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24 July 2008

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Daniel Wolf
1.

I don't know if Byrne likes or hates experimental music, but I do know that, no matter what surface similarities his work may bear to some experimental music, his own work does not experiment in the sense that he is not indifferent to the possiblity of failure, either artistically or commercially. Emptied of that reconciliation with risk, music that is ornamented with the signs and symptoms of an experimental aesthetic is often no more than a boutique product at the far end of the mall of musical commerce.

DJA
2.

Hmm. Indifference to the possibility of aesthetic failure is a prerequisite for music to be authentically "experimental"? That's a new one on me.

Regardless, over the course of his career, David Byrne has made music that is more genuinely experimental in its risk-taking -- and more aesthetically successful in its experimentalism -- than just about any living "classical" composer.

Daniel Wolf
3.

Yes, indifference: "the word "experimental" is apt, provided it is understood not as descriptive of an act to be later judged in terms of success and failure, but simply as of an act the outcome of which is unknown." (Cage, of course).

Where, precisely, in Byrne's music, do you locate such risk-taking? In the end, he's writing pop songs that do everything pop songs have to do to be distributed and played to a significant mass audience, and his career has been well-managed in a market that often values youth over the really new. His songs begin and a few minutes later they end, they fall within the increasingly flat dynamic curve permitted by pop recording, they are metrical and tonal, they have some bit of material that listeners can immediately grab onto, and sometimes they even get played on radio and MTV, if in the wee hours or at the far end of the FM dial. He may well be chipping at the definition of his genre -- extending it with unusual chord changes or rhythms or lyrics -- but nowhere is there a fundamental challenge made to the genre, let alone to the boundaries of musical production and listening in general.

This is not a criticism of Byrnes music; it's just rejecting the notion that it is experimental. He's practicing precisely the sort of incremental innovation made by most interesting musicians in most repertoire, pushing boundaries but not breaking them.

Which goes back to the big mistake in his critique of Die Soldaten. The problem with the Zimmermann opera is not that of the genre which it represents -- behemoths of the postwar European avant-garde -- but that it's neither a particularly musical or interesting example of the genera nor is it a piece that challenges the genera and offers something new. In other words, it was poorly composed. Basta.

DJA
4.

In the end, he's writing pop songs that do everything pop songs have to do to be distributed and played to a significant mass audience

And the overwhelming majority of "classical" composers aren't operating well within the bounds of an equally constricting set of constraints? (What kind of music do I write to get this grant, what kind of music do I write to get tenure, etc. etc. etc.)

Byrne has done a hell of a lot more to push against and subvert and expand the boundaries of what's possible in his world, while simultaneously preserving the stuff that is fundamentally valuable, than someone like, say, Ferneyhough, has done or ever will do.

If you can't hear the spectacular risk-taking in songs like "Animals," "Artists Only," "Memories Can't Wait," or even smash hits like "Burning Down The House," then (A) you probably don't listen to a whole lot of popular music, and (B) I can't help you with that problem.

I'm also not interested in music that is indifferent to whether it succeeds or fails, aesthetically, but I guess I'm just funny that way.

Daniel Wolf
5.

"And the overwhelming majority of "classical" composers aren't operating well within the bounds of an equally constricting set of constraints? (What kind of music do I write to get this grant, what kind of music do I write to get tenure, etc. etc. etc.)"

Absolutely -- as I indicated in my second post, most musicians, including most interesting musicians in any given genre work incrementally, not experimentally. And if you go down the lists of BMI and ASCAP and Pulizer-prize winners, or look to the professorate outside of maybe Wesleyan, Mills, and Cal Arts, risk takers aren't getting tenure. Hell, they're not getting hired in the first place. And let's not begin to talk about grants.

I admit that I'm not a pop music person, but jeez, I went to Santa Cruz in 78-83, and Byrne's was an unavoidable part of the atmosphere. But the fact that, in the end, even you readily identify the works as "songs" or "hit" illustrates the problem. But I'm still willing to be convinced otherwise: what, in precise, material terms are the elements of the music that you identify as experimental? and what, precisely, are the risks undertaken to produce this music?

James Hirschfeld
6.

Wow--you guys literally stayed up all night discussing this!

I guess the "problem" I have with the propositions is just the framing of "thorny music" in its own separate category, like it is an entirely different animal.

Like if one said, 1) not every Vermonter is a really good person and 2) Some Vermonters are very nice people and people who come to know them derive pleasure from their friendship.

I know the above is a total bullshit argument. You don't have to tell me. But as much as I agree with that statement, I just don't like the framing of it, because Vermonters are all different from each other and no different than Massachusians in that respect.

Going back to the blog entry about sports movies and genres, to me, classifying "thorny" music as a category is like putting all the black and white movies in a category and making a generalization about them.

