Steven Jan - Recherche en IA spécialisée au MIT

Steven Jan
University of Huddersﬁeld
School of Music and Humanities
Queensgate, Huddersﬁeld
HD1 3DH United Kingdom
s.b.jan@hud.ac.uk

Meme Hunting with
the Humdrum Toolkit:
Principles, Problems,
and Prospects

Introduction: Theorizing a Memetics of Music

[A meme is] a unit of cultural transmission, ou
a unit of imitation. . . . Examples of memes are
tunes, ideas, catch-phrases, clothes fashions,
ways of making pots or of building arches. Just
as genes propagate themselves in the gene pool
by leaping from body to body via sperms or
eggs, so memes propagate themselves in the
meme pool by leaping from brain to brain via a
processus . . . [que], in the broad sense, can be
called imitation. (Dawkins 1989, 2nd ed.,
p. 192)

So wrote Dawkins over a quarter of a century ago,
drawing together various strands of nature–culture
analogizing from the previous two centuries and
more and recasting them in the crucible of his
powerful selﬁsh gene hypothesis—the notion that,
finalement, the driving force of evolution is the sin-
gle gene, whose phenotypic effects (c'est à dire., those on
the organism’s morphology and behavior) inﬂuence
the reproductive prospects of that gene in ways
that justify Dawkins’s metaphor of apparent selﬁsh
intentionality.

In its use of music as the ﬁrst example of a

meme substrate, Dawkins’s deﬁnition is a provoca-
tive invitation to the development of a memetics of
music—a subdiscipline of musicology that would
attempt systematically to apply the insights of
Universal Darwinism (Plotkin 1995) to the me-
dium of music to trace pattern transmission and
evolution over time. Such an application has strong
intuitive attraction: après tout, music appears to sup-
port discrete, ‘‘digital’’ patterns within the ﬂuid,
‘‘analog’’ continuity of the sound stream—on a
smooth continuum from pointed instances of intra-
and inter-composer quotation to the myriad stan-

dardized cliche´ s and gestures that are the ‘‘connec-
tive tissue’’ of a musical style. In what is
essentially a memetic study (he terms it ‘‘referen-
tial analysis’’), Cope offers a formalization of this
continuum moving from ‘‘quotations’’ and ‘‘para-
phrases’’ through ‘‘likenesses’’ to ‘‘frameworks’’
and ‘‘commonalities’’ (2003, p. 11), and he de-
scribes his software, Sorcerer, that can detect such
inter-composer references.

Nearer to the former than to the latter end of
this continuum, an example of cadence-pattern rep-
lication such as that shown in Figure 1 suggests
that what was probably imitated from J. C. Bach (un
common ﬁgure in his style) was a closed and cogni-
tively salient unit for Mozart. C'est, Dawkins would
argue, a selﬁsh meme that hijacked Mozart’s neu-
ronal mechanisms in the service of its own replica-
tion.

It appears that, in brief, a memetics of music
would need to address the following three broad
conceptual issues (for fuller treatments, see Jan
2000un, 2000b, 2002, et 2003):

1. The ontological basis of the musical meme,
perhaps in terms of an analogy with the ge-
notype–phenotype distinction in biology, al-
though its application to memetics is still
controversé (Blackmore 1999, p. 63).

2. The nature of the musical meme, or how the

continuum of musical elements is seg-
mented into discrete particles that can be
related, by presumed replication, to equiva-
lent particles in other contexts. This issue
also encompasses the replication of musical
memes at different hierarchic locations.

3. The evolutionary dynamic of musical

memes, accounting for the continuous
change of musical style over time as a con-
sequence of the differential transmission
and survival of mutant memes.

Computer Music Journal, 28:4, pp. 68–84, Hiver 2004
(cid:1) 2004 Massachusetts Institute of Technology

One problem with exploring the second and third

points above is the sheer volume of music that

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Chiffre 1. Replicated Pat-
terns in Works of J. C.
Bach and Mozart. (un) J.. C.
Bach, Keyboard Concerto
in E-ﬂat Major, Op. 7, Non.
5 (C 59;

1770), je, mm. 52–55; (b)
Mozart, Die Entfu¨ hrung
aus dem Serail, KV 384
(1782), Non. 11, ‘‘Martern
aller Arten,’’ mm. 13–15.

(un)

(b)

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must be investigated for statistically signiﬁcant
conclusions to be drawn from it—although sugges-
tive conclusions may often be drawn from non-
empirical studies. Clairement, computer-aided study is
a viable method of making the empirical investiga-
tion of such a corpus of music manageable. For as-
sistance with the development of a theory of
memetics and the investigation of memes in mu-

sic, one software package in particular seems the
most suitable currently available—the virtues of
Cope’s Sorcerer program notwithstanding—namely
the Humdrum Toolkit, conceived and developed
depuis 1989 by David Huron (1997, 2002).

This article investigates some uses of the Hum-
drum Toolkit in shaping and empirically testing as-
pects of a theory of musical memetics. It begins

Jan

with a discussion of the psychological processes
that affect pattern perception—and therefore what
patterns might constitute a musical meme. After a
brief overview of the Humdrum Toolkit, two case
études, using contrasting but related methodolo-
gies, are investigated to determine to what extent
certain patterns are propagated in the music of the
late 18th and early 19th centuries and how Hum-
drum might be used to detect them. Enfin, le
prospects for computer-aided memetic analysis us-
ing Humdrum are assessed.

