Taking Issue with Alex Ross (or Jed Pearl)

Yesterday I finished reading “The Cults of Wagner,” the review that Jed Perl wrote about Alex Ross’ book Wagnerism: Art and Politics in the Shadow of Music for The New York Review of Books. Given that the book runs to 769 pages, Perl covered a lot of ground in his article. I would even say that his coverage was thorough enough that I can probably pass of reading the book itself. That said, there is one point where I would like to take issue; and, to be fair, I am not sure whether the issue is with Ross or Perl.

It concerns a single sentence:

What Ross believes, simply put, is that since life is disorderly, then art must be disorderly, too.

Given the argument that Perl develops across the paragraph that concludes with this sentence, I am inclined to believe that he has provided an accurate account of one of Ross’ beliefs. Regardless of the source, however, I am not sure there is much meaning in the premise that “art must be disorderly.” Indeed, I am not sure that there is much sense that can be derived from attempts to hang adjectives and adverbs on the noun “art.” In other words I have my doubts that art is anything and that it would be more appropriate to say that art provides grounds for experience. For those wondering, the answer is that this is not an original idea; rather it is one I picked up from John Dewey, specifically from the book Art as Experience.

What, then, is the “experiencing of art?” I would suggest that it is not that different from any other form of experience. The function of “mind” is basically to provide order to all the disorder that bombards us through stimuli. William James called this the “blooming, buzzing confusion” of sensory signals, which “mind” then tries to register as configurations of objects (often succeeding in unexpected ways that lead to phenomena such as optical illusions). No two minds need necessarily conceive of the same objects; but, at a much higher cognitive level, we have language to negotiate any disagreements. So it is that Ross turns to language to bring order to the disorderly stimuli created during a performance of Richard Wagner’s music and Perl does the same with the disorderly stimuli created while reading Ross’ book.

For some time I have been interested in those processes that enable bringing order to disorder. As I have written in the past, one of my primary sources has been a book by Friedrich Hayek entitled The Sensory Order, which seems to have had a serious impact on two researchers that have influenced me significantly: Marvin Minsky for his work on artificial intelligence and Gerald Edelman for his efforts to model what he called perceptual categorization. My guess is that neither Ross nor Perl have gone down either of these paths. Nevertheless, it is important to remember that the “experiencing of art” has more to do with the biological substrate of experience itself than it does with any properties of “art itself,” philosophical, biological, or otherwise.

This is not an injunction to advocate writing about making music or listening to it in terms of a biological substrate. Nevertheless, to go back to William James, both making music and listening are instances of experience. Unless we can anchor our thoughts to viable (if not necessarily valid) hypotheses about “how we experience,” we might as well just be juggling symbolic structures (such as the sentences we write) the same way we do when we try to solve a crossword puzzle!

Jazz for Brain Scientists

courtesy of Naxos of America

When I first learned about the album Yuko Mabuchi Plays Miles Davis, my curiosity was immediately piqued. Having spent almost a decade of my life at an “outpost” research laboratory in Palo Alto funded by a Japanese company, I quickly found more enthusiasm for jazz among my Japanese colleagues than I had encountered among Americans. Yarlung Records has provided an impressive platform for pianist Mabuchi and her trio, and it was hard to resist seeing what they would make of compositions that had been indelibly stamped with Davis’ unique approaches to creativity.

I quickly discovered that there was more to this album than I had anticipated. It turned out to be a concert recording taken from a performance in Cammilleri Hall on the campus of the University of Southern California on April 25, 2018. Cammilleri Hall, in turn, is in the building of the Brain and Creativity Institute (BCI); and Mabuchi’s gig turned out to be the last in a two-year series of concerts inspired by Davis in response to the hanging of his 1988/89 painting in the Cammilleri lobby. (The painting is reproduced in the booklet that accompanies Mabuchi’s album.) For the record, this is one of two USC research laboratories concerned with what pioneering researcher Warren Sturgis McCulloch liked to call “embodiments of mind.” The other is the Center for Neural Engineering, directed by Michael A. Arbib. BCI is led by Antonio and Helen Damasio, the former having written several perceptive books for lay readers on the relationship between brain and mind.

With all that as context, I found it hard to silence Davis’ own gravelly voice in the back of my head saying, “Jazz ain’t brain science, man!” Indeed, between the history of cognitive psychology and the various “wet brain” specialties, there is a long history behind trying to study “the mind behind the musical ear,” a phrase which happens to be the title of an excellent book by Jeanne Bamberger that was first published by Harvard University Press in 1991. During my tenure with Examiner.com, I wrote about a book entitled Music, Language, and the Brain by Aniruddh D. Patel, a Senior Fellow at The Neurosciences Institute in San Diego; and reading that book was not a particularly satisfying experience.

By way of a sidebar, I would like to observe that, when that San Diego campus first opened, its Director, Gerald Edelman, arranged a “launch seminar,” which included, as “entertainment,” a recital by the Juilliard String Quartet. It was on that occasion that I first met Antonio Damasio; and I have to wonder whether “jazz at USC” was his response to “chamber music in San Diego!” If nothing else, the Cammilleri concerts are a sign that brain scientists are still as occupied with music as they were two decades ago.

Where the music itself is concerned, the other members of Mabuchi’s trio on this new album are Del Atkins on bass and Bobby Breton on drums. They are joined by trumpeter JJ Kirkpatrick. I am afraid that Kirkpatrick was the weak link in this chain. I can appreciate that he was determined not to “channel” Davis through his own solo work; but he never seemed to find a distinctive voice of his own to add to the trio players. I was more interested in listening to Mabuchi and what she could do with not only Davis’ thematic inventiveness but also the impact of those themes on the pianist Bill Evans. Indeed, Mabuchi’s creative skills advanced beyond Davis’ legacy to take on three original tracks on the album, culminating in a concluding track entitled “Missing Miles.”

Ultimately, what I most appreciated was that Mabuchi provided me with a new context for listening to the five Davis “classics” included in her recital: “All Blues,” “Blue in Green,” “Milestones,” “So What,” and “Nardis.” For the record (so to speak), “So What” is the longest track on the album; and other Davis motifs creep in during its performance. The most recognizable of those motifs comes from “Four;” and it is introduced at the end of Kirkpatrick’s opening solo. A healthier share of that kind of free-association inventiveness would have been appreciated.

Visualizing the First Two “Razumovsky” Quartets

Having spent this past Friday writing about how Quatuor Ébène approached the performing (and recording) of the first two of Ludwig van Beethoven’s Opus 59 (“Razumovsky”) quartets, I decided to revisit Stephen Malinowski’s YouTube playlist of his visualizations of the Beethoven quartets to take a look at how he approached both of these quartets. Since this involved material with which I was familiar through both recordings and concert performances, I was curious as to how his videos would have an impact after one set of recorded performances was still fresh in memory. Once again, the experience had assets and liabilities.

Perhaps highest among the assets is the extent to which these visualizations provide a representation of one way in which the marks on the score pages may be parsed. It is important to bear in mind that there is no reason why any composition by Beethoven (or any other composer) should be parsed in a single way. Indeed, from a grammatical point of view, performance itself is a means of expressing a particular approach to parsing. In that sense Malinowski’s video interpretations take a syntactic structure arising from a recorded performance and add a second layer of parsing in the visual domain to the one that performance has established in the auditory domain. If nothing else, this is a highly inventive approach to how, with the proper tools, one might be able to document a listening experience by working in the same time-based domain that provides the foundation for listening itself.

This suggests that each of these videos reflects a highly personal interpretation. This is not meant as a criticism. Rather, it suggests that it identifies strategies that others might consider when trying to account for their own respective listening experiences, not necessarily by creating their own visualizations but, rather, by coming to appreciate what those visualizations express and then finding other means to express them.

