Saturday, June 5, 2010

Cultural Evolution 5: Rhythm Changes 2

In the previous post I took a look at Rhythm Changes, a memetic entity that has played an important role in jazz and, in particular, in bebop. FWIW, Rhythm Changes has also been used in the theme song for well-known some well-known cartoons, Woody Woodpecker and The Flintstones. In this post I want to do several things:
  • consider all the elements of “I Got Rhythm,” rather than just the chord changes,
  • think briefly about how pools of memetic elements function in defining musical styles, and
  • look briefly at how the chord changes to Gershwin’s tune became memetically active.
Taken together those discussions flesh out the role of memetic elements in music systems in the large. I conclude by
  • examining this discussion of memes in music in the context of a recent article by Evelyn Fox Keller and David Harel, Beyond the Gene, and not some broad thematic similarities between their discussion and mine.

I Got Rhythm, Whole

As I’ve indicated, Rhythm Changes is derived from, abstracted from, George Gershwin’s “I Got Rhythm.” Now let’s think about the whole tune, not just its harmonic trajectory, i.e. Rhythm Changes. In addition to that trajectory we also have a specific melody, the lyrics, the rhythmic framework, and the arrangement. The lyrics are optional; the tune can be performed without them, and among jazz musicians that is the typical, if not universal, performance practice. Note, however, that any consideration of the lyrics brings a whole other memetic field into consideration, that of language.

On the melody, Gershwin provided a specific melody, constructed on specific principles. We need not discuss those principles here. When others write tunes based on Rhythm Changes (e.g. Duke Ellington’s “Cottontail,” Charlie Parker’s “Dexterity”) they must provide melodies as well. Not only are these melodies different from Gershwin’s, but they may be constructed on different principles as well. Thus we have another body of memetic entities to deal with, albeit one that interacts quite closely with those governing the tonal trajectory.

And so it goes with rhythmic framework as well. Gershwin wrote his tune in 4/4 time and that is how it (and tunes derived from it) is generally performed, usually at a medium or fast tempo. The tune could, however, be performed in other meters (e.g. 3/4, 5/4), though I’ve never heard it done so. Beyond this we have to consider the particular rhythmic style. Gershwin wrote it in the swing style and most performances are in a swing style or a closely related bebop style. But it could also be performed as a bossa nova, or a rumba, etc. Another bunch of memes to consider.

As for the arrangement, I mean such things as whether or not a performance involves just a vocalist and piano, or a big band; what’s the introduction going to be? how many choruses, and so forth. In order to have a performance specific musicians must perform specific parts on specific instruments. These details are constrained by harmonic, melodic, and rhythmic matters, but not dictated by them.

My first point, then, is that in order to have a musical performance a great many details must be specified. While I don’t think all of these details have memetic status – in fact, I’m sure they don’t – a good many of them do. That is to say, a good many of them function broadly in musical culture and appear in many different performance. If Rhythm Changes, as abstracted from Gershwin’s tune, entails some 100s of memes, then a complete performance will entail an order of magnitude more memes – though whether that order of magnitude is a factor of 2, 10, or some other multiplier is anyone’s guess.

Styles and Meme Pools

An entire musical style, such as swing jazz or bebop jazz, is likely to have still an order of magnitude more memes. So, we could say that bebop performances are based on memes chosen from a pool of 10,000. That’s just a number and certainly not an accurate one. But I rather doubt that the bebop meme pool has as few as 1000 or 2000 memes nor do I believe it has as many as 1,000,000. Perhaps it has on the order of 100,000s, but I’m a little more comfortable thinking of it has having on the order of 10,000.

Whatever the number is, the meme pool is structured. You can’t create a performance simply by drawing 1,000 memes at random. You need memes distributed over various categories – rhythm, melody, etc. – and you need memes that are mutually compatible.

Whether or not memes persist in the repertoire depends on whether or not they are regularly used in performances,* the phenotypic entity of culture. It is performances that people create and listen to – and they do so intentionally, I might add. This is not a theory about how people are pushed around willy-nilly by pesky brain-hopping memes. If a given performance is particularly pleasing the musicians or audience may attempt to repeat it. The memes that facilitated the pleasurable performance are likely to appear in derived performances and so, over time, become entrenched in the musical system.

