Jan, S. (2000). Replicating Sonorities: Towards a Memetics of Music.
Journal of Memetics - Evolutionary Models of Information Transmission, 4.
http://cfpm.org/jom-emit/2000/vol4/jan_s.html

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Abstract

1. - Introduction: Music and The Memetic Paradigm

2. - Musical Memetics and The Linguistic Analogy

3. - Memetics and Musical Style

4. - Musical Memes and The Genotype-Phenotype Distinction

4.1. - The Memotype and (Extended) Phemotype of Musical Memes

4.2. - The Ontology of The Musical Work

5. - Defining The Musical Meme

5.1. - Particulateness

5.2. - Coequality

6. - Structural Hierarchies and The Musical Memeplex

6.1. - Pitch-Based Structural Hierarchies

6.2. - Structural Memes in Music

6.3. - The Psychological Organization of Musical Memes

6.4. - Topics

7. - The Transmission and Mutation of Musical Memes

8. - The Evolution of Musical Style

9. - Conclusion: Towards a Memetics of Music

Notes

Acknowledgements

References

Abstract

The memetic paradigm is herein applied to music. While memetics has been used to elucidate a wide variety of cultural phenomena, its concerns to date have largely been with memes in the realm of verbally-expressible concepts. In view of this, this paper represents an attempt to integrate the central concerns of analytical musicology with a neo-Darwinian meme-selectionist perspective. Such a viewpoint may be used, it is argued, to unify, under a systematic new paradigm, understanding of both local issues of musical structure and organization, and global issues of musical style configuration and its diachronic change. Against the grain of several suggestions in the memetics literature, a minimalist view of the musical meme is taken, seeing it as consisting, at the lower extreme, of configurations of as few as three or four notes. The hierarchic location of musical memes is a central concern here, both in cultural hierarchies - i.e., the replication of patterning at different strata within a culture - and in structural hierarchies - i.e., the replication of patterning at different strata within a work, including the level of the global structural archetype. Leonard Meyer's perspective on culture is employed to frame consideration of the first phenomenon, whilst the analytical method of Heinrich Schenker is employed to comprehend the second. In order to understand how musical memes partake of meaning in association with verbally-mediated concept memes, the semiology of Ferdinand de Saussure and Jean-Jacques Nattiez is employed. The article concludes with observations on the transmission and mutation of musical memes, and an account of how this process engenders the evolution of musical styles.

Keywords: Meme, memetics, memeplex, music, musicology, style, hierarchy, Meyer, Schenker, semiology.

1. Introduction: Music and The Memetic Paradigm

Nevertheless, Dawkins' now celebrated original definition of the meme was catholic, and indeed began with music, maintaining that "[e]xamples of memes are tunes, ideas, catch-phrases, clothes fashions, ways of making pots or of building arches" (1989: 192). One must therefore remember that our modern view of evolution is, in Dennett's words, substrate neutral, meaning that, in the algorithm of evolution by natural selection, "[t]he power of the procedure is due to its logical structure, not the causal powers of the materials used in the instantiation, just so long as those causal powers permit the prescribed steps to be followed exactly" (1995: 50-51; his emphasis). [note 1] This principle is the intellectual foundation of the `universal Darwinism' Dawkins outlined (1983b), which Plotkin has recently expanded upon (1995), and of which memetics is an important subset.

Given its broad applicability, and observing a niche, it is to music that I aim to apply the memetic paradigm here, attempting to understand the central concerns of musicology [note 2] from a neo-Darwinian meme-selectionist perspective in order to show how such a standpoint may be used to unify understanding of both local issues of musical structure and organization, and global issues of musical style configuration and its diachronic change. [note 3] Whilst I will largely use as my examples music written in the late-eighteenth and early-nineteenth centuries - a period of such stylistic clarity and coherence the epithet classical is deservedly applied to it by musicologists - many of the principles I adduce here are, I believe, applicable to all musics. [note 4] Moreover, I hope that some observations, given their necessarily contextualizing purpose, make a more general contribution to the debate on memetics, particularly some of the content of Sections 3, 4, 7, and 8. What follows is, however, only a brief outline of what I believe to be the central issues, and I hope to develop the points made here on other occasions.

I begin by examining briefly the relationship between memes in music and those in the verbal-conceptual realm in terms of the linguistic concepts of phonetics, syntax, and semantics. I then consider how memetics offers a means of understanding the characteristics of style in music and, indeed, in culture generally. After exploring the application to musical memes of the genotype-phenotype distinction from biology, I move on to the central parts of the article, which define what I understand as the memetic elements in music, including the nature and hierarchic location of memeplexes in music. The final sections of the article deal with the transmission and mutation of musical memes and the way in which this process engenders the evolution of musical style.

During the course of this article it will be necessary to use concepts and terms from music theory and analysis which may not be familiar to the reader. When these are used, notes provide what I hope are clear and non-patronizing explanations. For readers wishing to explore these concepts more fully, Bent and Drabkin 1987, Cook 1994, and Dunsby and Whittall 1988 are excellent sources. For more general information, Sadie 1980 is the most comprehensive reference source in English.

2. Musical Memetics and The Linguistic Analogy

...what is preserved and transmitted in cultural evolution is information - in a media-neutral, language-neutral sense. Thus the meme is primarily a semantic classification, not a syntactic classification that might be directly observable in "brain language" or natural language. In the case of genes, we are blessed by a gratifyingly strong alignment of semantic and syntactic identity: there is a single genetic language, in which meaning [i.e., what phenotypic feature(s) the gene codes "for"] is (roughly) preserved across all species.

Nevertheless, even though there is a long critical tradition [note 5] of conceiving music as in some sense akin to verbal language - with, accordingly, a distinct phonetic, syntactic, and semantic content - in reality music, unlike primarily referential symbolic systems such as language and painting, has the property of having no fixed semantic structure. To use the language of semiology, referential symbolic systems unite a signifier - a word or image - and a signified - an idea or concept. As Nattiez observes,

By making the sign a union of the signifier and the signified, Saussure conceived of the relationship between the two "faces" of the sign as stable and bi-univocal. Beyond this, the relationship is arbitrary[.]

In music, by contrast, a given configuration - a collection of pitches and rhythms, for instance - does not act as the stable signifier for a particular verbally-expressible signified, despite the propensity of music to exhibit to a degree of memetic coadaptation which permits specific musical patterns to become associated, in varying degrees of stability, with verbally expressible concepts. This question of music and the signifier-signified dualism - music as signified and music as signifier - is considered in more detail in Sections 6.3 and 6.4 respectively.

In this sense, music's semantic content is low, and its real substance could be said to inhere in its phonetic and syntactic structures. The phonetic presence of music is, as will be discussed in Section 4, a purely phemotypic property. Its syntax, however, whilst reflected phemotypically in, and only readily apparent from, the configuration of musico-graphical patterning in scores, and patterns of sound waves in performance, must presumably inhere at the level of the memotype, i.e., in the form of ordered, grammatical relationships between memes at the level of the neuron. Nevertheless, as Dennett implies, it seems the case that there is no "gratifyingly strong alignment" between neuronal configurations and the musico-syntactic structures they code for.

In contrast to the semantic aspect, the phonetic and syntactic realms are highly developed in the musics of all cultures, the sonorous (phonetic) field consisting of particles which have a combinatorial (syntactic) structure determined not by the constraints of verbal-conceptual logic but by the force of convention. In memetic terms, conventions arise from the differential replication of patterns. The most successful of these become to some degree evolutionarily stable, a concept examined in more detail in Section 8. Such patterns - Meyer terms them strategies played out within systems of rules (1989: 17, 20) - tend to oust rival configurations, which theorists, certainly in the western tradition, then belatedly condemn by deeming them aberrant.

As I hope will become evident from the following discussion, the rich phonetic and syntactic structure of music, together with its relative independence from the complexities engendered by the rich semantic content of verbal-conceptual memes, makes it an especially lucid medium for memetic analysis. Although the discussion of the memotype-phemotype dualism in Section 4 will indicate this is to be an oversimplification, I shall, in conducting this analysis, take the phonetic and, perhaps more importantly, the syntactic aspects of music to be adequately represented by the musico-graphical content of the printed score.

