I'm going to try to clarify the musical complexity issue. What we have now, left over from the previous post, is what I'll call the [David] Byrne argument: that a lot of incomprehensible, audience-alienating music has been written out of a kind of reverse elitism - and what I'll call the Nonken argument (after superb pianist Marilyn Nonken, who wrote in): that there's a lot of difficult, complex music that will never appeal to a wide audience, but it has its admirers, and they should be allowed to have it. On the face of it, these assertions both seem obviously true, and you'll notice they don't even contradict each other. But each of them comes with an assumed, unstated backside, a flipside, that is more questionable, and I'm going to see if I can dissociate those flip sides from the assertions themselves. I assure you I do this with malice toward none and charity toward all, so please don't write in with the intention of taking me down a peg for some supposed partisan advocacy on my part.

If we can agree on two propositions, I have some faith that all the rest will fall into place. Let's posit a musical idiom that I think most of you have heard or can imagine: thorny, complex, difficult-to-understand. Proposition 1: not every thorny, complex, difficult-to-understand piece that's been written is a masterpiece, worth listening to over and over again. Some pieces in that late-20th-century idiom are merely tedious and unclear, confusing rather than profound. I hope everyone concerned (except for Frank Oteri, who prides himself on a Zenlike appreciation for every piece that's ever come into existence, simply for existing) can agree on this much.

The second proposition may be a little more difficult to get universal agreement on among non-musicians. Proposition 2: at least some thorny, complex, difficult-to-understand pieces are beautiful and profound, and those listeners who come to know them well derive immense pleasure from them. In short, within the wide world of thorny, complex, difficult-to-understand music, we're going to draw a theoretical line. On the profound side of this line, for instance, I would place Bruno Maderna's Grande Aulodia, which is like ear-candy for me, and also Luigi Nono's late string quartet Fragmente: Stille, an Diotima. On the confused and unrewarding side of that line I might place as example Charles Wuorinen's Concerto for Cello and Ten Instruments, which I excitedly bought a score of as a teenager, and which ever since has served me as an emblem of pretentious musical gobbledygook. But it doesn't matter which pieces, or even which percentage of pieces, you put on which side of that line - as long as you'll simply agree with me that there's a line, we can continue.

All I'm asking you to do is dissociate the qualities complexity and quality. Complexity does not guarantee that a piece of music is great, nor does it guarantee that a piece of music is bad. Put that way, I don't think even our friend Frank can disagree.

(Already now, though, two people have written to express suspicion that if I think some complex music is no good, then I must secretly think that all simple music, or all tonal music is good. Aside from such assertions being patently ridiculous, there would be no logic whatever in such a leap of thought. Like, "You don't like some kinds of chocolate? Then you must love everything that's vanilla!" But in general musicians are not very good at logic, and this is the kind of fallacy that these arguments of musical style get caught up in.) [UPDATE: Darcy James Argue, in commenting on the above, makes a welcome clarifying point: "In practice, in certain circles... it is effectively impossible for anyone to make an argument that flows from Proposition 1 (especially: "this piece of thorny, complex, difficult-to-understand music is in fact a piece of shit") without people assuming that you are in fact launching a full-bore assault on Proposition 2 ("so you're saying that all my favorite thorny, complex, difficult-to-understand music is worthless???")"]

As is pretty clear, the Nonken argument does its level best to ignore Proposition 1 ("Vote NO on Proposition 1!"), and the Byrne argument ignores, or even disputes or refuses to acknowledge, Proposition 2. Yet to ignore either of them negates the deeply-felt experiences of large swaths of people. Of course there are thousands of musicians who have been deeply and positively affected by some thorny, complex, difficult-to-understand music that would have seemed opaque and unpleasant to my grandmother. Byrne's view (as he expressed it, and perhaps he doesn't believe it as simplistically as he said it, but he gave voice to a common formulation) is a cliche, the cliche of Evil Modern Music, but it is not a cliche that was made up out of whole cloth. Clearly a lot of people think music went off some kind of deep end in the 20th-century, and became (temporarily) self-delusional. As a critic, as a composer, as a person, I have an obligation to acknowledge both sets of opinions; I can't tell either my composing colleagues nor the musical audience I used to write for that their perceptions are totally neurotic - at least without losing credibility with one set or the other. Much of my life has been spent on this dividing line.

Let's take that opinion that classical music went off some kind of deep end in the 20th-century, and became self-delusional. There is absolutely no way to assess the sanity of this assertion without dividing the music alluded to into several repertoires with different reception histories:

Pre-WWII Modernism (early Stravinsky, Varese, Schoenberg, Webern, Bartok, Ives, Messiaen, etc): This music certainly disturbed older members of the audiences who first heard it, and it became the first repertoire of music shunned by orchestras. It definitely represents a split, apparently irrevocable, in the classical repertoire. That music exploded into a lot of musical areas that had been previously off-limits, using dissonance, complex rhythms, and atonality to express violence, anxiety, machinism, and anger. Of course, as is widely documented, today when orchestras play that music, the older crowd who loves their Brahms and Dvorak get irritated or stay away, but thousands of new, younger listeners pour in. The movies have done a lot to inure the modern ear to dissonance and arrhythmia, and also to associate it with analogous emotional states. For my students in general, the traditional relationship is now reversed: 19th-century symphonies seem tedious and unthinkingly conventional, while early modernism is entertaining and energizing, like the audio analogue of a video game. Reception history suggests to me that the jury is in on early modernism: arguing that it was a wrong turn seems as pointless an argument as any Luddite could make. Let us say no more about it in this context.

European avant-garde of the 1950s and '60s: This, as the rainbow of reactions to Zimmermann's Die Soldaten shows, is more problematic territory. That music hit the recording world when I was in high school, primed and ready for it, and I glommed it up with hungry ears, reading everything about it I could get my hands on - and even to me, some of it doesn't make sense. That music, too, used dissonance, atonality, and arrhythmia - but not always to express violence or anguish, often just to play with sound forms. My students get a perennial kick from Stockhausen's Gruppen, but whether its fragmented textures could ever cease to suggest anxiety to the untrained ear is something I would not want to speculate about. A lot of that music's drive was theoretical, and it trailed off into a thousand dead ends, a thousand pieces more remarkable for the pompous psychology of their program notes than for their sonic aura. Nevertheless, a core repertoire of tremendously beautiful and original works emerged from all that experimentation: Boulez's Pli selon pli and Rituel, Zimmermann's Photoptosis and Monologe, Berio's Sinfonia and Corale, and, you can make up your own list. If I were called upon to justify Darmstadt serialism to a general audience, I'd say, "Wait a minute - which pieces am I justifying here? Because I'm sure as hell not going to go out on a limb for all of them." I insist that there are pieces on both sides of the line in that repertoire, some gorgeous and some merely confused, but they are so unified by idiom that a general audience has to be forgiven for finding it difficult to make distinctions.

Comparing the reception history of this music with that of the next category is complicated by the fact that Europe and the U.S. have such different musical cultures. In Europe an immense festival culture grew up around serialism, which gave a convincing appearance that there was more public support for the music over there. Some Americans, like Rzewski, came to write more opaque music after expatriating to Europe, as though that had more success there, and it probably did. Nevertheless, I always think of the parents I once met of an exchange student at my son's elementary school. They were from Graz, Austria, and I mentioned that I was aware of a prestigious contemporary music festival there. They said, "Oh, the music they play there is terrible, all this horrible modern stuff. We go every year."

Academic 12-tone music of the 1970s and '80s: You may deny, if you wish, that in the period in question, thousands of student composers were encouraged by their professors, or perhaps pressured simply by their peers or the environment, to write abstract music of exploded textures in a 12-tone idiom, or something resembling it. Go ahead and deny it: an army of survivors will rise up to contradict you. Dissonance, arrhythmia, complexity, had, if you wanted, become completely dissociated from any specific emotional expression; it was often all just about pitch sets and sound structures. There is no need to demonize this period, which simply resulted from the collision of European serialism with an explosive expansion (in both size and influence) of academia in the directions of composition and analysis. But neither let us whitewash the fact that the "contemporary music concert" nurtured by academic culture became, for awhile, something of a chore. Even my fellow students and I, thoroughly indoctrinated into this culture, couldn't believe how bad most of the music was, semester after semester. Something was clearly wrong, and later that something got fixed to a certain extent. Just to take one example, student composer concerts I've heard in the last ten years are so infinitely better than student composer concerts of the '70s that someone should write a book about that phenomenon alone.

Whether you agree with my characterizations here is really not important. What's important is that contemporary classical music got a terrible public reputation in the mid-20th century, and while composers at first defended the music, at some point, even many of us began to concede that something had gone wrong. Where one draws the line that got crossed over (1945, 1970, serialized rhythm, pitch-set analysis) is immaterial. Certainly recent reception history suggests that some of that bad rep was unfair - and some, Frank, will argue that all of it is unfair, but many composers of my generation, myself included, cannot not go that far. Camus wisely said, "You are what other people think you are," and Morton Feldman's grandmother used to tell him, "When three people tell you you're drunk, lie down." There is a factual basis to the Byrne argument that it simply does not do us any good to ignore. At the same time, we need the Nonken argument so that we don't throw the baby out with the bathwater. In fact, those two arguments complete each other. We can't accurately describe the 20th century without both of them.

One of the arguments that composers bring up over and over again to buttress the Nonken argument is that all composers write the way they do from deep inner compulsion, and so there's nothing they (or you) can do about it. I simply don't buy this. It does not accord with my experience. It's true of some composers, and maybe they're the ones saying it, or perhaps it is a romanticization of the creative artist by their enablers. I've seen too much evidence to the contrary. I had a brilliant, ambitious student once who studied scores by composers who won prizes - thinking that if he could write the way they did, maybe he could win prizes too. I've known composition teachers who told their students, "Here's how you write a piece of music," and the student followed instructions and got in the habit of composing that way - often being well rewarded for doing so because the teacher, pleased with their obedience, afterward helped them get awards and commissions. Even I myself have been known to depart from my usual stylistic inclinations in order to accommodate the sensibilities of the people who gave the commission, who might want something more "classical-sounding" and emotive (or possibly just easier to perform) than my usual fare.