I know I am wandering here...your argument is that some people like all things complex, and fail to discern between a good piece that is complex and a bad piece that is complex. What constitutes a good piece of music has everything to do with perspective. Honestly, I don't know that I have ever heard a piece of music that offered "only thorniness, complexity, and difficulty, without the slightest regard for clarity, communication, and emotional resonance." What you look for in music (clarity, communication, emotional resonance) is your business, but I wouldn't say it is a universal metric on which to judge music. But of course, its your blog!

Full disclosure: I like David Byrne.

But I'd like to know what constitutes "spectacular risk" in music nowadays.

Does going to an unexpected chord constitute a risk? Is an irregular beat, or perhaps an odd meter a "risk?" These are aesthetic choices. You write what you hear. Anytime you write something, or "express yourself," you are taking a risk in someway...

David Byrne's "pipe organ building" is really not experimental. I'm not a curmudgeon...it's "neat," but it is not groundbreaking, shocking, or new. His fame does bring it to a larger audience. But it has a 100% guarantee of aesthetic success. Very safe art. NPR is all over that shit.

Chris Becker
7.

"...what, in precise, material terms are the elements of the music that you identify as experimental? and what, precisely, are the risks undertaken to produce this music?"

Hee, hee.

I think trying to make assumptions about the relative levels of "risk" each of us takes in creating our music is really presumptuous and not particularly helpful or (for me) interesting. And that tag "experimental" gets attached to my own music making - but for me, composing has more to do with personal honesty and the spiritual navigation of my moments in time on this planet. That said, to refer back to the Cage quote, composers plans, God laughs. And I usually enjoy being surprised.

Daniel, have you heard Byrne's soundtrack to Twyla Tharp's The Catherine Wheel (this performance was not given positive reviews when it played but I think it's a seminal work for both Tharp and Byrne)? Tharp's chapter in her autobiography Push Comes To Shove about the creation of this piece breaks down the various "risks" (some literally physical with regard to the piece's set and dancers) that she and Byrne took in its realization. Or My Life In The Bush Of Ghosts (which pushed the boundaries of what the recording studio was capable of doing in terms of combining sampling material with overdubs of percussion and other instrumental performance i.e. this was way before Ableton Live)? Or the first track from his score The Forest (composed for Robert Wilson) which is a bizarrely beautiful setting of sort of hamfisted Laibach styled orchestration against Byrne's own yodeling?

DJA
8.

But the fact that, in the end, even you readily identify the works as "songs" or "hit" illustrates the problem.

Daniel, it seems to me that you are prima facie unwilling to admit that pop songs can be experimental or take significant musical risks, simply by virtue of the fact that they are pop songs. And if that's your view... well, okay, that's your view. I think it's spectacularly wrong-headed and a bit tautological, but I suspect there's little I could do to convince you otherwise.

If however, you are willing to grant that expanding the horizons of what you can get away with in a pop song format is a legitimate form of experimentalism, then I don't really see how you could possibly deny that Byrne is one of pop's great experimentalists. Chris rightly brings up My Life In the Bush of Ghosts, which was constructed almost entirely of dense interlocking samples and concrète sounds, long before the technology (digital sampling, sequencers, MIDI) to make this kind of music had been invented -- so instead, the recording was painstakingly assembled by slicing up bits of analogue tape. (This is not unlike Nancarrow's punching his own player piano rolls.) It's not the first pop record to use sampling techniques, obviously, but it's the first to be built from them from the ground up, making the sampling the core of the music instead of a decorative element.

And the Talking Heads are a famously unusual group, one of the weirdest bands to ever achieve mass popularity. (I can't believe I actually have to spell this out.) Songs that are dissonant, polytonal, rhythmically dense and complex, structurally unusual, sonically and texturally rich, ambiguous in meaning, etc, are the norm for them. David Byrne hasn't written a straightforward lyric in his life, and his aberrant vocal inflection is like nothing else in pop. Talking Heads made by far the most successful integration of funk and Afro-Beat with edgy, nervous, stripped-down NYC punk rock. I forget who made this observation, but it's apt: they were simultaneously the whitest and blackest band to come out of the CB's scene. (You don't think it was ballsy for a bunch of ultra-nerdy white art school kids to tackle Al Green's "Take Me To The River"?) Most importantly, they are total conceptualists and their aesthetic choices, however unusual, are always in the service of the work as a whole.

If you want to talk about specific songs, go listen to some of the ones I mentioned in my previous post and then get back to me.

Daniel Wolf
9.

Chris wrote: "this was way before Ableton Live".

Sure, but it was also some 17 years after the Chamberlin (a tape loop-based sampler associated in particular with the San Francisco Tape Music Center) which features in Ramon Sender's 1964 piece Desert Ambulance, a multi-media work which combined overdubs of Chamberlin samplng with live instrumental performance (which was improvised live by a player following verbal instructions on a separate audio track).

I am familar with each of the pieces you've name, and while I can recognize in each other innovation with regard to the genre, none of it is innovative in terms of music in general.

DJA
10.

James,

your argument is that some people like all things complex, and fail to discern between a good piece that is complex and a bad piece that is complex.