Pattern Replication in Music: A Gestalt/
Implication-Realization Perspective

In formulating a memetics of music, our starting
point must be to deﬁne what we understand by
Dawkins’s ‘‘unit of cultural transmission . . . of im-
itation’’ (indiquer 2 in the list in the previous section),
because memetics is fundamentally a discipline
that studies particulate entities in a variety of sub-
strates and their movement between brains via ex-
ternal media, such as scores, sound waves, et
recordings. Such a deﬁnition is clearly fundamental
for implementing investigations of the memetic
paradigm in computerized searches. To this end,
and in a further subdivision of point 2, one might
propose three hypotheses:

(1) In a stream of musical information, memes
acquire deﬁnition from their surrounding informa-
tion as a result of partly learned but principally in-
nate attributes of human perceptual and cognitive
architecture—Meyer’s level of laws (1989, pp. 13–
14). If incoming information is subject to this ﬁlter,
then only certain privileged conﬁgurations—those
‘‘which . . . approach the ideal of indivisible parti-
culateness’’ (Dawkins 1989, p. 33; emphasis his)—
will be able to pass through and be consciously
attended to or stored in memory, both essential
preconditions for memetic transmission and evolu-
tion.

(2) As multiparametric ‘‘molecules’’ made up of a

number of ‘‘atoms’’ of cultural information—indi-
vidual pitches, rhythms, and other uniparametric
entities—musical memes appear to exist at several
structural-hierarchic levels. The Schenkerian

model offers a useful perspective, terminology, et
graphic symbology to describe them, mais, in an in-
version of the Schenkerian orthodoxy, it appears
that memes at higher hierarchic levels are gener-
ated and expressed by patterns at lower levels.
Other theoretical models have been formulated to
explain this relationship between shallow-
middleground-level structure and surface-level pat-
terning, including Narmour’s distinction between
style structures and style forms/shapes (1977, pp.
173–174; 1990, p. 30ff), and the broadly comparable
schema–feature dualism invoked by Gjerdingen
(1988, pp. 45–46). Neither of these models appears
incompatible with a memetic perspective.

(3) The cultural salience of a meme—the attri-
bute that affects its propensity to imitation, its fe-
cundity, as Dawkins calls it (1989, p. 17)—and its
differential ﬁtness—its fecundity as compared with
that of its memetic alleles or rivals—appear to be
partly a function of its relationship to its antece-
bosse (c'est à dire., the form from which it derives). A more
chromatic, rhythmically syncopated consequent
(mutation) of a given antecedent may, up to a cer-
tain degree of variation, be more likely to be imi-
tated than the antecedent itself—although simpler
versions may sometimes be more memorable. Le
element of variation is generally to be found in the
surface elements of the meme, the underlying
structure assuring the sameness of the two pat-
terns. Ainsi, as a general principle, a consequent
mutant meme is essentially the same meme as its
antecedent if the structural level above that which
is modiﬁed remains unaltered.

Although a complete computer-aided empirical
testing of the above hypotheses—and others devel-
oped from the list in the introduction—is beyond
the scope of this article, a preliminary exploration
of them might use two distinct but related method-
ologies, illustrated later in the two case studies us-
ing the Humdrum Toolkit.

The ﬁrst methodology identiﬁes a natural candi-
date pattern and then evaluates its prevalence in a
given idiom or dialect (Meyer 1989, pp. 23–24) ac-
cording to the criterion of ﬁt against the template
pattern. If matches are found, then the pattern is,
by deﬁnition, a meme, existing in the form of sev-
eral copies. It may then be fruitful to modify the

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original template pattern in the light of the original
search to locate other patterns that, while structur-
ally similar to the template, nevertheless manifest
certain evolutionary deviations from it.

The second methodology synthesizes an artiﬁcial
candidate pattern to predict what types of conﬁgu-
rations are likely to attain memetic status. Alors,
attempts are made to locate real instances of the
candidate in a given repertory. As with the ﬁrst
methodology, the hierarchic location and evolu-
tionary proﬁle of such ﬁgures may also be an ele-
ment of the search strategy.

It is well known that issues pertinent to the ﬁrst

hypothesis above were effectively theorized by
members of the Gestalt school of psychology in the
1920s and 1930s. In a reinvigoration of this tradi-
tion, their work informs two avenues of music-
theoretical investigation developed during the last
twenty years. Much of Lehrdahl and Jackendoff
(1983) relies on the insights of Gestalt psychology
for the formulation of metrical and grouping well-
formedness and preference rules. Temperley’s more
recent model (2001) of grouping structure in mu-
sic—a development of the preference-rule method-
ology of Lehrdahl and Jackendoff—also draws on
Gestalt insights but, unlike Lehrdahl and Jacken-
doff, subjects them to empirical testing via com-
puter models.

Perhaps the most comprehensive application of

Gestalt principles to music analysis, cependant, est
Narmour’s implication-realization (hereafter ‘‘i-r’’)
model (1977, 1984, 1989, 1990, 1992, 1999), lequel
draws strongly on the groundwork of Meyer (1956,
1973, 1989). Reviewing Gestalt grouping principles
and categorizing them into innate and acquired
phenomena, Narmour notes that

the separate registral and intervallic aspects of
small intervals . . . are said to be implicatively
governed from the bottom up by the Gestalt
laws of similarity, proximity, and common
direction. . . . [W]hat is important to notice
about the invocation of such Gestalt laws is
(1) that they have been shown to be highly re-
sistant to learning and thus may be innate . . .
(2) unlike the notoriously interpretive, holisti-
cally supersummative, top-down Gestalt laws

of ‘‘good’’ continuation, ‘‘good’’ ﬁgure, et
‘‘best’’ organization . . . the Gestalt laws of
similarité, proximity, and common direction
are measurable, formalizable, and thus open to
empirical testing. (1989, pp. 46–47)

It seems sensible to begin a computerized inves-
tigation of the grouping and ‘‘closural’’ structure of
music with the bottom-up Gestalt principles of
similarité, proximity, and common direction, comme
implemented in the i-r model. The top-down laws
of good continuation, good ﬁgure, and best organi-
zation are less consistent, being culturally condi-
tioned and therefore variable aspects of perception
and cognition. The beneﬁt of these insights to me-
metic research is that we can use the i-r model to
predict what forms memes are likely to take, et
then we can use these criteria to help design com-
puterized search tools to locate them in real musi-
cal contexts—the second pattern-searching
methodology discussed above.