3. Memetics and Musical Style

Here, intraopus style represents the style of - i.e., the totality of memes replicated within - a single work. Idiom represents the style of an individual composer within a particular cultural community, and is defined by the sum of the memes replicated within the totality of his or her intraopus contexts. A composer's idiom may, however, be subdivided into a number of chronologically-defined phases or style periods. [note 6] Dialect represents the style of a cultural community, defined in geographical (e.g., French, Viennese, Ghanaian) and/or chronological (e.g., Renaissance, Baroque, Classical) terms. Rules, the largest memetic aspect of the hierarchy, are the large-scale systems of musical organization, such as the modal system [note 7] or the major-minor tonal system, [note 8] the generative elements of which are replicated in a number of separate dialects. Finally, laws represent invariable, biologically-defined attributes of human perception and cognition which ultimately constrain our responses to music and therefore set limits upon the nature of the memes we assimilate and the profile of their interaction. The meme pool might be taken to consist of the totality of memes at the level of dialect or rules:

4. Musical Memes and The Genotype-Phenotype Distinction

Any cultural trait [meme] that is taken over by a given individual from another individual must accordingly be thought of as the transfer of a particular pattern of synaptic hotspots within the associative networks of one brain to the associative networks of another brain. Different traits must be thought of as being coded by topologically different hotspot patterns. That is, a given cultural trait borne by an individual is encoded informationally as a particular pattern of modified synapses in his brain. Naturally the hotspot pattern that a trait has in one brain will not be geometrically arranged in exactly the same way as the pattern that the same trait has in another brain...But functionally the two hotspot patterns would still be equivalent, at least to the extent that the effective memory contents representing the trait were identical.

 Acceptance of this point naturally suggests the application of the genotype-phenotype distinction - a differentiation between something hidden and its often far-reaching consequences - to the meme. Whilst care must be taken not to force our thinking on memetics into the straitjacket of earthly DNA, the assimilation of the genotype-phenotype principle is one area where analogizing seems warranted. [note 10]

4.1. The Memotype and (Extended) Phemotype of Musical Memes

This distinction is essentially that made several years before The Selfish Gene by Cloak (1973), who separated i-culture, the somatic cultural instructions, and m-culture, their resultant behaviour and artefacts. Whatever terms one uses, this perspective has the advantage of mirroring its biological analogue closely and being simple and clear-cut. Moreover, it loosely preserves the distinction Dawkins draws between replicators and vehicles, whereby the microscopic, invisible, units of replication are clearly distinguished from the large, visible, structures engendered by the replicants to facilitate replication (1983a: Chapter 6). It should be noted, however, that whereas in genetics, replicators are copied ("copy-the-instructions" - Blackmore 1999: 61-62), in memetics it is the vehicles which are copied ("copy-the-product").

Dawkins' concept of the extended phenotype enlarges the definition of the phenotype to incorporate

All effects of a gene upon the world. As always, "effect" of a gene is understood as meaning in comparison with its alleles. The conventional phenotype is the special case in which the effects are regarded as being confined to the individual body in which the gene sits. In practice it is convenient to limit "extended phenotype" to cases where the effects influence the survival chances of the gene, positively or negatively.

 While the phenotypic effects of the gene are both somatic and extrasomatic, the phemotypic effects of the meme are, as noted, almost entirely extrasomatic; and it is in the nature of the meme that one cannot usefully distinguish between its phemotype and its extended phemotype. To paraphrase Dawkins, one may indeed speak of "the long reach of the meme" (after the subtitle to 1983a), meaning that a meme, being at "...the centre of a web of radiating power" (1983a: viii), may both influence the behaviour of its host and also exert its effects at considerable geographical and temporal remove.

As an example of this wide compass, it is clear that memes which appeared initially in symphonies composed by Haydn in the isolation of the Palace of Eszterháza in Hungary in the 1770s continue to copy themselves into the brains of concert goers on the West coast of America in the 1990s; paper-based phemotypic forms of these memes continue to roll from the printing presses of the developed world; and tons of plastic are poured into moulds to make compact disks sustaining other phemotypic incarnations of them.

To draw these points together, Table 1 compares genes and memes in terms of the two pheno/phemotypic spheres, somatic and extrasomatic, offering examples of each category:
 

For a bird, for instance, some of its genes give rise to such phenotypic-somatic features as feathers, and to such phenotypic-extrasomatic behaviours as nest building and the resultant artefacts. For a human, some of its musical memes may give rise to culturally determined modifications to the body, such as the irreparable damage Schumann inflicted upon his hand as a result of using a crude device designed to strengthen the fingers (Daverio 1997: 77-79), and to such phemotypic-extrasomatic behaviours as composition, the artefacts of which are written and printed scores.

4.2. The Ontology of The Musical Work

...the work is a purely intentional object, immutable and permanent, whose heteronomous existence is no more than a reflection of its being: the existence of the work finds its source in the "creative act" of the performer, and its foundation in the score....The score constitutes the work's "schema," which guarantees its identity over the course of history, even though numerous elements not fixed by the score "play an essential role for the aesthetic Gestalt of the work"..., and even though the "schema" allows an enormous number of possibilities for the work's realisation.

 According to Siohan, however, the notation "...is a graphic element, is neither music, nor its reflection, but a solely mnemonic device. There is no music except in the state of sonorous manifestation" (in Nattiez 1990: 71).

In contrast to the score versus sound dualism underpinning these statements, the memotype-phemotype perspective indicates that the musical meme's principal state of being is the somatic neuronal configurations which define its information content. Despite being "...the thing that renders the work peformable and recognizable as an entity, and enables the work to pass through the centuries" (Nattiez 1990: 71), the score (and its resultant sound image) is, from the meme's perspective, merely a phemotypic "vessel" to convey it on certain stages of the "long odyssey" from brain to brain (after Dawkins 1989: 33). Seen in this way, one arrives not at a sound versus score dualism but rather one of neuronal matrix versus score/sound.

Thus, contrary to Nattiez's assertions, one might, in the light of the memotype-phemotype distinction, maintain music's "irreducible dimension" to be somatic memes, and sound waves to be just one of their extended phemotypic artefacts, albeit overwhelmingly the one of greatest importance to most cultures. On this reasoning, the large-scale memeplex that is the musical work exists fundamentally as a temporary alliance of memes in the composer's brain which is subsequently reconstituted in the minds of listeners exposed to its phemotypic products. The freezing of the work by its extended phemotype should not blind us to the fact that the memes that constitute it merely used it as a means of furthering their replication.

Despite this, work-memeplexes have attained a high degree of ontological singularity for us in the West, owing to a crucial memetic event which occurred some two hundred years ago. Goehr, without using the memetic paradigm in her argument, asserts that the closing years of the eighteenth century - not, controversially, the early years of the sixteenth - saw the evolution of a memeplex she terms the work-concept. This is an array of memes which cause us

...to see works as objectified expressions of composers that prior to compositional activity did not exist. We do not treat works as objects just made or put together, like tables and chairs, but as original, unique products of a special, creative activity. We assume, further, that the tonal, rhythmic, and instrumental properties of works are constitutive of structurally integrated wholes that are symbolically represented by composers in scores. Once created, we treat works as existing after their creators have died, and whether or not they are performed or listened to at any given time. We treat them as artefacts existing in the public realm, accessible in principle to anyone who cares to listen to them. And when called, finally, to give examples of works, we usually look to the tradition of western, European, classical, "opus" music, to works, in other words, of a "purely instrumental" or "absolute" sort.

The propagation of this memeplex in the nineteenth century and afterwards gave work-memeplexes a far greater cultural salience than they had hitherto enjoyed, according them the status of exhibits in the "imaginary museum of musical works" (Goehr 1992: 8). Before the time of Beethoven, pieces of music were generally seen as transient and ephemeral, the utilitarian products of craftsmanship and labour. After Beethoven - and because of the work-concept memeplex - many were seen in terms of the new category of artwork; they came to acquire a degree of permanence and stability, and were supposed the transcendental products of genius and inspiration.

5. Defining The Musical Meme

5.1. Particulateness

So far I have talked of memes as though it was obvious what a single unit-meme consisted of. But of course it is far from obvious. I have said a tune is one meme, but what about a symphony: how many memes is that? Is each movement one meme, each recognizable phrase of melody, each bar, each chord, or what?

The biological analogy, indeed the replicator concept, would seem to suggest that memes tend toward the latter end of the continuum Dawkins outlines - toward existence as simple rather than complex units. Thus, the more concise a musical meme the greater the likelihood that it will survive the travails of replication by imitation intact. Ultimately, one might assert that the meme shares with the gene the fundamental attribute that it is "...a unit of convenience, a length of chromosome with just sufficient copying-fidelity to serve as a viable unit of natural selection" (1989: 195).

Dennett, however, is reluctant to admit very small particles as memetic. His definition of the meme asserts that

These new replicators are, roughly, ideas....the sort of complex ideas that form themselves into distinct memorable units...Intuitively, we see these as more or less identifiable cultural units, but we can say something more precise about how we draw the boundaries - about why D-F-A isn't a unit and the theme from the slow movement of Beethoven's Seventh Symphony is: the units are the smallest elements that replicate themselves with reliability and fecundity. We can compare them, in this regard, to genes and their components: C-G-A, a single codon of DNA, is "too small" to be a gene. It is one of the codes for the amino acid arginine, and it copies itself prodigiously wherever it appears in genomes, but its effects are not "individual" enough to count as a gene. A three-nucleotide phrase does not count as a gene for the same reason that you can't copyright a three-note musical phrase: it is not enough to make a melody.