Much music, much good music, is written the way it is because the composer has gotten so excited about hitherto underused ramifications of the musical structures she's found in other people's music that she sees a wonderful creative opportunity to take music in a new direction based on those ramifications. That's probably the core paradigm (or at least, it's the more professionally realistic version of the composer "having something deep within her soul to express"). But a composer's idiom is influenced by a hundred forces, some unconscious, some carefully calculated, some financial, some vain, some noble, some inspired, some in habitual response to academic training. And the superficial impulses are no more guaranteed to produce bad music than the noble ones are to produce good music. The audience's reflexive skepticism toward new music is, in itself, no more unjust than the skepticism with which you are reading this article right now - waiting for me to show my hand, waiting to catch me in some fallacy.

It seems to me that I haven't said a controversial or non-commonsensical thing here yet, though I will. To create a healthy musical culture, we need a shared reality. The Nonkens need to admit to the Byrnes that upon occasion a composer has wasted the audience's time with a pompous, confused piece written in ambitious but misguided imitation of earlier works; the Byrnes need to admit to the Nonkens that music may be capable of wonderful large-scale effects that one needs experience and a well-conditioned ear to hear. Where audiences and where composers will tend to draw the line will always differ, and that's good: it gives us a big gray area to argue about, and art is always furthered by being argued about. But nothing is to be gained by claiming that the composers have never, ever been at fault, nor by denying that audience members could gain something from extending their listening capacities.

* * * * * * * * * * * * * * * * * * * * *

So far so good, I hope.

I read the first three chapters of Finnegans Wake once. I laughed, I cried, it was marvelous. For years I thought at some point I'd go back and finish the book, but with each passing year it looks a little more doubtful. It's an incredible, heady pleasure, like nothing else in the world, but fully absorbing that pleasure takes considerable time and energy. Maybe when I'm retired.

What if there were dozens of books like Finnegans Wake? I hear that there are. I haven't read any William Gaddis, I never finished a Thomas Pynchon novel, and I bought Hermann Broch's The Death of Virgil because of its connection with the composer Jean Barraque, but didn't get very far into it. And I'm a voracious reader, always have a couple of books going at least. I'm sure all those books are very good. If I were a literature professor or reviewer of books, I would have dutifully taken the time to get through all that stuff. But I'm just a pleasure reader, except for when I'm reading things for my own scholarship.

As a music aficionado and writer, I did do all that for many behemoths of 20th-century music. I combed Sinfonia for quotations, analyzed the entire tempo structure of Gruppen, listened repeatedly to Barraque's Sonata and looked at the score, went through Carter's Double Concerto countless times, devoured Boulez's On Music Today and painstakingly compared its prescriptions to Le Marteau, read Babbitt's articles and book, and did my homework. I sometimes notice, though, that the big, complex pieces that I've really gotten to know well were ones I studied back between 1973 and 1986, when I was in school and just afterward, before I started at the Village Voice, before my son was born, when I had plenty of time on my hands. The crazes for Helmut Lachenmann and Gerard Grisey came along later in my career. I've listened to their CDs at times and thought, "Well, if I had time to listen to this over and over, maybe I'd start to get more out of it." And, a couple years later, I've listened again - and put the CDs back with exactly the same thought. That today's grad students find Lachenmann and Grisey as exciting as I once found Wolpe and Maderna, and consider me something of an old fogey for not hopping on the bandwagon, makes perfect sense. They've got the time, and the available memory. New experiences make a deeper and quicker impression on them, as they once did on me.

The qualities of complexity and opacity do not guarantee that a piece is good, as we've established above, nor do they guarantee that a piece is bad, as we've also established. It takes time, working one's way slowly into each piece, work by work, to judge how good something is. The question is, of course: how much complex, opaque music can the world afford? How many more complex, opaque pieces can I be expected to internalize in my life than the couple hundred or so I've already absorbed? New CDs arrive in the mail every week. According to the paradigm by which musicians usually talk about music, when a CD contains simple music, I probably listen to it once, say "That's nice," and then put it on the shelf; and when the CD is of complex music, I listen to it over and over, getting more from each new exposure. But what actually happens is closer to the opposite: when the music is relatively simple, it has a visceral impact on me, and soon I want to hear it again, and it starts becoming part of my mental audio furniture, and I start writing about it and recommending it to people. And when the music is complex, I'm more likely to say, "Well, if I had time to listen to this over and over, maybe I'd start to get more out of it." Some of those CDs never get listened to again. For others, the second and third listenings are much like the first.

The defenders of musical complexity already have their angry fingers on the "comments" button, but wait - musical complexity needs no defense from me. I love Pli selon pli, remember? I bet I know more of Maderna's music than you do. That, at this point in my life, composers who can get their main musical ideas across in a listening or two get more of my attention than those who demand 12 or more listenings plus some reading and analysis is not a sign that I am superficial of soul. It is a sign that I am no longer a grad student, and that I am swamped with responsibilities. (I remember, when I studied with him in 1975, Morton Feldman being particularly caustic on this point. He'd criticize a student's piece as unclear, and the student would protest, "But you have to listen to it more than once," and Feldman would sneer, "Kid's 21, and he thinks I'm going to listen to his fuckin' piece twice.") (Maybe he didn't say fuckin', but it was clearly implied.) You can say, because it is one's duty to say so, that the pleasures that come from complex music run much deeper than those that come from simple music, and that the time spent getting familiar with a difficult masterpiece will pay off much more than the ten easier pieces I might have studied in the same span. But this hasn't uniformly been my experience. In my imagination, I think of Nono's Stille, an Diotima and Bill Duckworth's relatively simple Time Curve Preludes as being about equally great pieces; but the truth is, I haven't listened to the Nono in ten years, and I feel a need for the Preludes at least a couple of times a year.

Another popular escape hatch: "You don't need to understand complex music to enjoy it, just sit back and experience it." Yet something tells me that if I simply listened to Ferneyhough's [Ha! I mentioned him] Transcendental Etudes as passively as I do to Cage's Winter Music, I would miss many of the crucial things Ferneyhough put into it. (I actually heard Ferneyhough lecture about that piece at the U. of Chicago, so I know something of how it works. I like it OK. Don't listen to it often.) I think, too, that had I taken that Cagean approach years ago to Boulez and Stockhausen (or hell, Cage, for that matter), I wouldn't today enjoy their music on as many levels as I do. I'm not opposed to the idea that a repertoire might necessitate score analysis and book reading to fully appreciate it. I just don't know how many more composers I'm going to have time to do that with in my life, nor how many the avid lay music lover ought to be expected to study similarly. Nor do I, as a result, find composers I've done that with - like Boulez and Stockhausen - deeper or more appealing than composers like Virgil Thomson or William Schuman who never necessitated any such study.

Allow me a brief detour. There is an ancient tradition in aesthetics, and a wise one, I think, that simplicity in art is a virtue. I insist that one of the things we proved in the 20th century is that it is not a necessary virtue, that it may not be the best virtue - but it remains a virtue. Some will recognize the following quotations from my writing:

True genius is of necessity simple, or it is not genius.... The most intricate problems must be solved by genius with simplicity, without pretension, with ease; the egg of Christopher Columbus is the emblem of all the discoveries of genius. It only justifies its character as genius by triumphing through simplicity over all the complications of art.... Genius expresses its most sublime and its deepest thoughts with this simple grace; they are the divine oracles that issue from the lips of a child; while the scholastic spirit, always anxious to avoid error, tortures all its words, all its ideas, and makes them pass through the crucible of grammar and logic, hard and rigid.... - Friedrich von Schiller, "On Naive and Sentimental Poetry")

Simplicity is the most difficult thing to achieve in this world: it is the last limit of experience and the last effort of genius. - George Sand

In products of the human mind, simplicity marks the end of a process of refining, while complexity marks a primitive stage. Michelangelo's definition of art as the purgation of superfluities suggests that the creative effort consists largely in the elimination of that which complicates and confuses a pattern. - Eric Hoffer

Simplicity is the ultimate sophistication. - Leonardo Da Vinci

And allow me to add one more quote which will haunt you forever, my fellow Americans, a quotation that has appeared in countless books, and that will live as long as American music itself lives:

I began to feel an increasing dissatisfaction with the relations of the music-loving public and the living composer.... It seemed to me that composers were in danger of working in a vacuum... I felt it was worth the effort to see if I couldn't say what I had to say in the simplest possible terms.

Aaron Copland, of course, about the time he wrote El Salon Mexico. "I felt it was worth the effort," he says. Modernists draw a narrative around Copland that his thorny Variations for piano was a great, forward-looking work, while Billy the Kid was a terrible backsliding into mindless populism. But as Copland expert Larry Starr has aptly and truly written, "not only is this ballet score as sterling an illustration of Copland's basic methods as either the Piano Variations or Music for the Theatre; it also reveals these methods at a stage of greater maturity and refinement." Starr's right: study the scores, and you'll see that Billy the Kid is a more sophisticated score, gunfight and all, than the Variations. Copland did not weaken his music in simplifying it - he sharpened it.

You'll think, reader, that I've now shown my hand, and my discountable bias, at last, but not so fast. You may recall that Ives's Concord Sonata - a rather complex piece and not easy of approach by the novice - remains my favorite work, and I wouldn't for all the gold in the world subtract a note from it. Even now in late middle age I occasionally come across a complex, impenetrable piece that blows me away, such as the symphonies of Matthijs Vermeulen, and even more notably the Fourth Piano Sonata of Kaikhosru Sorabji, whose gorgeous and complexly multilayered Adagio came to obsess me before I'd ever read a word about the piece. I listen to it often, trying to capture its tricks, because if I ever untangle them, I have every intention of stealing them. Here's another quote, from Samuel Johnson: "The first duty of a book is to make us want to read it through" - which can easily be transposed to, "The first duty of a piece of music is to make us want to hear it through." Complex as Sorabji's Fourth Sonata is, it made me determined to hear it through. Simplicity is a virtue, but it is not a necessary virtue, and if a piece has compensatory virtues that are dazzling enough, it can get by without simplicity.

