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5. Tonality, Harmony, Philosophy

Rhythm Changes”. Notes on Some Genetic Elements in Musical Culture

William L. Benzon
p. 271-285


J’analyse ici, en tant qu’entité génétique dans la culture musicale, une entité connue sous l’appellation d’« anatole » (rhythm changes). On peut la qualifier de coordinateur, puisque sa fonction est de coordonner l’activité des musiciens qui jouent ensemble. C’est un coordinateur complexe dans la mesure où il est organisé à cinq ou six niveaux, chacun de ces niveaux contenant des coordinateurs qui fonctionnent dans d’autres contextes musicaux. Les musiciens n’acquièrent pas (c’est-à-dire n’apprennent pas à utiliser) un tel coordinateur à travers un transfert d’un cerveau à un autre. Ils apprennent en fait à le construire grâce aux diverses interprétations accessibles, circulant dans un milieu musical donné. Cette entité particulière provient d’une mélodie de George Gershwin « I Got Rhythm » (Jai le rythme), mais ne retient que la trajectoire harmonique de cette mélodie. Elle na toutefois obtenu de statut musical indépendant quaprès vingt ans dinterprétations. Le fait dêtre un coordinateur nest donc pas une qualité inhérente à lentité même, mais une fonction découlant de la manière dont elle sera utilisée dans le système musical. Une hypothèse récente suggère que les gènes biologiques se comportent également ainsi.

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1. Introduction: A Hunt for the “Genes” of Culture

1The last three decades or so has seen a resurgence of interest in culture as an evolutionary phenomenon, a theme that loomed large in the late nineteenth and early twentieth centuries, but then largely disappeared from view. At least some of this interest can be attributed to the eleventh chapter in Richard Dawkins’ The Selfish Gene (1976), where he introduced the term “meme” to designate the genetic entities of culture. The term quickly made its way into the popular realm where it has come to mean some bit of material that “goes viral” on the web.

2But serious scholars also began investigating cultural evolution. Some of this work was purely empirical, such as a recent investigation into the phylogeny of “Little Red Riding Hood” (Tehrani 2013). The problem Tehrani is addressing is whether or not “folktales are too fluid and unstable to be classified into groups based on descent” (p. 4). Using modern statistical techniques Tehrani studied 72 plot variables in 58 folktales, all of which are variants of two similar tales, “Little Red Riding Hood” (type number 333 in the standard Aarne-Uther-Thompson index) and “The Wolf and the Kids” (type 123). He concluded that descent can be reconstructed and that the African tales are of type 123, the East Asian tales are blends of the two types, and the European tales are of type 333.

3In doing this work Tehrani was not worried about whether or not the tale as a whole should be considered a meme (the word never appears in the article), or whether specific features of the tales are to be identified with memes. That kind of issue is of no concern to him. He has the tales and has identified plot variables of interest. That’s all he needs to do his analysis. There is a great deal of empirical work that is like that (much of it is summarized in: Mesoudi 2011). You can count traits and analyze their distribution without having to figure out what role they play in this or that model of cultural evolution.

  • 1 The general question of accuracy of replication of cultural items has received a lot of discussion. (...)

4But others thinkers have had different concerns. Daniel Sperber (1996, pp. 108 ff.) has argued for a cultural epidemiology and used “Little Red Riding Hood” as crucial example. The fact that the tale is not told the same way every time suggests to him it could not be a meme in Dawkins’ sense, because that requires accurate replication from one instance to the next. And that’s what we don’t see in the case of “Little Red Riding Hood” and many other tales; the details vary from between instances. Sperber posits the existence of an “attractor” in the “space of possibilities” (p. 112) as somehow accounting for the fact that the tale tends toward an “ideal” version, though he would balk at the word, which I have from Plato. He expects these attractors to be accounted for by various psychological and ecological factors (pp. 113 ff.).1

5Whether or not he is right in this and, if so, just what factors underlie “Little Red Riding Hood” is not, however, my concern here. I am interested in the fact of constrained variation. And my object is to provide a detailed discussion of a particular example, something that is lacking in the various discussions occasioned by Dawkins’ provocation in The Selfish Gene. While I am, like Sperber, ultimately interested in the underlying mechanisms, I believe that, at this point, it is more important to develop a repertoire of detailed examples than to propose mechanisms on the basis of casual examples. The current ratio of explanatory proposals to fleshed-out examples is too lopsided in favor of explanations for further discussion of them to generate more light than heat.