Dennett seems to suggest that whilst three notes can't be memetic, four can, for he maintains that

The first four notes of Beethoven's Fifth Symphony are clearly a meme, replicating all by themselves, detached from the rest of the symphony, but keeping intact a certain identity of effect (a phenotypic effect), and hence thriving in contexts in which Beethoven and his works are unknown.

Nevertheless, many listeners would recognize the following song, Johnny Burke's and Erroll Garner's `Misty' of 1955, from its distinctive opening vocal gesture ("Look at me..."), a collection of just three notes, b¹-g¹-d¹. If the memory of a melody can be accessed by hearing its opening notes, this implies that these notes themselves have independent memetic status: [note 11]

The issue is, however, not quite as simple as it is presented, for Dennett is blurring the musical parameters of pitch and rhythm. Even the shortest and most self-contained musical meme is seldom an indivisible particle, by which I mean divisible not horizontally (by length), or vertically (by pitch strata), but parametrically. Almost invariably, it is itself a complex of memes in different musical parameters, principally of pitch and rhythmic configurations, but also structures in the realms of dynamics (patterns of loud and soft) and texture (patterns of thick and thin sounds). Example 2 i below, for instance, consists of configurations in pitch - bracketed and labelled meme x - and rhythm - meme y - which, as shown in ii and iii, have independent existence owing to their replication in other contexts:

 
i) Memes x (pitch) and y (rhythm): Mozart, Piano Concerto in B major K. 456 (1784) I, bb. 1-4.

ii) Meme x: Pitch Analogue 231; [note 13] Mozart, Die Zauberflöte K. 620 (1791) no. 13, "Alles fühlt der Liebe Freuden," bb. 1-3, transposed, for ease of comparison, from C major to B major. [note 14]

iii) Meme y: Rhythmic Analogue ; Mozart, Piano Concerto in F major K. 459 (1784) I, bb. 1-4.

In order for syntax to exist..., successive stimuli must be related to one another in such a way that specific criteria for mobility and closure are established. Such criteria can be established only if the elements of the parameter can be segmented into discrete, nonuniform relationships so that the similarities and differences between them are definable, constant, and proportional.

In the western European tradition, at least, memetic structures have evolved most easily in the pitch and, less so, the rhythmic realms, the parameters of dynamics and texture lending themselves rather less readily to "...segment[ation] into discrete, nonuniform relationships....".

Having established the parametric interaction of musical memes, Dennett's example, the theme from the opening of Beethoven's Fifth Symphony, could be understood as not just four "notes" but, fundamentally, two pitches, g¹ and e¹, articulated by four rhythmic attacks, . One could even say that the most distinctive aspect of the theme is not the pitch content but this abstract rhythmic profile - bracketed and labelled as meme x - which, later in the first movement, becomes reduced to a three attack rhythm - , meme y - a memetic unit of wide currency at this time:

i) Meme x: Beethoven, Symphony no. 5 in C minor op. 67 (1808) I, bb. 1-5.

ii) Memes x and y: Beethoven, Symphony no. 5 I, bb. 179-190.

iii) Meme y: Mozart, Symphony no. 40 in G minor K. 550 (1788) I, bb. 146-150.

In the work of the composers who were Beethoven's contemporaries and successors, however, this theme, although also copied in their brains as a single-unit meme, was not imitated in their compositions en bloc, for what might be called the anti-plagiarism concept meme (prolific in western European culture certainly from the beginning of the nineteenth century) would have inhibited this, making it, in Dawkins' words, far too long to be a "...viable unit of natural selection" (1989: 195). Memorizing and then replicating whole chunks of the music of their predecessors and contemporaries is not what composers do: they tend, as I have shown, to replicate the small component units of the musical continuum - either remembered from musico-aural experience or viewed as musico-graphical symbols on paper - navigating the straits between the siren voices of memorability and the rocks of plagiarism.

On this reasoning, one would expect relatively short segments of the theme from the slow movement of Beethoven's Seventh Symphony to have memetic status. Indeed, as Example 4 illustrates, bb. 27-42 might be regarded as a memeplex, a collection of memes which assemble here into a larger pattern (this notion is taken up in more detail in Section 6). The example shows copies of just two of the memes - bracketed and labelled x and y in the example - which make up this melody: [note 15]

i) Meme x: Mozart, Piano Concerto in C major K. 467 (1785) I, bb. 413-417.

ii) Memes x and y: Beethoven, Symphony no. 7 in A major op. 92 (1812) II, bb. 27-42.

iii) Meme y: Schubert, Piano Quintet in A major D. 667 (`Trout') (1819) I, bb. 1-6.

i) Bach: Matthäus-Passion BWV 244 (c. 1729-c. 1744) no. 25, Chorale "Was mein Gott will, das g'scheh' allzeit," bb. 3-5.

ii) Bach: Matthäus-Passion no. 40, Chorale "Bin ich gleich von dir gewichen," bb. 9-11.

i) Mozart: Piano Sonata in D major K. 284 (205b) (1775) I, bb. 126-127.

ii) Beethoven: Piano Trio in D major op. 70 no. 1 (`Ghost') (1809) I, bb. 268-270.

Given these various qualifications, in defining the musical meme, one may therefore assert that any discrete musical segment which a composer assimilates from his or her environment may be held to be memetic, and that such a segment will tend to be the union of a short melodic fragment, a simple chord progression, or a concise rhythmic pattern. Thus, to demarcate musical memes one needs, in the words of Bent and Drabkin, "...to break the stream of music into component units (or 'unities' - i.e. units that either cannot be further subdivided or do not need to be because their sub-units never occur independently)" (1987: 96). Whilst offered as a summary of the working methods of distributional analysis, [note 16] this principle both holds for the definition of the meme, and neatly parallels that Dawkins gives for the gene.

5.2. Coequality

A coequal can exist at any level of the stylistic hierarchy discussed in Section 3, although in reality the coequal can exist in concrete form only at the level of intraopus style. Therefore a (musical) meme may exist abstractly at the level of dialect or idiom, but can only exist in reality at the level of the individual work. Here, as explained in Section 4, it manifests itself extrasomatically/phemotypically, but primarily derives from a somatic form in the composer's brain. In the absence of a proven coequal (or because the sheer magnitude of that which one has to investigate militates against identification of coequality, a particular problem in the memetic analysis of music), one might perhaps instead need to invoke a probabilistic perspective, positing the statistical probability of the existence of a coequal of given meme - without which, by definition, that mnemon would not attain memetic status - somewhere in the dialect at a particular point in time.

If the coequal of a mnemon Mn is identified one has to determine whether it is possible to verify if the coequal is the direct - i.e., causal - antecedent or consequent of Mn or whether the resemblance is adventitious. Dennett notes that "[t]his is the same epistemological problem, in the science of culture, that taxonomists confront when they try to sort out homology [resemblance due to direct descent] from analogy [resemblance due to fortuitous convergent evolution], ancestral from derived characters, in cladistic [species' family tree] analysis" (1995: 357). Ultimately, it may be impossible to resolve such questions, for the complexity of human communities and the convoluted modes of interaction between their members - particularly the admixture of horizontal and vertical modes of transmission - make verification of causality highly problematic. A workable definition of the meme probably ought not, in consequence, to contain a stipulation that a causal connection be verified between two equivalent particles, merely that a given particle has a coequal.

It is clear that a definition of coequality is more difficult in the case of two mnemons, Mn^x and Mn^y, which are similar in configuration but not identical to each other, for in such situations one must determine, using substrate-appropriate criteria, whether they merit the status of coequals, and hence memes. In such cases, Mn^y might be judged to be sufficiently different from Mn^x to be regarded as a mutant form of it, although it is not always apparent, even using chronological evidence, which is the antecedent and which is the consequent in a pair of mnemons in an assumed evolutionary relationship. If Mn^x and Mn^y are considered sufficiently different to preclude identity as coequals, their individual memetic status depends, of course, upon the existence of a coequal for each.

As Figure 3 illustrates, to regard Mn^y as a mutant form of Mn^x (or vice versa) implies direct evolution, by definition a causal process, whereas in reality the relationship might be one between independently generated variants of a single antecedent, Mn^a (Figure 3 i); or between two independently generated mnemons, each deriving from its own antecedent, Mn^a and Mn^b (Figure 3 ii):

It is often the case that a given span of music may contain two or more interlocking and/or nested memes, each segmentation of the pitch or rhythm matrix being defined and verified by reference to a coequal in another context - either the same work or a different one. Figure 4 represents this diagramatically, with a musical illustration of nesting given in Example 7 i-v. Here a phrase by Mozart is shown to contain several nested memetic melodic segments, bracketed and labelled with the letters a-d (Example 7 ii is transposed to the key of C, the key of Example 7 i, iii, iv, and v). Example 7 vi (transposed to C) and vii, whilst not demonstrating interlocking or nesting, are added in order to show the coequals - bracketed and marked e and f - of other memes in i:

i) Mozart: Five Divertimenti for Three Bassett Horns K. 439b (1783-1788) no. 1, III, bb. 1-9.

ii) Mozart: Serenade in B major K. 361 (370a) (c. 1781) I, bb. 15-18.

iii) Mozart: Missa Brevis in C major K. 220 (196b) (Spatzen-Messe) (1775) Agnus Dei, bb. 1-2.

iv) Mozart: Missa Brevis in C major K. 220 (196b) Gloria, bb. 7-9.

v) Mozart: Die Entführung aus dem Serail K. 384 (1782) no. 11, "Martern aller Arten," bb. 13-15.

vi) Mozart: Serenade in C minor K. 388 (384a) (1782) I, bb. 66-68.

vii) Mozart: Adagio and Rondo in C minor/major K. 617 (1791), bb. 1-2.