No. If it were just a matter of "like," it wouldn't be so problematic. Some people believe in (certain kinds of) complexity as a prerequisite for being taken seriously, and take complexity and inaccessibility as not just an end in itself, but as a marker of the highest form of artistic achievement.

Not to put too fine a point on it, but that's the kind of thing that gives bullshit a bad name.

Honestly, I don't know that I have ever heard a piece of music that offered "only thorniness, complexity, and difficulty, without the slightest regard for clarity, communication, and emotional resonance."

Then someone's led a charmed life!

Seriously, James, no offense, but I don't believe you. Unless you have adopted Frank Oteri's "Zenlike appreciation for every piece that's ever come into existence," then of course you have heard music that is unclear, uncommunicative, and emotionally barren. We all have.

But, if you want, although I can't imagine a less rewarding evening of music, I will even accompany you to the complete Babbitt string quartets at Miller this fall. Babbitt famously doesn't give a shit about clarity, communication, and emotional resonance, and I think he's done an admirable job throughout his career of writing music that is actively hostile to those virtues. But at the end of the night, you can let me know if, despite the best efforts of the composer, you honestly come away with an overwhelming impression of clarity, communication, and emotional richness.

Chris Becker
11.

But did Ramon Sender's piece make you want to shake your hips?

Daniel Wolf
12.

Daniel, it seems to me that you are prima facie unwilling to admit that pop songs can be experimental or take significant musical risks, simply by virtue of the fact that they are pop songs.

I may very well be wrong-headed (but if then spectacularly so) but I do have my own little book of favorite pop songs that do more than a pop song is supposed to do -- the continuous linear development in Orbison's In Dreams or Buarque's Construcao, the radical textural and dynamic breaks in the Cole/Kenton cover of Orange Colored Sky, Joseph Byrd's guitar-free ensemble in The United States of America, the thematic coherence of Randy Newman's early song cycles (aka albums), Zappa's framing of songs within larger pieces, and even Camper Van Beethoven's cover of the entire Fleetwood Mac Tusk.

Daniel Wolf
13.

But did Ramon Sender's piece make you want to shake your hips?

No, but that's because I shake my hips when I want to shake my hips, not when someone coerces me. In any case, hip shaking is — or usually is — harmless, and the Sender was something other than harmless: it changed the way I listened to music.

James Hirschfeld
14.

Darcy: But, if you want, although I can't imagine a less rewarding evening of music, I will even accompany you to the complete Babbitt string quartets at Miller this fall.

You have a DATE! I was planning on going to this concert. Seriously--let's go to this concert. There are going to be like 3 intermissions.

DJA
15.

No, but that's because I shake my hips when I want to shake my hips, not when someone coerces me.

Please don't confuse My Life in the Bush of Ghosts for the "Electric Slide." That's no good for anyone.

Chris's remark might have seemed facetious, but it's actually totally on-point. One of the great bits from this piece on Fear of Music (which is, you know, very much a song cycle) is: "But everything -- songs, performances, the pioneering videos on the 'Storytelling Giant' DVD included here -- started as music for the body." That's one of the most important things separating Talking Heads from their contemporaries and their would-be imitators.

DJA
16.

Seriously--let's go to this concert. There are going to be like 3 intermissions.

And you may say to yourself: "My God! What have I done?"

isaac
17.

I just wanted to chime in and say that the idea that David Byrne isn't experimental because he only moved pop music forward rather than the "music" forward seems to me spectacularly wrong headed, not only elitist in its privileging of one kind of music for another, but also completely misunderstanding how art works and moves forward.

To address the first part... the idea that Byrne isn't experimental on these grounds is elitist because it privileges one kind of music (the kind favored by the academy) over another kind (the kind favored by rock fans). There are plenty of things that happen in more academic circles of music that do nothing to move popular song forward, yet they still get branded as "Experimental". This belies an assumption that one counts as "Music" as an art form and the other is just "music" that shit that people listen to.

There's also this kind of cult-of-originality here thing that is a personal pet peev of mine. Nothing comes from nothing. Byrne/Eno (as Darcy has already discussed) trailblazed new forms and methods for pop music, in part by appropriating from what other artists in other forms of music had done. Guess what? For the most part, that's the only way art every progresses, when artists are creatively derivative-- taking what someone else has done and reinventing it through their own artistic voice. That's how artists work, by reinventing and adding to the past.

Furthermore the idea that experimentation means a specific kind of moving forward for an art form rather than an artist's attitude towards their own work is just kind of bizarre. We're not talking about theoretical physics here, we're talking about art, and frankly I believe that one of the more harmful things to happen w/r/t "experimental" art in the late 20th century is the idea that formal invention for its own sake is worth praise, even when that's the *only thing going on in the work of art*. I like me some formal invention, don't get me wrong, but it needs to be at least in part in *service* of something, communicating something or going towards some kind of meaning, or having some kind of effect on the listener/viewer/whatever, or being beautiful or really any other kind of artistic purpose beyond just formalist play.