Nevertheless, there are certain aspects that concern me because they might distract when they should be indicating. From a personal point of view, I find the frequent use of blurred images to be an almost painful distraction, even though I realize that, from Malinowski’s point of view, it is simply one of several means to express the variety of different approaches to performance. On the other hand I appreciate that Malinowski’s approach to “scrolling through time” does not always provide all “future information.” Every now and then events simply “spring out of the void;” and, from a rhetorical point of view, they tend to have the same effect as that of certain abrupt introductions of thematic material in the score itself.

Still, from an information theoretic point of view, there is an almost overwhelming abundance of content in both of the quartets being visualized, meaning that every movement, even when taken on its own, serves up considerable “bandwidth,” which then requires equally considerable “processing effort” on the part of the viewer. I would postulate that such effort is far greater than what is engaged when one watches the members of a string quartet perform these pieces. My explanation would be that the visual experience of performance reveals cues about how the performers are taking their “parsing of the score” and realizing it as a listening experience. They are not providing a blueprint. They are providing their impressions of that blueprint, and it is through those impressions that those of us on the audience side come away with an absorbing listening experience.

Thus, to return to the issue of a “fatigue factor” that continues to occupy my appreciation of Malinowski’s visualizations, I would say that the bandwidth of a concert experience is more manageable that that of watching those visualizations, particularly if one wishes to experience a single quartet from start to finish (as it would be performed). Mind you, the same issue arises when one is trying to follow the score. There are just too many bits on the printed page for mind to keep up with the steady flow coming in through auditory sensation. Thus, when we follow a score during a performance, we tend to select where we look because we want to look for certain features for the sake of understanding how they are interpreted. One cannot be that selective when viewing one of Malinowski’s visualizations; and, to be fair, I do not think he expects his viewers to approach his work that way.

Still, I have to grant that any one of those visualizations almost always calls my attention to a variety of features that have always registered with listening but may not have been appreciated for the full worth of their contributions to the overall design. There is no doubt that, for any of the Beethoven quartets, there is always likely to be more than “meets the ear,” whether the ear is in the concert hall or listening to a recording. Malinowski consistently provides insights into what that “more” may be. Sometimes, however, those insights tend to overwhelm the viewer, tempting him/her to close his/her eyes and just get “back to the Beethoven.”

James Tenney’s Final Thoughts on Harmony

In the last three of the chapters in the James Tenney anthology From Scratch: Writings in Music Theory, the author continues to wrestle with the nature of harmony and the perception of pitch. What is interesting is how each of Tenney’s essays on these matters tries to approach the subject from a different point of view, meaning that, by the end of the collection, one is reminded of the problems that three blind men have in trying to describe an elephant. “The Several Dimensions of Pitch,” written in 1993 and revised in 2003, tried to grab this particular elephant by its physiology, beginning with several informative pages that take a deep dive into what is happening in the inner ear. Of greatest interest is the explanation of the difference between hearing a simultaneity of individual tones and hearing them as a single unified stimulus, suggesting that, from an ontological point of view, a “chord” resides in a different category than a single tone.

In itself this is a rather profound insight. The problem is that Tenney does not quite seem to know where to take it. Part of the problem has to do with the fact that he never really reconciles the difference between the mathematical precision of integer ratio with the “fudge factors” of tolerance that arise when listening to real instruments playing their tones. As a result, I come away from Tenney’s speculations reminded of the old joke that the mathematical constant π, a transcendental irrational number, is equal to the integer 3 for very large values of 3.

The following chapter, “On ‘Crystal Growth’ in Harmonic Space,” also written in 1993 and revised in 2003, is the most problematic in the collection. It serves up an abundance of diagrams that get progressively larger and perhaps may be interpreted as a metaphor for crystal growth. For the life of me, I could not make heads or tails out of how to read those diagrams or what Tenney intended them to signify. It is as if he was in search of yet another metaphor to elaborate his thoughts, but it is almost immediately clear that his knowledge of auditory physiology was on much sounder ground than anything involving crystal growth.

The final chapter discusses Tenney’s composition “Diapason” and can be taken, without too much of a stretch, as a summing-up of the entire volume. The composition was clearly intended to make concrete many of Tenney’s abstract speculations on how the concept of harmony could “evolve” to accommodate new concepts of consonance and dissonance in the atonal repertoire. The “punch line” of those speculations is as follows:

Before harmony can evolve, the role of music itself must evolve. Otherwise we will simply be replaying an earlier scenario with minor, “cosmetic” changes in the details.

My own feeling is that there is too much to music to be crammed into a single context, let alone a “role” associated with that context. For my part, I would prefer to fall back on the “definition” that I think was attributed to Erik Satie by John Cage, which declares simply that music is what happens at concerts. I have now lived long enough to see the nature of the concert evolve in any number of imaginative ways, each with its own sense of context. Has music “evolved” along with the concert experience? From the Satie-Cage point of view, I suppose it has!

In the final paragraph of this chapter, Tenney turns his attention to the concept of form, which he declares should be treated “simply as another object of perception.” This takes me back to my own frequently-explored turf of the nature of mind as hypothesized by Gerald Edelman based on speculations by Friedrich Hayek. This involves the principle of “perceptual categorization,” which I discussed when writing about the “META Meta + Hodos” chapter in From Scratch. As I see it, what Tenney calls an “object of perception” is basically what Edelman calls a “perceptual category;” and, on the basis of what Edelman has written about the relationship between brain and perceptual categories, I am not yet convinced that the concept of form is one of those perceptual categories.

Tenney’s Rigorous Balance of Chance and Choice

Those who have been following my discussion of the articles by James Tenney collected in From Scratch: Writings in Music Theory should, by this time, appreciate how much rigor can be found in Tenney’s efforts, whether they are directed toward musical composition or toward imaginative reconceptions of practices that have come to be called “music theory.” When it comes to composition, there is a good chance that Tenney was inspired by John Cage, who could also be meticulously rigorous when called upon to explain the method behind the creation of one of his compositions. What is interesting about Cage is that, while many of those methods were based on a foundation of using a chance technique (such as the ritual for selecting passages to read from the I Ching), there could be prolific diversity in how that technique would be applied. The Silence anthology has two short articles about such applications, one published in 1952 and the other in 1957; and from these we may appreciate how the creation of method was as important to Cage as the creation of the music itself.

Cage’s approach would have an impact on other composers. The best known of these is probably Pierre Boulez. In 1958 Die Reihe published an article by György Ligeti that provided a deep dive into the creation of one of Boulez’ particularly challenging compositions. The title of the article was “Pierre Boulez: Entscheidung und Automatik in der Structure Ia” (Pierre Boulez, decision and automatism in “Structure Ia”); and evidence of Cage’s impact on Boulez is not hard to find. (The article appeared in the English-language edition of Die Reihe in 1960.)

As Ligeti’s title makes clear, much of the composition process is “automatic,” although it might be better to call it “algorithmic.” The connotations of the latter adjective allow us to appreciate that one cannot have an algorithm before first identifying input data, output data, and the relations that connect them. These are the issues that Ligeti addresses in the “decision” portion of his article.

Tenney’s article “About Changes: Sixty-Four Studies for Six Harps” is very much cut from the same cloth that served Cage and Boulez. However, where Boulez was concerned with serial techniques that could be applied to the twelve pitches of the equal-tempered chromatic scale, Tenney was more interested in exploring the pitches of the natural overtone series. He decided to do this by dividing the semitone into six equal micro-intervals, providing him with an equal-tempered gamut that would enable better approximations to upper harmonics, which could be represented terms of smaller “chromatic shifts” from the traditional pitch classes. (The reader should now appreciate why Tenney’s piece was scored for six harps; each harp had a different “micro-shift” in the pitch of its strings.)