6. Structural Hierarchies and The Musical Memeplex

6.1. Pitch-Based Structural Hierarchies

Example 8: Memes at Various Hierarchic Levels

i) Mozart: Flute Quartet in A major K. 298 (?1786) II, Minuet, bb. 1-8. [note 17]

ii) Voice-Leading Reduction of i.

iii) Mozart: Adagio in C major for Glass Harmonica K. 356 (617a) (1791), bb. 1-8, transposed to D major.

iv) Voice-Leading Reduction of iii.

v) Mozart: Flute Quartet in A major K. 298 II, Trio, bb. 1-8.

vi) Voice-Leading Reduction of v.

vii) Coequals of Memes 1-5, transposed to D major:

a) Meme 1: Beethoven, Symphony no. 9 in D minor op. 125 (1824) III, bb. 91-93.

b) Meme 2: Mozart, Symphony in C major K. 338 (1780) I, bb. 1-4.

c) Meme 3: Haydn, Die Schöpfung Hob. XXI: 2 (1798) no. 32, "Holde Gattin!", bb. 14-16.

d) Meme 4: Beethoven, Symphony no. 8 in F major op. 93 (1812) I, bb. 5-8.

e) Meme (1+) 5: Mozart, Piano Quartet in G minor K. 478 (1785) II, bb. 1-4.

To discount the single unit meme reading properly, it is necessary to ascertain the memetic status of the individual bracketed particles. Although one might only imply - on probabilistic grounds - the existence of other copies of these memes elsewhere in the dialect, it is prudent to attempt definitively to locate copies. Part vii a-e of Example 8 shows such copies, giving a coequal of each of memes 1-5 from other works from the dialect of Viennese Classicism.

Perhaps the best way to regard the passages in i and iii is to regard them as two copies of a coadapted meme complex or, to use Cees-Speel's term, a memeplex (in Blackmore 1999: 19). [note 18] As Dawkins notes,

Memes, like genes, are selected against the background of other memes in the meme pool. The result is that gangs of mutually compatible memes - coadapted meme complexes or memeplexes - are found cohabiting in individual brains. This is not because selection has chosen them as a group, but because each separate member of the group tends to be favoured when its environment happens to be dominated by the others.

Having ascertained the memetic status of the individual segments in the passages, the replication, in order, of the memes of extract i in the passage at iii allows us to speak with some confidence of the replication of a memeplex in these phrases. As a general principle, then, a memeplex may only consist of units which are also replicated independently of their preferred partners and which in association form a class of at least two. If a replicated complex of discrete units exists only in this form, one must regard this larger, encompassing, unit as the meme, in which case no memeplex exists. Conversely, what might initially appear to be two large single unit memes - as in Example 8i and iii - might be better regarded as memeplexes. Such a determination, however, hinges upon the hierarchic location of the replicated unit(s). A middleground structure - as in Example 8 ii and iv - might be regarded as a single unit meme, with copies existing at various hierarchic levels in other contexts, whereas the configurations generating this pattern may also demonstrate memetic existence independently of the memeplex into which they ostensibly assemble.

The `voice-leading reductions' at Example 8ii and iv strip i and iii down to their fundamental framework using a method of analysis developed by the influential Austrian music theorist Heinrich Schenker (1868-1935) in which notes deemed, on various criteria, to be of lesser importance are gradually removed. [note 19] It is evident that the foreground events of the passages in i and iii generate a middleground structure - the interrupted linear progression /I---/V|| /I---/V-/I [note 20] - which is essentially common to both passages, aside from a few minor details of voice alignment and disposition of scale degrees. Because this structure is replicated - it occurs more than once - it is, by definition, of memetic status. It is a meme at a deeper level of structure, but is not necessarily confined to that level; one might easily find examples of replicated patterns based upon this scale degree succession situated closer to or at the foreground level.

Part v of Example 8 shows the theme of the first half of the Trio of K. 298 III. Despite the fact that its foreground harmonic and melodic organization is quite different from that of the first half of the Minuet, i, and of the opening of the Adagio, iii, its middleground organization is essentially that of the passages in which the memeplex is replicated, ii  and iv. This illustrates the point that a meme at a level of structure below the foreground may be expressed by a variety of foreground configurations. In the present case, the middleground meme in ii  and iv is expressed both by a memeplex located at the foreground, i and iii, and by a sequence of foreground events, v, which - to my knowledge - is not a memeplex.

On the evidence of the above examples, it is logical to suggest that, in addition to foreground-located memeplexes, such complexes may also be situated at the middleground level. In such a situation, discrete middleground events in one piece would be replicated in sequence in another, both complexes generating a common background pattern. This is, of course, analogous to the situation presented in Example 8 i-iv, but located at one level of structure deeper (assuming, for simplicity's sake, three principal structural levels; in some analyses, Schenker often identifies more than one middleground stratum). Figure 5 represents these relationships diagramatically: [note 21]

At level iii of this hypothetical example, twenty foreground memes, M¹-M²⁰, each express (i.e., are principally based around) a single scale degree. These memes are shown as associating to form five groups. The first group of memes, M¹, M², M³, M⁴, and M⁵, for instance, might express the scale degrees , , , , and  respectively, giving rise to a middleground linear progression -, shown in Figure 5 ii a. Each of these middleground structures might, in turn, express a component (underlined in Figure 5 ii) of the ---- Urlinie shown in Figure 5 i. The fifth middleground structure, ii e, for instance, another - linear progression and itself generated by the group of memes M¹⁶-M²⁰, might express the final pitch, the , of the Urlinie.

It will be evident that each middleground structure in Figure 5 ii is a meme; examples may be found throughout the dialect of ---- middleground linear progressions, such as that expressed in bb. 18-22 of the first movement of Mozart's Piano Sonata in C major K. 545 (1788), illustrated in Schenker 1979 as Fig. 88 4 c. Moreover, if, by analogy with the foreground memes in the passage in Example 8 i, these five middleground structures a-e were replicated in sequence in another work at the same level, as is analogically the case in Example 8 iii, they would clearly constitute a middleground memeplex. As with the memeplex in Example 8 i and iii, such a memeplex will generate a meme at a still deeper structural level: in the same way that the foreground memeplex of Example 8 i and iii gives rise to the middleground meme of Example 8 ii and iv; correspondingly, the middleground memeplex of Figure 5 ii and its coequal in another work will give rise to the background meme of Figure 5 i and its coequal in that other work.

Furthermore, just as the middleground structure shown in Example 8 ii, iv, and vi was not dependent upon the specific set of foreground memes present for its expression - this being evident from the divergence at the foreground level between the passages in Example 8 i and iii on the one hand and Example 8 v on the other - so the background structure in Figure 5 i is not contingent upon a specific set of middleground memes for its expression. Indeed, one of the basic tenets of Schenkerian theory proposes a dualism between the limited number of background forms and the virtually unlimited number of middleground and foreground patterns. Nevertheless, it is logical to infer, as does the previous paragraph, that the replication of a middleground memeplex - whether or not it is itself engendered by a foreground memeplex - will give rise to identical background memes, just as the replication of a foreground memeplex will generate identical middleground memes. [note 22]

This relationship between proximate events and more remote phenomena is essentially that conceptualized by Gjerdingen as the schema-features dichotomy. Both Gjerdingen (1988) and Meyer (1989) have written at length on musical patterns they term variously archetypes and schemata. [note 23] These are perceptual/conceptual frameworks being determined by, and determining, the nature and disposition of a number of lower-level elements, termed features by Gjerdingen. Thus, "[s]chemata can be defined as meaningful sets of features, and features can be defined as meaningful elements in sets of schemata" (1988: 6). From the point of view of the composer, schemata are primarily synthetic, generative tools, guiding the creative process; from the point of view of the listener they are analytical aids, directing the processes of perception and cognition.

Implicit in the Meyer-Gjerdingen notion of a schema is the principle of recurrence: schemata are replicated patterns of relationships and are, by virtue of this replication, necessarily memetic. If one regards the schema as a middleground event and its constituent features as foreground phenomena, it will be evident, in the light of the discussion of Example 8 and Figure 5, that a diversity of foreground features may assemble to generate a specific middleground schema.

