Harmolodics and Holomorphy

Ornette Coleman died today.

And with him died any chance for an authoritative version of his treatise on harmolodics, which he had reportedly been working on for decades.  Oh, I daresay we may eventually see some fractured notes (pun intended) about harmolodics, but we will not see the definitive statement of what it is.

To be sure, it's entirely possible that any treatise about harmolodics would have been allusive and telegraphic at best.  Coleman was notoriously cagey about describing harmolodics, and players in Prime Time, Coleman's group, were obviously fearful of being pinned down to any concrete statement that might get back to Coleman (who understandably might be upset about his creation being characterized in a way not to his liking).

Practically speaking, harmolodics was what Coleman played with Prime Time, or at least aimed at playing.  He was said to have denied that any of his albums actually achieved harmolodic playing.  So we have no guarantee that any particular piece was exemplary of his musical philosophy.  In some sense, then, there might not be any ironclad difference between harmolodics and entirely free jazz.

Nonetheless, the nagging suspicion of many a listener was that there was something to harmolodics, that it didn't sound entirely free, that there was some structure lurking in there somewhere.  We might even imagine Ornette himself, driven by inspirations even he couldn't completely articulate, nonetheless moving the music in directions that felt "right" to him, if not specified or unique.  It's a tantalizing task to try to describe what that structure might be like.

If any authoritative vision of harmolodics died with him, so however did the possibility of being declared definitively wrong.  Musicology is in a sense freer now to come up with a descriptive notion of harmolodics, as opposed to what might have been Coleman's own more prescriptive one.  So here are my personal thoughts on harmolodics, based on a moderate amount of listening to Ornette Coleman recordings.

It's an odd idea, the concept of Coleman prescribing what harmolodics was, because even if it wasn't entirely free, he still viewed it as being freer than traditional jazz.  Still, he did seem to consistently assert that harmolodics was about denying the hegemony of harmony.  He viewed harmolodic music as equal parts harmony, melody, rhythm, dynamics, articulation, etc., all acknowledged as parts of a musical performance.  Granted, it's probably not possible to say precisely what "equal" means in this context (can you imagine measuring a particular piece to be exactly 75 percent harmony and 25 percent melody?), but it's hard to deny that traditional jazz performance is driven more by harmony—the chord changes—than by the melody in the head.  Presumably, that dominance is what Coleman wanted to counter; he frequently alluded to a "democracy" amongst the performers and the music they created.

One of the things that strikes me when listening to Prime Time and other ostensibly harmolodic groups play is that although any piece may seem to meander along aimlessly, individual segments of it typically do not.  That is, if you were to listen to any one-second snippet of a harmolodic piece, it "makes sense" in a way that we don't usually associate with harmolodics.  It sounds like it could come out of many a jazz piece.  So perhaps one thing that distinguishes harmolodics from other jazz forms is that the parts that make sense don't persist as long in harmolodics.

Let me try to make that more explicit by reference to traditional jazz pieces.  Suppose we're looking at a twelve-bar blues, the most traditional of the traditional jazz forms.  Everyone plays this at some point.  Even in a jazz setting, with its penchant for alteration, a fairly standard chord progression runs

| C7    | F7    | C7    | %     |
| F7    | %     | C7    | Em A7 |
| Dm7   | G7    | C7 A7 | D7 G7 |

Because everyone is playing to the same chart, whenever the bass is playing G7, so is the piano, so is the horn, etc.  It all "makes sense," because each performer is playing notes in the same scale.  We might characterize such playing as all taking place along the same line, or "linear."

What's more, the transition from, say, G7 to C7, although it's not exactly the same scale, is very nearly the same.  It differs in exactly one spot: The position occupied by B in the G7 scale becomes a Bb in the C7 scale.  So although it's not exactly on the same line, it's still diatonic.  We might say that it's in the same plane, to stretch (ever so slightly) a mathematical metaphor.  Thus it's not very surprising to hear.  Most of the other transitions in these changes are like that, and even those that aren't, are so familiar to our ears that we don't find them jarring at all.  On the contrary, those transitions are so familiar that it becomes jarring when we don't follow them.

It occurs to me that there is an analogue to be made here between the familiar plane of traditional jazz and harmolodics on one hand, and the familiar plane of Euclidean geometry and curved space on the other hand.

I've talked about curved space in other contexts before, where it's directly related to gravitation.  Here, obviously, the application is less precise, but I'll try to keep it from being wholly vacuous.  The idea is that when we say a section of music is diatonic, that's like saying it's flat—and I don't mean "flat" as in opposite of "sharp," or even that it's uninspired.  It simply means that it obeys the familiar rules of traditional jazz.