1.1. A Musical Example

6I have a number of reasons for choosing an example from music. In the first place I am a fairly skilled musician and have a great deal of practical experience with the example I’ve chosen, a musical entity known as Rhythm Changes. I know how this entity is used to structure performances, how one learns to use it, and I know something of its history. Furthermore, having written a book on music, one that examines the neuroscience, psychology, anthropology, and history of music, I have a reasonable sense of the broad intellectual environment in which my arguments exist.

7There are reasons, moreover, that have to do with the nature of music itself. The example I use is taken from instrumental music. There are no words to worry about. That’s important because memetics and memeticists are very concerned about how ideas, practices, attitudes and so forth get from one brain to another. That problem has one form when we are dealing with language, where the relationship between a word’s meaning and its physical form is arbitrary. How a word sounds to the ear or how it looks on the page has little or no bearing on what it means. The meaning is linked to the physical form by largely arbitrary social convention. The neural processes that both produce words through speaking or writing and that perceive them through hearing or vision thus do not thereby indicate what is meant. Meaning is mediated by a different set of neural processes. One can thus learn to mimic the sounds of a language without actually being able to comprehend or use the language; opera singers do it all the time.

8This problem doesn’t exist for instrumental music. The sound is all that there is. When a musician has learned to produce the sounds of Beethoven’s Moonlight Sonata, or a Chopin nocturne, what more is there? Music is fully mimetic, if you will, in a way that language is not. The downside of this kind of musical example is, of course, that it leaves the problem of meaning untouched. I am willing to defer that problem in the interests of offering a rich example.

9As partial compensation for this downside the musical example I have chosen is not a simple one. I’m not going to be talking about that pesky four-note Beethoven motif that shows up so often in memetics discussions, though I do have a few words about it later on, nor will I be talking about unanalyzed tunes treated as indivisible wholes. The example I have chosen is complex.

10As I’ve indicated, I’ve chosen an entity that jazz musicians know as Rhythm Changes. 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 tune. 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.

11Rhythm Changes is not a simple entity. It can be divided into parts at five or six levels depending on how you do it. The lower level entities are each constructed on standard patterns that are used in other tunes. Moreover it is a rather abstract entity. Unlike that four-note Beethoven motif, 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. It is not a trivial take-it-or-leave-it example. It has substantial internal structure that we can and will examine. Learning to identify it takes time and concerted effort. Learning to make your own music using Rhythm Changes takes considerably more time and effort.

12Finally, I need to say a bit about my terminology. When I originally drafted these remarks I was using “meme” as my term for the genetic entity in cultural evolution. I have recently changed my terminology, using the term “coordinator” instead. In the case of music this term is particularly appropriate because it designates the function these entities play; they help the musicians coordinate their interactions with one another in real time. Though it creates a bit of awkwardness here and there, I’ve tried to use my current terminology when referring to my own usage but have used “meme” where that is the term used by others.

1.2. Rhythm Changes Described

13Using a standard notation we might describe Rhythm Changes as follows (in the key of B-flat):

14The slash marks designate the beginnings of “measures” or “bars” and thus delimit 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.

15What’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 (B) 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 B), the first four bars would be:

| B7 G#7| C#m F#7| D#m7 G#7| C#m F#7|

16If 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|

  • 2 For the record, there is a standard way of representing this tonal trajectory independent of a part (...)

17The 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 that is Rhythm Changes.2

18In this sense we can think of Rhythm Changes as a relatively abstract property of the sonic object created by a musical performance. It is a perceptual invariant and, as such, is a bit like a Platonic ideal. 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.

19The point of improvising on Rhythm Changes is to demonstrate skill in devising clever ways of negotiating the changes. The trajectory thus has a normative value; one is judged on the ability to produce 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 that experts agree exhibit the property and another vastly larger collection of sonic objects that experts agree do not exhibit the property.

20So, Rhythm Changes is a fairly abstract musical entity. It is also a complex one. As it is thus not an atomic coordinator it might be better to think of it as a package of coordinators. “Package” is another term I’ve recently been entertaining.