Some performances may be considerably more elaborate than others, but even the simplest performance is going to involve a multiplicity of memes. Thus memes almost never appear individually, but generally in the company of other memes. We can identify individual memes only by analyzing performances and the brains and bodies that construct them.

Now let’s think about the relationship between various musical styles. Let’s say that bebop performances are based on a repertoire of 10,000 or so memes. Let us agree that two similar styles, swing and cool, are based on repertoires having roughly the same number of memes. Given that these are closely related jazz styles I would expect there to be considerable overlap between their meme pools. So, let’s say that in each paring of styles from among these three, each member of the pair shares 9000 memes with the other. Taken together the three might share, say, 8600 memes.

In a similar fashion I’ll assert that baroque music performances are based on a pool of 10,000 memes. How many memes are likely to be shared between bebop and baroque? These are moderately distant styles, but not utterly foreign. So let’s say they share 7000 memes. What about South Indian classical music (karnatic music)? I wouldn’t be surprised if, of its 10,000 memes, it shares, say, 5000 with bebop and 5000 with baroque, but not necessarily the same 5000.

Nor, for that matter, would I be all that surprised if the numbers in this section have to by multiplied by 10 to get in the appropriate order of magnitude. These numbers are simply crude guesses. However, if the notion of memes as units of cultural evolution is at all sensible, then it should one day be possible to make real estimates of these things. I don’t see this happening any time in the near future.

What’s a Meme (Two)?

Let’s return to Rhythm Changes. I’ve indicated why it interests me – it’s a fairly abstract and complex memetic entity – but I haven’t really explained why I think it’s a memetic entity. Could I, for example, have talked of Tunisia Changes as a memetic entity?

Dizzy Gillespie’s “A Night in Tunisia” is central to the bebop repertoire. Anyone at least moderately familiar with that repertoire recognizes the tune and any musician more or less competent to perform bebop can perform that tune. It has been recorded hundreds if not thousands of times. But I’ve never heard anyone talk about Tunisia Changes, nor have I ever read about them as such, though the changes can be found in many so-called fake books. It’s a relatively simple matter to analytically abstract the harmonic trajectory from the complex of melody, rhythm, harmony, and bass line (which is specified for this tune, but not generally so) that is “A Night in Tunisia.” But this has not been done by the group of people who perform and listen to bebop. As far as I know, anyone who wants to improvise over those changes does so by performing Gillespie’s tune. One can say the same about, for example, the harmonic trajectory for Thelonious Monk’s “Round Midnight,” or Tadd Dameron’s “Jordu.” These tunes are important in the bebop repertoire, but their chord structures have not been abstracted out and used as independent entities.

Thus those chord structures, those harmonic trajectories, do not have memetic status. This is a simple, and basic point. Not every element important to this or that musical performance has memetic status. Memetic status is a function of how some element or elements function within the music systems. All bebop tunes have some chord structure, but not all such structures have memetic status.

All of the tunes I’ve mentioned, however, do exhibit 32-bar AABA form. That would seem to be memetic. It is ubiquitous in the bebop and closely related musical repertoires. Similarly, all of these tunes use constituents which are themselves quite common and which appear in many different contexts. Individual chord types, two-bar and four-bar phrases of certain kinds, these are all common harmonic building blocks. Thus many of these constituents will have memetic status.

Now let’s consider that four-note Beethoven motif that keeps showing up in memetics discussions as a typical meme. This is the motif that Beethoven used at the beginning of his Fifth Symphony and that the British used in radio broadcasts during World War Two as a symbol for victory (the rhythm mimics that of the Morse code sequence for “v”). It is generally offered as a prototypical example of a meme; if anything is a meme, that surely is.

Well, maybe so. But it’s a relatively minor meme, at least in Western musical culture. Why do I say that? Because, it has almost no use outside of the symphony in which Beethoven used it. It’s not very productive. It seems likely that some jazz musician somewhere and some time has introduced it into an improvisation in such a way that one knows he’s quoting Beethoven (I’ve probably done it myself), and I know that a disco tune was based on Beethoven’s Fifth, but these are pretty minor uses. It’s a meme, but just barely so.

More generally, we can use the ordinary tools of musical analysis (which are by no means a coherent, consistent, and complete) to identify many features in real performances. Whether or not a feature is to be identified as a meme depends on its distribution in a body of performances, a body of performances that changes over time. Some features may never be used in more than a single performance, others may be used often by some particular performer, but never be used by other than that performer.