When it came time to specify what curved space means in physics, one of the central motivating tenets is that although it's globally curved, locally it's flat, in the limit.  That's why wherever you are in the universe, as long as you're relatively small (small compared to the curvature of spacetime), things behave more or less the way you're used to.  That's relativity.

In the same way, when you're listening to a piece of harmolodic music, although the whole of it doesn't constrain itself to any single musical plane, locally (that is, at any immediate moment), it does.  In particular, that means there aren't any immediately jarring transitions, but changes smoothly (differentiably, we might say!) from one moment to the next.  That's what gives harmolodic music the feel of being unanchored, and yet not having any moments of discontinuity, where what happens next is wholly divorced from what came before.

And how does one arrive at what comes next?  To my ear, that's where the democracy that Coleman was striving for comes in.  In traditional jazz, the lead chart—the chord sequence—dictates what comes next.  When I listen to harmolodic music, what I hear is an instantaneous bending of the musical fabric, where at any moment, any performer might play the note, or the rhythm, or even the articulation that changes the direction of the group and the music as a whole.  Maybe, if the recent actions of the rhythm section have pointed toward a C major scale, the horn might begin C-E-D-F—

—but then continue E-G#-F#-A-Ab-C-Bb-Db, following the intervallic motive of up a major third, down a major second, up a minor third, down a minor second, and then repeating a major third higher.  The bass and piano might follow suit—perhaps playing in double time for a moment to match the speed of the melodic line—but only for the moment, before one or the other of them again takes the lead in steering the music in yet another direction.

Obviously, carrying such an idea to fruition requires the performers to listen intently to each other, and to develop an almost preternatural intuition about their fellow musicians and their likely directions.  It's an interesting balance, though, since too little anticipation means that the music won't make sense for long stretches, while too much anticipation means implicitly restricting where the music can and can't go, and paradoxically limiting the very freedom that the approach was meant to foster.  Still, properly handled, it could enable a group to produce music that sounds cohesive and yet is freed from much of the shackles of traditional jazz.  To put it in the vernacular of the time in which harmolodics started, it would allow the music to ascend to a higher dimension.

I hope to make some time in the future to look at specific recordings and use them to substantiate the general framework I've described here.  (Also, I realize there's precious little reference to holomorphy here, other than the one mention of differentiability, but I couldn't resist the alliteration.)

The Limitations of Sense

As I've mentioned previously, I lived in the dorms in college.  In addition to balky vending machines, the dorms also had a number of lounges—common areas on selected floors for people to gather for the purpose of studying (if they didn't mind a bit of noise), watching TV, or generally screwing around.  And, from time to time, there was the occasional Bible study group.

I hasten to emphasize that the study group people (who generally lived in the dorms themselves) were very reasonable about their use of the lounge.  They were perfectly willing to wander around in search of a mostly unused lounge, and they asked the others instead of just plopping themselves down and using the space.  In my own turn, I was perfectly willing to move over to defrag the chairspace in the lounge and allow them their own section.

Once, though, they did manage to irritate me.

I had settled in with my Walkman, listening to an album.  (For the benefit of those of you who were born in this millennium: Songs used to be sold on physical media, called "vinyl" or "records."  These records could be "singles," or they could be multiple songs sold on one "album."  We had this innovation—developed by Sony, a company that existed even then—called a Walkman, which played "tapes," on which songs could be transferred from the record.  It was called a Walkman because you could walk around with it.  You could listen to a whole entire album and not be tethered to your "component stereo system," which was a collection of devices used to play music at a time when computers had memory sizes measured in kilobytes.  We thought it was great.)

Anyway, the Bible group came in and said they wanted to use the lounge and they promised not to be too loud.  Since I was the only other one in the room and I didn't want to be a complete jackass, I cheerfully agreed and moved over to the other side.  But in doing so, I took off my headphones.  And so, as they began discussing the Bible, I listened to them.  It was interesting, after all.

After some time, however, I guess it became increasingly evident that I was listening to them, and since it was apparently one of their objectives to spread the word to as many people as they could, they began working on me.  Now, I was brought up without any religious background.  (Oddly, I do recall that we had a napkin holder that had some strange incantation on it about "daily bread," although that was never explained to me.  I had to find out about it on my own.  But that's a story for another time.  Essentially, there was no religion in my upbringing, at all.)