Here's that escape hatch: Anyone who's an obsessed fan of a particular complex, opaque piece can always claim that what that piece expresses couldn't possibly be expressed any more simply, and it's a claim pretty much impervious to opposing rhetoric. Thank god for the ambiguity and subjectivity of art, and there will be no Q.E.D. at the end of this article. What he cannot claim, though, I think, is that music generally improves with complexity and opacity, nor that simplifying can't sometimes sharpen a composer's art. At the very least, complexity and opacity tend to withdraw a piece of music from the public sphere, while simplifying increases its public availablility. Ives's most public image, after all, is one of his simplest and (yet) most powerful pieces, The Unanswered Question.

Simplicity, Copland reminds us, requires effort. It is, for me, a sign of courtesy in a composer, of his urgency in wanting to reach me, that he is willing to work to sharpen his musical argument by simplifying it as far as he can without falsifying it. And before someone assumes that I am carrying arround some boneheaded, dumbass notion of simplicity, I do not mean reduction to quarter-notes and eighth-notes, but rather the streamlining and agreement of all elements of a piece to create a unified, singular impression. I hear now and then that some stranger thinks my Private Dances is my best piece; it is certainly my simplest piece, though there are some pretty hairy rhythms in it (including a dance in 29/4 meter). Like Copland, I sometimes take great pains to simplify what I try to say in my music for maximum public effect, and those pieces seem to get across well; other times, I want to do something that just won't reduce to simpler terms, and only my fellow composers realize what I've done. I've always thought Beethoven got the proportions right: he wrote an Eroica Symphony and a Ninth Symphony that showed the masses exactly what he was about, then a Grosse Fuge and an Op. 111 Sonata that made most of his contemporaries think he was mad. Had all of Beethoven's music been as dense and counterintuitive as his last sonatas and string quartets, we would still consider him a genius today, but he would have come down to us as a much smaller, more eccentric figure.

What does this portend for the would-be composer of complex, opaque music? Of course he is free to write what he wants, keeping aware that as the amount of complex, opaque music in the world grows, the time available for the dramatic needs of his own contribution shrink in proportion. He is content, of course - naturally! - to settle for a very small, very serious audience. Perhaps he is ambitious enough to think he can knock Gruppen off its pedestal, so that next year he'll be in the curriculum instead of Stockhausen. If such a composer wants his music to reach an avid but beleaguered music lover in middle age such as myself, the want of the virtue of simplicity will need to be made up for by some pretty dazzling compensatory virtues. Failing that, he will always have for his audience the grad students - who have time and incentive to decipher his intricacies, and who may well continue to love his music into their dotage for the intellectual challenges it provided them in youth.

COMMENTS:

Robert E. Harris says: July 23, 2008 at 11:48 pm - Thank you for writing this piece. The point about simplicity reminded me of reading Einstein's 1905 papers about quantum theory. My ability to read German was poor, but the simplicity of his arguments and mode of expression impressed me then and still do 45 years later. You have hit on a key feature of much excellent work in many areas.

Charlie Wilmoth says: July 24, 2008 at 12:02 am - Long-time listener, first-time caller here. You're A Great American! I'm a grad student, so I suppose it won't surprise you that I find Grisey and Lachenmann exciting, but it isn't, as you suggest, because I have more time than you to listen repeatedly and study scores. Both were thrilling the first time I heard them, and it seems odd to me that you imply that they are to my twenties as Boulez, Carter and Maderna were to yours. Both Grisey and Lachenmann make music that is, to my ears, very immediate-Grisey's gestures are bold and his spectral harmonies twist the ears, and the Lachenmann's sounds seemed so wild when I first heard them that I was attracted to them right away. In contrast, I never liked Carter's music until I played in a performance of A Mirror On Which to Dwell and I could really appreciate all the details. Of course there are Lachenmann pieces that aren't so immediate, but I think you sell him and Grisey short. Then again, I'm apparently part of their target audience, so maybe I'm being myopic.
KG replies: Perhaps, had I heard Grisey and Lachenmann as a grad student, I would have fallen in love at first listen. Thanks.

David Kulma says: July 24, 2008 at 1:29 am - Wonderful! I know you mentioned some works in the post, but I would be interested if you would give a couple of lists. The first of complex works you enjoy, and the second of one's that fail to meet the mark.
KG replies: Well, let's see: in addition to what I mention, I love Pousseur's Votre Faust; Schnebel's Schubert-Phantasie; Stockhausen's Mantra most of all his works, Klavierstuck IX, and some of his new opera Licht; Ligeti's San Francisco Polyphony, Double Concerto, and Monument-Selbstportrait-Bewegung; anything by Berio based on other music, plus his Points on a Curve to Find; Boulez's Repons, maybe Derive; Nono's Contrappunto dialettico alla mente and Sofferte onde serene; those come to mind. I'm on record as liking Babbitt's vocal music and Carter's music from 1948-52. As for the other side, it would be cruel to the composers to list them, and worse, I'd have to do some listening to make sure, which would be cruel to me.

petemaskreplica says: July 24, 2008 at 6:12 am - Excellent post. Your comments about simplicity remind me that whenever I heard Stockhausen talk about his music the thing that really impressed me was that, contrary to what academia would have me believe, he made me realise that at heart his music was actually very straightforward. Something similar happened for me with "Trout Mask Replica", a difficult listen that one day I realised was, beneath the surface, actually very simple. That Feldman quote makes me think of all the composer workshops I've been at; I don't know how it is in the U.S. these days, but on this side of the pond there's a definite attitude instilled in students about writing music that needs lots of listens to be understood, and I think it'd be much more educational to knock it into them very quickly that they don't have that luxury, and they'll be lucky if anyone listens to their piece once, let alone fuckin' twice.

lawrencedillon says: July 24, 2008 at 7:58 am - In a word: yes.

David Toub says: July 24, 2008 at 8:59 am - Thanks, Kyle. I think it's critical for folks to realize that whether a piece is simple or complex doesn't have any relation to quality. I love Webern and Scelsi not because of their complexities but because for whatever reason, their music connects with me. I have deep affection for a lot of Cage not because of its apparent simplicity but again, because I just do. Indeed, the whole notion of what qualifies as "simple" and "complex" is arbitrary. Some folks would consider Reich's Piano Phase to be pretty simple compared with Babbitt's stuff. Yet just yesterday I came across some paper analyzing the hell out of Piano Phase in terms of rhythmic and pitch structure. Who knew? Some folks undoubtedly would look at some of my own recent scores that have a steady stream of eighth notes and one dynamic level as "simple" but it was anything by simple to compose. Beyer wrote some pretty incredible and beautiful music that was derided as lacking technique. How ridiculous was that? I've seen the attitude that if somethng isn't in the mold of Elliot Carter or Boulez then it isn't worth listening to. I also have seen the attitude that if something is less transparent, say like Gunnar Berg, it also isn't worth the time. Both attitudes are unfortunate. It isn't as black and white as all that. Why I dig Schoenberg and detest Carter has nothing to do with complexity. Why I like early Adams vs later Adams also has nothing t do with simplicity. The distinctions, convenient and well meaning though they are, are artificial in the long run .

Marilyn Nonken says: July 24, 2008 at 10:10 am - Perceived complexity and perceived simplicity are in mind of the listener. This is where my interest lies: in the personal, immediate experience of a piece of music, the vulnerable state in which listeners place themselves when they enter a new musical environment. Musical perceptions of opacity and transparency, expectations, and preferences evolve in the listener's mind, as a result of human psychological mechanisms and all that the individual brings to bear on the experience. I see your argument drifting away from the experience of the music towards the reception of the repertoire, and it's important to distinguish that reception is a more abstract concept, reflecting the social or cultural behaviors of groups of listeners, as interpreted by others over time. Considering reception, we abandon the individual listener and begin to see the audience as something of an abstraction. In my own work, I try to stay closer to that listener's personal experience, purposefully avoiding what I see as a kind of Marxist description of Music as a dynamic of mass consciousness, ideologies, material conditions, and means of production….because I play for individuals, not large swaths of people, and I play work created by creative individuals (and whether or not they are "true geniuses" isn't one of my more pressing concerns). Music is not self-delusional; individuals are deluded, and everyone (listeners, composers, performers, and critics) creates their own fictions. Music does not waste our time; we waste our own time, or upon experience see our time as wasted or well-spent. As you note, I don't find generalizations about audiences and composers useful. Debates that depersonalize the musical experience do something of a disservice to (and underestimate) all involved. The more we generalize about music and those involved in the experience as abstract forces or cultures ("tribes), we deny the individuality of musical experience and imply a limit to its possibilities. "How much complex, opaque music can the world afford?" We need to consider, whose or what world we are talking about and question its reality.
KG replies: Otherwise OK?