21Before going on to consider the “internal” structure of Rhythm Changes, however, I would like to offer a rough biological comparison. I suggest that we think of Rhythm Changes as comparable to a biological notion such as the body plan of carnivores, though I don’t know where one would find this in the genome-the Hox complex?3 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.

22It 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 “coordinators specifying Rhythm Changes”.

23Let us now think about how we might begin analyzing Rhythm Changes into constituent elements. 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 that has made the core repertoire; it has been performed year after year, decade after decade by tens of thousands of musicians. “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.

24Thousands of tunes have been written having a 32-bar AABA form. Thus we might consider the AABA form itself to be a coordinator. 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 abstract even further and consider 32-bars divided into four 8-bar phrases, where each can have any internal structure, to be a coordinator? The question isn’t an urgent one, and we’ll return to the matter a bit later.

25Note that in treating AABA form as a coordinator 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? In point of abstract principle you could divide an eight-bar phrase into a five-bar and three-bar phrase, or into two three-bar phrases and one two-bar phrase; other divisions are possible. But they don’t happen in practice, not in this musical tradition. Rather, each eight-bar phrase consists of two four-bar phrases, each of which in turn consists of two two-bar phrases.

26This tradition uses two-bar phrases as a fundamental building block; there are standard ways of constructing harmonic structures for two-bar phrases. That is, there are harmonic coordinators that are two-bars long, lots of them. Finally, given that we are talking about harmonic structure, our simplest unit is simply the chord, a set of pitches (to be) sounded simultaneously. Chords consist of various types, major and minor triads, dominant 7ths, major 7ths, and so forth. These are coordinating entities as well.

27I do not know what sorts of things we’ll end up with as the atomic or simplest coordinators 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. The psychological validity of these analytic efforts is questionable (thus 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 coordinating entity, one constituted by a rather fuzzy collection of perhaps some 10s or maybe even 100s of more limited coordinating entities in some structured relationship.

2. Coordinators 1: How They Work

28The psychological language of the preceding paragraphs should not be taken as an abandonment of my belief that the genetic elements of culture are to be considered as things in the external world, not as structures and processes in brains (Benzon 1996). Rhythm Changes is a property that some sonic objects exhibit, but most do not. Similarly, those constituents of Rhythm Changes that are used in other harmonic trajectories (e.g. the I7 VI7 ii V7 phrases in the A section, the ii V I phrases in the B section) are properties of a good many sonic objects. And so it is with the other coordinators I identify below. All are to be considered properties of sonic objects.

29Notice, however, that while I have previously characterized these genetic entities as physical things I am now talking of them as being properties or attributes of physical things. Though I’m not quite set on this way of thinking, I do rather like it.

30I 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). 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.

  • 4 This last distinction seems like the one linguists and anthropologists make between etics and emics (...)

31Just as nervous systems are sensitive only to some of the properties and attributes of physical objects and events, so cultural processes only respond to some of the properties and attributes detectable by human nervous systems.4 These properties and attributes can function as coordinators. The only way to identify the properties and attributes that function as coordinators is to examine cultural processes-a matter I’ll comment on a bit later.

2.1. Learning from the Inside

32“But what”, the orthodox memeticist (such as Dawkins himself) asks, “what happens in people’s brains? Surely that’s where memes reside?” For the orthodox memeticist talks as though memes propel themselves from brain to brain and thus propagate themselves.

33I have spent a great deal of time reading and thinking about what goes on in human brains and, of course, believe that it 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.

34Such talk seems to presuppose what Michael Reddy (1993) has called the conduit metaphor for human communication. Reddy’s article is based on 53 example sentences. Here are the first three (p. 166, italics in the original):

  1. Try to get your thoughts across better

  2. one of Mary’s feelings came through to me with any clarity

  3. You still haven’t given me any idea of what you mean

35Reddy’s argument is that many of our statements about communication seemed to be based on the notion of sending something (the thought, idea, feeling) through a conduit, hence he calls it the conduit metaphor. He knows that communication doesn’t work that way, but that’s not his central issue. His central concern is to detail the way we use the conduit metaphor to structure our thinking about communication.