In terms of method, Tenney was far more rigorous than either Cage or Boulez. His expertise in higher mathematics allowed him to make rigorous specifications of subtle variations. This was most evident in his effort to extrapolate principles of harmony into the domain of his 72-pitch equal-tempered gamut. Nevertheless, I think it would be fair to say that almost every reader of this article will come away with absolutely no sense of what it would be like to listen to the results.

(Back when I was living in Los Angeles, I had the opportunity to listen to a tape that Tenney played of an excerpt from a performance of Changes. I had as much trouble making sense of my listening experience than I had encountered during my “first contact” with “Structure Ia!” I gather that there is now a performing version six guitars, taking the same approach to chromatic tuning; but I missed out on an opportunity to listen to that music played at the Center for New Music.)

It would be easy to dismiss Tenney’s project as “much ado about not very much.” The fact is that it is very difficult to establish the relationship between Tenney-the-composer and Tenney-the-listener. That relationship was always much clearer in Cage’s work: There was none! Cage simply created the “sonorous materials” for a listening experience; and the listener was free to make of those materials whatever (s)he wished.

Tenney, on the other hand, seems to have been motivated by a desire to explore how one could work with pitches based on the overtone series through techniques consistent with pre-existing knowledge of counterpoint and harmony. Those who have followed this site for some time know that he is far from the only composer to be so motivated. The two composers that have probably received the most attention in my writing have been Ben Johnston and, more recently, Harry Partch. Of these three, Partch has struck me as the one that gave the most thought to the sorts of listening experiences that would arise from his techniques. In that context Tenney occupies the space at the other extreme of the pendulum swing, a claim that I shall be happy to withdraw if convinced by sufficient experience in listening to Tenney’s music, rather than reading about his approaches to composition!

Thomas Clifton’s Impact on James Tenney

My journey through From Scratch: Writings in Music Theory, the University of Illinois Press collection of articles by music theorist and composer James Tenney, has now come to what quickly became the most significant of my encounters with Tenney’s writings. Readers may recall that my last article examined a five-year period of “struggle” (my word choice) to develop a theory of harmony that would apply to contemporary music as effectively as it did to the traditions of the nineteenth and preceding centuries. The year after that period seemed to have marked Tenney’s awakening from “metaphysical slumbers” (paraphrasing the traditional account of David Hume’s impact on Immanuel Kant) by virtue of his reading and reviewing the book Music as Heard: A Study in Applied Phenomenology by Thomas Clifton. Clifton died in 1978, and this book was not published until 1983. Tenney’s review appeared in the Journal of Music Theory in 1985.

In the second paragraph of his review, Tenney described the book as “at times brilliant, insightful, and thought-provoking; at other times irritating, exasperating, even embarrassing.” Nevertheless, Tenney is impressively persistent in seeking out the insights while glossing over the exasperations, reminding me of my favorite admonition from one of the pioneers in studying the relationship between brain and mind, Warren Sturgis McCulloch, “Don’t bite my finger, look where I am pointing.” Tenney clearly wanted his readers to grasp just where Clifton was pointing. Over 30 years later I still feel that he did an admirable job, but returning to that review also left me disconcerted at how little has been done to follow up on Clifton’s phenomenological stance.

Indeed, having presented the reader with both pans of the balance required for reading Clifton’s book, Tenney then makes it clear why he believes the book is so important:

A new kind of music theory is needed that deals with the question of what we actually hear when we listen to a piece of music, as well as how or why we hear as we do. To the extent that music theory involves the development and application of a descriptive language for music, this means that both the things named and the relations between things described by such a language must be much more precisely correlated than they are now with things and relations actually perceived or experienced.

Ever since I created this site, I have struggled with the challenges confronting anyone trying to describe “music as heard.” Those who have followed that struggle known that I have, from time to time, tried to take a phenomenological stance; but, at the end of the day, I feel as if what I have been doing all these years amounts to anthropological field work. There are, of course, anthropologists who respect the insights of phenomenology; and some of them have had a definite impact on my own efforts. Nevertheless, as I know from my interactions with “working musicians,” there is a wide gulf between the thought processes behind making music and those behind listening to it; and neither phenomenology nor anthropology currently goes very far in efforts to narrow that gulf.

As those who know a thing or two about phenomenology may guess, Clifton’s primary influence came from, as Tenney puts it, “the methods, insights, and terminology of Edmund Husserl.” Tenney goes on to name others; but Husserl was the one to get the ball rolling, so to speak, particularly through Vorlesungen zur Phänomenologie des inneren Zeitbewusstseins (lectures on the phenomenology of the consciousness of internal time), which was published in 1928, based on Martin Heidegger editing notes taken from Husserl’s lectures. The best source in English is the translation by James S. Churchill in 1964, The Phenomenology of Internal Time-Consciousness, published by Indiana University Press. Tenney’s chapter-by-chapter examination of Clifton’s book suggests that Tenney himself was at least adequately, if not sufficiently, acquainted with both Husserl in general and the question of time-consciousness in particular.

Nevertheless, when one gets to the end of Tenney’s review, the major “lesson” is that there are no easy answers to questions about what happens between ears and mind during acts of listening to music. Presumably, Clifton did not live long enough to take the next steps along the path delineated by his book; and, on the basis of the remaining chapters in From Scratch, I would suggest that Tenney was more interested in pursuing the composition of music than in picking up the baton that Clifton had prematurely dropped. Personally, I feel as if I continue to acknowledge the phenomenological stance, even if I do not follow Husserl’s discipline faithfully, whenever I try to account for my own acts of listening to music; and rereading Tenney’s review has given me an encouraging boost to keep at my own efforts, even when they do not (yet?) seem to yield deep insights!

Tenney’s Five-Year Struggle with a Theory of Harmony

If it seems as if it has been a while since I have continued my writing about From Scratch: Writings in Music Theory, the University of Illinois Press collection of articles by music theorist and composer James Tenney, it is because I have been deeply occupied with four consecutive chapters (and one appendix), which collectively account for a five-year period during which Tenney tried to develop a theory of harmony that would apply to contemporary music as effectively as it did to the traditions of the nineteenth and preceding centuries. The texts that occupied my attention for so long are the following:

• Chapter 10: Introduction to “Contributions toward a Quantitative Theory of Harmony” (1979)
• Chapter 11: The Structure of Harmonic Series Aggregates (1979)
• Chapter 12: John Cage and the Theory of Harmony (1983)
• Chapter 13: Reflections after Bridge (1984)
• Appendix 3: Excerpt from A History of ‘Consonance’ and ‘Dissonance’ (1988)

As can be seen from the first of these titles, Tenney’s orientation throughout these chapters is primarily quantitative. His methods are grounded in mathematics, but it is a mathematical orientation that reflects his experiences in using computers to manipulate properties that are fundamentally numerical in nature. It is from that foundation that he believed that there can be “a quantitative theory of harmony.” So it is that we encounter this sentence in Chapter 10:

Unless the propositions, deductions, and predictions of the theory are formulated quantitatively, there is no way to verify the theory and thus no basis for comparison with other theoretical propositions.

This is a rather unfortunate attempt to apply the methods of formal logic to quantitative properties. Sadly, it leads to a misunderstanding of what formal logic can and cannot do. While those who work in formal logic will use terms such as “truth value” casually, Tenney seems to have overlooked that such logicians are not constrained by dictionary definitions of the noun “truth.” The “mission” of formal logic is never anything more than a means to establish whether a collection of propositions is consistent; and deductions involving the determination of truth values is the tool for seeking out an inconsistency. (It takes only one inconsistency for the whole collection to dissolve into uselessness.)