Samuel Vriezen says: July 24, 2008 at 11:21 am - Kyle, congratulations on another well-written and provocative post. I think it's a good idea to look at what you could call the logistics of complexity, in the sense of how much time you can give to a difficult work, etc. However, I do feel that you're skirting some of the more complex issues you could encounter in opposing complexity and simplicity. Let's focus on Feldman and Copland. They knew each other, and I guess they appreciated each other's work. But certainly I think their aims in simplifying must have been different. Copland's simplicity is about establishing contact with "the" music-loving public; Feldman's demand for simplicity is simply about one student and one (advanced) listener, who is Feldman. There's a very different economics involved here. And clearly, Copland's work was reaching wider audiences than Feldman's. For all his simplicity, Feldman remains a composer more on the order of Lachenmann in terms of audience. And in fact, Feldman stands in for a whole area of music in which you find a great deal of the music that interests me most these days: a music that is simple, in that the ideas are presented with maximum clarity, but that is still so ‘weird' from the point of view of "the" musical language that "the" public understands that its audience will be quite specialist. Just one of the most recent examples that I came across recently is Michael Pisaro's disc "an unrhymed chord" on edition wandelweiser records, which is gorgeous, not very likely to become ‘popular', though the clarity of the idea and the beauty of the result could make a bigger audience in theory entirely possible… So I would say there must be a third term between ‘complex' and ‘simple'; or, that two oppositions should be distinguished, between ‘complex' and ‘simple' on the one hand and ‘sufficiently conventional to merit wide distribution' and ‘hard to sell' on the other hand. (in addition to the third dimension of ‘good' and ‘bad', which indeed is a different thing again). When I'm putting "the" in quotation marks, it's because that's for me the most problematic point here: in fact, I would prefer simply not to speak of "the" audience at all. To make claims about "the" audience is to essentialize it. I take Marilyn to have a related issue in mind when she writes that she plays for ‘individuals, not large swaths of people' - which I understand to be less about numerical criteria than about what one might assume about the character of an audience. This is also why I found myself raising an eyebrow when you write "To create a healthy musical culture, we need a shared reality." - if this ‘shared reality' is of any more specific content than the simple fact that we share a planet and a physionomy, I just can't agree. I'd be very happy to disagree on basic aspects of culture with David Byrne, Marilyn, Feldman, Ferneyhough, you, or anybody, should the occasion arise. If we are to be granted real freedom, we should be granted the right not to admit anything. The resulting disagreements may lead to some heated debate; it may also lead to people simply working on their own project in some type of isolation; but it's the condition under which there is at least some hope for something valuable to emerge.
KG replies: We need a shared narrative with the audience. It hasn't been good for composers to go one way, lay music-lovers another, completely disagreeing about what happened and resentful of each other for not understanding. You're talking about the 106th floor, and I'm in the lobby. I started out in PR, ya know. Also, I first wanted to include a whole other section on "simple-but-difficult" music like Phill Niblock and Eliane Radigue, but even without that it got up to 4700 words. And who's got time to read all that? Grad students?

David McMullin says: July 24, 2008 at 12:26 pm - This is a great post, and I strongly agree with your premise. I've never thought that there could only be one kind of good music. Regarding simplicity vs. complexity, there isn't necessarily a one-dimensional spectrum between these two extremes, and the same piece can be simultaneously simple and complex in different ways. I respond best to - and try to write - music that operates on several levels at once, where there's something clear and powerful enough to grab an uninitiated listener at first hearing, but also enough mystery to leave you feeling that there are important forces at work beneath the surface. Even if you don't ever listen to the piece again, that sense of subliminal depth is still important. And if you do listen again and again, then each time you'll get more, but still feel that there's more to get. Your reference to Beethoven is apt here. It's not just that he wrote some simple pieces and some complex pieces. Even in his simplest pieces, there are all sorts of nuances and subtleties, and even in the most enigmatic pieces, he's not afraid to hit you over the head with gestures that are pretty obvious.
KG replies: Thanks. Of course I'm aware it's not a one-dimensional spectrum, but there's only so much you can do in a blog entry, and I feel like I already stretched the limit.

syro0 says: July 24, 2008 at 12:52 pm - Thanks for a great article. I agree with your views to an almost unlikely degree, yet I feel (it's more of a gut-reaction than an actual argument) that the word "simplicity" has an unfortunate negative ring to it. As you thankfully indicated, simplicity in art is fundamentally different from everyday simplicity in dealing with problems. There is no word for the concept, but to me it includes shades of "apparent effortlessness" (though not as slick) and "inevitability" (though not as in brainless so-called commonsense; the german "folgerichtigkeit" comes to mind). of course, some technically complex procedures (as related to the average use within a craft) may equally result in clumsiness, or brilliant logic. some fairly simple decisions may lead to staggering perceived complexity. One more quick thought: What makes the discussion a little more difficult when it comes to music (as opposed to literature, for instance), is that music may (and will) of course be perceived as sound as much as process. Either of the two aspects can define the quality of a piece, as can both at once, or none. Nobody admires the shape of letters on a page, except in rare instances. This is marvellous, of course, and there is no end of wonder. Yet, with the heated formal discussion that started in the mid-20th-century, I sometimes fear that - in its strange resemblance to the theories of the duality of man - the history of western thought is written all over yet again. In truth, however, I don't really fear, I am deeply amused (pleasure more than ridicule), while often thoroughly engrossed by the back and forth of opinions.

Richard Mitnick says: July 24, 2008 at 1:37 pm - On Tuesday, John Schaefer had one of his "smackdowns". It was new music vs the old lovelies in the concert hall making one group or the other miserable. Well, it is a new world, with no limits. The argument is irrelevant because of the wonderful availability of streams like your Post-Classical, Iridian, Counterstream, Philip Blackburn's Innova.mu and the like. I asked in the comments to John's show, who knew of Charlemagne Palestine, whose work you have presented. The point is to get music out to a public which can then ignore it or support it. I personally enjoy a great deal of new music, and I have been heavily influenced by the early American geniuses, Nancarrow, Partch, etc., brought to the public by American Mavericks. We will support what we like, we will spend money to support artists, and even Amazon with their .mp3 downloads makes it easy as pie. Marvin Rosen at WPRB, Princeton, just did a five hour tribute to Henry Brant. When I looked at the play list and saw that most of it was from a nine-CD collection from Innova, I went right to Amazon and guess what, it was there and I bought it. There is no need for an argument over style, it is all there, you have proved it, and, a lot of it is even presented on wnyc2.

Gerrit Roessler says: July 24, 2008 at 2:49 pm - Thank you for this great post. As has been commented before, I think you give a very fair and balanced account of the relationship between composer, audience and the somehow artificial expectations of music criticism that seem to be alienated form the actual musical experience. I also agree with Nonken's comment that the line between a worthwhile listen and a waste of time is determined by the listener. Moreover I think your analysis takes a big weight of the shoulders of people like me, who are dedicated listeners but are as performers and composers very much on an amateur level. From now in I don't have to feel guilty if I do not give a piece a third or twelfth chance just because it has been celebrated in current art circles, I do not have to feel bad if my own pieces are enjoyable and simple but I don't have to feel bad for intuitively enjoying Lachenmann and Zimmermann either. It feels very liberating. Thank you!

Richard Lainhart says: July 24, 2008 at 5:23 pm - An interesting read, Kyle - thanks. One thing I'd like to add is that I find, when discussing the kind of "simple" music you refer to here, that a more effective descriptor is "elegant". I studied with Joel Chadabe, and I think the most important thing I learned from him was to always strive for elegance in composition - elegance in the scientific sense of the clearest, most refined expression of an idea. This, to me, is what Minimalism is all about - stripping away all the extraneous stuff that gets in the way of clear expression in order to expose the music's fundamental nature. "Simplicity", especially when contrasted with "complexity", has some connotations that I feel "elegance" avoids. And I would say that both Niblock and Radique write elegant music.
KG replies: I completely see your point. However, it makes me mad that the connotations of "simplicity" are looked down upon in the academic world, and I like rubbing the word in their faces as often as possible.

Samuel Vriezen says: July 24, 2008 at 6:33 pm - Kyle - of course you have a point there, and I certainly agree that resentment is not a very useful emotion, I'm certainly not one to resent anybody for not liking my work - but really what I'd like most of all to tell "the" audience is that it doesn't exist. I feel that's what it needs to realise, that's what would be the liberating thing to tell it. I hope you'll write something about how "simple-but-difficult" composers fit into the scheme; I'm very interested to see your views on this (and though no grad student, I promise I'll actually read it!)
KG replies: Well, yes, I'd love to tell every single music lover out there that there is no such thing as "the" audience, and that his father really loved him but just didn't know how to show it, and that all the qualities that made him feel weird as a kid will make him perceived as all the more special after he's 40. But in a music history book, I'd settle for acknowledging that in the 1980s, many composers came to agree that late 12-tone music had become off-puttingly technical.

andrea says: July 25, 2008 at 11:24 am - What grad students are you hanging out with? I barely have time to read this blog (but I am always compelled to do so, because I learn so much from it), with the three jobs, the non-profit chamber ensemble, the other two groups, the flute that needs to be practiced, the girlfriend that needs to be loved, and the dissertation that may get written someday. These grad students that you mention clearly need to get a life… =)
KG replies: I know, when I was a grad student I was scheduled 20 hours a day, and had to squeeze all my drinking into the remaining four hours. But somehow - maybe it was mostly undergrad and just after finishing my D.Mus., when I suddenly *really* had a lot of time on my hands - that was the era in which I figured out how all that complex music worked.

Bill says: July 25, 2008 at 1:57 pm - I'll also jump on the bandwagon and say this is great writing (are you listening Pulitzer?). I was thinking of other possible shared criteria, and the one that's common to the modern music I love is ‘hope'. Everything cycles, and I'm looking forward to a generation that revolves around simplicity and hope rather than 20th century complexity and angst.

