathetically incapable of walking the walk.

To be fair, many years later, shortly after my doctoral thesis had been approved, I met a pianist that was preparing a Babbitt composition for recital. I sat beside him on his bench while he did a run-through, and I was quite impressed with how he had endowed all of those marks on paper with expressiveness. When it came to our talking about the what, why, and how of his approach to performance, mathematics never reared its head.

Cover of the album being discussed (courtesy of AMT Public Relations)

All of those paragraphs were written to establish a mind-set for an album of Babbitt compositions that was released by New Focus Recordings at the end of this past October. The title of the album is Milton Babbitt: Works for Treble Voice and Piano. The 21 tracks are performed by soprano Nina Berman and pianist Steve Beck. The six-movement “A Solo Requiem” requires two pianos, and the second pianist is Eric Huebner.

The good news is that the listening experience was rich enough that my mind never lapsed into thoughts of higher mathematics. On the other hand, when I consulted Babbitt’s Wikipedia page, I discovered that his list of compositions was divided into three periods. These covered the intervals of 1935–1960, 1961–1979, and 1979–2006, respectively. All of those periods are represented on Berman’s album. However, if I were to play this CD in “shuffle mode,” I doubt that listening alone would allow me to identify which tracks resided in which interval.

All that I can say for sure is that the demands made on the performers could not have been more intense. (That was the same impression I had listening to the pianist prepare for his recital.) As a result, it is hard for me to avoid suggesting that, regardless of what track one first encounters, all of the other tracks will come across as “more of the same.” It would probably be fair for the reader to then ask, “The same what?” The only answer I can give is, “Darned it I know!” As to whether or not Babbitt will be remembered for his cryptic ventures into higher mathematics, I can only say that, in the mid-Seventies, a colleague of mine in the Music Department at the University of Pennsylvania declared, with no uncertainty and with a fond memory of Milton Berle, “Nobody is afraid of Uncle Miltie any more!”

“Meta + Hodos” After a Decade

In working my way through the writings of music theorist and composer James Tenney collected in From Scratch: Writings in Music Theory, some of my more extended efforts went into situating Tenney’s Master’s thesis, “Meta + Hodos: A Phenomenology of Twentieth-Century Musical Materials and an Approach to the Study of Form” in the context of how issues of phenomenology in general and time-consciousness in particular have evolved since that thesis was completed in 1961. Tenney himself took his own retrospective view of his thesis but only after over ten years of experiences and cogitations had ensued. The result was his follow-up essay “META Meta + Hodos,” written in 1975 but not published until 1992, when Frog Peak Music coupled it for publication with the original “Meta + Hodos” document.

The preface to the retrospective document begins as follows:

“META Meta + Hodos” represented an attempt to organize certain ideas first presented in Meta + Hodos in 1961, incorporating insights and revision that have emerged since then. The writing was initially motivated by the desire to provide an outline of my ideas and terminology for use by students in a class in formal perception and analysis at the California Institute of the Arts.

The result is not quite the sort of systematic outline that many of us learned to create in secondary school. However, it amounts to a reasonably well-organized collection of propositions, whose contents are elaborated through systematic definitions. Both propositions and definitions are then further elaborated by comments. For most readers this is hardly a page-turner; but Tenney’s attempt to be systematic facilitates homing in on the ways in which more recent insights reflect on the ideas brewing both in 1961 and subsequently in 1975.

One of my key conclusions about “Meta + Hodos” was that Tenney would probably have altered the path he was following had he been aware of Friedrich Hayek’s book The Sensory Order: An Inquiry into the Foundations of Theoretical Psychology. This book was first published in 1952; and, while it did not cross my path until around 2005, I quickly discovered that it had influenced two of the most perceptive thinkers concerned with the nature of mind that I had been fortunate enough to encounter. One of them was my doctoral thesis advisor Marvin Minsky, a pioneer of artificial intelligence back in the days when understanding the nature of mind was more important than hacking together software that could fool enough people about its inherent “wisdom.” The other was Gerald Edelman, who was inspired to seek out biological processes that might validate what for Hayek was never anything more than mere speculation.

The very first Proposition in “META Meta + Hodos” involves the hierarchical organization of temporal gestalt-units. However, this is quickly qualified with a comment that suggests that the organization does not necessarily follow the strict “tree formation” of a hierarchy. (In abstract mathematics we would call the structure Tenney had in mind as a “partially-ordered set.”) The absence of such strict hierarchies is a significant issue in the biological model that Edelman developed based on a principle he called “perceptual categorization.” Put simply, perceptual categories are not neatly nested, nor, for that matter, are they stable. Indeed, those who have been following these “commentary” articles should know by now that the Necker cube is one of the easiest observed instances of unstable category definition.

Where things start to get a bit dicey, however, is when, in spite of the fluidity of the underlying nature of perceived categories, Tenney succumbs to the influences of his background in working with computers and ventures into a domain he calls “Musical Parameters.” Unfortunately, there is a slippery slope here. The very idea of there being parameters presumes that sound (and, therefore, music) is produced by what in computer-speak we would call a functional module, which has one or more control inputs. “Parameters” are neither more nor less than the quantities passed through those inputs.