Byrne's approach to his own career has been resolutely and relentlessly experimental (except for much of the second half of Talking Heads' discography which is kinda lame). He's written song cycles, a disco opera, done visual art work, invented and reinvented himself with startling amounts of creativity. This to me (as a working theatre artist) is a far more useful way of talking and thinking about what it means to be "experimental"... namely "taking an experimental attitude towards the art that someone is creating".

James Hirschfeld
18.

Darcy--you may not believe me re: never having heard a piece of music that offered "only thorniness, complexity, and difficulty, without the slightest regard for clarity, communication, and emotional resonance," but it is true! Maybe it is a charmed life! Complaints I have about concerts are usually with regard to the performance (lack of preparation, lack of energy, etc). The single most important factor in my appreciation of a piece is my mood going into it. If I am coming from a rehearsal and had a terrible train ride, then I am probably not going to be too receptive to a challenging piece of music. But I do like to be challenged! In all sorts of ways. When I listen to Babbitt, the compositional process does not concern me. The music can speak independently of the composer. The performers can communicate through their interpretation. Listening to Babbitt's 6th string quartet last night, I was struck by its incredible beauty. Which one of us is right about Babbitt? What a silly argument that would be.

Honestly, Babbitt's music is far less complex than say Xenakis or Lachenmann, or even Berio (in my opinion!). In fact, I don't really find Babbitt's music complex at all when compared to those composers.

Isaac: I believe that one of the more harmful things to happen w/r/t "experimental" art in the late 20th century is the idea that formal invention for its own sake is worth praise, even when that's the *only thing going on in the work of art*. I like me some formal invention, don't get me wrong, but it needs to be at least in part in *service* of something, communicating something or going towards some kind of meaning, or having some kind of effect on the listener/viewer/whatever, or being beautiful or really any other kind of artistic purpose beyond just formalist play.

I feel like if you're going to say something like this, as many others have said before you on this blog, you should tell us specifically who and what you're talking about. What is an example of formal invention that is NOT "at least in part in *service* of something, communicating something or going towards some kind of meaning, or having some kind of effect on the listener/viewer/whatever, or being beautiful or really any other kind of artistic purpose beyond just formalist play?"

I simply cannot imagine such a thing that does not communicate anything, or has no meaning, or has no effect on the listener, though I am willing to be enlightened.

isaac
19.

I'll hazard a few examples. Two caveats however:

(1) although honestly I think I might've in true bloggy fashion overstated the point a wee bit, in that it is hard to think of experimentations that have *literally nothing else* going on, but it's not hard to think of work where the other stuff, as Darcy said (clarity, communication, emotional resonance" or that I talked about (communication, meaning, beauty etc.) is so secondary (or tertiary or whatever) to the work as to not really matter to it.

(2) any of the artists I name below you may not feel the same way about, because objectivity w/r/t art is impossible. So you may find (or from my POV invent) all sorts of depths and meaning into the work that i find shallow empty formalist play (or to your view have a shallow understanding of).

So the few that come to the top of my head immediately: (1) Robert Ashley. (2) The Fiery Furnances after their first album, (3) Richard D. James, (4) much of John Zorn's scores for dance .In theater, I'd say the work of Needcompany, and much of the Royal Court's in-yer-face theater movement, particularly the early plays of sarah kane. I am very much in a minority in drama on the latter, however.

There's also another problematic set... artists who get called experimental not because they actually experiment with anything but because the set of conventions they are obeying are not mainstream and therefore the only term applied to them is experimental. A good example in theater would be Robert Wilson and an okay (if too easy) example in music would be Philip Glass.

Random Joe
20.

I don't understand the idea of "complexity" as a goal. Wouldn't it only mean adding ever more intricate patterns? And that ultimately it is formulaic, measurable even. (I am sure somebody will come up with fractal analysis of music work, just as it is for painting.)

It will be more a cute project, asking how "dense" a music composition can be before it becomes deafening sound wall. (eg. metal, gabber, big band all dabble in that direction for a moment before nobody cares about it anymore)

Or by complex it means very long non repeating pattern. then the ultimate non repeating pattern is randomness.

or is it finding that maximum complexity a type of composition can have before everything falls apart (unplayable, unlistenable, or nobody cares)

DJA
21.

Honestly, Babbitt's music is far less complex than say Xenakis or Lachenmann, or even Berio (in my opinion!)

Hey James,

Remember when I said, in the original post:

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???")

Well, you kind of proved my point just there. I don't hate complex music. I write lots of complex music (as you know all too well). And when I say that Babbitt's music does nothing for me, and one of the reasons it doesn't reach me is that the complexity/density/serialized rigor doesn't seem in service of anything visceral, I am not criticizing all complex music. Just Babbitt's.

But we shall see if exposure to five Babbitt string quartets in a row will do anything to change my view.

James Hirschfeld
22.

Let’s just say I agree with the one’s right to criticize a piece and not have that criticism extend to all pieces of a particular genre. No argument.

I probably shouldn’t say anything more, BUT I can’t resist:

I think you’re right that people often assume that you are in fact launching a full-bore assault on Proposition 2 when an argument flows from Proposition 1.