In brief, the i-r model offers a means of assessing

the bottom-up, note-to-note implicative ﬂux of a
passage and identifying its points of procession and
closure at various hierarchical levels. Narmour pro-
poses a number of basic i-r functions, to which he
applies a distinctive terminology and symbology.
His fundamental premise is that, in melodic mo-
tion, an interval of a perfect fourth or smaller mov-
ing in a given registral direction implies a
continuation of similar intervallic magnitude in
the same direction (a phenomenon termed process
and symbolized by ‘‘P’’); whereas an interval of a
perfect ﬁfth or larger moving in a given registral di-
rection implies a continuation of smaller interval-
lic magnitude in the opposite direction (termed
reversal, ‘‘R’’). Most importantly for this study,
these implicative potentials may not be fulﬁlled,
being terminated by durational interference (‘‘d’’),
harmonic interruption (‘‘h’’), or metric (beat) differ-
entiation (‘‘b’’), which serve to deﬁne the bound-
aries of a perceptual/cognitive grouping (Narmour
1989, pp. 45–51; 1990).

Although Narmour’s theory is not universally ac-

cepted, in their evaluation of the predictive power
of the i-r model (using the Humdrum Toolkit as

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their analytic engine), Thompson and Stainton con-
clude that ‘‘a combination of these principles can
predict much of how Bach and Schubert composed
(or ‘realized,’ in Narmour’s terminology) notes fol-
lowing implicative intervals. . . . [C]omposers may
be abiding by some basic rules, learned or innate,
regarding melodic expectancy’’ (1996, p. 33). Si le
results of this and other studies (such as Schellen-
berg 1996) are to be believed, then a Gestalt per-
spective, reﬁned by the precepts of the i-r model,
would appear to be a fundamental element in both
pure and empirical memetic research.

It is worth noting that effective use of the toolkit

in its ‘‘raw’’ state requires a degree of facility with
UNIX that many musicologists without technical
backgrounds are unable or unwilling to devote time
to acquiring. Andreas Kornsta¨ dt’s JRing program
(2001) circumvents this difﬁculty by providing a
graphical front-end to the Humdrum tools which
should increase their accessibility, albeit with the
loss of some ﬂexibility. The investigations de-
scribed below, cependant, use Humdrum in its origi-
nal form.

Overview of the Humdrum Toolkit

The Humdrum Toolkit is a suite of software tools
for UNIX systems. It encapsulates a central UNIX
design philosophy in that, although each of the
over 70 tools is fairly modest in its individual ef-
fects, great analytical sophistication can be
achieved by connecting several tools in pipelines.
The tools can also be incorporated into shell scripts
to facilitate the processing of lengthy pipelines and
expedite large processing tasks.

Beyond the tools themselves, Humdrum provides
a syntax for representing music—that is, a series of
formal conditions that stipulate how music may be
represented in a manner comprehensible by the
tools. The default representation scheme is
‘‘**kern,’’ which provides a means of encoding the
fundamental elements of common-practice West-
ern notation. Essentially, pitches are represented by
their letter names (CC–BB, C–B, (middle) c–b, cc–
bb, etc.), rhythm values are indicated by integers
(‘‘4’’ (cid:2) quarter-note, ‘‘8.’’ (cid:2) dotted eighth-note,
etc.), and parts/voices are organized in spines (tab-
separated columns of data), with leftmost spines
representing lower parts and rightmost representing
upper parts. Each horizontal line of the **kern
score, called a data record, represents a simultane-
ity in the music, being divided into as many data
tokens as there are spines (Figure 3c later in this ar-
ticle shows two bars of music represented in
**kern). More detailed overviews of Humdrum
and the **kern encoding are given in Huron (1997,
2002).

Pattern Searching with Humdrum

In investigating musical memes, two of the Hum-
drum tools have particular signiﬁcance. Le
broadly similar patt and pattern tools, as their
names imply, are pattern-locating utilities. Both
tools search the representation of the music under
investigation using a template that deﬁnes the pat-
tern sought. Templates use UNIX regular expres-
sion syntax to stipulate what the target ﬁle may or
may not contain in order for a positive (c'est à dire., un
match or hit; see Temperley 2001, p. 74) to be reg-
istered.

The chief difference between patt and pattern

is in the latter’s implementation of record-count
metacharacters, c'est à dire., characters that specify how
many records containing a sought pattern may oc-
cur in the target ﬁle for a positive to be registered—
namely one or more (speciﬁed by ‘‘(cid:3)’’), zero or
plus (‘‘*’’), or zero or one (‘‘?’’). Patt does not sup-
port record-count metacharacters, interpreting
them as literals.

A useful feature of patt is its echo option,
which is not supported by pattern. This shows
the results of the search by displaying only those
segments of the **kern score containing the found
pattern. An alternative option is to specify that
patt tag the score under investigation by the in-
sertion of an additional rightmost ‘‘**patt’’ spine,
which places a user-speciﬁed keyword (tel que
‘‘meme’’) at those points in the encoding where the
sought pattern occurs. Pattern, by contrast, sim-
ply outputs a list of line numbers indicating where
the pattern is found, and the researcher must then
peruse the input to locate these occurrences.

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The essence of a successful search using patt or
pattern lies in designing a parsimonious and efﬁ-
cient template. Having provisionally formulated
such a template, it is essential to test it out on pas-
sages—either synthetic examples or extracts taken
from real pieces—in which the sought pattern is
known to exist. This is to verify that the template
will not register a false negative, c'est à dire., will fail to
ﬁnd an instance of the pattern, despite its occurring
in the music. Such a test may also indicate if the
template would record a false positive, c'est à dire., would
register a pattern match for conﬁgurations that the
musician’s judgment would reject as unconvincing.
Given these two potential problem classes, it is un-
wise to begin investigations of real repertories
without such simulations conducted in controlled
and circumscribed conditions.

Meme Hunting with the Humdrum Toolkit:
Principles and Problems

I now describe two case studies that illustrate the
application of Humdrum to some of the theoretical
problems outlined above and exemplify the two
methodologies for computer-aided pattern replica-
tion analysis outlined in the second section.