Whoa, there. I follow you so far, but you aren’t really telling us why a feature becomes a meme. You’re just showing us how to identify that it has done so. Why does this feature become a meme, and that one not?

Good question, one for which I don’t have an answer. It’s about pleasure, pleasurable performances. I devoted chapter 4 of Beethoven’s Anvil to pleasure, but I don’t know whether or not I want to reprise that discussion in one of these posts. I will say this, however, that I reached the conclusion that pleasure is a function of the operating dynamics of the whole nervous system and not the result of stimulating so-called pleasure centers in the brain. Following Walter Freeman, Karl Pribram, and Jaak Panksepp, I argue that the notion of pleasure centers is a mis-interpretation of the experimental work.

That sounds pretty vague and holistic to me, “the operating dynamics of the whole nervous system.”

Holistic, yes. Vague, at the moment. That surely can be clarified and made more precise. But not by me, that will take more mathematics than I’ve got.

Becoming Memetic

What’s interesting, however, is the possibility that a feature that doesn’t have memetic status at some time may acquire it at some later date. Thus, the tonal trajectory Gershwin used in “I Got Rhythm” didn’t have memetic status immediately. The tune was written for a Broadway musical, Girl Crazy, which opened on 14 October 1930 and was sung by Ethel Merman. The orchestra was led by cornetist Red Nichols and included such eventual jazz luminaries as Benny Goodman, Glenn Miller, Jack Teagarden, Jimmy Dorsey, and Gene Krupa. A bit later in the year Nichols recorded the tune with his own band, the Five Pennies, and with Dick Robertson singing the vocal. It rose to fifth place in the charts. A Louis Armstrong version rose to 17 in 1932.

Had Rhythm Changes acquired memetic status by that point? I don’t know the relevant musical history well enough to answer that question, though I suspect not. One thing we need to know is when derivative tunes began appearing. Lester Young recorded “Shoe Shine Boy” with Count Basie in 1936 and wrote his own “Lester Leaps In” in 1940, the same year Duke Ellington recorded “Cotton Tail.” These tunes are based on Rhythm Changes. The existence of “Shoe Shine Boy” in the mid-30s is evidence that at least some musicians had abstracted the chord changes from the whole tune. Does that mean they’d attained memetic status? I’d say that’s a matter of definition. Obviously more abstracting had been done by 1940. Did audiences routinely recognize the lineage of these derived tunes? I don’t know. Is the question relevant to the issue of memetic status? Probably not, but I’ve not thought the matter through.

By the mid 1940s, however, enough beboppers had written their own tunes to Rhythm Changes, Charlie Parker in particular, that we can say Rhythm Changes had assumed memetic status at least within the bebop style, if not within jazz or swing more generally.

This thumbnail analysis suggests that musical memes don’t have a special formal features. You can’t identify something as a musical meme by hearing it. You can only identify it as a meme by considering the body of performances in which it functions. Rhythm Changes is the same entity in 1945 as it was in 1930; it has the same characteristics. But it plays a function in the musical world of 1945 that is different from that it played in 1930. One might even think of this as an example of emergence involving a population of thousands of people interacting with one another through tens of thousands of performances. Some relatively few elements are selected from performances here and there and incorporated into other performances. Those are memes.

Conclusion: Memes, Genes, and Denes

At this point you might be thinking, That’s all well and good. But this meme concept is pretty vague. I don’t see how we can do much of anything with it. Yes, it’s vague, whether or not its uselessly so, that’s another matter. It’s worth pointing out, however, that the biological concept of a gene is not so distinct as one would like it to be. For a population geneticist the gene is an abstract entity that plays a certain role in the life of a population. Identifying those abstract entities with a physical object, however, is rather difficult. The notion of the gene as an organic bead on a string is gone.