The question is: why?

Is it because there are certain circles made up of shallow people who value complexity over elegance? Or is it because certain snobs feel the need to express their musical elitism by choosing a form of expression that is so esoteric, that if you don’t like it, you must not be smart enough to understand it?

Or is it because too often, difficult music is cast by the wayside—not even listened to once before being judged? Is it the fact that in general, people really DO lump all “complex” music into one category and then make generalizations (“I don’t like that stuff”)? Or is it because certain people, by their own free will, sacrifice so much (money, family, sanity) to pursue their perhaps eccentric artistic goals, only to find a society that is largely indifferent to their work?

When you talk about Babbitt, I don’t think there is anything wrong with your opinion, even if I don’t agree with it. I don’t want to force you to go to a concert that will probably be incredibly unpleasant to you. I trust you’ve listened to enough Babbitt and given it as much time as you’re willing. But, most people haven’t. They’re talking about shit they don’t know anything about. For every one person who has listened to Babbitt and doesn’t like it, there are a hundred people who HAVEN’T listened to Babbitt and don’t like it.

Now I really shouldn’t say anything more, BUT again, I can’t resist:

I actually think I disagree with part of Proposition #1. While I don't think that all music ever written constitutes a masterpiece, I do think that probably 85% of music is "worth listening to over and over again." And I do think that this is particularly important with what you call "thorny, complex, difficult-to-understand" music.

We agree that music may fail to "get" you the first time through. And we agree that that music may NEVER "get" you no matter how many times you listen to it. But you will never know that UNLESS you listen to it repeatedly. And if it never "does anything for you," what have you lost? Do you wish you could have back the time that you spent listening to Babbitt? (Maybe you do!) But you have gained something through that experience, more than just the knowledge that you don't like Babbitt, I hope.

DJA
23.

Hey James!

First, I already said I'd go to the Babbitt marathon. I don't really know the string quartets so what the hell -- maybe it will be revelatory, you never know. And I think Gil Evans used to say he learned just as much from listening to music he didn't like, so...

Is it because there are certain circles made up of shallow people who value complexity over elegance?

Yep.

Or is it because certain snobs feel the need to express their musical elitism by choosing a form of expression that is so esoteric, that if you don’t like it, you must not be smart enough to understand it?

Uh-huh.

Or is it because too often, difficult music is cast by the wayside—not even listened to once before being judged?

I am saying that just because difficult music is often underappreciated, that in no way justifies the first two attitudes you cite. And honestly, I could not think of a more effective method of driving away well-intentioned listeners than that kind of knee-jerk snobbery -- telling bright, curious listeners that their visceral reactions are invalid because they aren't smart enough to "get it" is pretty heinous in my book.

I also think that music should at least make a good-faith effort to grab you the first time through. (I love the Feldman anecdote Gann mentions: ""Kid's 21, and he thinks I'm going to listen to his fuckin' piece twice.")

Random Joe
24.

found the little paper.

how one can determine 'randomness'.

(complex information cannot be represented in simpler manner without loosing its information. There is a limit how small one can compressed information. randomness is part of complexity.)

so for eg. a song containing "abc, abc, abc" is clearly less complex than "aba, acb, cbc"

then there is also fourier transform.

http://www.cs.umaine.edu/~chaitin/sciamer.html

Limits of Formal Systems
Since complexity has been defined as a measure of randomness, this theorem implies that in a formal system no number can be proved to be random unless the complexity of the number is less than that of the system itself. Because all minimal programs are random the theorem also implies that a system of greater complexity is required in order to prove that a program is a minimal one for a particular series of digits.

The complexity of the formal system has such an important bearing on the proof of randomness because it is a measure of the amount of information the system contains, and hence of the amount of information that can be derived from it. The formal system rests on axioms: fundamental statements that are irreducible in the same sense that a minimal program is. (If an axiom could be expressed more compactly, then the briefer statement would become a new axiom and the old one would become a derived theorem.) The information embodied in the axioms is thus itself random, and it can be employed to test the randomness of other data. The randomness of some numbers can therefore be proved, but only if they are smaller than the formal system. Moreover, any formal system is of necessity finite, whereas any series of digits can be made arbitrarily large. Hence there will always be numbers whose randomness cannot be proved.

mclaren
25.

Kyle's original discussion and this one too prove unsatisfactory insofar as everyone is 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, my posts have bibliographies, 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 highly 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 low, 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 acfording to the music's redunancy, so for highly redundant music, the span of immediate attention can be a long period of time, whereas if you have lotz 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 timrbe repeated, and audiences will not have much of a problem. 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 parsing the result. 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, the listeners will get bored and jittery.

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 msuis 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.">http://www.musanim.com/miller1956/">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.


DJA
26.

Hi mclaren,

I appreciate all your detailed research -- fascinating stuff!

When Kyle talks about "thorny, complex, difficult-to-understand music," I take that to generally mean music with a very high level of pitch complexity, hardly any repetition, and no audible pulse. So we were not actually talking about "complexity" as a big lump, it's just that the kind of distinctions you write about, we were taking as a given.

