two-for-the-show

Wild Replicator’s Got Funky Rhythm, Part 1

Now that the replicator meme is out and about I’ve got more to say. I’m going to republish two more posts from my 2010 cultural evolution series. These posts are about music. I have various reasons for using music as my cultural evolution conceptual sandbox. For one thing, it means that I don’t have to contend with semantic meanings arbitrarily associated with bits of music. In music, all we’ve got is the physical signal.

In these two posts I choose, not a simple musical example but, rather, a complex one, something jazz musicians know as Rhythm Changes. While I could talk about the four-note motif Beethoven used to construct the first movement of his Fifth Symphony, which is a memetic favorite, that’s too easy. Thinking about it won’t stretch our intuitions about the memetic properties of mere physical things. That motif has four notes, with specific durations and specific note-to-note pitch relationships.

Rhythm Changes isn’t like that. It’s an abstract property of a sound stream. There is now specific number of notes, no specific durations, and no specific note-to-note pitch relationships. Thousands upon thousands of specific musical streams, many quite different from one another, have exemplified the properties of Rhythm Changes.

In the previous post (in this series) I argued memes, the cultural parallel to the biological gene, are those physical properties of objects, events, and processes that allow different individuals to coordinate their participation in those things. In this view, memes are not physical objects, like genes, that spread through a population. Rather, memes are about sharability; they are physical properties that can easily be identified by human nervous systems and thus be the basis for shared (cultural) activity.

In that post I considered a very basic case, people making noise at regular intervals. In that case we have two memes, period (the interval between “hits”) and phase (the relationship between streams of hits by different individuals). Now I want to consider a considerably more complex case, the entity jazz musicians know as Rhythm Changes. This entity assumes that, for a given performance, period length and phase value are agreed upon. In fact it assumes a lot more. We’re dealing with a whole lot of memes here.

But I don’t want to get hung up in those details. I just want to characterize Rhythm Changes in a reasonable way and explain just why I insist that we regard Rhythm Changes as a structured collection of physical properties that can be ascribed to a stream of sound. While it would be nice to characterize Rhythm Changes using the language of acoustics, it’s not at all clear to me that we’ve got the necessary concepts. In any event, if we do, I don’t know them. Instead, I’ll couch my description in the schematic terms jazz musicians tend to use when talking about their craft; these terms are derived, in part, from descriptive and analytic concepts developed for European art music (i.e. classical music).

I’m going do this in two posts, the first will be confined to Rhythm Changes itself. The second will consider how Rhythm Changes came into being and how it functions in the popular music system.

Rhythm Changes: A harmonic trajectory

By changes I mean chord changes, the basic harmonic structure of a piece considered as sequence of chords (whatever they are). In this context “Rhythm” designates George Gershwin’s tune, I Got Rhythm. Thus Rhythm Changes is the harmonic pattern Gershwin used for that particular. Gershwin’s tune was a smash hit during the 1930s and became a favorite of pop and swing musicians and fans. Jazz musicians, mostly of the bebop era (from roughly the early 1940s through the 1950s), have abstracted the changes from the tune and written new tunes for them, and then have based innumerable performances on these various tunes. Rhythm Changes are thus well known and readily identifiable within the jazz world.

I have various reasons for choosing Rhythm Changes as the an example for extended consideration. For one thing, it’s a rather abstract entity. Yes, it is an aspect of a physical event; it’s not abstract in the sense of, say, charity, mana, or democracy. But it’s not a relatively simply property of sound, like pitch, loudness, or timbre. Unlike that pesky four-note Beethoven motif that keeps turning up in memetic discussions, you can’t “point” to Rhythm Changes in an easy way. It’s not something you can hum, though you can hum any number of musical lines that conform to rhythm changes. And yet, if a bunch of musicians are jamming on Rhythm Changes and a newcomer enters the room, she can hear the changes instantly and join right in without any difficulty.