Case Study 1: The ‘‘Glass Harmonica’’ Pattern

A pattern occurs in mm. 1–2 of Mozart’s Adagio in
C Major for Glass Harmonica, KV 356 (617un) depuis
1791, that is essentially a chromatically altered
interrupted cadence. We might hypothesize that
ﬁgures such as this derive from evolutionarily sim-
pler forms—those outlining a diatonic interrupted
cadence and, finalement, those outlining a perfect
cadence (with or without a terminal 4ˆ –3ˆ appoggia-
tura)—such as are represented in Figure 2.

This distinctive ﬁgure seems a good starting

point for a study following the ﬁrst pattern-
searching methodology, and it might well be a
meme in the non-trivial (‘‘strong’’) sense of having
been propagated within the dialect of the European
late 18th century. (The trivial—‘‘weak’’—sense as-
cribes memetic status to it on the grounds that the

pattern is replicated in contemporary musical cul-
ture in the minds of present-day listeners to the
Adagio.)

My segmentation of the music is based on the
fact that, as well as exemplifying a clear melodic
processus, the ﬁgure clearly satisﬁes all three of Nar-
mour’s criteria for closure (c'est à dire., termination of im-
plicative potential). D'abord, in Figure 3a, the left-hand
dotted half-note in m. 2 creates durational interfer-
ence; second, the unit is harmonically interrupted
owing to the resolution of the vii7/vi in the fourth
beat of m. 1 to vi in the ﬁrst beat of m. 2; and ﬁ-
enfin, the rest in the right hand in m. 2 effects met-
ric (beat) differentiation. This segmentation also
satisﬁes Temperley’s ‘‘PSPR 1 (Gap Rule)’’ and
‘‘PSPR 3 (Metrical Parallelism Rule)’’ (2001, pp. 68–
71), the latter on account of the recurrence of the
unit in the same metrical position at mm. 5, 21,
et 25.

Chiffre 3 shows three representations of these
measures, the ﬁrst a score with an overlaid i-r anal-
ysis, the second a voice-leading reduction showing
foreground and shallow-middleground elements (à
which I shall return later), and the third a **kern
encoding.

When designing a template to search for the
‘‘Glass Harmonica’’ pattern, we begin with the
premise that it is likely to be independent of key,
and therefore the search process must be conducted
in terms of scale degree and not absolute pitch. Le
repertoire under investigation must be converted
à, and the template conceived in terms of, le
Humdrum ‘‘**deg’’ representation. The encoding
in Figure 3c appears as in Figure 4 when converted
to **deg, in which all rhythmic information is re-
moved (numbers being used instead to indicate
scale degrees) and in which ‘‘(cid:3)’’ and ‘‘(cid:4)’’ indicate
chromatically raised and lowered versions, respecter-
tivement, of the diatonic pitch. En plus, data are
propagated downwards into null (vide) tokens to
indicate the effect of the ditto command.

Having arrived at a **deg version of the pattern,
a patt template suitable for locating the conﬁgura-
tion shown in Figure 4, which might be stored as a
ﬁle called glass.patt, may be extrapolated from
it, as shown in Figure 5.

This template would only locate examples of the

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Chiffre 2. (un) Diatonic per-
fect cadence in Mozart,
Clarinet Quintet in A Ma-
jor, KV 581 (1789), III,
mm. 1–8; (b) Diatonic in-

terrupted cadence in Mo-
zart, Divertimento in F
Major, KV 138 (125c;1772),
II, mm. 1–3.

(un)

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pattern in the tonic key, unless they occurred in a
passage whose departure from the tonic was so ex-
tensive or signiﬁcant as to warrant a new key tan-
dem interpretation (par exemple., ‘‘*G:’’) indicating the
changed tonal center (and therefore the status of
the new local tonic note as 1ˆ , as far as deg is con-
cerned). To locate examples in the dominant key—
the most probable other key in which the pattern
might occur—then an analogous ‘‘transposed’’ tem-
plate would have to be employed.

For ease of use, the commands that implement

this search may be placed in a shell script,
memeﬁnder1.ksh. The script is available online at
mitpress2.mit.edu/e-journals/Computer-Music-
Journal/memeﬁnder.tgz. If this archive is not ex-
panded automatically, the Unix command tar

xzvf memeﬁnder.tgz will extract its contents.
Memeﬁnder1.ksh repeats its operations on all
.krn ﬁles in the current directory, rendering it
suitable for searches of a large repertory. The ﬁnd-
ings are successively appended to a single memere-
sults ﬁle that may be inspected by the researcher
after processing is completed. The operation of the
script is summarized in Figure 6.

In conducting a search for the pattern it seems
reasonable to restrict an initial investigation to Vi-
ennese music of the late 18th century. It was de-
cided to use those string quartets of Haydn and
Mozart that are publicly available from the
CCARH Muse Data Web site (www.musedata.org),
which contains the vast majority of Haydn’s quar-
tets (apart from some of the early works) and all of

Computer Music Journal

Chiffre 3. Three representa-
tions of Mozart, Adagio in
C Major for Glass Har-
monica, KV 356 (617un;
1791), mm. 1–2.

(un) Implication-
Realization Analysis;
(b) Voice-Leading Reduc-
tion; (c) **Kern Encoding.

(un)

(b)

(c)

Mozart’s quartets, together with a small selection
of various other chamber works of Mozart.

A patt search using memeﬁnder1.ksh and the
template glass.patt produced the results shown
in Table 1.

The examples from Mozart’s KV 298 and KV 478

are the most salient, being clearly demarcated by
durational interference, harmonic interruption, et
metric (beat) differentiation. The passages from
Mozart’s KV 458 and Haydn’s Op. 71, Non. 1 sont, par
contraste, relatively open, ‘‘processive’’ tonicizations
of vi in the context of larger descending I–vi–IV se-
quences (possibly itself memetic) and lack the de-
marcation engendered by Narmour’s three closural
criteria. Our musical judgment might be inclined
to reject these latter examples for not representing
clear examples of the pattern. As for its ‘‘strong’’
memetic status, we might reserve judgment on the
‘‘Glass Harmonica’’ pattern at this stage, insisting

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Chiffre 4. The **deg ver-
sion of Figure 3c.