I think almost everyone intuitively understands that certain kinds of complexity are easier to grok than others -- for instance, we all get that rhythmic complexity against an audible grid is easier to understand than rhythmic complexity without any audible reference point. (Obviously, it's good to have the hard research to check against our intuitions.)

So Kyle was definitely not talking about totalist/metametric works (like Michael Gordon's Trance) when he refers to "thorny, complex, difficult-to-understand music." He's talking about high modernism -- generally, serial or densely chromatic music with no perceptible pulse and no audible redundancy or repetition.

I also appreciate and basically agree with this paragraph:

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.

Miro
27.

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, the listeners will get bored and jittery.

I think this is highly depended on what language listeners are using.

for eg. several asiatic language using more than 9 tones, while several uses no tone whatsoever. (which is why some music can be used as torture device)

I would guess basic western music to people who uses more than 9 tones would probably sounds a little limited, a little like us hearing pentatonic.

(of course since most modern music performance are for english speakers, this is a pointless side note)

http://en.wikipedia.org/wiki/Tonal_language

There are numerous tonal languages in East Asia, including all the Chinese dialects, Vietnamese, Thai, Lao, and Burmese (but not Mongolian, Khmer, Malay, standard Japanese or standard Korean). In Tibet, the Central and Eastern dialects of Tibetan (including that of the capital Lhasa) are tonal, while the dialects of the West are not.

mclaren
28.

Sorry, Miro, but that claim involving the pitches of tonal languages is unbelievable tripe. It contradicts all the available evidence about the human ear-brain system as well as the known evidence from ethnomusicology and music history. No surprise, since the wikipedia article you cited is marked with THE ACCURACY OF THIS ARTICLE HAS BEEN DISPUTED.

Evidence for the limit to 9 or fewer modal pitches as a worldwide invariant throughout history converges from mmany sources. One source of evidence comes from ethnomusicology. We find no indigenous native culture anywhere in the world that uses more than 9 modal pitches as a basic melodic subset. For example, Chinese music uses the pentatonic, the Kwaiker peoples use 7 roughly equal pitches, the Balinese use 5 pitches (slendro) or 7 pitches (pelog) which are non-just and non-equal, the Are-Are people of the Solomon Islands use 7 equal pitches, Americans/Europeans have traditionally used 7 modal pitches (the diatonic scale), the people of India use 7 pitches out of 22 theoretically unequal sruti, and so on. There is no record of any indigenous culture anywhere in the world that uses more than 9 modal pitches as a basic melodic set. Even 9 pitches is unusual: we find 9 pitches used in the West by combining the asecnding and descending melodic minor scales, and we find similar differing sets of ascending and descnding 7 pitches which, put together, yield a total of 9 pitches in certain Indian srutis.

Even giving credit for 9 modal pitches in Western or Indian music is a stretch. It's arguable whether the ascending + descending melodic minor scale really adds up to 9 pitches total, since we're really talking about 7 pitches going up and a different 7 pitches going down. In real music in the real world, you typically only hear 7 of those pitches at any given time during the span of immediate attention.

More evidence for Miller's limit comes from music history. When we study music history back to the Hurrian Hymn (ca. 1300 B.C.), we find 7 or fewer modal pitches being used. Once again, whether we're talking about the Greek tetrachords which get combined to produce 7 modla pitches, or later European hexachords, we always encounter a limit of 7 modla pitches plus or minus 2. It's inadvisable to bring up Claudius Ptolemy's Greater Perfect system because that shows a lack of knowledge of music history. Ptolemy's Greater Perfect system was never used in actual performance: it is a theoretical construct only, used in very late Greek music theory of the Silver Age, after the first century A.D. These sorts of theoretical musical constructs abound, and have no connection with actual musical composition or performance: A. J. Ellis' duodenarium (1874) likewise represents another example of pure theory which was never put into practice, and was never intended to be put into practice. When we turn to records of music that actually gets composed and performed, we always encounter Miller's limit of 7 plus or minus 2 pitches.

Of course even more evidence for Miller's limit as a universal invariant comes from the peer-reviewed experimental literature from cognitive psychology.

Miller's original 1956 paper itself cites well over a dozen previous peer-reviewed journal articles each detailing the experimental results that led to his concludion.

So trying to deny Miller's results already involves trying to deny more than a dozen published experiments. However, many peer-reviewed articles confirming Miller's 1956 results have been published since then, so you've really got a steep hill to climb if you want to deny the limits Miller deduced about human short-term memory.
Here are some recent papers confirming Miller's limit of 7 plus or minus 2 on human short-term memory:

Simon, Herbert A., "Invariants of Human Behavior," Annual Review of Psychology, Vol 41, January 1990, pp. 1-20

Craik, F.I.M., "Human Memory," Annual Review of Psychology, Vol. 30, No. 1

Waldrop, M. "The workings of working memory," Science, Vol. 237, 1987, pp. 1564-1567.