36There is no transfer of patterns in the sense that computers can transfer information from one machine to another. We have learning from public models, and we have interplay, negotiation, and mutual adjustment. How individual musicians achieve these results, what goes on in their brains, is a secondary matter. Whatever it is, it isn’t a matter of either sending or receiving information.

37Following 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. Culture is not something foisted upon people by pesky and intrusive memes.

38In the case of music, let me suggest that how different musicians understand Rhythm Changes is irrelevant as long as they can stay together while performing together. Charlie Parker’s neural patterns for Rhythm Changes may have been different from Dizzy Gillespie’s or Miles Davis’s or Bud Powell’s, but that doesn’t matter as long as they’re together on the bandstand. That is something they can judge perfectly well in performance, as can listeners. The question of how accurately patterns are “transferred” from one brain to another is mistaken.

39I’ll go so far as to say that even when a neophyte is learning from a master, there is no transfer of patterns from the master’s brain to the neophyte’s. Rather, as they play together, the neophyte responds to what the master is doing and figures out, in his own (neural) terms, how to match or complement, as the case may be, what the master is playing. The student will make mistakes, the master will make comments, and they will try again.

40What musical culture provides though coordinators, then, is the technical means by which independent performers can coordinate their real-time interaction. In agreeing to adhere to these conventions the actions of musicians become coupled into a single acting system where some signals pass between individuals in the form of mechanical vibrations in the air while many other signals are completely internal to individual nervous systems (cf. Benzon 2001, pp. 47 ff.). While these two sets of signals place constraints on one another, it makes little sense to talk of the one-way passage or transfer of information from one individual to another.

2.2. From Gershwin’s Tune to Musical Styles

41As I’ve indicated, Rhythm Changes is derived from George Gershwin’s I Got Rhythm. But how do we think about the complete tune as opposed to its harmonic trajectory? In addition to that trajectory we also have a 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, mode of performance. Note, however, that any consideration of the lyrics brings a whole other cultural field into consideration, that of language.

42On the melody, Gershwin provided a specific melody, constructed on specific principles. We need not discuss that melody or those principles here; we need only note their existence. 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, e.g. those of bebop as opposed to swing. Thus we have another body of coordinators to deal with, albeit one that interacts quite closely with those governing the tonal trajectory.

43And 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 collection of coordinators to consider.

44By 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 an actual 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.

45At this point we have a musical entity that is as fully specified as a performance of a folk tale, such as the example we began with, “Little Red Riding Hood”. But just as “Little Red Riding Hood” can retain its identity in different tellings, so I Got Rhythm can maintain its identity in different arrangements. The identities of such cultural objects generally do not depend on the full set of physical traits necessary for a given realization. That identity is furthermore decomposable into other entities which can maintain their individual identities under a wide variety of physically different manifestations.

46My first point is simply 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 independent status as coordinators, 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 performances. If Rhythm Changes, as abstracted from Gershwin’s tune, entails some 10s of coordinators, then a complete performance will entail an order of magnitude more of them — though whether that order of magnitude is a factor of 2, 10, or some other multiplier is anyone’s guess.

47An entire musical style, such as swing or bebop, is likely to have still an order of magnitude more coordinators. So, I could say that bebop performances are based on coordinators 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 coordinators 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.

48Whatever the number is, the coordinator pool is structured. You can’t create a performance simply by drawing 1,000 coordinators at random. You need coordinators distributed over various categories, and you need coordinators that are mutually compatible.

  • 5 Keep in mind that simply listening to a recording is a performance in the sense I am using the term (...)

49Whether or not coordinators persist in the repertoire depends on whether or not they are regularly used in performances.5 It is performances that people create and listen to. If a given performance is particularly pleasing, the musicians or audience may attempt to repeat it (at some other time).

50Some performances may be considerably more elaborate than others, but even the simplest performance is going to involve a multiplicity of coordinators. Thus coordinators almost never appear individually, but generally in the company of other coordinators. We can identify individual coordinators only by analyzing performances and the brains and bodies that construct them.