In pursuing that mission, whether or not a proposition is “formulated quantitatively” is not relevant. Identifying an inconsistency is a matter of symbol manipulation, the manipulations being the workings of deduction. As I have previously observed, had Tenney enjoyed the benefit of an intellectual community in which “computing” was more concerned with manipulating symbolic structures, rather than evaluating complex numerical forms, he would have realized that the role of numbers in a “theory of harmony” is only part of the story, a story that is more concerned with finding useful symbolic constructs to represent the nature of signals that must be processed when either making or listening to music.

As a result, even after Cage had radically broadened Tenney’s view to accept that a “harmonic structure” may involve any simultaneity of sounds, Tenney continues to be obsessed with the integers that represent the overtone series. This is understandable, but it also distracts from where the real questions reside. Consider, for example, some of the ways that Cage worked with a piano (both with and without “preparation”). Clearly, he understood that composition and performance needed to deal with simultaneities of sounds. However, Cage was willing to deal with a sequence of such simultaneities as if it were a progression no different from the progression of chords in a four-voice hymn setting. In Cage’s case, however, one could not reduce that progression to a sequence of Roman numerals or figured bass integers.

Tenney clearly appreciated this quality of Cage’s music; but, by the end of Chapter 12, one gets the impression that he had not quite figured out what, in his capacity of theorist, he should be doing about it. The good news is that he was aware that there are actually (at least) two different kinds of simultaneity. In one case, such as in those hymn settings, one is aware of both the individual notes and the chords that they form. In another case, such as one of Henry Cowell’s tone clusters, the individual notes “fuse” into a single “sonorous object,” whose “signal” is an integrated whole, rather than a superposition of recognizable parts.

The good news is that, by the time Tenney wraps up Chapter 12, he is beginning to appreciate that time-consciousness is more relevant to perception than “score reading,” associating correlations between auditory constructs and symbols on staff paper. Once again, however, I need to be fair to Tenney. He was writing at a time when few were focusing on issues of time-consciousness raised by Edmund Husserl and Martin Heidegger, and even fewer were trying to relate their focus to the cognitive foundations behind listening to music. Those who read From Scratch today are better equipped to consider going down roads not taken by Tenney; and, if Tenney’s efforts did not lead very far, they may yet provoke a new generation of readers to seek out new paths.

Tenney’s Effort to Move from Theory to Practice

The ninth chapter of From Scratch: Writings in Music Theory, the University of Illinois Press collection of articles by music theorist and composer James Tenney, seems to be the second-longest in the book: “Hierarchical Temporal Gestalt Perception in Music: A Metric Space Model (with Larry Polansky).” This was written in 1978 and was subsequently published by the Journal of Music Theory in 1980. It basically involves first distilling a hypothesis out of the theoretical speculations that first emerged in Tenney’s “Meta + Hodos” Master’s thesis and then testing the hypothesis by implementing its content in a computer analysis program, which was written by Polansky and executed on input from three scores of twentieth-century music compositions.

Before discussing the model, the hypothesis behind the model, and the testing of the hypothesis, however, I want to call attention to a published review of “Meta + Hodos.” This took place after “Meta + Hodos” itself was published as a monograph by the Inter-American Institute for Musical Research in 1964. The Spring 1966 issue of the Journal of Music Theory published a review of the monograph by A. Wayne Slawson, which was pretty devastating.

Slawson provided the reader with a paragraph explaining the the “birth” of Gestalt psychology as a result of observations made by Max Wertheimer in 1912. However, Slawson then accused Wertheimer and his colleagues of oversimplifying the theory they developed, concluding that “the Gestalt movement failed to go beyond a particularly apt and persuasive presentation of new questions.” This was the stick he used to subject “Meta + Hodos” to a rather merciless beating.

Thus Tenney’s effort to develop a model that could then be realized through software-based testing amounts to a response to Slawson’s review. The fact is that this was a time when painfully little was known about the “wetware” of a brain embedded in the larger complex system of the human body. Thus, even a precept as straightforward as Donald O. Hebb’s famous postulate that “neurons that fire together wire together” could not be tested in the absence of technology for observing the “wiring.” One of the reason’s that I have been citing the work of Gerald Edelman is that he recognized that his own theory of perceptual categorization could not be tested through direct observation; so, as an alternative, his team developed a computer-based simulation model of Hebb’s “wiring” process. Tenney’s model, on the other hand, was based on an attempt to turn the theoretical speculations of “Meta + Hodos” (a product of the theoretical speculations of Gestalt psychology) into practice.

At this point I feel it is important to note that the term “metric space” that appears in the title is never explicitly invoked in the article’s text. Nevertheless, there is an implicit sense of “distance” that Tenney seeks to apply to his “temporal gestalt-units” (TGs), focusing primarily on those constructs captured by the terms “element,” “clang,” and “sequence.” The model requires a quantitative representation of the amount of difference that distinguishes two TGs. A metric space is a topological construct that defines the concept of distance in terms of four criteria:

1. The distance from a point to itself is zero.
2. The distance between two distinct points is a positive number.
3. The distance from point A to point B is the same as the distance from point B to point A.
4. For any point C, the distance from A to B is less than or equal to the sum of the distance from A to C plus the distance from C to B.

(That last criterion is sometimes called the “triangle rule” because the length of the hypotenuse is always shorter than the sum of the lengths of the other two sides of a triangle.)

As we liked to say as freshmen at the Massachusetts Institute of Technology, these properties were “intuitively obvious to the most casual observer.” However, those of us who went on to major in mathematics discovered that the most interesting insights were those involving counterexamples to the constraints of those criteria. Every math major knew about the book Counterexamples in Analysis by Bernard R. Gelbaum and John M. H. Olmsted and the critical role it played when trying to solve homework problems. So, in the interest of seeking out counterexamples, it is important to determine whether or not the concept of distance can actually be applied to comparing two TGs.

Let’s start with something simple. Imagine music as it is printed on score pages. Imagine, then, that you take a pencil and draw circles around groups of notes that you wish to identify as TGs. You can then take a ruler and measure distances between TGs on the score page. Even if those distances are somewhat rough (since a TG is not a simple point on the page), it is easy to see how the four distance criteria are satisfied.

However, as we all know, the marks on the score pages do not constitute the music. The music only exists through the experience of listening to a performance, even if that performance involves playing a recording. I would now suggest that the time-consciousness required for such listening involves awareness of differences that do not necessarily satisfy the distance criteria.

To make my point, I need to appeal to the reader’s imagination. Think of a flowing stream. Now, imagine that every point along that stream can be established as a fixed position (through a very precise measurement of latitude and longitude, for example). Suppose, now, that “distance” is not measured by difference in latitude and longitude but in the amount of time it takes a reference object, such as a fish, to swim from one point to another. By virtue of the flow of the river, the third property of a distance metric is violated because swimming “downstream” takes less time than swimming “upstream,” even though the beginning and ending points are fixed! I would argue that the passing of time is like the flowing of that stream and that Tenney’s model, while it looks good on paper (such as score pages), does not adequately capture the phenomenology of difference in a situation requiring the dynamic nature of time-consciousness.

After I first performed this exercise, I realized that I had been about as merciless in approaching Tenney’s work as Slawson had been. The reason is that the model that provided Tenney’s point of departure was required a quantitative foundation based on the topological properties of distance. Even the hypothesis being tested in his article, involving relationships among elements, clangs, and sequences, had been undermined in the absence of how those relationships could be represented quantitatively; and, if the hypothesis was no longer sound, then testing it was out of the question.