Using a standard notation we might describe Rhythm Changes as follows (in the key of B-flat):
/ Bb7 G7/ Cm F7/ Dm G7/ Cm F7/ Bb / EbM Ab7 / Dm G7 / Cm F7/

/ Bb7 G7/ Cm F7/ Dm G7/ Cm F7/ Bb / EbM Ab7 / BbM F7/ BbM /

/ Am / D7 / Dm / G7 / Gm / C7 / Cm / F7 /

/ Bb7 G7/ Cm F7/ Dm G7/ Cm F7/ Bb / EbM Ab7 / Cm F7 / BbM /
The slash marks designate the beginnings of “measures” or “bars” and thus demark equal units of time. The alphanumeric symbols designate chords; roughly speaking, chords indicate quasi-ordered sets of pitches from which one can choose notes to play. Notice that some bars have two chords while others have only one.

What’s characteristic of Rhythm Changes is the relationship between the chords in the sequence; it is a certain trajectory through tonal space, one somewhat different from that found in, e.g. Back Home in Indiana, or How High the Moon. Gershwin wrote the song in the key of B-flat, where the pitch B-flat (Bb) is understood to be the tonic or “anchor” tone for the whole song. Just what that means is not terribly important at the moment, but we do need to know that the same set of chordal relationships, the same tonal trajectory, could be realized in any key. To do so, however, means that we’ve got to transpose the chords up or down as appropriate. Thus, if we wanted to play Rhythm Changes in the key of B (up a half step from Bb), the first four bars would be thus:

/ B7 G#7/ C#m F#7/ D#m G#7/ C#m F#7/

If we wanted to play Rhythm Changes in the key of A (down a half step from Bb), the first four bars would be:

/ A7 F#7/ Bm E7/ C#m7 F#7/ Bm E7/

The relationships between successive chords are the same in all three cases. As we can realize this set of relationships in all twelve keys of the chromatic scale, there are thus twelve sets of rhythm changes; that is to say, twelve different ways of realizing this set of tonal relationships. It is the abstract set of tonal relationships which is Rhythm Changes.


For the record, there is a standard way of representing this tonal trajectory that is independent of any specific tonal center. In this notation the first four bars of Rhythm Changes becomes:

/ I7 VI7/ ii V7/ iii7 VI7/ ii V7/

Roughly speaking, the Roman numerals indicate the position of a chord in tonal space. Capital letters indicate major chords while lower case indicate minor chords. Music psychologists sometimes conceptualize harmonic structure as an abstract space (e.g. Longuet-Higgins 1987) and some have even begun to map that space onto cortical structure (see Janata 2002, Zatorre 2002).


In this sense we can think of Rhythm Changes as a relatively abstract property of the sonic object created by a musical performance. Any number of specific sonic objects can display this property, each different from the others in many ways, some of which may be minor while others are extreme. Despite all their surface differences, all these conform to the properties of Rhythm Changes.

The point of improvising on Rhythm Changes is to demonstrate skill in devising clever ways of negotiating the changes. This particular trajectory thus has a normative value; one is judged on the ability to producing interesting and even surprising melodies that, nonetheless, conform to the trajectory of Rhythm Changes. It may well be a matter of individual judgment or taste as to whether or not a given sonic object exhibits this property – Rhythm Changes – or not. Still, there will be a large collection of sonic objects which experts agree exhibit the property and another large collection of sonic objects which experts agree do not exhibit the property.

Rhythm Changes is not, of course, an “atomic” meme. It is an ordered collection of memes. Before going on to consider how to think about the constituent memes of Rhythm Changes, however, I would like to offer a crude biological comparison. I suggest that we think of Rhythm Changes as comparable to a biological notion such as the body plan of, say, carnivores. While zoologists always examine the bodies of individual members of specific species, the idea of the body plan for carnivores in general is a perfectly sensible anatomic notion; it characterizes a real entity which can be observed in the world – as Rhythm Changes designates a real entity.

It is also sensible to think about the genes responsible for that body plan, provided that one is appropriately careful. There’s no reason to think that all of those genes exist in a continuous sequence on a particular chromosome; nor does it even make much sense to think of some set of genes such that they and only they do nothing but specify the carnivore body-plan. However linguistically specific it may be, the extension of the entity specified by the phrase “genes specifying the carnivore body plan” is rather fuzzy. So I suggest it is with the notion of the “memes specifying Rhythm Changes.”