What's more, I had by this time become fascinated by science, and the scientific method.  I didn't have a firm idea, perhaps, of how science got done, exactly, but I did have the notion that people were fallible, and experiments were conducted so that we could find things out without relying solely on fallible humans.  And it seemed to me that the more fantastical stories in the Bible (as opposed to the moral precepts, say) simply would not stand up to any kind of scientific inquiry.  I did not believe that there existed anything like the Christian god.  And I'm sorry to say that, somehow, that came out.

Well, the floodgates opened up after that.  And I just could not get them closed back up.  For some reason, I was made to answer for the slightest failing or shortcoming of science as it pertained to anything, and I mean anything, in the Bible.  To be sure, I was not blameless in this; at that age, I had not learned to adopt the sort of detached self-doubt that I can effect these days, and I was unfoundedly certain about the points I made, which landed me in some hot water.

I don't remember how I managed to extricate myself from the "discussion," but I do know that it took a couple of hours, after which I went to my room and lay down.  I was exhausted.

A few of them came up to me the next day, and apologized for their aggressiveness.  I said I understood, and apologized for my unseemly certainty.  But it set me to thinking: I did feel pretty certain about my atheism.  Why?  What made me feel so certain?  I had some vague sense that it had something to do with a kind of epistemological conservatism (though I wouldn't have known to put it in such a way)—the idea that one believes in as few things as is possible to understand the world—and the proposition that extraordinary claims require extraordinary evidence.

It took me some years, however, before I could fully work out what my situation was with regard to atheism, and agnosticism, and all that.  It came about like this:

Much later, I was talking to this fellow, and I mentioned some of this mess I got in with the Bible study group.  And so he asked me, what did make me so certain?  He thought that people who could feel so certain that there was no god were just as scientifically irresponsible as those who could feel certain that there was one.

Fortunately, by this time, I had read Wittgenstein (I'll bet that's the only time you'll hear anyone consider it fortunate to have read Wittgenstein, and by the way, he looks just about that crazy in every picture of him I've ever seen), and I knew he had, too, so I could express it a bit more concisely.  I said that I was about as certain that there was no god as Wittgenstein was that he had a hand.  What good ol' Wittgenstein—and I, by extension—meant by that was that the knowledge that one has a hand represents an upper limit of certainty: a limit imposed by our senses.  We know it not because it is logically proven beyond a shadow of a doubt, but because doubt itself is pointless in this regard.  In other words, the degree to which we know it is a milestone of certainty—in a very real sense, defines it.  In fact, I think Wittgenstein says as much, right at the very start of his final work, On Certainty:

If you do know that here is one hand, we'll grant you all the rest.

My friend was satisfied by that, I believe, and he walked away.  As he walked out, though it hit me that that was it—that the limitations of my senses were the basis of my "certainty" that there was no god.

To begin with: From time to time, some atheist wag will remark that we have no more evidence for the existence of the Christian god than we do for, say, the Flying Spaghetti Monster.  Which is true, so far as it goes, but it doesn't really establish atheism (the belief that there is no god) as it does agnosticism (the lack of a belief that there is a god).

So then, the hypothetical line of questioning goes, what would it take to establish the existence of a god in any kind of scientific way?  Because, as I tell others, if you take a position against something, then as a self-check, you must ask yourself what it would take to convince yourself you were wrong.  Because if there's no amount of evidence that would do it, then your position isn't a scientific one; it can't be falsified.

I thought about all the miracles that are said to be the work of some god or another, all the things that happened that could not be explained.  In most cases, I rather thought that these were evidence less for a god than for the selective ingenuity of humans: If people wanted to believe in something, they were remarkably ingenious about how they managed to assemble evidence in its favor.  But if they didn't want to believe it, that ingenuity mysteriously went away.  In other cases, I couldn't come up with a plausible explanation, except to say that the people who related these stories (thousands of years ago, remember) were either mistaken or, possibly, exaggerating.  That might not have satisfied anyone who was truly on the fence, but it satisfied me.

It boiled down, therefore, to what I could personally witness that would convince me I was wrong.  What could a supernatural being do that would sway me?  It quickly occurred to me that whatever evidence could possibly support the claim to existence of a god had to be much more extraordinary than the possibility that my senses were fallible.  When it came to the existence of a god, I could not grant that I had a hand.

We hear "Seeing is believing," but we see things all the time that, it later turns out, aren't true.  And so, not as an expression of any desire, but simply as an acknowledgement that my senses can fail, catastrophically at times, I flatly admit an incapacity to believe in a god, any god (as normally represented—I obviously don't mean just a super-powerful being, but someone who brought about the world).  It's a personal incapacity, not one that I could possibly extend to anyone else, but it's insuperable just the same.