6.2. Structural Memes in Music

Cook argues, on the basis of several empirical studies, that these structures seem to have little tangible reality for listeners, suggesting that

...few people actually experience musical compositions as such, in the sense of constituting them as fully co-ordinated, objective structures. Unless they have both the training and the inclination to track the form of a piece of music in theoretical terms as they listen, people experience recurrence without actually observing what it is that recurs; they experience coherence but not the unitary organization in terms of which a theorist or analyst would explain that coherence. People enjoy musical compositions, in other words, without really perceiving them at all; rather than listening to them...they "just listen."

Nevertheless, they apparently had clear existence for composers, for as Drabkin notes, apropos of Beethoven:

...we know that he studied the music of his predecessors Haydn and Mozart and modelled a number of sonata-type works of the 1790s and early 1800s on specific works by Mozart [Beethoven's String Quartet in A major op. 18 no. 5 (c. 1799) is, for instance, closely modelled on Mozart's String Quartet in A major K. 464 (1785)]. If a piece by Mozart could suggest to Beethoven a set of procedures to be followed - with modifications - to produce another piece, then he probably did not regard the growth processes in a particular piece as the exclusive property of that piece.

This is equivalent to saying that Beethoven - indeed probably most composers working in traditions with strongly developed notions of form and genre - perceived a fairly clear separation between a work's global organization and its detailed content. He realized that a given structural configuration might receive many instantiations each of which was unique in its local details but all of which shared broadly analogous "growth processes."

Given this process of replication by repeated instantiation, it is a small step to the view that the fundamental archetypes of music are memes - structural memes - at the largest dimensions and highest hierarchical levels of musical organization; they are, to use Gjerdingen's terminology, superordinate schemata which may be instantiated by a diversity of subordinate features. Given this, one can conceive of interplay, perhaps indeed tension, between the top-down processes of the structural memes (which require and perhaps select memes at lower hierarchic levels for their generation and replication), and the bottom-up processes of the memes at lower hierarchic levels (which selfishly pursue their own replication without regard for the structural memes which they generate and replicate). Moreover, one might even envision a process of allelic rivalry between lower-level memes in the competition to occupy the loci in a structural archetype.

How structural memes should be conceptualized and described has been one of the great debates of music theory and, latterly, music analysis. These disciplines have, moreover, had to keep pace with the evolution of structural memes over the last four hundred years. Conceptual memeplexes assembled to account for such configurations include, in roughly chronological order, Quintillian rhetoric (Burmeister, c. 1600), phrase assemblage (Koch, c. 1780), formal models (Marx, c. 1840), voice-leading strata (Schenker, c. 1930), motivic elaboration (Réti, c. 1950), and Chomskyan generative grammar (Lerdahl and Jackendoff, c. 1980). [note 24] It will be realized that these conceptual memeplexes are themselves subject to variation and selection (including by the criterion of fit with that which they aim to elucidate) over time and, as a result, undergo evolution in association with the structures they endeavour to describe.

I hope to return to this question of deep structural archetypes in music and their evolution - the musical analogue to Dawkins' `blind watchmaker' principle (1991) - on another occasion. [note 25] Before leaving the issue, however, it should be noted that structural memes clearly retain the fundamental characteristics of memes at lower hierarchic levels, in that they are composed of a relatively small number of discrete components in a clear and distinct relationship with each other. The observations made in Section 5.1 on the implications of the memetic attributes of copying fidelity and fecundity would therefore appear to apply to memes irrespective of the hierarchic level at which they are propagated. Whether one chooses to speak in terms of traditional formal models, such as binary, ternary, or sonata form; [note 26] the Schenkerian Ursätzen -, -, or -; or the normative prolongational structure proposed by Lerdahl and Jackendoff, [note 27] one is essentially dealing with small memes - particulate entities consisting of relatively few elements - despite their generally expansive temporal arch.

6.3. The Psychological Organization of Musical Memes

Semantic/categorical memory takes the form of an associative network of information-encoding memory nodes (memes) and their interconnections. Delius notes that "[s]uch plastic synapses have to be thought of as the critical components of neural networks that function as associative arrays" (1989: 44; see also his Figure 2; and Gjerdingen 1988: Figures 4-1, 4-2). The memory patterns for foreground features such as memes 1-5 in Example 8 i and iii would seem to be subject to this type of organization. In contrast, episodic/schematic memory structures the recall of discrete events anchored in linear time. The memory patterns for a middleground schema such as that shown in Example 8 ii, iv, and vi, with its clear sequence of component events, would seem to be subject to this type of organization. These two models of memory organization may be represented diagramatically as follows:

Having outlined their differences, Gjerdingen asserts that

These two types of memory organization commingle if we allow the term feature for event schema to coincide with the term concept for semantic[/categorical] networks....[I]n music, dominant seventh chord, for example, can be both a concept linked to the memory nodes instability, dissonance, and so on, and a feature in the [episodic/]schemata[tic] perfect authentic cadence....

In the light of the discussion of Example 8, one might suggest that foreground-orientated memes (features) are coded by the individual neural nodes in a semantic/categorical associative network; and that middleground-orientated memes (schemata) are the consequence of the organization of these nodes into sequential configurations fixed in and mediated by episodic/schematic memory. Moreover, these middleground memes then act as features coded by the nodes of a higher-order semantic/categorical associative network; these are themselves fixed sequentially into a superordinate episodic/schematic configuration (the highest level schema), of which the Ursatz is one representation. In this sense, the hierarchic, embedded, nature of memory organization gives rise to the hierarchic, embedded, nature of musical organization.

 Despite its congruence with observed musical phenomena, Gjerdingen's synthesis of the two forms of memory organization in the extract cited above tends to blur the distinction between signifiers and signifieds. One method of clarification would be to regard the spoken (verbal-phonetic) and written (verbal-graphical) patterning `dominant seventh chord' as the phemotypic products of somatic memes which act as signifiers. [note 29] To this category one should add the memes antecedent to such phemotypic products as the written (musico-graphical) patterning of the dominant seventh chord:

Together, and in coadaptation with an array of other memes, these form the matrix of concept memes - the network of interlinked notions Peirce termed interpretants (in Nattiez 1990: 6) - which structure our verbal-conceptual cognition of this chord.

Whilst to some extent independent, these three signifier memes also exist in coadaptation with the somatic sonority meme, our mental image of the sound - i.e., the sound internalized (`heard') in the brain - which operates as their signified and whose phemotypic product, via the intercession of musical instruments, is the physical sonority through which the dominant seventh chord impinges upon us most directly. This complex relationship is illustrated below: [note 30]

It will be understood that in verbal signification systems, the somatic signifier - the verbal-phonetic and/or verbal-graphical memes antecedent to the language-specific spoken and/or written word - and the somatic signified - the idea or concept with which they are stably united - give rise to a unitary phemotypic manifestation, a spoken and/or written verbal configuration. In music, by contrast, a separation is maintained, in that the somatic signifier - the memes antecedent to the verbal-phonetic and/or verbal-graphical phrase `dominant seventh chord' and/or the musico-graphical image shown in Figure 7 - and the somatic signified - the memes antecedent to the physical sonority - give rise to separate manifestations which preserve the signifier-signified dualism at the level of the phemotype.

6.4. Topics

A topic, T, may be defined as a musical sign. Each T embodies the union of a signifier and a verbally mediated signified. Signifiers are purely musical dimensions such as texture, timbre, rhythm, melody, and harmony in a particular disposition....The signified or concept is represented by an arbitrary label drawn from [the] U[niverse of] T[opic and] normally point[s] to dimensions of historical or sociocultural specificity, including the elements of a contemporary compositional code.

An example of a topic is the chromatic descending tetrachord pattern, which consists of the motion from the tonic of the key to its dominant (the fifth note) downwards by semitones. [note 31] From Monteverdi to Beethoven, this meme was regularly replicated in coadaptation with texts expressing death, grief, and the funereal. In the following passage from Purcell, the tetrachord is bracketed:

i) Musical Signifier: Purcell, Dido's Lament from Dido and Aeneas (1689), bb. 6-12.

Text: When I am laid in earth, may my wrongs create no trouble in thy breast.

ii) Verbal-Conceptual Signified: Coadapted Concept Memes

As Figure 2 indicates, the topic exists at the level of dialect - the association of musical meme with concept meme is copied in all the brains of the members of a given cultural community - but also shares the meme pool with analogous memeplexes consisting of personal associations of musical memes and concept memes at the level of idiom. A composer may, in other words, replicate a private association between musical patterning and verbal concepts in his or her works which remains inscrutable to the wider musical community.