Let us now think about how we might begin analyzing Rhythm Changes into constituent memes.

Constituents of Rhythm Changes

Notice that when I spelled out Rhythm Changes (in the key of Bb) I did so on four lines. That was quite deliberate. If you examine those lines you’ll notice that lines 1, 2, and 4 are identical except for their last two bars. Line 3 is different. You will further notice that each line consists of eight bars. Gershwin’s I Got Rhythm is a specific instance of a kind of tune known in the trade as a “32-bar AABA standard.” A “standard” is simply a tune which has made the standard repertoire; it has been performed year after year, decade after decade. “AABA” designates the form, where “A” designates one longish phrase while “B” designates a different longish phrase. Lines 1, 2, and 4 consist of the A phrase while line 3 is the B phrase; the B phrase is often known as the bridge or the channel. Each of these phrases is eight bars long, making the whole form 32 bars long.

Thousands of tunes have been written having a 32-bar AABA form. Thus we might consider AABA form itself to be a complex memetic entity. As such it contrasts with other 32-bar forms. Embraceable You and How High the Moon have an ABAC form; Autumn Leaves is AABC; and Yesterdays is ABCD. Given these possibilities do we also wish to consider 32-bars with 4-phrases-of-equal-length to be memetic? At this point I don’t really know, nor do I see any urgency in the question.

Note that in treating AABA form as memetic we specify nothing about the internal structure of the A and B strains. Once we begin to think about that, we have another whole arena open for analysis. Just how does one construct an eight-bar phrase suitable for use in 32-bar AABA tunes? For the most part, one does it by using two four-bar phrases, each of which, in turn, consists of two two-bar phrases. And there are standard ways of doing those things as well; I should think that we’ll find various memetic entities here. Finally, given that we are talking about harmonic structure, our simplest unit is simply the chord. Chords consist of various types, major and minor triads, dominant 7ths, major 7ths, and so forth. These may be memetic entities as well.

I do not know what sorts of things we’ll end up with as the atomic or simplest memes constituting something like Rhythm Changes. Music theory and musicology have devoted considerable effort to similar issues, but this has been done without regard either to psychology or to neuropsychology. Thus the psychological validity of these analytic efforts is questionable (we should not get too attached to the chord notation I used to describe Rhythm Changes). While there is a rich psychological and neuropsychological literature on these matters, that literature is not yet prepared to deal with something as complex as Rhythm Changes. This not withstanding, I still feel that it is sensible to think of Rhythm Changes as a memetic entity, one constituted by a rather fuzzy collection of perhaps some 10s or 100s of simpler memetic entities in some structured relationship.

To get it right, however, we’re going to have to understand what’s going on at the neural level.

What Happens in Peoples’ Brains?

If I’m correct in this approach, then memes are not going to turn out to be an entirely new class of entity – such as Robert Aunger has posited in his (rather unfortunate) Electric Meme. In the case of music, I warrant that we already know quite a bit about such entities, but we haven’t been conceptualizing them as memes. We’ve simply been conceptualizing them as the stuff of music.

I tend to think of physical objects and processes as having an unbounded number of properties or attributes. J. J. Gibson might talk of their affordances. As I indicated at the end of my previous post (and in the ensuing discussion), others talk of emics vs. etics. Perceptual systems evolve to respond reliably to some of these properties. The properties to which nervous systems are sensitive may not always be readily described in the language of physics or chemistry (color is a simple and notorious example), but they are nonetheless properties of physical objects or events.

Just as nervous systems are sensitive only to some of the properties and attributes of physical objects and events, so cultural evolution is sensitive to only some of the properties and attributes exhibited by objects and events. These properties and attributes are memes. The only way to identify properties and attributes which function as memes is to examine cultural processes – a matter I’ll comment on in the second post on Rhythm Changes.

“But what,” the orthodox memeticist asks, “of what happens in peoples brains? Surely that’s where memes reside?” For the orthodox memeticist believes that memes flit about from brain to brain and thus propagate themselves.