2.3. Styles and Coordinator Pools

51Now 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 coordinators. Let us agree that two similar styles, swing and cool, are based on repertoires having the same order of magnitude. Given that these are closely related jazz styles I would expect there to be considerable overlap between their coordinator pools. So, let’s say that in each pairing of styles from among these three, each member of the pair shares 9000 coordinators with the other. Taken together the three might share, say, 8600 coordinators.

52In a similar fashion I’ll assert that baroque music performances are based on a pool of 10,000 coordinators. How many coordinators 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 coordinators. What about South Indian classical music (karnatic music)? I wouldn’t be surprised if, of its 10,000 coordinators, it shares, say, 5000 with bebop and 5000 with baroque, but not necessarily the same 5000.

53Nor, for that matter, would I be all that surprised if the numbers in this section have to be multiplied by 10 to get in the appropriate order of magnitude. These numbers are simply crude guesses. However, if the notion of coordinators 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.

3. Coordinators 2: Emerging from a Sea of Sounds

54Let’s return to Rhythm Changes. I’ve indicated why it interests me — it’s a fairly abstract and complex musical entity — but I haven’t quite explained why I think it warrants being treated as a coordinating entity. Could I, for example, have talked of Tunisia Changes as a coordinating entity?

55Dizzy 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 thousands of times. But I’ve never heard anyone talk about Tunisia Changes, nor have I ever read about them as such, though chord changes for A Night in Tunisia can be found in many so-called fake books. It is 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 particular 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 chord 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 they do not have coordinator status in the musical system.

56All of the tunes I’ve mentioned, however, do exhibit 32-bar AABA form. That would thus seem to play a general coordinating role. 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 coordinator status.

57Now let’s consider that four-note Beethoven motif that keeps showing up in memetics discussions as a typical meme-to return to the term that is generally used in these discussions. 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, the thinking seems to go, that surely is.

58Well, maybe so. But it is unimportant in the musical system at large, 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 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 coordinator (to return to my preferred term), but just barely so. It isn’t very fruitful.

59More generally, we can use the ordinary tools of musical analysis (which are by no means coherent, consistent, and complete) to identify many features in real performances. But that doesn’t mean that each and every feature is a coordinator. Whether or not a feature is a coordinator 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 never be used by other than a single performer.

3.1. Coordinators Emerge from the Larger Pool of Sonic Materials

  • 6 On the history of “I Got Rhythm”, see Crawford (2000, pp. 213-236).

60What’s interesting, moreover, is the possibility that a feature that doesn’t have coordinator status at some time may acquire it at some later date. Thus, the tonal trajectory Gershwin used in “I Got Rhythm” didn’t acquire coordinator status immediately. The tune was written for a Broadway musical, Girl Crazy, which opened on 14 October 1930 and was sung by Ethel Merman.6 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.

61Had Rhythm Changes acquired coordinator 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 all 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 coordinator 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 coordinator status? Probably not, but I’ve not thought the matter through.

62By 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 coordinator status at least within the bebop style, if not within jazz or swing more generally.

63This thumbnail analysis suggests that musical coordinators don’t have special formal features. You can’t identify something as a musical coordinator by hearing it. You can only identify it as a coordinator 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 the one 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 coordinators.

3.2. Coordinators, Memes, Genes, and Denes

64At this point you might be thinking, That’s all well and good. But this coordinator concept is pretty vague, just like the meme concept is. I don’t see how we can do much of anything with it. Yes, it is vague, whether or not it is uselessly vague, that’s another matter. It is 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, has proven to be difficult. The notion of the gene as an organic bead on a string is gone.

65In 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.

66Notice that they think of the dene as a property, which is how I have defined coordinators. Musical coordinators are properties of the sound stream that individuals can use to coordinate their performance of that sound stream. Similarly, the 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.

67Let’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.

68First, note the talk of heterogeneity and recall the discussion of all the constituents of “I Got Rhythm”.

69It’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.

70I 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 coordinator (or, for that matter, a meme) as unclear does not seem entirely warranted, not if the lack of clarity is contrasted with the mythical clarity of the biological gene. I think further exploration is warranted. In particular, I think we need to take a close and detailed look at many specific examples, many of which are readily at hand in the literatures of various humanistic disciplines, musicology, literary criticism, and art history among them. It is foolish to argue fundamental theoretical issues on the basis of a few poorly defined examples.