7. The Transmission and Mutation of Musical Memes

The center of our theoretical models is the concept of transmission: for biologists, and in particular geneticists like ourselves, the centrality of the concept of transmission to evolutionary thinking is patently obvious. In biological material, however complex, there exists an almost perfect mechanism of genetic transmission. Evolution is the result of mutational exceptions to perfect transmission and the differential success of the products of this imperfect transmission.

In cultural material, the "mechanism of transmission" is less perfect than is the case with biological material and, as a result, the "mutational exceptions to perfect transmission" are more numerous. These deficits in copying-fidelity are thus intrinsic to all replicants, but are a particular propensity of the meme; the parlour game of `Chinese Whispers' represents this process in isolated and compressed form. The tendency towards miscopying makes available memes which are variants of existent forms - i.e., mutations - and which are subject, as are all memes, to the pressure of `cultural selection', the analogue, proposed by Cavalli-Sforza and Feldman, to the natural selection which regulates the replication of genes within living systems. They define this as

...the rate or probability that a given innovation, skill, type, trait, or specific cultural activity or object - all of which we shall call, for brevity, traits - will be accepted in a given time unit by an individual representative of the population.

Like natural selection, cultural selection works upon the totality of memes (traits, in the terminology of Cavalli-Sforza and Feldman) within a cultural community and leads to their differential replication. That is, if a meme arises which is a clear variant of an existing meme it may persist and increase its representation or it may become extinct, according to whether it is more or less susceptible to imitation as a result of the changes it has undergone. The net result of this process of cultural selection is change in the relative frequency of memes in the meme pool over time. The concept of susceptibility to imitation is directly analogous to the biological notion of reproductive fitness; it is an index of the replicant's capacity for replication which Cavalli-Sforza and Feldman term `cultural fitness' (1981: 17). In biological replication, a gene's fitness is contingent upon the phenotypes it plays a role in engendering. In cultural replication, an analogous situation obtains, for a meme is not selected directly; rather, it is selected by virtue of its phemotypic consequences. [note 32]

Figure 9 represents the processes of memetic transmission and mutation schematically. Because cultural products are transmitted from a producer to a receiver via an intermediate (phemotypic) form, one means of representing the process is to adapt the Molino/Nattiez notion of the semiological tripartition (Nattiez 1990: 10 ff.). The figure traces the movement of memes as they pass between the poietic, neutral, and esthesic levels and across the somatic-extrasomatic boundary which bisects the diagram. [note 33] Five individuals, or hosts, are shown; these individuals, 1-5, need not be in immediate geographical or chronological relationship with each other, although they often are:

Here meme M, shown located in the brain of the first host, 1, is situated at the poietic level and, initially, exists in somatic form. The process of conversion into the extrasomatic form, a musico-graphical or musico-aural version, first moves the meme across the somatic-extrasomatic boundary (the vertical line bisecting the diagram) within the poietic level - at this stage the meme may exist in the context of compositional sketches and drafts - and then across to the neutral level, where the meme exists as part of a completed, notated (or even improvised) composition. The second host, 2, initially encounters the meme from the standpoint of the esthesic level, either by hearing the meme in its musico-aural form or by seeing the meme in its musico-graphical notation. The movement from the esthesic back to the poietic level within the second host corresponds broadly to the two principal stages of memetic transmission identified by Cavalli-Sforza and Feldman: awareness followed by adoption (1981: 62-65).

Once the adoption stage is accomplished, meme M now resides in the brains of both the first and second hosts and may then be transmitted to other hosts. Of course, a meme is never imitated with complete accuracy over any length of time; some changes, albeit very slight, are almost inevitable during this process. As the diagram shows, a third host, 3, might encounter M and subject it to alteration at some stage in the course of its progress through the sectors esthesic-somatic (awareness), poietic-somatic (adoption), poietic-extrasomatic (compositional sketches), and finally neutral-extrasomatic (the musico-graphical and/or musico-aural phemotypic form). The sectors of the diagram within which mutation can occur are indicated by dotted brackets. The changes imposed on M might be intentional, accidental, or indeed obligatory. In the latter case, this is determined by the new context into which the meme must be inserted, for memes, as has been seen in Section 6.1, are rarely transmitted singly but as components of larger memeplexes.

At its inception, the mutant is a mnemon, Mn, rather than a meme, for if a particle defined as or assumed to be memetic gives rise to a mutant form, the mutant, at its moment of genesis, is not memetic; at this moment it is theoretically unique, unimitated. When the mnemon is copied into the brain of a subsequent host - 4 in Figure 9 - the particle attains memetic status, as meme M¹. The mutant form may overwrite the original meme in the brain of the third host or coexist with it. It may even be (re-)encountered by the first and second hosts and copied into their brains, possibly overwriting the original copies of M or coexisting with them. As Figure 9 shows, meme M¹ is then subject to further imitation, and possible mutation, by a fifth host, 5, and subsequent hosts ad infinitum.

This account hopefully makes clear that, whereas the gene is propagated non-phenotypically (ultimately genes, not bodies and other gene products, reproduce themselves), the meme, of necessity, must be propagated phemotypically. To recall Blackmore's terminology cited in Section 4.1, memetic propagation is an example of "copy-the-product," as opposed to the "copy-the-instructions" of genetic transmission (1999: 61).

8. The Evolution of Musical Style

...the best way too look at evolution is in terms of selection occurring at the lowest level of all....the fundamental unit of selection, and therefore of self-interest, is not the species, nor the group, nor even, strictly, the individual. It is the gene, the unit of heredity.

Given that the principle of Universal Darwinism holds that these remarks must be taken to apply analogically to all replicators, the same considerations must be applied to memetics. Thus, the single unit meme is the fundamental unit of selection, and not any larger configuration. Without wishing to labour analogies between genetics and memetics, it is nevertheless interesting to note that Meyer's hierarchical view of cultural structure outlined in Section 3 maps fairly neatly onto the biological hierarchy Dawkins describes, helping us to comprehend more clearly the implication of the unit of selection principle to musical memetics:
 

Here, the cultural analogue for the species may be taken to be the dialect; a group of organisms within the species can be compared with either the composer's personal style, with a musical genre (such as the symphony, the string quartet, or the opera), or with a formal-structural type (such as those considered in Section 6.2); and the individual organism maps onto the self-contained musical work, the individual representative of a genre. Lastly, the memes whose phemotypic products constitute a musical work are analogous to the genes whose phenotypic products constitute the individual organism.

It is, of course, intuitively clear that the meme is the unit of selection in the evolution of musical style: whole dialects, such as the Austro-German Classical style, are not selected for or against; neither are the styles of composers, musical genres, or formal-structural types; and neither are whole works. What are selected are the memes which constitute those works. In this view, cultures evolve from the bottom up, not the top down, the nature of the system being a function of the properties of the units at the lowest hierarchic level.

In the evolution of musical style, a mutant meme appears in the work of a composer, the level of intraopus style, by means of the processes discussed in Section 7. Providing it possesses high longevity, fecundity, or copying-fidelity, it may then be copied in other works of that composer, thereby moving to the level of idiom. Further imitation might disseminate the meme among the composers in a community, taking it to the level of the dialect, the configuration of the which is slowly and subtly changed.

However, it is the case, as Gatherer observes apropos the evolution of jazz, that

New memes, such as novel chord patterns, rhythmic changes, or alterations in instrumentation are subject to scrutiny as to how they cohere with the pre-existing whole. Sudden innovation is not permitted but small innovations may cumulatively have large results.

This point is developed by Dawkins in a passage in which the word `meme' may be substituted for `gene' throughout. He asserts that

The gene pool will become an evolutionarily stable set of genes, defined as a gene pool that cannot be invaded by any new gene. Most new genes that arise, either by mutation or reassortment or immigration, are quickly penalised by natural selection: the evolutionarily stable set is restored. Occasionally a new gene does succeed in invading the set: it succeeds in spreading through the gene pool. There is a transitional period of instability, terminating in a new evolutionarily stable set - a little bit of evolution has occurred....Progressive evolution may be not so much a steady upward climb as a series of discrete steps from stable plateau to stable plateau. It may look as though the population as a whole is behaving like a single self-regulating unit. But this illusion is produced by selection going on at the level of the single gene.

 The notion of the evolutionarily stable strategy (ESS), formulated by J. Maynard Smith, is a concept fundamental to understanding cultural evolution. In biological evolution, an ESS is essentially a behavioural strategy which, "...if most members of a population adopt it, cannot be bettered by an alternative strategy," "[a] strategy that does well in a population dominated by the same strategy" (Dawkins 1989: 69; 1983a: 286). Many patterns of animal behaviour, including aggression and territoriality, in which the conflicting self-interests of the members of a group reach an equilibrium, are understandable in terms of this notion. Individuals deploying deviant strategies against the majority strategy generally cannot better it, and they and their strategies are consequently penalized by natural selection.