Baddeley, A., "The magical number seven: still magic after all these years," Psychological Review, Vol. 101, No 2., pp. 353-356, 1994

Kane, M. J. and R. W. Engle, "Working-Memory capacity and the control of attention: the contributions of goal-neglect, response," Journal of Experimental Psychology," Vol. 132, No. 1, pp. 47-70

Cowan, N., Chen, Z. and Rouder, J. N., "Constant capacity in an immediate serial-recall task: a logical sequel to Miller (1956)," Psychological Science, Vol. 15, No. 9, pp. 634-640

Cowan, N., "Evolving conceptions of memory storage, selective attention, and their mutual constraints within the human information-processing system," Psychological Bulletin, 1988, Vol. 104, No. 2, pp. 163-191.

Marois, R. and J. Ivanoff, "Capacity limits of information processing in the brain," in Trends In Cognitive Sciences, 2005, Elsevier Inc.

Along with the dozen or so original peer-reviewed journal articles cited in Miller's original article, I've now added 8 more. If all these results are incorrect and there's a vast mass of citations in the peer-reviewed experimental psychology literature contradicting my claims, it should be easy to prove it. By the well known rule of four, it should be easy for you to find at least 4 peer-reviewed journal articles contradicting my claims for each reference I've cited.

Therefore please cite those 80 peer-reviewed journal articles specifically rebutting the above references. I'll wait.

Whoops! You can't cite such references, since they don't exist. Miller's limit the consensus of the avilabale cognitive science research. There is no evidence to rebut it because it's a documented fact. Alas, I know this scientific literature, but you don't.

It would be a good idea to familiarize yourself with this material before you make claims which systematically contradicxt the known facts about the human ear-brain system.

Frankly, it's irritating to have to debunk claims made by garbage sources like wikipedia, since, as Kyle Gann has pointed out, wikipedia is a cesspool of junkthink, bogus rumors, and garbled sources. Wikipedia can't be taken seriously because: [1] there's no attribution to any known author, so the credibility of the person who wrote the article can't be assessed; [2] there's a near-total lack of citations, so the validity of the claims usually can't be checked against the peer-reviewed scholarly literature; [3] wikipedia articles constantly get re-written garbling and scrambling valid claims based on the scholarly literature by insertion and deletion of random junk by people with no knowledge of the subject and no authority and no expertise. (I've written enough stuff in wikipedia about microtoanlity to know first-hand how valid information gets garbled and scrambled, my references get removed, and the entire article turned to sludge by musicians with an axe to grind. JI fanatics hate my citation of references showing that the limits imposed by the human ear/brain system are relatively wide and flexible and do not require the use of "natural" overtones to produce good music, while hardcore modernists despiste my citation of evidence that some (albeit flexible) limits on the perception of music exist. So both types of musical ideologues edited my wikipedia article into sludge. After that, I gave up, because (like Kyle) I have better things to do with my time. Kyle had the same experience watching his articles about minimalism and totalism get turned to junk by other musicians who disliked the facts he stated. Hardcore modernists hated Kyle's documentation of the existence of downtown music, while extreme minimalists loathed the inclusion of trends like postminimalism and totalism and strove to edit those out of Kyle's article.)

I know, I know...everyone tells me it's a waste of time even to bother to refute the bogus claims of people who cite nothing more than a worthless wikipedia article. But I still do it, just for the sake of accuracy. Someone should be stating the documented facts, somewhere. Someone should provide peer-reviewed references that can be checked. Someone should give the principal authors of these experimental studies so that their reputations can be verified and their results confirmed.

What's really sad about this kind of worthless garbage citation of a piece of wikipedia junk is that there are real issues involving music and short-term memory. Miller's discussion of "chunking" plays an important role in music. You could have cited that, and it would have added to the discussion. But nonsensical claims that human short-term memory in music is somehow dependent on the number of pitches in non-Western tonal languages remain absolute twaddle.

Really, innate cognitive limitations on the perception of modern music is an important subject in music, and we deserve to have a serious discussion about it. Tossing in wikipedia garbage whose factually accuracy is disputed isn't the way to do it.

Concerning "chunking," see the peer-reviewed journal article:
Gobet, F., Lane, P. C. R., Croker, S., Cheng, P. C. H., James, G. Oliver, I., and Pine, J. M., "Chunking mechanisms in human learning," Trends in cognitive sciences,, Vol. 5, No. 6, 2001, pp. 236-243.

Chunking operates hierarchically in the human ear-brain system. Themes and motifs can be "chunked" after extensive repetition, effectively extending our ability to perceive musical structure. However, note that when we talk about reptition, we're moving away from short-term memory to retrieval from long-term memory. The same process is at work when you memorize your full 10-digit phone number with area code. How can we remember 10 digits if our short-term memory is limited to 7 digits plus or minus two? Because constant repetition forces the information from short-term into long-term memory, and long-term memory is not limited to 7 items plus or minus two.