Chiffre 5. The glass.patt
template for the ‘‘Glass
Harmonica’’ pattern.

The template shown in Figure 7, glass.pattern,

is designed to ﬁnd versions of the pattern that, al-
though broadly based on the middleground struc-
ture shown in Figure 3b, synchronize the two
component linear strata in various ways. Un
might in particular speculate on a possible variable
alignment of the upper-voice 4ˆ against its support-
ing harmony, or the omission of the diatonic lower-
voice 5ˆ ; both seem likely evolutionary alterations.
The use of record-count metacharacters in the tem-
plate—essential to account for these two scenar-
ios—necessitates the use of pattern as the search
tool.

If such a pattern template is derived from a
patt template to account for unpredictable surface
elaborations of an underlying structure, then it will
lose some of the precision of the patt template
owing to its use of record-count metacharacters to
account for the unknown extra elements—the dim-
inutions that are symptomatic of memetic evolu-
tionary change. Although Humdrum pattern
searches are in principle suitable for locating stable
middleground patterns beneath a changing fore-
ground, such searches inevitably increase the
chance of producing false positives. By this, we are
referring to patterns that, although perhaps appear-
ing to be descended from the antecedent at the
foreground level, do not correspond at the middle-
ground level, and are therefore—according to the
rule given under point 3 in the second section—not
consequents of the given antecedent. As may be
seen by comparing Figure 5 with Figure 7, all but
the ﬁrst line of the pattern template contain vari-
ously the ‘‘(cid:3),’’ ‘‘*,’’ and ‘‘?’’ symbols or the Bool-

that a copy be found in the work of another com-
poser, thus implying connection in a nexus of imi-
tation.

As noted earlier, after a preliminary search based
on the conﬁguration of a candidate pattern, it may
be instructive to revisit the search template and
consider ways of modifying it to account for vari-
ants that are derived from the antecedent form dur-
ing the course of a diachronic-evolutionary process.
As mentioned, it might be hypothesized—accord-
ing to the rule given under point 3 in the second
section of this article—that such variants will re-
tain the shallow-middleground-level structure of
the meme (Figure 3b) but will manifest a degree of
variability in the foreground-level patterning that
generates that middleground structure. Such vari-
ability of surface patterning might, par exemple, af-
fect the rhythmic synchronization of components
of the pattern.

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Chiffre 6. Flowchart illus-
trating the operation of
Memeﬁnder1.ksh.

Tableau 1. Search Results (je) for the ‘‘Glass Harmonica’’ Pattern

Haydn

String Quartet in B-Flat major, Op. 71, Non. 1 (1793), III

Mozart

Flute Quartet in A major, KV 298 (1778/1786?), II
String Quartet in B-Flat major KV 458 (‘‘Hunt’’; 1784), II
Piano Quartet in G minor KV 478 (1785), II

Pattern found in

mm. 37–38

Pattern found in

mm. 5–6
mm. 4–5; 24–25
mm. 1–2

ean OR operator (‘‘|’’). Clairement, any modiﬁer that
allows for a multiplicity of often very loosely de-
ﬁned elements, the absence of an element, or ‘‘al-
ternativity’’ between elements, will tend to register
as positives a great variety of middleground struc-
photos.

Humdrum ultimately cannot ‘‘know’’ the

structural-hierarchic location of a given pitch (à
my knowledge, no software yet available can per-
form Schenkerian analysis); patt and pattern do
not have the higher-order algorithms necessary for
this task. This type of complex determination,
which often vexes seasoned Schenkerians, must be
the task of the researcher. Cependant, given that
middleground elements often have greater metrical
(accentual) and durational (agogic) weight than ele-
ments at the foreground level, then searches may
be adjusted to account for these factors. The posi-

tion of the bar line—which often directly precedes
a structurally important pitch—can easily be fac-
tored into a search template. For this reason, le
template shown in Figure 7 adds barline signiﬁers
(‘‘^(cid:2)’’) before ‘‘^1.*5$’’ and before ‘‘^6.*4$’’ be-
cause these elements are markers of pitches inter-
preted, in Figure 3b, as having middleground status.
Nevertheless, the second of these components of

the template is qualiﬁed by a metacharacter in
such a way as to make its presence non-obligatory.
Glass.pattern deliberately casts the net widely,
yet this lack of precision has its advantages: le
template registers a positive for the decorated and
syncopated version of the pattern in mm. 25–26 of
Mozart’s Adagio that glass.patt cannot detect.
Owing to this attribute, and because a middle-
ground 3ˆ /vi may not necessarily directly follow a
bar line, use of this template necessitates a subse-

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Chiffre 7. Le
glass.pattern template
for the ‘‘Glass Harmonica’’
pattern.

of the pattern, from the opening of the slow move-
ment of Haydn’s String Quartet in F major, Op. 74,
Non. 2. Given the distinct instances of the pattern
in Mozart’s KV 298, 478, et 356 (617un), and in this
work of Haydn’s, we are now justiﬁed in regarding
it as a meme in the ‘‘strong’’ sense, for it is a par-
ticulate unit that would appear to have been trans-
mitted (spontaneous generation aside) by imitation
from Mozart to Haydn (or to Haydn by means of
some other nexus of imitation).

The passage from Haydn’s Op. 74, Non. 2 dem-

onstrates the attributes mentioned above in
connection with likely evolutionary variants of
the pattern (c'est à dire., variable alignment of the upper-
voice 4ˆ against its supporting harmony and omis-
sion of the diatonic lower-voice 5ˆ ). In ﬁnding a
passage that glass.patt missed but which our
musical judgment tells us is a clear example of the
unit, glass.pattern appears to strike an appro-
priate balance between an overly narrow and an
overly broad speciﬁcation of the sought conﬁgura-
tion.