I am quite aware that a laot goes on in human brains and, of course, believe that that activity is central to the processes of human culture. Similarly I know perfectly well that, in order for culture to be propagated from one generation to the next, or from one group to another, something must be learned by the recipients of culture – though this does not mean that the propagators engage in explicit teaching; they may or may not. The propagation of culture requires systematic and extensive changes in brains. I just don’t think that talking about memes flitting from brain to brain tells us anything about this process; on the contrary, such talk prevents us from thinking seriously about how culture operates.

Following the neuroscientific work of Walter Freeman (1999) I believe we must think of brains as self-organized systems. Brains construct culture “from the inside” as it were. They do so to serve the purposes of the individuals in which they reside – I’m aware of notions of group selection, but that’s more than I want to deal with here. Culture is not something foisted upon people by pesky and intrusive memes.

References

Aunger, R. (2002). The Electric Meme: A New Theory of How We Think. The Free Press

Freeman, W. J. (1999). How Brains Make Up Their Minds. London, Weidenfeld and Nicholson.

Janata, P., J. L. Birk, et al. (2002). “The Cortical Topography of Tonal Structures Underlying Western Music.” Science 298(5601): 2167-2170.

Longuet-Higgins, H. C. (1987). Two Letters to a Musical Friend. Mental Processes: Studies in Cognitive Science. Cambridge, MA, MIT Press: 64-81.

Zatorre, R. J. and C. L. Krumhansl (2002). “Mental Models and Musical Minds.” Science 298(5601): 2138-2139.

3 thoughts on “Wild Replicator’s Got Funky Rhythm, Part 1”

  1. Again, nice article Bill — especially so, given that it’s on the topic of music (something that’s not really been addressed, with one or two exceptions). On the general topic of memes, I was wondering if you’re familiar with the work of Dan Sperber on attractors: points or areas in the space of possibilities that are abstract objects, with all variants of a given item tending to graviate around the same attractor point. As Sperber said in a recent short essay over at Edge:

    Well, bits of culture — memes if you want to dilute the notion and call them that — remain self-similar not because they are replicated again and again but because variations that occur at almost every turn in their repeated transmission, rather than resulting in “random walks” drifting away in all directions from an initial model, tend to gravitate around cultural attractors. Ending Little Red Riding Hood when the wolf eats the child would make for a simpler story to remember, but a Happy Ending is too powerful a cultural attractor. If a person had only heard the story ending with the wolf’s meal, my guess is that either she would not have retold it at all — and that is selection — , or she would have modified by reconstructing a happy ending — and this is attraction. Little Red Riding Hood has remained culturally stable not because it has been faithfully replicated all along, but because the variations present in all its versions have tended to cancel one another out.

  2. I’ve not read that particular essay, but I’m familiar with Sperber’s usage. He developes the attractor notion in one of the chapters of his 1996 Explaining Culture, where he talks about Little Red Riding Hood. The notion is from nonlinear dynamics where it is used to indicate a point or a trajectory in a system’s phase space to which the system is driven by its internal dynamics. Just what that means, well Sperber doesn’t explain it in the book (he doesn’t even mention nonlinear dynamics) and this comment is not the place to explain it either. (This Wikipedia entry may help.)

    I don’t think Sperber develops the notion very well in the book. He just says the space a possibility space, but doesn’t say what’s driving the dynamics of that space. So you’re left thinking that these attractors are, well attractive, you know, like moths to light, and that’s not terribly useful. He explicitly denies that’s what’s going on, but doesn’t give you any other way of thinking about the space or the attractors in it.

    Now, in my book on music, Beethoven’s Anvil, I start with Walter Freeman’s nonlinear neurodynamics where the phase space is that of the brain and begin by developing the concept of a collective neural phase space for a group (Ch. 3 “Fireflies: Dynamics and Brain States”). If a given performance is a pleasurable one (Ch. 4 is about pleasure), then the group is likely to (attempt to) repeat it. The trajectory of such a performance then becomes an attractor in the group’s collective neural phase space. I then go on, in a later chapter in the book to argue that such trajectories are, in function, cultural phenotypes (pp. 192-193). You can read a quick and dirty version of that argument in this post.

    So, what makes it possible for people in a group to collaborate together in creating a pleasurable musical performance? Memes, that’s what. And Rhythm Changes is a modest, but organized, little pile of musical memes.

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