In cultural evolution, the ESS may be understood as an index of the resistance of a meme pool to incursions by mutant memes. However, because the meme "...is already achieving evolutionary change at a rate that leaves the old gene panting far behind" (Dawkins 1989: 192), even a year of memetic evolution is comparable to many millions of years of genetic evolution. Consequently, the generation and propagation of mutant memes, and the resultant motion from "stable plateau to stable plateau" as one ESS is supplanted by another, occurs at a rapid, and probably indistinguishable rate. This process is represented, in simplified form, below:

Acceptance of this perspective forces one to question Meyer's notion of dialect, which he defines as "...substyles that are differentiated because a number of composers...employ (choose) the same or similar rules and strategies" (1989: 23). This differentiation may be on the basis of geography, nationality, cultural movements, social class, or function within the culture; "...but most often dialects are distinguished historically" (1989: 23). From this one might interpret the period c. 1700-c. 1900 as comprising three historical dialects, the Baroque (the period of Bach and Handel), Classicism (the period of Haydn, Mozart, and Beethoven), and Romanticism (the period of Schumann, Wagner and Brahms), operating within the constraints of a single set of rules, that of tonality. Yet whilst no musicologist would claim a strict articulation between these periods, if one regards the evolution of musical style as driven by a fluid meme pool configuring itself into a succession of transient ESSs, then the notion of discrete historically distinguished dialects cannot logically remain tenable. The meme pool of Bach's time evolved through a near infinity of ESSs until it became transmuted into that of Brahms'.

Moreover, scepticism is needed concerning the rigidity of the distinction Meyer draws between diachronic changes from one dialect to another, which he terms trended changes (for example, between Classicism and Romanticism, which occurred c. 1800-c. 1820); and changes from one system of rules to another, which he terms mutational changes [note 34] (for example, between tonality and serialism, [note 35] which occurred c. 1900-c. 1920). He conceives this distinction as one between differences of degree and kind respectively, asserting that the two modes of style change are not necessarily related (1989: 102), and suggesting that "[i]t does not follow...that the trend caused the mutational change, only that the stylistic/cultural situation created by the trend made it possible for the mutation to endure - be replicated....Nor is it supposed that if a stylistic consensus takes place, the new rules (mutations) will be a result of prior trends or strategies" (1989: 103, notes 79, 80).

Whilst there is no teleological inevitability of a given rule change's arising from antecedent changes in the dialect(s) it encompasses, it must be the case - accepting the bottom-up perspective of memetic evolution - that the large-scale reconfiguration represented by a change in rules can only be defined in terms of the changes occurring upon lower hierarchic levels. A neo-Darwinian, meme-selectionist perspective would regard mutational changes as the inexorable outcome of cumulative trended changes, the latter acting not only as a necessary condition for the former but also as determinants of the configuration of the new higher-order system. In this respect, cultural evolution again parallels biological evolution, for "...all sane Darwinians are gradualists in the extreme sense that they do not believe in the de novo creation of very complex and therefore statistically improbable new adaptations like eyes. This is surely what Darwin understood by the aphorism 'Nature does not make leaps'" (Dawkins 1983a: 287-288). [note 36]

Lastly, just as the notion of distinct, historically sequential dialects is undermined by a view of musical style as a succession of transient ESSs, so the idea of distinct, historically sequential systems of rules cannot logically be sustained. Whilst the division of style along the vertical (synchronic) axis of rules, dialects, and idioms is a useful intellectual tool for structuring a complex field, retaining its clarity at any given point in musical time, when considered in association with the horizontal (diachronic) axis representing temporal progression its categories of rules and dialects are ultimately blurred by the inexorable, random gradualism of memetic mutation.

9. Conclusion: Towards a Memetics of Music

Whilst commentators such as Dawkins and Dennett have seen musical memes as, to re-employ the linguistic analogy, comparable with sentences, I have attempted to show that they are more akin to the individual word - that music is made up of small units of pitch and rhythm which, by virtue of their replication, should be regarded as memetic.

The examples have illustrated that music is a rich field of interacting parameters, some of which are capable of sustaining memetic replication. Whilst I have largely confined myself to the parameter of pitch, in common with the practice of much analytical musicology, a comprehensive memetics of music must account for these individual parameters and, more importantly, their interaction in the form of parametric memeplexes.

In the realm of pitch, music, perhaps more than any other symbolic system, sustains the propagation of memetic structures at a variety of hierarchic levels, from its immediate surface to more remote levels. At the deepest levels of structure are propagated structural memes, the superordinate configurations repeatedly reinstantiated by composers as the guiding architectural frameworks of their compositions. The analytical method of Schenker is an effective, although by no means unproblematic, method of representing these structures. Whilst not discussed here, it seems the case that rhythmic memes are similarly propagated at several hierarchic levels - a subject to which Yeston 1976 is addressed, although not in terms of the memetic paradigm.

I hope to have shown that, as with all cultural evolution, the evolution of music occurs because of the differential selection and replication of mutant memes within idioms and dialects. Slowly and incrementally, these mutations alter the memetic configuration of the dialect they constitute. Whilst gradualistic, this process eventually leads to fundamental changes in the profile of the dialect and, ultimately, to seismic shifts in the overarching principles of musical organization, the rules, propagated within several dialects.

Finally, I hope to have indicated that the application of musicological insights to memetics and the memetic paradigm to musicology offers considerable benefits to both areas of inquiry. To memetics, music offers a field of study in which the units of selection are, arguably, clearer and more amenable to analysis than verbal text- and concept-based memetics. To musicology, memetics offers a new viewpoint on its concerns, one which has the power to unify a variety of disparate musical subdisciplines - composition, performance, improvisation, listening, notation, theory and analysis, history and criticism, musical style and style-history, music-psychology, aesthetics and philosophy, and influence [note 37] - under the cool logic of a neo-Darwinian, meme-selectionist perspective.

Notes

2. The various strands constituting the discipline of musicology are surveyed in Kerman 1985.

3. Gatherer's (1997) contribution to the development of a memetics of music is acknowledged. A longer treatment of the subject of musical memetics than the present article may be found in my forthcoming article `The Selfish Meme: Particularity, Replication, and Evolution in Musical Style' (2000). A few paragraphs in the present article, particularly in Section 8, are adapted from `The Selfish Meme.'

4. Constraints of space prevent the discussion of music outside the western European art canon. Traditional and popular musics are, I believe, readily amenable to examination in memetic terms, although arguments presented here involving notation are not always pertinent to non-western musics, in which graphical fixation often plays little or no role. This is partly a consequence of the fact that the western trichotomy between composer, performer, and listener is rarely so sharply drawn in non-western musics.

5. See Scruton 1997: Chapter 7 for a detailed examination of the relationship between music and language.

6. The works of Beethoven (1770-1827), for instance, are generally divided into three style-periods, albeit with very fuzzy boundaries at c. 1803 and c. 1815.

7. Modality is the organization of the seven pitches C, D, E, F, G, A, and B into a number of different scale patterns, each with its own distinctive internal intervallic (i.e., pitch spacing) pattern. It was the system of pitch organization employed during the Medieval (c. 500-c. 1450) and Renaissance (c. 1450-c. 1600) periods, but has its origins in the music of ancient Greece.

8. Tonality is the organization of the twelve pitches of the chromatic scale into a hierarchy centred around one note, the tonic or key-note. It was the system of pitch organization employed during the Baroque (c. 1600-c. 1750), Classical (c. 1750-c. 1820), and Romantic (c. 1820-c. 1900) periods. Boundaries between these periods, and between modality and tonality and between tonality and serialism (see note 35), are, for reasons discussed in Section 8, highly fluid.

9. The concept of topic referred to in this Figure is examined in Section 6.4.

10. Sereno 1991 offers a stimulating critique of interdisciplinary analogy.

11. A now-defunct game show featured a competition (`Name that Tune') between two finalists to name a well-known melody, the contestants gambling on being able to name the melody on hearing only a few of its notes, within a range of one to seven. Some, I believe, were able to name melodies having heard as few as the opening two notes. Accepting the element of fortune here, and the fact that the themes were played fully harmonized, some melodies clearly begin with distinctive three-note memes.

12. Abbreviations used in musical examples in this article are as follows: b. N = bar N; bb. N-N = bars N-N inclusive; I, II, etc. = movement number of a multi-movement work.

13. The up and down arrows and associated integers indicate the direction of melodic movement and its size in semitones (the octave, in western music, is divided into 12 semitones). It seems logical to suggest that intervallic structure, in addition to absolute pitch location, should be a criterion in the establishment of memetic equivalence classes. On this principle, the opening gesture of `Misty' could be represented, independently of key, as 35.

14. In many of the examples here, particularly Example 8, I have transposed pitch memes from passages in different keys into one key in order to facilitate comparison, but it is worth noting that a given meme in two different keys is essentially the same meme, in that, by definition, it retains its internal intervallic structure; what differs is the absolute pitch location.