Of course, those parameters can be applied to do a variety of things, meaning that they do not all “look alike,” so to speak. Thus, computer science recognizes that parameter values need to be classified, so that they can be distinguished as involving different categories. Those categories are usually called data types. (For the record, in 1975 I was teaching this sort of stuff to both undergraduates and graduate students!)

With such terminology at our disposal, it is easy to appreciate one of Tenney’s Comments:

There is not, in general, a one-to-one correspondence between musical and acoustical parameters.

This can only be appreciated if it is generalized to the above terminology. Given any two data types, does a relationship exist that defines one in terms of the other? From a computational point of view, that relationship needs to be expressed as a function. However, in the language of mathematics, that function may be injective (different inputs mean different outputs), surjective (different outputs mean different inputs), or bijective (both injective and surjective). (A bijective function is also known as an isomorphism.) Until we tease out the mathematics behind it all, any “correspondence between musical and acoustical parameters” can be little more than vague speculation.

Tenney then moves on to a domain that he calls “On Formal Perception and Description.” This is where he probably would have benefitted from a previous encounter with Hayek. As might be expected, The Sensory Order has a good deal to say about “forms” and how they “are formed,” so to speak. Hayek even distinguishes “simple” and “complex” “forms of classification,” the latter having the sort of dynamic qualities we associate with the Necker cube. In that context it seems to be fair to ask whether form, as such, as actually perceived or whether it is essentially a framework for expected perceptions. The latter seems more consistent with Edelman’s model of perceptual categorization, which, in turn, has little to do with Tenney trying to identify state, shape, and structure as “aspects of form.”

To those who may be chafing from my invocation of terminology from mathematics and computer science, I apologize. For better or worse, if we are trying to explain something, it always helps to have a vocabulary that facilitates the process of explanation. Readers may recall my earlier citation of the programming language LISP. An early pioneer of computer science Edsger W. Dijkstra, once praised the language for its ability to allow us to think previously unthinkable thoughts. Decades later a natural language researcher observed, in the middle of a talk he was giving, that it is often easier to explain what you are doing with a LISP program, rather than in text. The bottom line is that you cannot undertake explanation without terminology, and I have tried my best to evoke terminology that is appropriate without being dangerously confusing.

I make this point because, towards the end of the “META” article, Tenney begins to abandon it. There is an entire section of the text based on the mathematical property of ergodicity. However, he does not explain that term; nor does he interpret it the same way that any well-educated mathematician would. (To be fair to Tenney, Milton Babbitt had a tendency to play similar games in applying the terminology of abstract mathematics to his arguments about serial music. Several mathematicians I know have looked at his paragraphs and dismissed them as mere bunk.) The good news is that Tenney enlists such terminology to elaborate on those properties of state, shape, and structure; and the really good news is that those who follow in the footsteps of Hayek and Edelman need not worry about the specifics of those properties. The same can be said about the final section of the “META” article devoted to entropy, which seems to have originated from misconceptions that Tenney probably picked up from Lejaren Hiller at the University of Illinois.

A Coincidence of Contradictions

Milton Babbitt died yesterday at a hospital in Princeton at the age of 94.  I was never a great fan of his music, but this was due in no small part to the sparse opportunities to hear it.  I also suspect that Babbitt had as much right to fall back on the same observation that Arnold Schoenberg once made:

My music is not modern;  it’s just badly played.

Nevertheless, I doubt that anyone would question that there is something very challenging about playing a composition in which the composer can claim a rigorous logical argument behind every note.

However, where this reduction ad absurdum of Schoenberg’s serial techniques is concerned, I think that Virgil Thomson made the right call in one of his pieces in The New York Review.  The article was primarily about John Cage, and Thomson noted Cage taking the opposite strategy that every note in a composition would be determined by a rigorously applied aleatoric process.  (Where Cage was concerned, that process usually involved tossing three coins to select a reading from the I Ching.)  Thomson made the claim that the ear could not tell the difference between a product of absolute logic and one of absolute chance, and I think there is a sound point to make.

The reason probably has to do, once again, with the fact that the music is not in the notes.  It is in the actions that go into making music.  As soon as a composer abstracts away from those actions, there are no perceptual criteria that can distinguish the absolutely determined from the totally random.  Artificial life researchers used to say that this was a phenomenon that occupies just the right middle ground between these two extremes, describing that area as “the edge of chaos.”  I find that more poetic that useful, as if it is yet another way to punt on how little we know about motivated action.

The irony is that the time of Babbitt’s death may have coincided with a concert of compositions by Witold Lutosławski.  The focus of the concert was on works based on aleatoric techniques!  We thus had two events occupying opposite sides of a major aesthetic argument during the twentieth century.  Lutosławski died in 1994;  so I assume he has been waiting patiently in heaven to resume that argument with Babbitt.  I wish both of them well in the afterlife!