Case Study 2: The ‘‘I-R Process’’ Pattern

To begin, one must devise a musical pattern that
contains some combination of realized and/or de-
nied implications and satisﬁes one or more of Nar-
mour’s criteria for closure. Chiffre 8 shows a
suitable pattern.

This simple shape (which may exist, as indicated
by the permutation slashes [‘‘/’’] in the example, dans
a variety of chromatic and rhythmic forms) is de-
marcated before its initial pitch and closed after its
terminal pitch by rests, which enforce closure by

quent manual interpretation of the results. Ulti-
mately, in making such judgments, one is treading
the ﬁne line between false positives and false nega-
tives: sifting and eliminating false positives arising
from a less-discriminating template makes more
effort for the researcher (undermining, to some de-
gré, the beneﬁts of computer-assisted investiga-
tion); cependant, false negatives are more serious,
compromising the integrity of a set of results.

Using this revised template, glass.pattern, un
pattern search using memeﬁnder1.ksh (Chiffre 6)
produced the results shown in Table 2.

The second search found an additional example

Tableau 2. Search Results (II) for the ‘‘Glass Harmonica’’ Pattern

Haydn

String Quartet in B-Flat major, Op. 71, Non. 1 (1793), III
String Quartet in F major, Op. 74, Non. 2 (1793), II

Mozart

Flute Quartet in A major, KV 298 (1778/1786?), II
String Quartet in B-Flat major, KV 458 (‘‘Hunt’’) (1784), II
Piano Quartet in G minor, KV 478 (1785), II

Pattern found in

mm. 37–38
mm. 1–2; 5–6; 75–76

Pattern found in

mm. 5–6
mm. 4–5; 24–25
mm. 1–2

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Chiffre 8. Candidate pat-
tern.

metric (beat) differentiation, establishing it as a dis-
crete perceptual/cognitive unit. As a rising scale
pattern, it exempliﬁes Narmour’s notion of process,
the implication of the initial motion c–d(ﬂat) être
realized by continuation of the ascent to e(ﬂat) et
then f(sharp). Further continuation to g is sup-
pressed owing to the durational interference of the
dotted quarter-note (or longer) F(sharp) and/or the
metric (beat) differentiation of the rest, which neu-
tralizes the implicative charge and closes the
grouping. Clairement, the pattern is not as distinctive
or salient as that of Figure 3—it is a ‘‘commonal-
ity’’ on Cope’s continuum—but its closural attrib-
utes nevertheless allow it to exist as a meme.

It is most efﬁcient to conceive this ‘‘I-R Process’’

pattern in terms of its intervallic structure and (comme
indicated by the permutations in Figure 8) to allow
for a variable sequence of major and minor seconds,
so the pattern essentially represents a tetrachord
starting on any degree of the diatonic or chromatic
scale. One could specify more accurately its inter-
vallic structure, but for present purposes, a wide
variety of conﬁgurations will be accommodated;
plus tard, ﬁner distinctions will be made. In conceiving
a template, it is again necessary to convert the mu-
sical information to a representation independent
of absolute pitch: most parsimonious would be to
use the melodic interval or ‘‘**mint’’ representa-
tion, which indicates the direction of motion (‘‘(cid:3)’’
(cid:2) en haut, ‘‘(cid:4)’’ (cid:2) down), interval category (‘‘M’’ for ma-
jor, ‘‘m’’ for minor, etc.), and interval size of a me-
lodic progression. Chiffre 9 shows the pattern in
both **kern and **mint representations.

An appropriate template ﬁle must contain regu-

lar expressions capable of identifying patterns in
which the terminal pitch is a quarter note or longer
followed by a rest. Without this capacity, motifs
that terminate on note values shorter than a quar-
ter note and/or with no terminal rest—and which

are therefore not, in Narmour’s view, closed by
durational interference and/or metric (beat) differ-
entiation—will also be recorded as positives. Sur
the basis of our working hypothesis, such patterns
may not have sufﬁcient end-closure for indepen-
dent memetic existence.

To ﬁnd patterns that match the sought interval-
lic criteria and closural properties, it is necessary to
use the Humdrum assemble tool vertically to
align the original **kern spine against the derived
**mint spine (the result resembling Figure 9), et
then to devise a template that can distinguish be-
tween the presence of integers in the **kern spine
(which signify rhythmic values) and integers in the
**mint spine (which signify intervallic steps).

A suitable template, i-r_process.pattern, est

shown in Figure 10. In the penultimate line, it
speciﬁes that the ﬁrst ‘‘4,’’ ‘‘4.,’’ ‘‘2,’’ or ‘‘2.’’ to be
encountered must be followed directly by a pitch.
C'est, it must be only a **kern quarter note,
dotted quarter-note, half-note, or dotted half-note
and not, donc, a **mint intervallic signiﬁer,
the desired values of which are speciﬁed at the end
of this line by ‘‘((\(cid:3)M2)|(\(cid:3)m2)).’’ For this
recherche, pattern must be used, because record-
count metacharacters are employed in several lines
of the template, including ‘‘*’’ in lines 2, 4, 6, et 8
to account for the presence of any null data tokens
interspersed between **mint signiﬁers. These, dans
this context, would indicate the presence in other
spines of rhythmic values shorter than those of the
sought pattern.

As with the ﬁrst case study, the pertinent com-

mands may be placed in a shell script,
memeﬁnder2.ksh (also available at mit-
press2.mit.edu/e-journals/Computer-Music-Journal/
memeﬁnder.tgz), a variant of memeﬁnder1.ksh
(voir la figure 6). Unlike memeﬁnder1.ksh, cependant,
this script extracts each spine of the input ﬁle in
turn and subjects it individually to the actions of
pattern to ensure that the sought pattern exists
within a single spine and is not spread ‘‘diagonally’’
across two or more parts. The operation of the
script is summarized in Figure 11.