Once again I find myself thinking about the problems with Tenney being ahead of his time in terms of the tools available for his efforts. This particular paper predates the earliest efforts that would eventually lead to MIDI. For all of its shortcomings, MIDI provided a symbol representation that could capture not only marks on score pages but also the time-dependent factors inherent in any performance involving the interpretation of those marks. As a result of MIDI representations, it has been possible to investigate structural questions that go beyond music notation and enter the realm of time-dependent interpretations of the notation. It is in those interpretations that we need to seek out patterns and make sense of both what they are and why they are, and it is a pity that Tenney did not have such tools at his disposal when he first set off down his phenomenological path of inquiry.

“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.

James Tenney’s Formal Thoughts about Form

In “Form in Twentieth-Century Music,” written between 1969 and 1970 and the sixth essay in From Scratch: Writings in Music Theory, James Tenney returns to matters of phenomenology after accounting for his computer-based research activities that took place between 1961 and 1966. This is a relatively short essay that, more than anything else, reminded me of a caustic remark made by Arnold Schoenberg in a letter to René Leibowitz:

I do not compose principles, but music.

The good news is that Tenney avoids making Leibowitz’ mistakes. He is fully aware that the prize on which he must keep his eyes is that of music (as opposed to, for example, music theory).

Mind you, he resorts to philosophy-speak to establish this point:

Actually, the “thing-in-itself” doesn’t even exist in music apart from our perception of it. All that may be said to “exist” are various partial manifestations or symbolic representations of it, and even these must be mediated by perception.

However, we are on a slippery slope here. There is, of course, the problem that “thing” is a notoriously vague weasel-word (Does “Ding an sich” sound classier just because that is what Immanuel Kant wrote?); but, even more problematic is that fact that it is a noun.

The wording of Tenney’s next sentence seems to recognize the distinction between nouns and verbs:

So it is really the form of the musical experience that must be dealt with.

Nevertheless, as the essay proceeds, one finds that Tenney’s argument is linked to the fact that “experience” is also a noun, suggesting the premise that the attribute of form only applies to noun-based constructs. That slippery slope seems to be pulling us into a pit in which terms that we use comfortably, such as “perfect cadence” or “recapitulation” have more to do with “forms” perceived on score pages than with the experience of listening to the “music-in-itself,” an experience that must, of necessity be verb-based.

To the best of my knowledge, the earliest studies of perception dealt with the “processing” of visual stimuli. That processing involved how the “blooming, buzzing confusion” of sensory signals registered by the retina (as William James put it) are ultimately registered by mind as configurations of objects. However, the operative phrase in that last sentence is “registered by mind.” Perception is in the mind of the perceiver, so to speak; and mind is always in the midst of processing, whether or not the stimulus is static.

The best example of such ongoing processing may be found in the response to the stimuli of the Necker cube. This is a line drawing of a cube in which it is possible to interpret two different squares as the front face of the cube. The Wikipedia page for this optical illusion illustrates that ambiguity of interpretation as follows:

What is important is that the ambiguity is dynamic. Mind can flip back and forth between those two interpretations, even though the stimuli themselves never change.

When we shift from visual to auditory stimuli, the dynamic nature of perception is further confounded. We are no longer trying to reduce the process of vision to a “scene analysis” consisting of a configuration of static objects. Rather, the sensemaking that emerges over the course of listening involves ongoing dynamic interpretations of stimuli that are, themselves, dynamic. To push that theatrical metaphor, one is not only occupied with the “scene” but also with the “actions (physical and verbal) of the “actors performing” in that “scene.” Mind is no more occupied with trying interpret musical stimuli in terms of static marks on score pages than it is with trying to reconstruct the text of the script while experiencing the play being performed on the stage.

To be fair, the very nature of the noun “form” carries connotations of a static object. The significance of the Necker cube, however, is that, even when the stimuli are static, mind is never anything less than an ongoing dynamic process that terminates only with death. To be fair, when Tenney wrote this essay, there were not very many cognitive scientists dealing with the dynamics of brain that enable what we call “mind;” and, on the philosophical side of the coin, very little had been documented to go beyond Edmund Husserl’s lectures on time-consciousness other than Martin Heidegger’s proposition that “being” was a verb-based phenomenon, rather than a noun-based one.

As we learn more about brain dynamics, we are less inclined to reduce listening to the noun-based foundations of scene analysis. Nevertheless, the infrastructure of listening to music remains elusive. Those actually making the music probably have some advantage, since they experience the in-the-moment nature of relating what they are doing to what they are hearing. However, when it comes to describing those experiences, they are probably no better at it than those of us trying to account for the “audience perspective” of those same experiences.

I often refer to this site as my “laboratory notebook” for my efforts to understand better just what such description entails. (I also frequently call going to concerts my “field work.”) Whether or not I have yet learned anything of significant value from the pages of that notebook remains to be seen!

James Tenney Encounters Computers: 1961–1966

My last report on the essays of music theorist and composer James Tenney, compiled by the University of Illinois Press in the book From Scratch: Writings in Music Theory, concerned his pursuit of, in his words, “A Phenomenology of Twentieth-Century Musical Materials.” That quotation comes from the title of his Master’s thesis at the University of Illinois, which he completed in 1961. The University of Illinois also provided him with his first serious encounter with digital computers and the technical skill of programming those devices. The three essays that follow his Master’s thesis in From Scratch document his experiences in working with computers and the impact of those experiences on this thinking about music and “musical materials.” The titles of those essays are “Computer Music Experiences, 1961–1964” (completed in 1964), “On the Physical Correlates of Timbre (1965), and “Excerpts from ‘An Experimental Investigation of Timbre—the Violin’” (1966). (The excerpted document was a grant proposal.)

Once again, I appeal to the reader to allow me to put these dates in a personal context. My freshman year at the Massachusetts Institute of Technology (MIT) began in September of 1963. My very first elective during that first semester was a course on computer programming, almost all of which was focused on working with machine code. I hated it. Programs had to be given as input to the computer as decks of punched cards, and the slightest error meant that the deck would be ejected without yielding any results. Since we were allowed only four attempts for each assignment, the pressure was maddening; and I came away with little more than the ability to decipher the “Principles of Operations” manual for an IBM computer.

Fortunately, that was enough to get me a summer job at the University of Pennsylvania. Initially, I was simply assisting a graduate student with data entry for a long program written in a long-forgotten programming language (IPL-V). After I had been there for about a week, another graduate student asked me to help him with writing the code for the system he was developing as part of his thesis research. Free of the constraint of getting everything right within four attempts, it did not take me long to get into a comfortable groove of implementing useful code.

That same graduate student then told me that I could use the computer for any other project that interested me. I told him that, having been instructed in the rules of counterpoint, I was curious to see if those rules could be translated into software. He encouraged me to go ahead with the idea and directed me to the book Experimental music: composition with an electronic computer by Lejaren Hiller and Leonard Isaacson. (Hiller had founded the Experimental Music Studios at the University of Illinois at Urbana-Champaign by the time Tenney was beginning to work on this thesis.) Thus, I made my first steps down the rabbit hole in the summer of 1964.

This was a good time to be at MIT. The Compatible Time-Sharing System (CTSS) had first been demonstrated in 1961; and it provided ways to program a computer through a keyboard (basically a repurposed teletype, some models of which could both read and write punched paper tape). It also supported a programming language called LISP (LISt Processor) that allowed you to type in programs as symbolic expressions and run them from the keyboard. There were also computers with interactive systems to support writing long programs (text editors) and testing them in “debugging” environments. By the time I had reached my senior year, I was enjoying the facilities available at the MIT Artificial Intelligence Laboratory, whose Director, Marvin Minsky, supervised my senior thesis work around developing software for playing music.