Samuel Vriezen says: July 25, 2008 at 2:19 pm - Kyle, I would probably subscribe to that bit about the 80s (not being in the US I have a more hazy idea of that music, of course); but I think the challenge is to make that exact point /without/ reference to a shared musical culture and to "the" audience. It will only make the point stronger. In fact, I would argue that the weakness of stuffy styles like, as you have it here, 80s academic 12-tone music, is in fact exactly its "shared" language and its complete lack of risk-taking in terms of audience creation. (I believe audiences don't just sit there but are always *created* along with styles and performance traditions - not in the sense of being designed; audiences grow along with them)

Matthew says: July 25, 2008 at 4:52 pm - If such a composer wants his music to reach an avid but beleaguered music lover in middle age such as myself I'm buying most of what you're saying (and from a pro-complexity standpoint—well, really a pro-everything standpoint) but, come on, that's a bit of an escape hatch in itself. Even as a jest, it's glossing over the fact that, no, you are not just a "music lover," you're a professional critic and educator, the fact of which means that people who aren't professionals—or aren't yet professionals—are going to take your opinions as the word of someone who presumably does take more time than they might to determine whether a piece of music is worthwhile or not. It's kind of like when politicians insist they're not politicians.
KG replies: Well, I'm certainly not going to disrecommend the music without getting into it deeply, and I'm rather unlikely to get into it deeply if it's a lot of trouble and I don't hear anything that initially attracts me. Since I no longer review CDs, and I don't write as a critic, I have no professional obligation to comment on or familiarize myself with any particular disc. I'm just a blogger. You're right insofar as, had Fanfare magazine sent me the disc years ago, or had I included it in a Voice Consumer Guide, I certainly would have put the amount of time into it that I needed to to do it justice.

Rodney Lister says: July 25, 2008 at 8:18 pm - To quote Virgil Thomson: "I read it, every word of it. I could have put it down, but I didn't." Which doesn't mean I didn't think it was brim full of good sense, because I did. I whole heartedly agree that neither complexity nor simplicity, in and of itself, justifies a piece or style or makes it good, but I bridle at the notion that somebody can tell me that I can't like Schoenberg or Babbitt on one hand or Virgil or Grainger on the other of Cage or Feldman on yet another or Vaughan Williams or Britten or Elgar simply because one can't like that kind of music. (Not that I'm accusing you of doing that.) I'm often very upset by the kinds of blythe assumptions that people want to make about the intention of some of those composers. I grew up more or less in the cradle of East Coast Academic music, and I saw first hand, both in the way my teachers looked at the music I was writing and the comments they made about it, and the way they talked about their music and the pains they took with it, that people like Donald Martino and Milton Babbitt and Martin Boykan and Seymour Shifrin and Arthur Berger were vitally concerned with what their music sounded like and how it would be and was received by an audience, and how much they insisted that I as a student also would be concerned with those things-and I can attest that over and over again I was told that the fact that some point in a piece of mine could be explained by some system didn't mean that that moment could be justified by said explanation. Having had the experience of seeing how much they cared about all that, I get upset by people who don't like their music (which they're, of course, perfectly entitled to do) trying to justify the fact that they don't like it by claiming that those composers were only interested in some kind of mathematical thing and didn't care what their music sounded like and had contempt for players and audiences and….etc., etc. It seems to me that every composer deserves the assumption that they're making a good faith effort to write the best music they can do and that they want to make it as beautiful, expressive, meaningful, interesting-whatever word you want to use (fill in the blank)—as they can do, until they're proven guilty of doing anything else-including the most unforgivable thing, tiring our sense (as Pope put it), and that every piece deserves to be judged on terms of how well it does whatever it's trying to do, regardless of what style or tonal language it might be in. Also everybody is entitled to like or dislike anything they choose, but it would be good if everybody could lay off the ad hominem attacks. Now I guess we can all join hands and sing Cum Ba Ya or Shall We Gather at the River or Serenity or (maybe best of all) Exaltation, or something.
KG replies: Rodney, I would rarely accuse a composer of not acting in good faith, though I can think of a handful of examples. I don't think our field is *entirely* free of charlatans and opportunists. (I remember one Downtown composer who, when grant organizations all went multicultural, suddenly rounded up a slew of drummers of color from different continents to improvise with, so his grant proposals looked really multicultural.) But I think it's far more common for a composer to pick up, often from a teacher, some idea about composing that really isn't very artistic, without realizing that. For instance, I was on a panel once with a woman composer in mid-career, and every pronouncement she made about a score began with the words, "My teacher always told me that you should do such-and-such," and "My teacher said never to do *this*," and I finally thought, "Good lord, woman, here you are in your late 30s, haven't you ever learned to think for yourself?" I don't think she was acting in bad faith, but she was still following what some professor told her to do as though it was a recipe. Some of the worst music I've ever heard (and I'm thinking of Downtowners at the moment) was made by people who were absolutely sincere. But sincerity never precludes the possibility of being absolutely mistaken. Nor is it impossible for an insincere but shrewd craftsman (I'm thinking of Bernstein's Harvard lectures now) to come up with a damn good piece. Complexity guarantees nothing, and I'm tempted to think that sincerity doesn't guarantee much more. (Was there an ad hominem attack in my essay? I thought I put in one line - "And the superficial impulses are no more guaranteed to produce bad music than the noble ones are to produce good music" - that finessed that issue.) But thanks for writing in at such length. I rarely disagree with anything you say.

Tom Brennan says: July 26, 2008 at 1:37 am - Ordinary conversation is incredibly complex. Linguists struggle to no end trying wrap their brains around even the simplest turns of phrase, the meanings of which are easily understood by the vast majority of people, including small children. Language is commonplace. So is music. But complexity is also commonplace. I think the completeness and/or relevance of our music theory for prescribing compositional practice is horribly exaggerated. The problem is that we aren't approaching this scientifically enough to realize that we're the lab-rats in this experiment. If you have something to say, say it. The theory comes in the analysis after the fact. The so-called "complexity" we're all talking about here is a copout excuse for the real complexity we've chosen to ignore by fetishizing the notational aspects of music and refusing to cultivate the innate musicality we all acquired before we even went to college.
KG replies: That mistakes the kind of simplicity I'm referring to, as I tried to clarify in the penultimate paragraph: "I do not mean reduction to quarter-notes and eighth-notes, but rather the streamlining and agreement of all elements of a piece to create a unified, singular impression." Someone else here called it elegance, R.H. Blyth would have called it Zen, meaning spontaneity. It is, of course, extremely complex to try to describe a simple, intuitive, natural phenomenon via analytical means. It would take an extremely complex algorithm to fully account for my piece Private Dances, but it remains - perceptually, and for the listener - a very simple piece. Often, simple (meaning linear and more consistent) compositional means result in more perceptually complex pieces (12-tone, etc.).

Tom Brennan says: July 26, 2008 at 11:41 am - The "extremely complex algorithm" would be a theory of everything. Also, what is being called "perceptually complex" might be to a linguist called "ungrammatical". Otherwise, I understood your penultimate paragraph, and my last comment was just chiming in to assert that complexity in design is extra-musical currency. But it is cultural currency, nonetheless. You encounter this a lot in non-western art, where the overt design of a certain textile, for instance, may be simple, but the technique of making it, which everyone in that community is acutely aware of, provides the majority of its value as an indicator of social status, etc. I think of prescriptive music theory in this sense—that it imbues a certain privileged quality to the artwork in the eyes of a community, which uses it partly to create a sense of elevated social status.

Robert Davidson says: July 26, 2008 at 4:51 pm - This is great and very stimulating. I think another idea that has a lot of bearing on this is the whole area of cognitive constraints (quite nicely summarised in Leonard Meyer's 1998 essay "A Universe of Universals" in the Journal of Musicology), which I hope you will forgive me for quoting at length: "The kinds of relationships that can be perceived and processed by the human mind are limited by neuro-cognitive universals. And these constraints account for many features of music-non-Western as well as Western. To take an obvious case, the minimum distance in frequency between pitches in a scale depends on human auditory discrimination. As a result, intervals smaller than a half-step almost always serve to inflect structural tones. "More importantly, the amount of information that the human mind can process is constrained by human cognitive capacities. In general, cognitive overload, which can be a matter either of amount or of speed of stimulus input, creates confusion and anxiety. In our age of electronic resources, this hazard has become very real. Vastly to increase the amount of information the mind must process-for instance, playing recordings of a number of different symphonies simultaneously-is to court the vacuousness of white noise. And speed of both information processing and muscle response are similarly limited. "More specifically, the number of elements in any comprehensible relationship is limited by the cognitive capabilities of the human mind - by what psychologist George Miller called "The Magic Number Seven, Plus or Minus Two." The repertory of tones in the music of most cultures is constrained by this universal. So, too, is the number of elements that make up patterns on the various levels of a musical hierarchy-the number of motives in phrases, of phrases in themes, themes in sections, and so on." Perhaps some modernist complexity represents an unusual departure because it makes a conscious effort to move beyond the contraints of non-encultured, biologically-endowed human perception, and may find it difficult to ever find a non-specialist audience as a result.
KG replies: Uh-oh - I thought the magic number, pitch-wise, was 37. Long quote well worth it.

Rob Davidson says: July 26, 2008 at 7:02 pm - I agree with Tom Brennan I think - that's a good point about social status being a major driver in motivating people to follow prescriptive musical grammars. John Carey's enlightening and sometimes infuriating book "What good are the arts?" deals with this topic.

Vadim says: July 27, 2008 at 11:06 pm - Oh my, how times have changed! Thoughtful music writers like yourself agonize over why they do or do not "get" this or that piece by this or that composer. They search for reasons and explanations, analyze their possible perceputal biases, and what they do say in the end still has the flavor of a hypothesis rather than an apriori truth. Which brings me to this: Some twenty plus years ago Harold C. Schonberg attended the premiere of Roger Session's 8th Symphony (NY Phil, conducted by Steinberg) on behalf of his employer The NY Times. On the basis of that one hearing of Sessions' composition, he confidently declared in the next day(?) NY Times review that the piece had everything going for it except originality and individuality. And he was on record stating that for an "experienced critic" one hearing is perfectly sufficient to assess the merits of a new musical composition and render his firm judgment the next day. Oh my… how times have changed… P.S. I discovered your blog by accident a couple of days ago, and I want to thank you for much pleasure your writings have given me already.