15. In the passage from the `Trout' Quintet, meme y appears in the key of A major, whereas in the Beethoven symphony it appears in C major, at the point where the melody modulates from the tonic (home) key of A minor to C, its relative major (i.e., the major key with the same key signature).

16. Distributional analysis is a method of analyzing music developed by musical semiologists such as Jean-Jacques Nattiez and Nicolas Ruwet in which, as with the analysis of language, music is segmented into its component phonetic units (paradigmatic analysis) and then the syntactical (grammatical) distribution of those units is determined (syntagmatic analysis).

17. The minuet movement of a Classical multi-movement work (such as a symphony or a string quartet) is tripartite, consisting of the minuet proper, a central trio section (i.e., a contrasting minuet), and a closing repeat of the minuet.

18. The `parametric complex' discussed in Section 5.1 is, of course, a memeplex composed of elements in different parameters; that considered here exists in only one parameter, that of pitch.

19. In the 1920s and 1930s Schenker developed a theory which conceived music as consisting of three interrelated levels (Schichten): the foreground (Vordergrund), the immediate musical surface; the middleground (Mittelgrund), a deeper level revealed by the removal of superficial, decorative notes; and the background (Hintergrund), the most remote and fundamental level. Forte and Gilbert 1982 and Neumeyer and Tepping 1992 are good introductions to his thinking, presenting the essence of Schenker's seminal work, Der freie Satz of 1935 (1979), in accessible form. The following Schenkerian conventions are adopted here: the degrees of the scale are indicated using Arabic numerals topped by the caret symbol (, , , etc.); and important harmonic steps (Stufen) are indicated by Roman numerals (I, IV, V, etc.).

20. A linear progression (Zug) is a stepwise melodic motion generally spanning the intervals (gaps) of a third, fourth, fifth, sixth, or octave. The forward slash, in Schenkerian analysis, indicates both vertical alignment and structural synchrony. Thus, /I-- means that whilst the tonic (I) chord is operative, the scale degree  is sounded, followed by the descending motion --. In an interruption (Unterbrechung) - symbolized by "||" - the upper line descends to /V and then returns to the pitch from which it began its descent. This is then followed by a second descent which reaches the/I averted by the interruption.

21. Schenker proposed that all tonal pieces could ultimately be reduced to one of three Ursätzen, or fundamental structures. The Ursatz is a two-part structure, consisting of a lower voice or Bassbrechung (bass arpeggiation) outlining the harmonic progression I-V-I, and an upper voice or Urlinie (fundamental line), expressing the linear progression -------, or ----, or --. It will be realized that the three Ursätzen, repeatedly reinstantiated by a variety of foreground and middleground memes, are memes at the deepest levels of musical structure (see Section 6.2 for further treatment of this concept). A memetic view of musical structure tends, however, to overturn Schenker's view that "...all the foreground diminutions, including the apparent 'keys' arising out of the voice-leading transformations [of the middleground], ultimately emanate from the diatony [i.e., the Ursatz] in the background" (1979: 11). Instead of this top-down perspective, memetics suggests the bottom-up generation of middleground structures by patterning at the foreground and, in turn, the generation of background structures by middleground events.

22. From this discussion, it will be understood that `Schenkerism' is a rich memeplex of musical and extra-musical memes fronted by a set of graphical memes. As such, one must be aware that it filters, and inevitably colours, the memes that make up the music which is its subject and with which it interacts. In other words, the view of musical structure one formulates via Schenkerian analysis is, possibly, as much an artefact as those distortions which sometimes result from the treatment of samples in preparation for electron microscopy. Throughout this article, my reliance on Schenkerian memes is a testament to their virulent infective powers; no other comparable music-analytical memeplex has such high fecundity at present. Nevertheless, I am fortunately also a host to other memes which impart to me some degree of critical detachment, and I hope the reader is likewise infected. For vigorous arguments contra-Schenker, see Narmour 1977.

23. See Meyer 1989: 50-54 for a consideration of such schemata, which "...are patterns that, because they are congruent both with human perceptual/cognitive capacities and with prevalent stylistic (musical and extra-musical) constraints, are memorable, tend to remain stable over time, and are therefore replicated with particular frequency" (1989: 51). Meyer also uses the term archetype to refer to structural classes which are the result of innate rather than learned responses; in practice the distinction is often difficult to draw (Gjerdingen 1988: 46 f.).

24. For a comprehensive survey, see Bent and Drabkin 1987, Chapters 2 and 3; see also note 22.

25. It is worth observing that in distinguishing between the process of memetic conglomeration which gives rise to the individual work of art and the long process by which the structural archetype instantiated by that work evolves, we mirror the clear biological parallel between ontogeny - the (embryonic) development of the individual organism - and phylogeny - the development of the species of which the organism is, in a sense, an instantiation.

26. Binary form consists of two repeated sections, the first of which (A) moves from the tonic key to a contrasting key, the second (B) from this contrasting key back to the tonic. Ternary form consists of three sections, the first (A) being a closed unit, the second (B) offering a strong contrast, and the third being either identical to A or a modified version (A¹) of A. Sonata form may be understood as an evolutionary descendant of binary form in which the B section of the binary form becomes divided into two distinct phrases, the second of which recapitulates the A part of the form (A | B A¹). This summary is, however, highly oversimplified: see Rosen 1988 for a full discussion of the relationships between eighteenth-century binary forms and sonata forms.

27. A normative prolongational structure is "...specified in terms of relationships of prolongational connection among structurally significant events, not in terms of any specified sequence of events" (Lerdahl and Jackendoff 1983: 248).

28. Constraints of space prevent my addressing the burgeoning neuroscientific literature on music, central as this will be to further research in musical memetics. See, especially, Bharucha 1999, in which a neural net model of musical organization is examined. Such models "...have a number of properties that recommend them as models of music cognition....they can account for how we learn musical patterns....their assumptions are either known or plausible principles of neuroscience....they are capable of recognizing varying shades of similarity and are therefore well suited to modeling similarity-based accounts...of tonality or modality....[and] they can discover regularities in musical styles that may elude formal music-theoretic analysis..." (1999: 413). Moreover, "...a neural net can learn temporal composite patterns so that they function as schemas and as sequential memories" (1999: 424).

29. The particular signifier `dominant seventh chord' would, of course, be propagated principally in the brains of anglophones. Owing to language differences, the same signified musical meme would have been associated with different signifying concept memes in the brains of, for instance, Mozart, Rameau, and Vivaldi.

30. This account clearly oversimplifies matters considerably by ignoring the motor-control memes which govern the muscular actions engendering writing, speaking, and the production of musical sounds.

31. Another example is the coadaptation between the rhythmic meme  (seen in Example 2 i and iii, where it is labelled meme y) and verbal-conceptual memes articulating notions of pompous militarism.

32. To speak of a single gene's or meme's fitness is somewhat artificial: these replicators are selected and propagated as complexes and exert their pheno/phemotypic effects in concert. A given pheno/phemotypic effect may be engendered by several genes or memes; conversely, several effects may be brought about by a single gene or meme. To use terms from population biology, musical memes would appear to be subject to r-selection, which is "[s]election for the qualities needed to succeed in unstable, unpredictable environments..." (Dawkins 1983a: 293). K-selection, by contrast, is "[s]election for the qualities needed to succeed in stable, predictable environments..." (1983a: 288).

33. Nattiez defines these three levels as follows: "(a) The poietic dimension: even when it is empty of all intended meaning...the symbolic form results from a process of creation that may be described or reconstituted. (b) The esthesic dimension: 'receivers,' when confronted by a symbolic form, assign one or many meanings to the form.... (c) The trace: the symbolic form is embodied physically and materially in the form of a trace accessible to the five senses. We employ the word trace because the poietic process cannot immediately be read within its lineaments, since the esthesic process...is heavily dependent upon the lived experience of the 'receiver.' Molino proposed the name niveau neutre [neutral level] or niveau matériel [material level] for this trace" (1990: 11-12; his emphases).

34. Meyer is using the term mutational in a different sense to that used in this article: a memetic standpoint regards trended changes as just as much the result of mutations as mutational changes.

35. Serialism is the organization of the twelve pitches of the chromatic scale into a relationship of equal status. It is a system of organization developed by Arnold Schoenberg (1874-1951) by the early 1920s and employed in the works of many later twentieth-century composers.

36. Thus, whilst many commentators see the appearance of the serial system as a revolutionary change, in the gradualist interpretation advocated here it is an evolutionary transformation grounded in antecedent developments, particularly the steady attenuation of tonality in the decades after Wagner's Tristan und Isolde (1865), and its eventual disintegration into "free atonality" in the works of progressive composers c. 1910.

37. Studies of influence - now often subsumed under Kristeva's term intertextuality (1969) - in music, such as Korsyn 1991 and those sources listed in his note 5, are increasingly common in the musicological literature. To my knowledge, however, none invokes the memetic paradigm.

Acknowledgements

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