That last paragraph is important, because Tenney does not seem to have had the luxury of working with such interactive systems for writing, testing, and running computer programs. Wherever he was based, he had to live in a world of “batch processing,” which seriously impeded the whole nature of research as an ongoing process of the interaction of ideas and their implementation. The present-day reader of the essays Tenney wrote between 1964 and 1966 will probably be inclined to ask, “Why didn’t he just …?” The answer is, “Because he worked in an environment that would not support his doing that sort of thing!”

Each of those three essays presents an admirable account of finely disciplined hypothesis-and-test thinking. Unfortunately, that discipline was seriously impeded by work habits that had to be developed to accommodate computer systems that had not been designed for “user interaction.” The most significant consequence of those work habits was a need to limit the hypotheses one could pose on the basis of which ones could be realistically tested. As a result, when Tenney sought to investigate timbre, he tended to focus on data consisting of individual tones, whose analog recording could then be transformed into digital data. His working environment was simply not up to “capturing” an actual performance of music as digital data; and, as a result, his hypotheses never tried to address the dynamic interactive relationship between an instrument’s timbre and what the player of that instrument is actually doing.

In other words we have come a very long way since Tenney wrote those essays. Indeed, the distance is so long that it is unclear that there is much value in these texts. The one thing that interested me was that his account of his work at Bell Labs probably had some connection to a piece by Princeton composer James K. Randall entitled “Lyric Variations for Violin and Computer.” As I recall, Randall wrote an article for Perspectives of New Music in which he chronicled the tortuous path he had to follow to get the computer at Bell Labs to make even the slightest peep of a sound. My guess is that this was a serious cri de cœur; but, to his benefit, he managed to maintain a sense of humor in documenting his experiences. Tenney was a much more serious writer; and, considering what he had to endure, I wish he had cultivated a better sense of humor.

Tenney’s First Venture into Phenomenology

The largest single essay in From Scratch: Writings in Music Theory, the University of Illinois Press collection of the writings of music theorist and composer James Tenney, is “Meta + Hodos: A Phenomenology of Twentieth-Century Musical Materials and an Approach to the Study of Form.” This was originally written as Tenney’s Master’s thesis at the University of Illinois at Champaign-Urbana, which he completed in 1961. It received relatively little circulation until it was published (along with the follow-up essay “META Meta + Hodos”) by Frog Peak Music in 1992. For its current publication Larry Polansky, one of the four editors of From Scratch, incorporated Tenney’s own corrections and revisions to the Frog Peak publication.

To call Tenney’s thesis groundbreaking would be a bit of an understatement. In 1961 only a few of the writings of Edmund Husserl, one of the major sources for phenomenological study, had been translated from German into English. Because any act of listening, including listening to music, is time-dependent, the most important Husserl source is probably Vorlesungen zur Phänomenologie des inneren Zeitbewusstseins (lectures on the phenomenology of the consciousness of internal time), which was published in 1928, based on Martin Heidegger editing notes taken from those lectures. This would be translated into English as the book On the Phenomenology of the Consciousness of Internal Time (1893–1917) (whose title provides the dates of Husserl’s lectures). The translator was J. B. Brough, and his book was first published in 1928. Here in the United States Indiana University Press published a new translation by James S. Churchill in 1964, and that now tends to be the source most readily available.

While Tenney never loses sight of the fact that sound is a time-dependent construct, he tends to avoid the extent to which listening must, of necessity, be a time-dependent action. Thus, while his essay postulates the need for “sounds and sound-configurations” (his italics) to serve as his “primary units” of study, he tends to avoid the issue of how perceiving those units requires time-consciousness. Indeed, the deeper he gets into his study, the more he seems inclined to seek out foundations in the symbolic constructs used to notate music than in any effort to account for (to paraphrase the title from a famous study about the physiology of vision) “what the listener’s ear tells the listener’s brain” (see below for citation).

As a result, a curious reader today (who would probably have already stoked his/her curiosity by reading David Lewin’s “Music Theory, Phenomenology, and Modes of Perception”) will probably be disappointed that a “verb-based” behavior like listening is overlooked in favor of acts of interpreting configurations of static symbols (as in marks on pieces of paper that are then interpreted by performers). An apologist might suggest that Tenney had the misfortune of hanging out with the wrong crowd at the University of Illinois; but, on the basis of my own educational experiences, I would suggest that, in those years prior to 1960, it is unclear that one would be able to find “the right crowd” at any American university (and, perhaps, any university where English is the primary language).

These days I tend to suggest that those more interested in listening than in notations would do well to consult The Sensory Order: An Inquiry into the Foundations of Theoretical Psychology by Friedrich Hayek. Yes, this is the same Hayek whose approach to economics has won the hearts and minds of conservatives around the world; and, to be fair, he was very up-front about calling The Sensory Order a speculative book. Nevertheless, his speculation led him to try to think about perception as a process, rather than some kind of mathematical mapping that would correlate the firing of a configuration of neurons with some “concept of an object.”

There are any number of places in Tenney’s text in which he seems to be dipping his big toe in the waters of process. He even admits that his own construct for a “unit” of listening, his clang, must (in his words) “include both a ‘dynamic’ and a ‘static’ aspect.” However, he never lets the “waters of the dynamic” get more than ankle-deep, perhaps because he could not conceive of a useful symbolic representation of a dynamic phenomenon.

In other words it will be fair to say that anyone who has “gotten the message” of The Sensory Order is likely to read “Meta + Hodos” with a very skeptical eye. On the other hand I, for one, believe that one should read everything with a very skeptical eye. That is how we “learn things” (in the immortal words of Dwayne “King” Cassius Pride). Following the wisdom of Warren S. McCulloch (one of the author’s of the pioneering essay “What the Frog’s Eye Tells the Frog’s Brain”), I am less inclined to bite Tenney’s finger than I am to see how the “finger” of “Meta + Hodos” may point to Tenney’s subsequent writings.

Ellen Lockhart and the Music of Animated Statues

from the Amazon.com Web page for the book being discussed

Last year the University of California Press published a volume whose title almost read as if it had been generated by a computer. In fact, however, Animation, Plasticity, and Music in Italy, 1770–1830 was the published version of the doctoral dissertation written by Ellen Lockhart to conclude her graduate studies at Cornell University. The book presents Lockhart as a researcher who is not afraid to dive deep into her sources and then return to the surface to account for her findings in clearly accessible language. On the other hand the very nature of her subject matter stands as an indicator of how difficult it has become to come up with original thesis material than can be discussed and defended through a degree-worthy dissertation.

Given the clarity of Lockhart’s writing, it seems proper to reproduce her own words describing the thesis topic that she has chosen to present and justify:

I argue that from 1770 to 1830, the animated statue was not only a figure of spectatorial engagement—as an object shaped like a human body, inviting aesthetic attention from the human body, and curing a corresponding animation within the human body—but also a means of understanding the relation of human senses to the self and to the very matters and materials of the fine arts.

Those who follow this site know that I am not one to recoil from a lengthy sentence; and, for what it is worth, the adjective “spectatorial” can be found on an Oxford Living Dictionaries Web page, even if it is there only as the adjectival form of “spectator!” More interesting, however, is the universality of the topic, extending beyond music to the fine arts in general.

This past summer, when writing about the Profil album of the complete operas of Pyotr Ilyich Tchaikovsky, I recalled the joke about a one-sentence book report written by a sixth grader: “This book told me more about penguins than I would ever want to know.” When it comes to animated statues, most of us think immediately (if not exclusively) of Wolfgang Amadeus Mozart’s K. 527 opera Don Giovanni. First performed in 1787, that opera fits comfortably into Lockhart’s time frame; but it receives relatively little attention in her book. Pride of place instead goes to the musical dramatization of the Pygmalion myth, best known from Ovid’s account in his Metamorphoses. However, Prometheus also figures in the examples that Lockhart explores, which include Ludwig van Beethoven’s 1801 Opus 43 score for the ballet The Creatures of Prometheus, based on a libretto by Salvatore Viganò.