Alex Temple says: July 28, 2008 at 2:29 pm - This post is one of the most nuanced discussions of this issue I've seen on the blogosphere — fantastic! I find that the highly complex pieces I fall for are usually ones that, in one way or another, grab me immediately. Many of them I don't entirely understand or fully follow the structure of until many more listens — but *something* makes me want to come back. A lot of the composers whose names come up when the topic of discussion is "difficult modernism" have a few pieces that grab me in this way and many that don't. For example, the first time I heard Lachenmann — it was years ago and I don't remember what the piece was — it didn't grab me and I didn't listen to it again. Then a few years later I heard "Tanzsuite mit Deutschlandlied" and it got me from the first note (or rather, the first note and then the insanely long pregnant pause that follows it). Same thing with Ferneyhough: I listened to "La chûte d'Icare" a bunch of times and eventually gave up; the first movement of the Third Quartet didn't click with me until the ninth listen (and when it did I felt like Neo seeing that the Matrix is really made of green floating numbers), but the thing is, there were certain chords and gestures that fascinated me the very first time I listened to it, and if I'd followed my intuition, I probably could have predicted that that piece would click, and that "La chûte" wouldn't. My favorite example of this is actually not one from music: it's David Lynch's film "Inland Empire," which I wasn't wild about the first time I saw it, but which had enough in it that haunted me in the months that followed that I went back for a second viewing, and I loved it the second time. I've now seen it five times, love it more with each viewing, and have figured out most of its abstruse, bizarre, opaque structure. But what made me come back in the first place wasn't the thought that "Hmm, maybe on further study I'll understand this better" — it was the fact that there were specific details that I felt compelled on a gut level to see again. (All of this is, of course, very similar to what you said about the Sorabji piece.) By the way, you might try Pynchon's "The Crying of Lot 49 if you haven't. It's short, not at all as difficult as his later books, and often very funny.

Rob Deemer says: July 30, 2008 at 3:07 am - Thanks for this, Kyle. It's given us all a lot to chew on. I'm going to enjoy discussing this article with my comp studio in September…