Using the same repertoire as that employed for
the ﬁrst case study, a pattern search using meme-
ﬁnder2.ksh and the i-r_process.pattern tem-
plate produced the results shown in Table 3. À

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Chiffre 9. **kern and
**mint encodings of the
‘‘I-R Process’’ pattern in
Chiffre 8. (un) **kern
encoding; (b) **mint
encoding.

(un)

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distinguish between the various forms of this ﬁgure
(which the i-r_process.pattern template spe-
ciﬁcally did not), values in square brackets after bar
numbers indicate the internal interval classes of
the particular pattern, the careted superscript be-
fore these indicating its starting scale degree.

Ignoring rhythmic factors for present purposes,
all intervallic variants of this pattern appear to be
memes in the ‘‘strong’’ sense. Every type found in
the Haydn movement also occurs in the three Mo-
zart examples, suggesting their connection in a
nexus of imitation—albeit a very broad one, given
that this is such a basic ﬁgure, and one surely not
restricted to Haydn and Mozart. Correlating this
observation with initial scale degree, we see that
7ˆ1–2–2 and 5ˆ2–2–1 are common patterns in this
sample. Nevertheless, there is clearly insufﬁcient
evidence to extrapolate wider conclusions about

the prevalence of this pattern and its variants in
the dialect as a whole, given the small size of the
results group and the distorting effect of intra-work
repetition. De plus, one should perhaps be careful
not to make too much of such ﬁne structural dis-
tinctions, owing to the limited number of conﬁgu-
rations available within the diatonic tetrachord, un
function of the intervallic characteristics of the
major and minor modes.

Conclusion: Prospects

It seems clear that there is much to commend the
use of the Humdrum Toolkit in developing a the-
ory of memetics. The following conclusions can be
drawn from the above investigations. D'abord, a theory
of musical memetics will be complex and multifac-

Computer Music Journal

Chiffre 10. Le
i-r_process.pattern
template.

Chiffre 11. Flow chart illus-
trating the operation of
Memeﬁnder2.ksh.

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Chiffre 11

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Tableau 3. Search Results for the ‘‘I-R Process’’ Pattern

Haydn

Pattern found in

String Quartet in F-Sharp minor, Op. 50, Non. 4 (1787), je

mm. 5 [1ˆ2–2–1; 3ˆ2–1–2], 15 [7ˆ1–2–2], 120 ((cid:2) m. 5) [1ˆ2–2–1;

Mozart

String Quartet in F major, KV 158 (1773), III
String Quartet in A major, KV 464 (1785), IV
String Quartet in D major KV 575 (1789), je

3ˆ2–1–2]

Pattern found in

mm. 28 [5ˆ2–2–1], 29 [7ˆ1–2–2]
m. 4 [2ˆ2–1–2]
mm. 6 [7ˆ1–2–2; 5ˆ2–2–1], 14 [7ˆ1–2–2; 5ˆ2–2–1], 122 ((cid:2) m. 6)

[7ˆ1–2–2; 5ˆ2–2–1], 130 ((cid:2) m. 14) [7ˆ1–2–2; 5ˆ2–2–1]

eted, requiring for its formulation both synchronic-
structural and diachronic-evolutionary
perspectives. Computers offer sophisticated means
of facilitating research in both dimensions.

Deuxième, one of the central problems in develop-
ing a theory of musical memetics is the necessity
to formulate a robust, psychologically valid model
of pattern perception. Narmour’s i-r model, et le
Gestalt principles upon which it is based, are argu-
ably the best candidates at present.

Troisième, two useful strategies for verifying the me-
metic status of candidate patterns are 1) to identify
a natural candidate pattern and then evaluate its
prevalence in a given repertory; et 2) to synthe-
size an artiﬁcial candidate pattern using Gestalt/i-r
principles and then attempt to locate real instances
of it in a given repertory.

Fourth, the Humdrum Toolkit’s patt and pat-
tern utilities are powerful tools for searching rep-
resentations of musical information and locating
memes and are amenable to both the above strate-
gies. The regular expression syntax they implement
is well suited to memetic investigations on ac-
count of its ﬂexibility and precision.

Enfin, the results of such searches may be used
both qualitatively and quantitatively. C'est, ils
can foster analytical and critical discussion of spe-
ciﬁc musical works and the memes they contain,
and they can facilitate statistical evaluation of the
frequency and distribution of memes within idioms
and dialects.

I hope to have shown that it is in the nature of
computer-aided research that, perhaps more impor-
tant than making a complex task more managea-

ble, the highly structured approach required by the
enterprise forces the researcher to interrogate as-
sumptions, to rethink methodologies, and to reﬁne
the hypotheses upon which the investigation is
based. In considering the prospects for this re-
recherche, three issues in particular deserve mention.

The Geographical Distribution of Memes and the
Generic Mapping Tools

The second part of the last point above suggests
that memes might be tracked as they spread geo-
graphically. A mechanism for implementing this
already exists, pour, as described in Aarden and Hu-
ron (2001), Humdrum can be integrated with Wes-
sel’s and Smith’s Generic Mapping Tools (available
online at gmt.soest.hawaii.edu). This linkage
might, in theory, permit the detailed memetic pro-
ﬁling of musical styles, allowing their transmission
and evolution over time to be charted.

The Humdrum Simil Tool

As suggested earlier, the ‘‘Glass Harmonica’’ meme
might be regarded as a mutation of a normative di-
atonic V–I or, less modiﬁed, a V–vi progression (figue-
ure 2). The concept of mutation can usefully be
described in terms of the notion of edit-distance,
c'est, the number of changes (additions, deletions,
and substitutions) required to move from the ante-
cedent to the consequent form. This scale, le
Damerau-Levenshtein edit distance metric, has al-

Computer Music Journal

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ready been implemented by Keith Orpen in the
Humdrum simil tool (Orpen and Huron 1992) et
may prove useful in memetic research.