For the most part, however, many readers will find most of the names that emerge in this book to be as unfamiliar as Viganò’s. Personally, I feel that the one name that deserves more attention is that of Étienne Bonnot de Condillac, whose Traité des sensations was written in 1754. A disclaimer is appropriate here: When I entered the Massachusetts Institute of Technology (MIT), I was informed that those of us with knowledge of French had the option of taking our four semesters of introductory humanities in French, rather than in English. As a result I was fortunate enough to encounter Condillac’s treatise in the spring of my freshman year, and my copy of that book is still on my shelf!

Given the state of knowledge in the middle of the eighteenth century, Condillac was a major pioneer in the domain of psychology as we now know it and the philosophical side of what has come to be called “cognitive science.” His treatise took a “bottom-up” approach to an analysis of sensation. He begins by asking the reader to imagine a statue. He then augments that statue by providing it with a single sensory organ, the nose and describes the effect this partial animation, so to speak, will have on the statue. He then works he way systematically through the other four senses before then turning to what happens when the sensory organs then interact among each other.

(Fun fact: The shortest path from the “outside world” to the brain goes through the nose. I learned this from a lecture given by Gary Lynch to a cognitive science seminar series at the University of California at Los Angeles. As Lynch put it, “There are only three neurons between your brain and air.” Think about that the next time you inhale the scent of someone’s marijuana joint!)

Lockhart basically treats Condillac’s analysis as a “recipe” for the sort of “animation” she cites in her title. Ultimately, however, I did not come away convinced that Condillac’s insights had much to do with the musical examples she presented, particularly the operatic ones. Far more significant were the examples she cited of how a “statue figure,” such as Galatea, acquires a sense of self and the ways in which different composers could lend expressive power to the delivery of a mere first person pronoun.

It is through this issue of how self is established that we encounter another familiar name among the composers that Lockhart discusses. It involves a significant transition in which the regular rhythms of vocal music from the eighteenth century and earlier begin to bend to the more flexible rhythms of speech:

It is in the music of Vincenzo Bellini that we may hear the speech-like song … in its purest form. This declamation is most evident in Bellini’s early operas and was identified immediately by startled spectators, who (for reasons that should now be clear) called the style “philosophical.” His operas for La Scala bear a number of strong family resemblances to the first essays in melodramatic opera, Through large portions of Il pirata (1827) and La straniera (1829), Bellini employed vocal lines that were so austere and so resolutely speech-like that one contemporary critic wondered whether they should be called canto declamato (spoken song) or declamazione cantata (sung speech). An emphasis on “the rhythms of the spoken word” resulted in brief lyric portions that eschewed ornamentation and repetition, taking their melodic forms directly from the verse …. Perhaps more striking, though, are the fluid musical forms that play host to this song. Bellinian “numbers” like Gualtiero’s aria in act 1 of Il pirata feature a continuous texture, devoid of extended ritornelli but defined instead by a constant interchange between accompanied recitative, arioso, and orchestral gesture; a single number might encompass dozens of tiny shifts of character, tempo, and key, and a few larger ones. (John Rosselli called this music “startlingly Wagnerian.”)

(Readers may recall that I invoked the latter part of this passage last weekend when writing about Franz Liszt’s paraphrases of operas by both Bellini and Richard Wagner.)

Lockhart also includes a chapter on sensory deprivation, which struck me as valuable for shifting the domain of discourse from general questions of self to the more specific issue of time consciousness. She pays particular attention to how the blind can only perceive objects “diachronically,” usually by applying the sense of touch to different parts of the object over a span of time. She then asks whether there might be a “spatial” way to perceive music the way a sighted person recognizes an object in an instantaneous glance.

This is the one place in which Lockhart’s background scholarship turns out to be lacking. There is (and has been for some time) a shape-based approach to the representation of a time-dependent audio signal. It is known as a sonogram. It is basically a graph with time as the horizontal axis and frequency on the vertical. It essentially provides an instant-by-instant representation of the spectral content of a sound. I once attended a lecture by a specialist in computer-based speech recognition, who supposedly could look at a sonogram and “read” the text being uttered by the data sample; but I never saw him actually demonstrate this skill. (The MIT Media Lab explored the possibility of accounting for mapping two independent dimensions along the time line through a rectangular solid called a “micon.”) Andrew Bregman wrote an entire book entitled Auditory Scene Analysis: The Perceptual Organization of Sound about the interpretation of sonograms, but the book never made a convincing case that his techniques would account for perceiving music.

Personally, I am not entirely convinced that Lockhart’s book follows through on the thesis statement quoted above. On the other hand it presents a highly engaging account of both social and intellectual contexts during that period of transition from the eighteenth century to the nineteenth. If most of the members of Lockhart’s “cast of characters” tend to be obscure, the roles they played in a changing artistic frame of reference are still worthy of consideration.

Naive and Sentimental Musical Sensemaking

Readers who have followed this site for some time know that I have a tendency to fall back on the noun “sensemaking” when talking about the nature of listening to music. While this word is not in the Oxford English Dictionary (although the hyphenated version “sense-making” is), it had been adopted by several of my former research colleagues to address the rising problem of being able to extract “useful meaning” from very large bodies of data. The Oxford definition of the hyphenated version does little more than echo the two component words; but, if we look back about half a century, we find that Friedrich Hayek was dealing with the same issue when addressing sensory data, rather than databases. The term he introduced was “sensory order,” the biological drive to find order in what William James called the “blooming, buzzing confusion” of sensory signals.

from the Amazon.com Web page for Comparing Notes

With that as context, I found it hard to resist reading the book Comparing Notes: How We Make Sense of Music by Adam Ockelford. Ockelford is Professor of Music at Roehampton University (in England). He also directs the university’s Applied Music Research Centre. He occasionally makes reference to his doctoral studies in music, suggesting that he got his advanced degree in music. However, much of his research has involved the acquisition of musical skills among young people with sensory or cognitive disadvantages. His practices thus keep one foot in music and the other in psychology.

That sort of background should, by all rights, have made this book both fascinating and valuable reading. For my part, however, I was profoundly dissatisfied; and that dissatisfaction can be traced back to the second word of Ockelford’s title. At the end of the day, he has little to say about anything other than those marks on paper that all practicing musicians are expected to be able to decode. What that as his foundation, he dwells on that tiresome question of what music actually is, how it “works” (whatever that means), and, ultimately, how we “make sense” when it comes to either performing the music or listening to it. Only at the beginning of his final chapter does he cite sociomusicologist Christopher Small’s contention that music is not some kind of “thing” but, rather, “an activity, something that people do.”

My decision to devote personal time to writing about music owes much to my ability to spend a fair amount of time hanging out at the San Francisco Conservatory of Music (SFCM), which is only about half a dozen blocks from where I was living. Through my own experiences in higher education, I have come to a naive but probably useful conclusion about where who learns what. In universities we learn about theories about music; in conservatories we learn about how music is practiced.

Universities occupy their curricula with things, to such an extent that one might almost say that education can be reduced to a knapsack of noun phrases. Ockelford’s noun phrases come from a wide variety of sources, almost all of which have to do with academic publications that may or may not signify to anyone beyond other academics. The grammatical infrastructure of the conservatory education, on the other hand, is build on verb phrases. One emerges (hopefully) with refined skills for doing, often without necessarily verbalizing (or, for that matter thinking about) what one is doing.