Grasping at Genius

No, this isn't about me trying to become a genius. My aim is a lot more modest: trying to draw a bead on what genius is. Partly this is motivated by my last post about music, but mostly it came out of a discussion I had several years ago with a co-worker over whether athletes could be geniuses at their sport. I thought they could, and he thought not. He conceded that they had some outstanding skill, but felt that it would be demeaning the word "genius" to call it that. I was willing to be a bit more expansive with the term. One does have to be a little careful—probably half the parents out there think their precious little ones are geniuses—but limiting genius to a specified list of fields seemed unnecessarily restrictive to me.

The discussion more or less had to end there because we never really grappled with the larger issue of what genius really is, and without that any debate over whether it means anything in sports is putting the cart before the horse. I want to tackle that now, so I can go back and win the original argument.

First of all—because I'm sick and tired of hearing about it, even now—what is genius not? It is not a high IQ, or intelligence quotient. Lots of folks are intimidated by numbers (especially, but not exclusively, those who do not feel comfortable around them), to the point that any description using them feels more objective and unassailable. Well, they might be that, but what's lost when a number is attached to anything is the process by which that number was derived. If you don't know and understand that process, the number—while not exactly meaningless—is not as reliable as it sounds.

In the case of IQ, the formula is generally straightforward; what's not so clear are the principles on which questions are selected for IQ tests. If you've ever taken one, you know that questions on such tests are fairly narrowly circumscribed: which one of these things doesn't belong, how many blocks are there, numerical or word analogies, etc. The only thing that we can be sure IQ tests measure is how well someone takes IQ tests. Beyond that patently circular assertion, it gets hazy. Does it measure intelligence? How about genius? There are lots of folks who have very high IQs (Marilyn vos Savant—really? that kind of name?—comes to mind) who nonetheless evince no obvious signs of genius. To her credit, vos Savant doesn't make any claims of genius for herself.

If we can't rely on a test to identify genius, we are back to Potter Stewart's famous dictum (in his concurring opinion in Jacobellis v. Ohio regarding hard-core pornography): "I know it when I see it." So where do we see it?

If we start with the so-called hard sciences (physics and chemistry), plus mathematics, I think you'll find little argument that folks like Archimedes, Isaac Newton, Carl Friedrich Gauss, and Albert Einstein were geniuses. Expand that to all of letters and sciences, and you embrace other noted geniuses, such as Charles Darwin, Louis Pasteur, and B.F. Skinner. But maybe these get a little dicier. These are great scientists, to be sure, but what about them promotes them beyond the ordinary rabble?

You might expect that things would get dicier still when we go to the fine arts, but at least in my experience I find less argument about ascribing genius to artists like Leonardo da Vinci (also an engineer), William Shakespeare, Auguste Rodin. How about musicians? Ludwig van Beethoven, Richard Wagner, and Igor Stravinsky all wear the mantle of genius, and wear it rather comfortably at that. (Yes, I realize these are all dead white dudes. I'll get to that in a moment.)

Let's pause a while and take stock of what we have. Accepting for the sake of discussion that these people are all geniuses, what makes them so? They don't just do what ordinary people in their professions do, only better—although by and large, they do do those things better. They also don't just do what ordinary people can't do—although, again, they do do that, too. What sets them apart is that they do things that ordinary people in their profession could never even conceive of, before the geniuses did. Arthur Schopenhauer put it this way:

"Talent hits a target no one else can hit; genius hits a target no one else can see."

I must emphasize that innovation is a vital part of this. One of Newton's most important contributions to physics was a mathematical demonstration of the law of universal gravitation (the so-called "inverse square law" of gravitation) from Kepler's observations and laws of planetary orbits. That same law is derived countless times over by students in undergraduate physics classes around the world (albeit using analysis, rather than the essentially geometrical means that Newton employed). That doesn't mean that any of them, let alone each of them, is a budding Newton, for likely none of them, plucked at birth and set down in a pre-Newtonian world, could have done what Newton did. Newton's genius lay in blazing the trail that future scientists and students would follow.

In that context, then, let me add a few other names to the list: Charlie Parker, Miles Davis, Herbie Hancock. Jazz is an art form, among others, that combines composition and performance in a single moment, adding for the first time—to my list, anyway—the element of dynamism. (I don't mean to slight other performance geniuses, such as actors and stand-up comedians, but I'm trying to make a point!) Although jazz tunes are composed to a certain extent, a fundamental aspect of jazz performance is improvisation. No two jazz performances are ever exactly the same—not, at any rate, to the extent that classical music performances are alike. The music is constantly written and rewritten by each new performer that approaches it, and each new performer must contend not only with the structure of the music, but with the performers around him or her, in an endeavor that is, in the best of cases, at once collaborative and competitive. And genius denotes the ability, moment to moment, to conceive and perform what others in that situation could not even imagine.