mclaren says: August 4, 2008 at 10:54 am - Discussing complexity in music seems incomplete as long as everyone keeps talking about "complexity" as a big lump, an undifferentiated thing. There exist different kinds of complexity in music. And it makes a huge perceptual difference which kind of complexity you're talking about. Lots of complexity of one kind actually winds up being perceptually simple, while complexity of another kind quickly turns into the perceptual equivalent of static on a TV screen tuned to a dead channel. The best overall discussion of this remains Meyer's 1998 article "A Universe Of Universals," so you should really read that article (cited below) for all the details. Absent a full reprint of that entire article as this post, let me try to give some specific examples. Rhythmic complexity differs radically from pitch complexity. Timbral complexity differs radically from pitch and rhythm complexity. Dynamic complexity (lots of different discrete levels of loudness) differs radically from pitch and rhythm and timbre complexity. Why? Because 70 years of psychoacoustic experiments have shown that the human ear/brain system has radically different perceptual precision depending on whether you're talking about timbre, rhythm, pitch, or loudness. Many psychoacoustic experiments have shown that the human ear/brain system can detect pitches to an accuracy of about 0.2% in the most sensitive region of the auditory range, which turns out to be the region around 2 kHz. That's about an octave and half down from the highest key on a piano. In that range, the human ear/brain system can identify a tremendous number of different pitches. Estimates based on psychoacoustic experiments show that the human ear/brain system is capable of identifying around 280 different pitches per octave. However! As George Miller's 1956 paper "The Magic Number Seven, Plus Or Minus Two: Some Limits On Our Ability To Process Information" (complete citation in bibliography below — yes, this post has a bibliography, sorry, but it's necessary) shows, we also have a cognitive limitation on the total number of pitches we can deal with at any given time. Now, the phrase "at any given time" turns out itself to involve some subtleties, because we are talking about the span of immediate attention. This is the span of time over which short-term memory operates in music. And that's not a fixed time window: if the music is not redundant in the sense of Shannon's information theory, that span of immediate attention (i.e., the time window over which we can hear and recognize and parse things going on) is very short, whereas if redundancy is high, the span of immediate attention is very long. That limit turns out to be around 9 pitches. So when you go beyond 9 pitches over the span of immediate attention (whatever those pitches are — they don't have to be taken from the conventional 12 logarithmically equal pitches used in modern western music), you get problems. Notice that this does not limit you to 5 or 7 or 9 pitches in the entire composition, only to 9 distinct pitches over the span of immediate attention, which varies depending on the other things going on in the music, including the redundancy. So this is not a prohibition against chromaticism or a limitation on the total number of pitches that can be used in a composition as a whole, it's a limitation on the total number of pitches that can be used within the span over which human short-term memory operates effectively in the context of that particular composition. This explains why some classical music uses a whopping huge amount of chromaticism yet still retains audible organization, while other so-called "post-tonal" music uses relatively fewer pitches yet because of much lower redundancy exhibits no audible organization, viz., Milton Babbitt's post-partition cosets. Grey did psychoacoustic studies on timbre at Bell Labs back in the 60s and 70s, so we now know a great deal about the human ear/brain system's ability to process timbre. It turns out that there are basically three relevant dimension of timbre, and we can recognize and identify a lot of different variations among those three timbral dimensions, thousands in fact. So our ability to recognize and identify timbres is hugely larger than our ability to recognize and identify pitches. The human ear/brain system has almost no ability to finely discriminate dynamic levels. We basically have loud and soft, and that's it. If you play, say, 15 different precisely gradated dynamic levels and test listeners' ability to reliably discriminate ‘em, you'll find people have almost no fine discrimination in loudness levels. Our perceptual granularity for dynamic levels in music is crappy. We have about 2 bits of resolution, maybe 2.5 bits at most. We hear loud and soft and that's about it. If you push hard you can get most listeners to discriminate a third dynamic level, "in-between," but that's it. Psychoacoustic tests show, for example, that humans just cannot reliably recognize and discriminate (for instance) 12 different precisely gradated dynamic levels. The human ear/brain system just doesn't have anywhere near the kind of fine resolution for dealing with loudness that we have with pitch or rhythm or timbre. As for rhythms, it turns out that if you use a constant or near-constant rhythmic pulse, the human ear-brain system can accept and recognize a lot of different simultaneous rhythms. For example, it's easy to hear 4 against 5 against 6: likewise, it's easy to to hear 4 against 5 against 6 against 7, and it's easy to hear much more complex rhythmic resultants. Kyle Gann uses 6 overlapping in his Yamaha Disklavier piano piece The Waiting, I think 3 against 5 against 7 against 11 against 13 against 17. (Might be wrong, I'm just working from memory here. But there are 6 simultaneous mutually prime meters going on.) The result doesn't sound complex — it sounds straightforward. The human ear/brain system has a tremendous capacity to accept high levels of rhythmic complexity as long as the overlapping meters use a regular pulse. If you break up the regular pulse, the human ear/brain system rapidly loses the ability to parse rhythmic complexity. Take a specific example: 4 against 5, a pretty trivial polyrhythm. But now shotgun out 6 pitches in the top line and then play one and then shotgun out another 7 and then play one, etc., and on the bottom line delete 8 pitches in a row and then play one and then delete 9 and then play one, and so on. If you play the resulting polyrhythm it suddenly sounds incomprehensible. You get what sound like random herky-jerky rhythms with no rhyme or reason. What's going on there is that you have removed the regular pulse. As long as you have a regular pulse, the human ear/brain system can accept huge amounts of rhythmic complexity, 6 or 7 or 10 or more simultaneous tempo-streams, and you'll still be able to parse it and make sense of it. But get rid of the regular pulse, and the rhythms stop being rhythmic and start sounding chaotic. You can't recognize or make sense of the rhythm, it all sounds like spastic junk with no audible organization. Various researchers have hypothesized that this is due to an autocorrelation process in the brain during rhythmic perception. We don't know the details of the cognitive processes yet, but we do know that removing a regular pulse reduces and eventaully destroys the ability to hear what's going on rhythmically. See the Sloboda and particularly the Povel & Essen and Tiovianen references cited below for more details. The same applies to pitch — you can use up to 9 highly microtonal pitches as a melodic mode, and the human ear/brain system accepts ‘em right off. No problem. But as soon as you start going beyond that many pitches in a melodic mode within the span over which short-term memory operates within the context of that composition, the ear/brain system quickly gets overwhelmed. Note that the span of immediate attention varies according to the music's redundancy, so for highly redundant music, the span of immediate attention can be a long period of time, whereas if you have lots of notes with complicated rhythms whizzing past you at high speed, the 9-pitch limit really closes in on you. Beyond 9 pitches in a melodic mode at the absolute outside within the span of immediate attention, you can't recognize any audible organization, it all just sounds like wildly chaotic junk. Note also that highly chromatic patterns remain comprehensible if they're highly correlated, i.e., if you get regular monotonic patterns like an ascending or descending chromatic line. So let's summarize: The human ear/brain system has a tremendous capacity to parse timbral complexity. You can throw huge numbers of different timbres at a musical audience and it won't phase ‘em. In fact, you can compose pieces in which every single note uses a different timbre with no timbre repeated, and audiences will not have much of a problem. Webern's famous re-orchestration of the Bach piece offers an obvious example. There will be some minor problems in auditory stream segregation if the timbres are wildly different on each note, as Bregman has shown. However, in general, an will find such the underlying organization of music that is very timbrally complex fairly easy to perceive. The human ear/brain system has a more limited capacity to parse pitch complexity: 9 melodic modal pitches at a time, but they can be chosen from up to 280 pitches per octave, which makes the possible range of pitches very large. You just can't throw more than 9 of ‘em at the audience within the span of immediate attention (a time window which depends on the redundancy of the music), otherwise the music breaks down and becomes perceptually incoherent. Note also that you can use way more than 9 pitches in the entire composition, but not more than 9 at any given time unless they're highly correlated — i.e., some regular ascending or descending pattern of chromatic pitches. This is really just a fancy way of saying "modulating between different keys using melodic modes of 9 or less pitches sounds comprehensible, while using all 12 pitches as a melodic mode sounds destroys the audible organization." The human ear/brain system has a huge capacity to parse rhythmic complexity provided that you use regular pulses and not intermittant isolated notes. No one has done psychoacoustic experiments yet to demonstrate the perceptual limits of rhythmic complexity, but we know from successful compositions like Nancarrow's and Gordon's and Lang's and Gann's that the level of rhythmic complexity possible possible in music that does not overrun the human ear/brain system's capacity for recognizing patterns is very large. 6 or 7 or 8 simultaneous mutually prime tempo-streams at least, and probably more. Audiences can hear that and have no trouble with it as long as you use constant rhythmic pulses. The human ear/brain system has a very low capacity for parsing dynamic level complexity, that is to say, complexity produced by organizing lots of precisely gradated levels of loudness. Humans just can't parse more than 2 or 3 loudness levels reliably, we simply can't recognize and reliably identify lots of different loudness levels. There's an added caveat to pitch complexity: if you use regular monotonic patterns, the human ear/brain has no problem parsing the result. For example: if you play a constant ascending chromatic scale of 12 chromatic notes over and over again, even though there are a lot more than 9 pitches in the melodic mode, the human ear/brain system has no problem hearing exactly how the melody is organized. So the 9 pitch melodic mode limitation is somewhat flexible to the extent that regular monotonic patterns provide an exception. If you toss all 12 pitches in with a random order, no, listeners can't parse that, it degenerates into an undifferentiated mass of chaotic-sounding pitches. But a continuously ascending or descending or some other similar monotonic pattern using all 12 pitches, that, the human ear/brain system can readily recognize and identify and it doesn't cause problems. So what does all this mean? It means that musical complexity might or might not present problems for the listener according to what kind of complexity we're talking about. Organizing a composition by using lots of precisely gradated loudness levels is going to fail because it's much too complex for the human ear/brain system. If your musical composition depends on listeners recognizing and reliably identifying, say, 17 different precise levels of loudness of musical notes, your composition will lack audible organization. The audience will hear an undifferentiated mass of notes and get bored and antsy. Even moderate levels of complexity in the organization of loudness of individual notes fails insofar as it's crucial for organizing your composition. Once again, a caveat: if your complicated system of dynamic levels isn't necessary for perceiving organization in your composition, then it won't matter if listeners can't hear it. This limitation only applies to loudness levels used as the sole or primary means of organization in a composition. Organizing a composition by using more than 9 modal melodic pitches within the span of immediate attention (a time window which varies according to the music's redundancy), regardless what they are, will likewise fail…unless you use monotonic regular patterns of pitches, like ascending or descending chromatic scales, etc. If you move to a melodic mode of 12 pitches per octave, as the serialists did, the human ear/brain system can no longer parse this and the result will sound more like hail on a tin roof than like familiar western music. You'll hear an undifferentiated mass of chaotic pitches with no audible organization. Once again, typical listeners will get bored and jittery. (Atypical listeners may enjoy the experience. They won't be a large percentage of the population, however.) Organizing a composition by using huge amounts of rhythmic complexity will not present a problem for listeners, provided you use more or less constant rhythmic pulses. Even wildly extreme amounts of rhythmic complexity, such as 5 against 7 against 11 against 13 against 17 against 19 with embedded tuplets, will not be a problem for the audience, as long as you use a more or less regular rhythmic pulse. However, if you use intermittant pitches with large blocks of rests, the result will turn to spastic chaos. It will sound chaotic and disorganized and once again the typical audience will fidget and jitter and get bored fast because they won't hear any audible organization. Organizing a composition by using enormous amounts of timbral complexity is essentially never problematic, though it does tend to disrupt the perception of auditory streams as Bregman shows (see reference below). A composer can throw virtually any level of timbral complexity at the audience and it won't faze them. Audiences just don't have a problem with a large number of radically different timbres being used in a composition, so timbral complexity basically seldom presents an issue unless you have two very close or intertwining polyphonic melodic lines and the organization of your compositions makes it crucial for the audience to reliably distinguish twixt those 2 auditory streams. Now let's look at what totalists do, as opposed to what serialists do, and we can see that the kinds kinds of complexity we're talking about are radically different, and have radically different effects. Totalists typically use lots of rhythmic complexity, but with a more or less regular rhythmic pulse. In a typical totalist composition, you're got a bunch of instruments playing different meters, but constantly, with notes going in all parts pretty much all the time. This is easy for listeners to parse. It's not a problem. So even though it's notationally complex, the auditory resultant is relatively simple. Serialists typically use lots of different chromatic pitches, all mixed up according to pitch-class set calculations or other exotic methods of organization, so that you've got all 12 pitch-classes being used a melodic mode, and the order of the pitches is permuted in complicated ways. This is impossible for listeners to parse. The human ear/brain system can't discern any audible organization in that kind of composition. So the audience gets bored fast and fidgets and jitters. The kind of complexity has a crucial impact on the audience's ability to hear what's going on. Totalists write rhythmically complex music, but in pitch terms, totalists use a lot less pitch complexity than the typical serialist, or even than late-period Wagner or a composer like Max Reger or Carl Ruggles. So totalist music, while nominally complex, is complex is a way that listeners find easy to deal with. Audiences have no problems recognizing the patterns and grasping the musical organization of pieces like Michael Gordon's Trance. But serialists write music which not only has very high pitch complexity (which by itself makes it impossible for listeners to hear audible organization), the total serialism crew threw in organization by 12 different gradated dynamic levels and 12 different rhythmic patterns on top of that. Moreover, because of the way total serialist music is composed, you don't get a regular rhythmic pulse. So the net result for total serialism is very high pitch complexity and very high rhythmic complexity but without any regular pulse and very high complexity of loudness levels. When you throw all that at an audience, the human ear/brain system just can't cope with it. It's not a matter of "educating" the listeners, when you toss that much complexity of those kinds at listeners, the limitations of the human nervous system kick in. Listeners simply cannot parse that much information presented in those ways. To make matters even more complicated, there are strong indications that complexity in the different parameters of music is perceptually cumulative. In other words, if you have a great deal of rhythmic complexity, you need to reduce pitch complexity to prevent the music from turning into a glob of undifferentiated chaotic "stuff." This applies with different force to different musical parameters, however. High pitch complexity does not require as much low timbral complexity as it requires low rhythmic complexity and low dynamic-level complexity. So in this sense, you can think of musical complexity as a rough constant area in a 4-dimensional cube: if pitch complexity goes up along one axis, rhythmic complexity must go down along the other axis, and so on. The 4 musical dimensions here are pitch, rhythm, timbre and loudness (dynamic level from fffff to ppppp). So I really think the discussion needs to deal with the fact that it's just how complex a piece of musc is…it's what kind of complexity you're talking about. Musique concrete composers discovered that phenomenally high levels of timbral complexity did not present a problem for listeners. Totalist composers discovered that enormously high levels of rhythmic complexity can still yield easy-to-hear and readily understandable forms of musical organization, provided that a more or less regular rhythmc pulse gets used to let listeners hear the different simultaneous meters going on in the piece. But serialists discovered that even moderately high levels of pitch complexity or complexity of dynamic levels (in which compositions are organized according to arcane schemes of the loudness of musical notes) fail completely. These kinds of organizational schemes prove inaudible. The listeners just don't hear audible organization in these kind of pieces. Instead, listeners hear chaotic herky-jerky random arbitrary spatters of notes that come and go willy-nilly, without any discernible pattern. These documented facts about the human ear/brain system do not carry aesthetic implications. Stating these documented facts about music perception is not an attempt to use psychoacoustics or cognition research to draw conclusions about whether serialism is "better" or "worse" than totalism. You can't make aesthetic judgments based on laboratory tests. The fact that serial music sounds like herky-jerky random spatters of notes without discernible organization isn't a value judgment: some listeners love that kind of music. If so, great. By all means, listen to it, compose it, these facts don't dictate the kinds of music we should compose. These facts about the human ear/brain system, which come from 70 years of psychoacoustic research, dont' tell us what kind of music people ought to compose or should like. It just tells us the auditory results of certain types of musical complexity. Even high levels of rhythmic or timbral complexity are easy to parse, whereas even moderate levels of pitch complexity are impossible to parse. Note that I say "moderate" levels of pitch copmlexity when talking about 12-tone serialism because, of course, it's entirely possible to use microtonal tunings to get more than 12 pitch classes, and do serialism with that expanded set of pitches. The guy who's in charge of Harry Partch's musical instruments right now, Dean Drummond, does serial music using more than 12 pitch classes. Drummond uses just intonation to do serialism, and he makes use of lots more than 12 pitch classes, so the level of pitch complexity involved in 12-tone serialism is only moderate. You could easy use, for exmaple, all 31 pitches of a 31 equal tuning to do serialism, and that would have pitch complexity much higher than anything you get in 12-tone serial music. We really need to get a little more specific in these kinds of discussions, though, when a general term like "complexity" gets tossed around. The specific kind of musical complexity a composer uses has a crucial impact on how the music sounds. Pierre Schaefer created music of extremely high timbral complexity, but it's easy on the ears. Michael Gordon creates music of extremely high rhythmic complexity but it's easy on the ears. Milton Babbitt creates music of high pitch and rhythmic and dynamic-level complexity, and it simply doesn't sound as though it has any audible organization, so it's very difficult on listeners. Once again, this is a matter of hardwired limitations on the human nervous system, it's not a matter of education. These limitations on the human ear/brain system are imposed by nature, not nurture. You can't "educate" listeners to reliably reocgnize 12 different finely gradated dynamic levels — it's just not humanly possible. Music organized in that way will not sound organized. So the moral of the story is that the kind of complexity makes a huge difference to how the music sounds. References cited or discussed in this post: Bregman, A. S. (1990). Auditory Scene Analysis: The Perceptual Organization of Sound. MIT Press, Cambridge, MA Brown, B. Determination of meter by autocorrelation. Jouranlf othe Acoustical Society of America, 1993, Vol. 94, pp. 953-957. Butler, D. The musician's guide to perception and cognition, 1992. Deutsch, Diana. The Psychology of Music. 2nd ed., 1992. Dowling, W. J. and D. L. Harwood. Music cognition, 1986. Eck, D., Meter and autocorrelation, 10th Rhythm Perception and Production Workshop, Montreal. Link. Grey, J. M. (1975): Exploration of Musical Timbre. Stanford Univ. Dept. of Music Tech. Rep. STAN-M-2. Handel, S. Listening: An introduction to the perception of auditory events. MIT Press, Cambridge Mass., 1993. Howell, P., I Cross, R. West. Musical structure and cognition. 1985. Krumhansl, Carol, Cognitive Foundations of Musical Pitch, 1990. Lee, C. S. (1991). The perception of metrical structure: Experimental evidence and a model. In P. Howell, R. West, and I. Cross, editors, Representing Musical Structure, pages 59-127. Academic Press, London. Meyer, Leonard B. A Universe of Universals, The Journal of Musicology, Vol. 16, No. 1, pp. 3-25, Winter 1998. Miller, George A. The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information, The Psychological Review, 1956, vol. 63, pp. 81-97. Link. Parncutt, R., A PErceptual Model of pulse salience and metrical accent in musical rhythms, Music Perception, Vol 11, 1994, pp. 409-464 Povel, D. and Essens, P., Perception of temporal patterns. Music perception, Vol. 2, 1985, pp. 411-440. Pring, Linda and Jane Walker, The Effecst of uncovalized music on short-term memory, Current Psychology, VOl. 13, No. 2, June 1994 Shannon, Claude. Information theory. 1948. Sloboda, J.A. The Musical Mind, 1994. Toivianen, P. and Eerola, The role of accent periodicities in meter induction: a classification study. In Lipscomb, S. Ashley, R. Gjerdingen, R., and Webster, P., editors, The proceeedings of hte eighth international conference on music perception and congition, Adelaide, Australia, 2004. Volk, A. Exploring the interaction of pulse layers regarding their influence on musical accents. In Lipscomb, S. Ashley, R. Gjerdingen, R., and Webster, P., editors, The proceedings of the eighth international conference on music perception and congition, Adelaide, Australia, 2004. Wessel, David L. Timbre Space As a Musical Control Structure. Rapports IRCAM 12/78, 1978. Link.