In view of this situation Evelyn Fox Keller and David Harel recently offered some new concepts to replace the old and battered concept of the gene. Their paper, Beyond the Gene, was published in PLoS ONE in 2007. I have no intention of examining their article in any detail, but I would like to quote two passages. First:
Accordingly, the first thing we’d like to do is to offer as a replacement for the gene a concept that is closely related, even if of a different kind, which we shall call the dene. Like the gene, our notion of dene is intended to capture the essence of genetic transmission, but, rather than being confined to denoting a discrete chunk of DNA, it is far richer and more expressive. A dene is, in fact, a general kind of statement about the DNA—what logicians call a predicate or a property. Denes can be used to represent vastly more intricate characteristics of the DNA sequence than the simple statement that it contains a particular subsequence. Also, even though we choose (for now) to focus on the material structure of DNA because of its obvious importance in heredity, it should be obvious that everything we say about DNA (and denes) would also apply to other inheritance systems.
Notice that they think of the dene as a property, which is how I defined a meme in the previous post. Musical memes are properties of the sound stream which individuals can use to coordinate their performance of that sound stream. Similarly, their phrase “vastly more intricate characteristics of the DNA sequence” resonates with what I’ve been doing with Rhythm Changes. Rhythm Changes specifies a very intricate characteristic of some sound stream, far more intricate than, e.g. the four opening notes of Beethoven’s Fifth Symphony.

Let’s look at another passage:
Returning to our list of examples, surely its most striking feature is its heterogeneity: At one end of the spectrum, it includes the very entities that were used not very long ago to think of as defining the gene, namely, continuous sequences of nucleotide encoding a protein (we think of this entity as the semi-classical gene). It also includes more recent ‘genomic’ conceptions of genes as exon containing entities that are not continuous, perhaps not even confined to a single chromosome, but from which proteins are constructed (we might call these genomic genes). And then, there are ncRNA genes, associated not with the production of proteins but purely with regulation. Lastly, though not finally, our list includes untranscribed (or unexpressed) collections of nucleotide sequences that acquire function in the cellular economy purely by virtue of their physical-chemical properties. We say ‘not finally’ because we assume that over time researchers will surely discover other ways in which properties of nucleotide sequences can inform function, just as biological systems, also over time, will learn other ways of making function out of sequence in the course of their evolution.
First, note the talk of heterogeneity and recall the discussion of all the constituents of “I Got Rhythm.”

It’s that last phrase, however, that’s got my attention: “. . . just as biological systems, also over time, will learn other ways of making function out of sequence in the course of their evolution.” That seems to imply that a given sequence might not function as a dene at some moment in time but that, at a later moment, it acquires such functionality. That seems roughly parallel to Rhythm Changes. They weren’t memetic when Gershwin wrote them and when they first appeared in performance; but they acquired memetic status over time.

I hesitate to draw any strong conclusion from this parallel beyond simply noting that things seem to be somewhat up in the air. In view of the current situation in biology, rejecting the notion of a meme as unclear does not seem entirely warranted, not if the unclarity is contrasted with the mythical clarity of the biological situation. I think further exploration is warranted.

* Keep in mind that simply listening to a recording is a performance in the sense I am using the term. The listener’s nervous system is enacting the music, that is, performing. If that performance is pleasurable people will want to repeat it. In the case of a listener, they will want to replay the recording, or perhaps seek out other recordings of the same song, or by the same artist. And so forth.


Fox Keller E, Harel D (2007) Beyond the Gene. PLoS ONE 2(11): e1231. doi:10.1371/journal.pone.0001231

Previous Posts in This Series

Cultural Evolution 1: How “Thick” is Culture?

Cultural Evolution 2: A Phenomenological Gut Check on Gene-Culture Coevolution

Cultural Evolution 3: Performances and Memes

Cultural Evolution 4: Rhythm Changes 1


  1. Rather grand speculations. There are 12 tones per octave, and while I imagine some creative jazzers use every note on a piano (88) it's a safe bet they limit themselves to like 3 or 4 octaves. So that makes a total of count-'em, 48 notes, that is 48 note-memes, with most of those repeated in the harmonies. A bit less than 10,000. And I wager Beethoven's 5th taken in its entirety uses a rather larger amount of notes and more harmonic combinations (as well as rhythmic patterns, dynamics, etc). As far as complexity goes (with something like more complexity--at least done correctly-- equals ...more intelligence), Ludwig Van quite outdoes Goishwun (or the jazz types playing it)

  2. yr babbling, not to say a reductionist even beyond Dawkins. And you even admit the "meme" is vague.

    You've never quite understood what human thinking implies.

  3. So, tell me, in 25 words or less, plus a Wheaties box top, what does human thinking imply? Your entry must be post marked by midnight 11 June 2010. Bots and other non-humans not eligible.