"Chunking" comes in when you're able to extract features of (say) a phone number and compress them into smaller chunks. Suppose your area code was 111; you chould memorize your 10-digital phone number by chunking it as "triple 1," and then then 7 digits. That 2 items (triple + 1) plus 7, giving you 9 all told.

"Chunking" can operate with music, so this once again makes the constraints involving a musical mode somewhat flexible. Suppose you had a musical theme that consisted of (say) 8 repeated Cs, then 8 repeated E's, then 8 repeated G's, and now 8 repeated c#s, 8 E#'s (F's) and 8 G#s, and so on, progressively upward. That theme can be chunked as C-E-G, C#-E#-G#, D-F-A-, and so on. Note however that chunking requires regular repeated patterns, which tends to impose a sense of tonality.

Also, when we're dealing with chunking in music we're no longer dealing with a pure melodic mode, but instead with repeated melodic figures which are quite different from the underlying melodic mode.

Miller's limit in music is a human invariant. It operates across all cultures, and throughout all known history. Short of space aliens genetically engineering us to enhance our short-term memory for musical perception, the limits I cited remain universal, invariant, and incontrovertible.

It's worth asking why musicians and music theorists keep trying to deny this stuff. Why do musicians continue to flail away in the futile attempt to disprove these well-documented scientific results about musical human short-term memory and the musical limits of the human ear-brain system's information processing capacity?

Stephen Pinker has pointed out that Westerners the "blank slate" notion, which denies limits on human abilities and which found its musical expression in serial atonality and total serialism and the New Complexity and other po-mo variants, irresistably attractive:

"With so much seemingly at stake in so many fields, it is no surprise that debates over nature and nurture evoke more rancor than just about any issue in the world of ideas.
During much of the twentieth century, a common position in this debate was to deny that human nature existed at all -- to aver, with Jose Ortega y Gasset that `Man has no nature, what he has is history.' The doctrine that the mind is a blank slate was not only a cornerstone of behaviorism in psychology and social constructivism in the social sciences, but also extended widely into mainstream intellectual life."

Pinker, S., "Why nature and nurture won't go away."

In retrospect we can see that the denial of any sorts of innate limits on musical perception (which formed the basis of the serial atonal movement in modernist music) was just part of the much larger denial of innate limits in society, literature, government, etc. Stalin's "New Soviet Man" which sought to eliminate all traces of religious impulse or aesthetic preference or family bonding from the Soviet worker was part of the same project as the effort to eliminate all traces of tonality, perceptible rhythmic pulse, functional harmony and audible organization from music. All these various social and artistic experiments came a-cropper starting in the 1920s because of innate limits imposed on how human beings think and feel. Soviet collectivism failed because people want to own property and have families; communes failed for the same reason; laissez-faire capitalism is failing because the things people value most in life can't be bought (children, family, a sense of pride in one's work, etc.).

Pinker has aptly pointed out the enduring appeal of the incorrect "blank slate" hypothesis about the human mind:
"If nothing in the mind is innate, then differences among races, sexes, and classes can never be innate, making the blank slate the ultimate safeguard against racism, sexism and class prejudice. Also, the doctrine ruled out the possibility that ignoble traits such as greed, prejudice and aggression spring from human nature, and thus held out the hope of unlimited social progress." [op. cit.]

We can translate these utopian hopes into musical terms:

If nothing in music is innate, then diferences among composers can never be innate, making the blank slate in music the ultimate safeguard against musical prejudice and narrowmindedness. Also, the doctrine of the musical blank slate ruled out the possibility that traits such as musical tonality and a need for a regular rhythmic grid spring from human nature, and thus held out the hope of unlimited music progress.

The bad news is that the utopian dream of unlimited musical progress turned out to be a myth; we can't boundlessly extend the complexity of rhythms or the number of pitches in a melodic mode without encountering perceptual limits hardwired into the human nervous system.
Remember that Schoenberg initially questioned why any elements of music needed to be repeated. At the very start of his exploration, he hoped to produce a new music entirely without repeated motifs -- he thought this would produce music that sounded limitlessly fresh and constantly exciting. Alas, he discovered that it actually produced music without any distinguishing perceptual features at all, so he settled on some repetition involving all 12 chromatic pitches as a minimum requirement.

The good news is that the serial atonal escapades of the 1910s through the 1970s showed us that the human ear-brain system is far more flexible and much more subtle than anyone ever suspected. As a result, the period from 1910 through roughly 1975 gave 21st century composers a tremendous treasure trove of new musical techniques and new musical forms to explore, even though much of what was tried in music between 1910 and 1975 turned out to be a flop. So on balance, the serial atonal adventures represnted a big net positive for 21st century music. Even though most of it didn't work musically or perceptually, it hugely expanded the range of emotions and forms and techniques available to composers and to audiences. Even without exploring new frontiers like microtonality, the musical resources introduced since 1910 offer plenty of raw material for composers to produce exciting new work with for, oh, at least the next several centuries. This is arguably the most exciting time to be a composer or a music aficionado, ever.

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