Samuel Vriezen says: August 5, 2008 at 3:34 pm - Great post, McLaren - just one thing: there have been cases of people who trained themselves to hear very extraordinary things. There have been documented cases of Stockhausen hearing a serial piece for the first time, and half way through *singing the series along with the piece* (a piece by Jan van Vlijmen). He seems to have found a way to surpass the pitch limits (likewise, his sense of dynamics, absolute pitch and absolute tempo was uncanny). What I would assume is that part of it is that he managed to reduce the window of ‘attention span' by training sufficiently to allow for extensive parsing. Much of the most succesful serial music I think will avoid the impression of chaos through careful phrase organisation, which makes it possible to cram in more ‘moments' (units of attention span) in the second.

Rob Davidson says: August 17, 2008 at 9:26 am - Hey mclaren - wow, I think that's the first referenced comment I've ever seen. Some really thought-provoking topics covered. I'm curious about the 9-category limit in the immediate attention span. I wonder if it's derailed somewhat by register - only that I've been playing with spaced-out all-interval chords (over five-and-a-half octaves - using each pitch class and each interval once) and they sound very agreeable and non-chaotic. I think it might be because each interval occupies its own register. Similarly, if you play a big stack of fifths, using up all 12 equal tempered pitch classes, it sounds very easy on the ear - not giving that result of too much information that I think you're describing from these perception studies. I wonder what the hell's going on with that? The fact that we're just hearing fifths? Or again the register separation giving each pitch class its own space? Rob Davidson

mclaren says: August 18, 2008 at 8:11 pm - Samuel: Both Stockhausen and Boulez claimed to have extraordinary auditory perceptual capabilties. The thing is, I've never seen any A-B-X objective double-blind listening test results from Stockhausen and Boulez done under controlled conditions. These guys claimed they could perceive lots of amazing things, but as far as I can tell, no one ever put these guys into a double-blind test of the kind you get in lab experiments. Instead, we get anecdotal evidence. As the saying goes, the plural form of "anecdote" is not data. I would have to see A-B-X double blind listening tests done on Stockhausen and Boulez before I were willing to believe these kinds of claims. This isn't to say these sorts of claims can't be true: I'm just from Missouri. I have to be shown. Preliminary studies of memory enhancement from the anti-sleep drug modafinil appear to add one bit to the capacity of human short term memory, when fresh non-sleep-deprived volunteers took the drug. See this reference and this reference about the apparent effectiveness of modafinil in enhancing short-term memory. It would be interesting to have a group of composers get prescriptions for modafinil and then have ‘em compose music while on the anti-sleep drug and then do a double-blind A-B-X psychomusicological test to determine if ordinary listerens could reliably hear any difference between such compositions and the rest of the composers' output. To my knowledge, no one has done this. Hey, grad students, here's your doctoral thesis in music perception right here… Rob: What's going on with widely spaced all-interval chords is well known and was explained in Plomp & Levelt's classic 1965 paper "Tonal Consonance and Criticial Bandwidth." The width of the critical band above 150 Hz is slightly larger than a just 7/6, roughly 270 cents or so. Plomp & Levelt found that maximum acoustical roughness is perceived when two partials coexist within 1/4 of the critical bandwidth, which works out to around 90 cents or thereabouts. Strong sustained beats within 1/4 of the critical bandwidth sound viscerally disturbing, Plomp & Levelt found, with some caveats. This is hardwired into the human ear-brain system and is not a mattter of nurture. You can't learn to hear strong sustained beats within 1/4 of the critical bandwidth as sounding acoustically smooth. What's going on with widely spaced all-interval chord is that the individual pitches are spaced far enough apart in cents that only the higher overtones of the piano (or whatever instruments you use to play the all-interval chords) fall within 1/4 of a critical bandwidth of the other notes of the chord. But since the higher overtones are much less loud than the lower overtones for instruments like a piano, the beats that clash within 1/4 of the criitical bandwidth are quite weak, and thus not disturbing. This explains why widely spacing almost any type of tone cluster or all-interval set on an acoustical instruments like a piano sounds nice and agreeable, whilst a loud sustained gob of two or three chromatic pitches (like B-C within the span of 100 cents) on (say) a pipe organ sounds intensely rough and disagreeable. To take a specific example: if you spread the above B-C dyad out and play B two octaves below middle C and then a C two octaves above middle C, only the 16th overtone of the lower note B will fall within 1/4 of a critical bandwidth of the higher note C 4 octaves above. (4 octaves = a frequency ratio of 16, that is, 2^4.) All the other overtones of the lower note B, from overtones 1 through 15, will not rise high enough to coexist within 1/4 of a critical abandwidth of the upper note C 4 octaves above. But on most acoustical instruments (such as a piano or a pipe organ), the 16th overtone is much much less loud than the fundamental of the musical note, so in this case such beats as coexist within 1/4 of a critical bandwidth will be very weak and thus any acoustic roughness they cause won't sound disagreeable, and may well be inaudible. Every musician should at least skim Plomp and Levellt's classic paper. The precise reference is: Plomp, R. & Levelt, W.J.M. (1965). Tonal consonance and critical bandwidth. Journal of the Acoustical Society of America, Vol. 38, pp. 548-560. Direct link here. It might seem tempting at this point to ascribe consonance and dissonance entirely or even primarily to acoustical interactions of overotnes, but that simply doesn't work. Musical consonance and dissonance are influenced by acculturation as well as acoustical beats within the critical bandwidth. The reason why the simplistic leap of acoustics = musical consonance doesn't work is illustrated by your second example, because, as mentioned, the human ear/brain system is very complex, so we can't jump to overly simple conclusions like "intensity of beats between partials within 1/4 of the critical band governs musical consonance." The caveat triggered by your second example is that if you toss so many partials into the critical bandwidth that the human ear/brain system gets overwhelmed, it stops noticing or caring about any two partials that beat strongly within 1/4 of the critical bandwidth because there are zillions of partials within the critical band. This is what happens when a tone cluster of dense closely spaced pitches get played. Dense tone clusters represent one of the great discoveries of modernist music and added wonderfully to the modern musical vocabulary. Xenakis (in compositions like Eonta and Kraanerg), Ligeti (in compositions like Atmospheres and Volumina), Penderecki (in compositions like De Natura Sonorem and Threnody for the Victims of Hiroshima) all made successful use of dense closely-spaced tone clusters which don't sound disagreeable at all, yet which contain vast numbers of strong partials coexisting within the critical bandwidth. It's worth mentioning that the tone cluster explosion was started by early pioneers like Henry Cowell and Charles Ives, though they've seldom been given the credit they deserve. The moral of the story is that some modernist compositional innovations, like tone clusters, were an unqualified musical success, while other modernist compositional innovations, like serial tone rows, proved musically problematic. This is why we can't take seriously such books as Henry Pleasants ‘ The Agony of Modern Music (1955) today. Some modernist innovations worked very well, others fell flat, still others had a spotty track record depending on lots of different factors. People who reject high modernism as a whole just aren't making the necessary distinctions to capture the sophistication and breadth of the high modernist moverment in music.

Kyle Lynch says: August 30, 2008 at 10:13 am - Well, I finally got around to reading this essay, and I'm really glad I did. There's a lot here that makes sense and which I agree with. As a young would-be grad student [long story], I feel like I've been shirking my duty by not studying a lot complex music. Off to the library.

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