In his academic context it is understandable that Ockelford cannot get his head out of all those notes on staff paper. He has some clever ideas (which he calls his “zygonic conjecture”) about a foundation based on replications and transformations of patterns; but these are just familiar concepts dressed up in a new notation. As a doctoral student I was taking the same sort of approach to music in my thesis, except that my patterns were modules of computer code and the transformations resulted from parameters passed to those modules.

As a result of observing master classes at SFCM, I came to appreciate just how limited my perspective had been. Apparently, Ockelford has yet to encounter that revelation. Nevertheless, to be fair, shifting attention from nouns to verbs is no easy matter. Even the very idea of how one describes grammar for verbs has major qualitative differences from the almost computer-like formality of noun grammar. However, Ockelford never seems to accept that sensemaking cannot be anything other than an ongoing process. Like sound itself, if you try to freeze it in a single moment of time, it all vanishes.

When I read Ockelford’s title, I approached his book in the hope that someone had finally come up with, if not an underlying theory, at least a usable roadmap for negotiating the complexities of verb-based thinking. Instead, I encountered that very noun-based song-and-dance that I have been trying to escape for at least a decade. My guess is that those music-makers who really “get” the verb-based activity of their work are too occupied with the work itself to waste any time theorizing about it.

Kyle Gann Tries to Reinvent Tonality

courtesy of Other Minds

A little over a week ago, Other Minds released its latest recording, a two-CD album of Kyle Gann’s seventeen-movement suite Hyperchromatica. On the strength of numbers alone, this marks a significant addition to the ranks of compositions whose creators have chosen to reject equal-tempered tuning in favor of working with natural harmonics. The tuning systems for such efforts are known collectively as just intonation. In such systems all intervals are based on integer ratios, usually with a limit on the number of integers involved.

The movements in Hyperchromatica are based on 13-limit just intonation. Thus, the integers used in forming the ratios range from 1 to 13 along with different combinations arising from multiplication. Put in another way, all of the ratios have numerators and denominators that arise from multiplicative products of the prime numbers 2, 3, 5, 7, 11, and 13.

Those who read my extended essay about listening to integer ratios, written when I was trying to get my head around Lou Harrison’s compositions based on just intonation, may recall that the thirteenth harmonic has rich history. Benjamin Britten singled it out in the horn solo that begins and concludes his Opus 31 serenade, requiring that the horn be played without the use of valves. As might be guessed, that solo involves an abundance of tonic-to-dominant perfect fifths. However, towards the end of the solo, the dominant pitch is approached by stepwise motion from above; but the “step” is neither a semitone or a whole tone. It is somewhere between the two; and the result can be spooky, provocative, or downright disturbing, depending on the personal disposition of the listener. That result is the movement from the thirteenth harmonic to the twelfth (two octaves above the third harmonic, the basis for the so-called “perfect fifth”).

Britten wrote that daring passage in 1943 for Dennis Brain, the leading horn player of his day. Some 75 years have elapsed since then, during which Harrison emerged as only one of several composers bent on turning to just intonation to explore new ways to think about the fundamental foundations of musical composition. Remember, this was a time when many composers were wrestling with how to approach composition after Arnold Schoenberg had “emancipated” the concept of dissonance. Schoenberg himself saw that emancipation as a liberation from harmonic progression, meaning that the primary foundation of his own work was polyphony; but his was a polyphony that was similarly “emancipated” from the strictures of species counterpoint, which had is own rules based on a distinction between consonance and dissonance.

45 years on we now have Gann, who has written in his notes for the booklet accompanying Hyperchromatica, that his goal “is no less than to reinvent tonality.” I have to confess that this quote sticks rather uncomfortably in my craw. I prefer to think that tonality was discovered, rather than “invented.” Making music is a behavior that probably goes back to the earliest practices of prehistoric social groups. During those prehistoric times, there was probably the emergence of a fundamental precept that, if you liked something you did, do it again. Eventually, when our ancestors were not hunting or gathering, they would assemble in a group to tell stories, or sing them, or perhaps even sing them while others provided “instrumental accompaniment.” Not too long thereafter, those “instrumentalists” realized that they could “perform” just as well without “accompanying” the singers!

It probably took many centuries before mind developed to a point where one could consider these practices and recognize them as instances of some systematic infrastructure. Such systematic thinking dates back (at least) to Socrates (or Plato’s documentation of Socrates’ wisdom). However, it was only in the Middle Ages that more extensive efforts at such documentation advanced. Those efforts would eventually work their way into educational curricula. However, for a long time educational practices seemed to lack the ability to recognize the difference between a document that was descriptive and one that was prescriptive. So it was that the confusion between rules to be followed and descriptions of past practices first emerged; and, on the basis of some of Schoenberg’s more caustic writings, it would appear that all too many practitioners are still laboring under that confusion.

I am not sure where Gann stands in the midst of that confusion, but I think that one way to establish a point of view is by going back to the basics behind practices of making music. Put another way, what was Gann actually making in the process of creating each of the seventeen movements of his suite? At the most fundamental level, he was writing MIDI programs for Disklaviers. MIDI, of course, was based on the equal-tempered tuning of twelve semitones, all the same size, to the octave, the usual way in which most pianos are tuned. In order to deal with just intonation Gann had to alter the hardware of his Disklaviers to synthesize pitches they had not been designed to synthesize. Furthermore, to account for a gamut of 33 pitches per octave, he needed three of those Disklaviers to account for all of the pitches. In other words what Gann made was an extensive library of software to run on an array of hardware, which he had made specifically for that software.

All that probably sounds so dry that many readers may wonder, “What does that have to do with making music?” It is therefore to Gann’s credit that I have to say that, if one puts all thoughts of theory aside and just listens to these two CDs, it is not difficult to imagine that Gann was playing at some non-standard keyboard, perhaps even improvising, rather than building a software library. In other words, while his methods were not actually products of the tight coupling between listening and making, he has successfully created the illusion of that coupling.

Having accepted that illusion, what is the listening experience that emerges from these recordings? The overall impression is one of exploration, often involved with establishing some “seed” of content and then playing around with different approaches to expressing that seed. Those who have listened to (and enjoyed) many of the prolonged improvisations that have been recorded of Keith Jarrett’s solo piano work can appreciate this approach to listening; and, for the most part, Gann works on durational scales that are not quite as extended as Jarrett’s.

On the other hand everything we listen to in the present is informed by what we have listened to in the past. One of my first counterpoint teachers (from the days of that “great confusion” between description and prescription) would consistently come down on all of his students for writing what he called “slimy chromaticism.” Gann has a frequent tendency to run through long strings of consecutive “micro-semitones” in his gamut that would escalate my former teacher’s sense of “slimy” to a level he could not have imagined.

However, Gann’s “hyperchromatic” runs may be the tip of a more imposing iceberg. Over the course of these seventeen pieces, there is little sense of hierarchy in what Gann is playing. The durational value of individual notes often serve as a clue to which of his notes are basically embellishments, but it is not always clear just what they are embellishing. As one who continues to have considerable respect for the theoretical writings of Heinrich Schenker, I feel that the absence of a clear distinction between the embellishing and the embellished reduces much of what Gann is doing on these recordings to another term that my counterpoint teacher used to throw at us: noodling.

To be fair, I am sure that Jarrett has any number of critics that would throw that same term at many (all?) of his prolonged improvisations. For that matter, there are any number of reasons to believe that Miles Davis felt the same way when John Coltrane launched into one of his longer improvised takes on whatever tune they happened to be playing. In other words the experience of listening to Hyperchromatica may, for better or worse, simply be similar to that of my recent account of listening to the world premiere of Lera Auerbach’s Labyrinth, in which I cited Henry Miller’s definition of “confusion” as “a word we have invented for an order which is not understood.” Fortunately, a recording provides ample opportunity to eventually home in on an order that is not yet understood!