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Benzon, W.L. (1996), “Culture as an Evolutionary Arena”, Journal of Social and Evolutionary Systems 19/4, pp. 321-362.

Benzon, W.L. (2001), Beethoven’s Anvil. Music in Mind and Culture, New York, Basic Books.

Crawford, Richard (2000), The American Musical Landscape. The Business of Musicianship from Billings to Gershwin, University of California Press.

Dawkins, Richard (1976), The Selfish Gene, Oxford University Press.

Dennett, Daniel (2005), “From Typo to Thinko: When Evolution Graduated to Semantic Norms”, in Levinson & Jaisson (eds.), Evolution and Culture, The MIT Press.

Fox Keller, Evelyne and Harel, David (2007), “Beyond the Gene”, PLoS ONE, 2/11: e1231. doi:10.1371/journal.pone.0001231.

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

Gil-White, Francisco J. (2008), “Let the meme be (a meme): Insisting too much on the genetic analogy will turn it into a straightjacket”, in Botz-Bornstein (ed.), Culture, Nature, Memes, Newcastle upon Tyne, Cambridge Scholars, pp. 158-190.

Janata, Petr et al. (2002), “The Cortical Topography of Tonal Structures Underlying Western Music”, Science, 298/5601, pp. 2167-2170.

Longuet-Higgins, Hugh C. (1987), “Two Letters to a Musical Friend”, Mental Processes: Studies in Cognitive Science, MIT Press, pp. 64-81.

Mesoudi, Alex (2011), Cultural Evolution. How Darwinian Theory Can Explain Human Culture & Synthesize the Social Sciences, University of Chicago Press.

Reddy, Michael J. (1993), “The conduit metaphor – a case of frame conflict in our language about language”, in Ortony (ed.), Metaphor and Thought, Cambridge University Press, 2nd ed., pp. 164-201.

Sperber, Dan (1996), Explaining Culture. A Naturalistic Approach, Oxford, Blackwell Publishers Inc.

Tehrani, Jamshid J. (2013), “The Phylogeny of Little Red Riding Hood”, PLoS ONE, 8/11: e78871. doi:10.1371/journal.pone.0078871.

Zatorre, Robert J. and Krumhansl, Carol L. (2002), “Mental Models and Musical Minds”, Science, 298/5601, pp. 2138-2139.

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1 The general question of accuracy of replication of cultural items has received a lot of discussion. If you wish to follow that discussion I suggest, beyond Sperber, Dennett (2005) and Gil-White (2008).

2 For the record, there is a standard way of representing this tonal trajectory independent of a particular key. In this notation the first four bars of Rhythm Changes become:
| 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 et al. 2002, Zatorre 2002).

3 Wikipedia URL:

4 This last distinction seems like the one linguists and anthropologists make between etics and emics. We can use the methods of phonetics to characterize the difference between /l/ and /r/. That distinction is phonemic in English (that is, it is linguistically significant), but not in Japanese.

5 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.

6 On the history of “I Got Rhythm”, see Crawford (2000, pp. 213-236).

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William L. Benzon, « Rhythm Changes”. Notes on Some Genetic Elements in Musical Culture »Signata, 6 | 2015, 271-285.

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William L. Benzon, « Rhythm Changes”. Notes on Some Genetic Elements in Musical Culture »Signata [En ligne], 6 | 2015, mis en ligne le 31 décembre 2016, consulté le 20 mars 2023. URL : ; DOI :

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William L. Benzon

Bill Benzon is an independent scholar whose career runs from cognitive science, through art, music, and the web. He published Beethoven’s Anvil: Music in Mind and Culture in 2001 and is on the scientific advisory board for the Institute of Music and Neurologic Function in New York City. Previously he was a Senior Scientist with MetaLogics, Inc., where he worked on knowledge representation and information design for web-based health services. Bill has taught in the Department of Language, Literature, and Communication at the Rensselaer Polytechnic Institute and has published scholarly articles, reviews, and technical reports on African-American music, literary analysis and theory, cultural evolution, cognition and brain theory, visual thinking, and technical communication. In conjunction with Richard Friedhoff he has written a book on computer graphics and image-processing entitled Visualization: The Second Computer Revolution.

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