From that point, how far of a step can it be to arrive at sports? I'm going to talk about basketball, because it's the sport with which I'm most familiar, but similar arguments could be made for other sports. (Imagine, for instance, the shots that Tiger Woods can execute that others would never even attempt, or the sudden volley, deft but fierce, of Pete Sampras.) Basketball, like jazz, requires the constant attention of the athlete to the ever-changing state of the game, from the highest level down to the smallest detail, and the ability to respond to that state, all on the spur of the moment. Where's that pick going to be in five seconds? What are the possible tactical options available to me, given the current score and time remaining? Seeing the passing lane halfway down the court is a geometric exercise in negotiating tangled world-lines in the four dimensions of space and time; to actually complete the pass, when everyone else is watching, one must summon the legerdemain of a practiced conjurer.

We think of sports as an essentially physical activity (which is probably why my co-worker could never attach the genius label to an athlete), but in its own way it is as demanding on the intellect as the most abstruse mathematical theorem, and unlike the mathematicians, who can return now and again to their labors when it suits them, the athlete has only the splittiest of split-seconds to act—or else the instant is gone. Who are we to say that genius could not act here, as well as anywhere else?

We may debate whether or not Wilt Chamberlain, Michael Jordan, or Magic Johnson merit the label of genius, whether or not what they do exceeds the conception of their colleagues. But not, in my opinion, whether the question makes sense. Even we non-geniuses can see that, I think.

The Sound of Music

I've always been intrigued by music; there's something almost incomprehensible about its appeal, which, nevertheless, you desperately want to comprehend. At least I do. And the best I can do is sort of nibble 'round the edges.

For one thing, it's a temporal art form. Mostly you experience it over time, however long it takes to hear a performance (or a recording thereof). And if you feel its impact, be it sadness, suspense, gladness, or even a kind of horror, that too is felt over the duration of the music. It never happens that a piece of music saves up all of its emotional impact for a single whap in the face, like a painting or a sculpture might. Yes, I'm aware that those art forms have nuances that can take extended or repeated viewings to appreciate. But for those forms, it is possible for the entire gestalt to strike you at a single moment, followed by a sustained decay of gradual discovery.

To be sure, trained musicians can look at a musical score and apprehend it. But even then—unless they are familiar with the music, and sometimes even then—they hear the music in their head, once again over time.

And the emotions you feel—oh! Music seems to speak to us in a language that is uniquely suited, not for communication, but only for emotional transference. A strain of music can connote hope or despair, struggle or triumph, seemingly no matter your roots or background. You almost think that if only somehow that universality could be harnessed, you could solve the world's problems in a single swoop—but then, that sounds like a travesty to be visited on music. At times I feel as though it should be protected from that kind of directed use.

Music stays in us. We have a tune stuck in our head. As much as we may appreciate the Mona Lisa or the David, how often do we complain that one of those (or their modern counterparts) are stuck in the same way? Maybe music gets a leg up from being a primarily auditory art form. We get so much of our information about the world from our eyes; our ears are generally accompanists, not the featured performer. As a result, though, it works its magic subliminally, providing a soundtrack for us. Seeing a visual art form may put us in an ecstatic trance of exploration, but rarely does it pull something directly out of us, something we recognize. Whereas surely all of us have songs that invariably draw forth some sharp memory. Music makes us aware that we have a story.

None of which brings me much closer to being able to comprehend its appeal in any meaningful way.

Inconsequence (A Jazz Tune)

Something a little different. A test of the video embedding, I guess. (Could it have picked a more objectionable thumbnail?)

An original composition. In my Walter Mitty fantasy world, this is part of a stage musical and is performed twice; the reprise has slightly different lyrics. For my own nefarious purposes, I have Frankensteined the two into one.

Here we are, you and I,
Face to face, eye to eye.
Shouldn't time give a soul
Who while wondering was blundering
A chance to be whole...?

...Hold that thought, just a mo,
Never mind, let it go.
Doesn't matter what we do
From here on, from here on I'll smile
In consequence of you.

This song is Copyright © 2009 by Brian Tung. All rights reserved. Product may have settled during shipping. Do not incinerate. Objects in mirror may be closer than they appear. Operate in a well-ventilated environment. Handle with care. Do not taunt Happy Fun Ball. Contents under pressure. Do not inhale.