Investigating the Hierarchic Location of Memes

A third development—touched upon in the ﬁrst
case study—would be to search for patterns at
deeper levels of structure. The patterns examined
here have been short ﬁgures of foreground orienta-
tion based on simple shallow-middleground-level
frameworks. The use of record-count metacharac-
ters with pattern facilitates the identiﬁcation of
more distributed, ‘‘virtual’’ conﬁgurations that, si
replicated, can still be regarded as memetic.

Remerciements

I am grateful to Michael Clarke for his constructive
comments on an earlier version of this article and
to the two anonymous reviewers who suggested
further improvements.

Les références

Aarden, B., and D. Huron. 2001. ‘‘Mapping European

Folksong: Geographical Localization of Musical Fea-
tures.’’ Computing in Musicology 12:169–183.

Blackmore, S. J.. 1999. The Meme Machine. Oxford: Ox-

ford University Press.

Cope, D. 2003. ‘‘Computer Analysis of Musical Allu-

sions.’’ Computer Music Journal 27(1):11–28.

Dawkins, R.. 1989. The Selﬁsh Gene, 2nd ed. Oxford: Ox-

ford University Press.

Gjerdingen, R.. Ô. 1988. A Classic Turn of Phrase: Music
and the Psychology of Convention. Philadelphia: Uni-
versity of Pennsylvania Press.

Huron, D. 1997. ‘‘Humdrum and Kern: Selective Feature
Encoding.’’ In E. Selfridge-Field, éd. Beyond MIDI: Le
Handbook of Musical Codes. Cambridge, Massachu-
setts: AVEC Presse, pp. 375–401.

Huron, D. 2002. ‘‘Music Information Processing Using

the Humdrum Toolkit: Concepts, Examples, and Les-
sons.’’ Computer Music Journal 26(2):11–26.

Jan, S. 2000un. ‘‘Replicating Sonorities: Towards a Memet-

ics of Music.’’ Journal of Memetics—Evolutionary

Models of Information Transmission 4(1). Available
online at jom-emit.cfpm.org/2000/vol4/jan_s.html.
Jan, S. 2000b. ‘‘The Memetics of Music and Its Implica-

tions for Psychology.’’ In J. Sloboda et al., éd.. Proceed-
ings of the Sixth International Conference on Music
Perception and Cognition. Keele, ROYAUME-UNI: Université de
Keele Department of Psychology.

Jan, S. 2002. ‘‘The Selﬁsh Meme: Particularity, Replica-
tion, and Evolution in Musical Style.’’ International
Journal of Musicology 8:9–76.

Jan, S. 2003. ‘‘The Evolution of a ‘Memeplex’ in Late Mo-

zart: Replicated Structures in Pamina’s ‘Ach ich
fu¨ hl’s.’ ’’ Journal of the Royal Musical Association
128(2):330–370.

Kornsta¨ dt, UN. 2001. ‘‘The JRing System for Computer-

Assisted Musicological Analysis.’’ Proceedings of the
Second Annual International Symposium on Music
Information Retrieval. Bloomington: Indiana Univer-
sity Press, pp. 93–98.

Lerdahl, F., et R. Jackendoff. 1983. A Generative The-
ory of Tonal Music. Cambridge, Massachusetts: AVEC
Presse.

Meyer, L. B. 1956. Emotion and Meaning in Music. Chi-

cago: University of Chicago Press.

Meyer, L. B. 1973. Explaining Music: Essays and Explora-

tion. Chicago: University of Chicago Press.

Meyer, L. B. 1989. Style and Music: Theory, Histoire, et
Ideology. Philadelphia: University of Pennsylvania
Presse.

Narmour, E. 1977. Beyond Schenkerism: The Need for

Alternatives in Music Analysis. Chicago: Université de
Chicago Press.

Narmour, E. 1984. ‘‘Toward an Analytical Symbology:

The Melodic, Harmonic, and Durational Functions of
Implication and Realization.’’ In M. Baroni and L. Cal-
legari, éd.. Musical Grammars and Computer Analy-
sis: Atti del Convegno. Florence: Olschki, pp. 83–114.
Narmour, E. 1989. ‘‘The ‘Genetic Code’ of Melody: Cog-

nitive Structures Generated by the Implication-
Realization Model.’’ In S. McAdams and I. Delie` ge,
éd.. Music and The Cognitive Sciences. Londres: Har-
wood, pp. 45–63.

Narmour, E. 1990. The Analysis and Cognition of Basic
Melodic Structures: The Implication-Realization
Model. Chicago: University of Chicago Press.

Narmour, E. 1992. The Analysis and Cognition of Me-

lodic Complexity: The Implication-Realization Model.
Chicago: University of Chicago Press.

Narmour, E. 1999. ‘‘Hierarchical Expectation and Musi-
cal Style.’’ In D. Deutsch, éd. The Psychology of Mu-
sic, 2nd ed. San Diego, California: Academic Press, pp.
441–472.

Jan

D
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o
un
d
e
d

F
r
o
m
h

t
t

:
/
/

d
je
r
e
c
t
.

je
t
.

e
d
toi
/
c
o
m

j
/

un
r
t
je
c
e
–
p
d

F
/

2
8
4
6
8
1
8
5
4
2
2
3
0
1
4
8
9
2
6
0
4
2
7
2
8
4
0
3
p
d

b
oui
g
toi
e
s
t

o
n
0
8
S
e
p
e
m
b
e
r
2
0
2
3

Orpen, K. S., and D. Huron. 1992. ‘‘Measurement of Sim-
ilarity in Music: A Quantitative Approach for Non-
Parametric Representations.’’ Computers in Music
Research 4:1–44.

Plotkin, H. 1995. Darwin Machines and the Nature of

Knowledge: Concerning Adaptations, Instinct and the
Evolution of Intelligence. Londres: Manchot.

Schellenberg, E. G. 1996. ‘‘Expectancy in Melody: Tests

of the Implication-Realization Model.’’ Cognition
58:75–125.

Temperley, D. 2001. The Cognition of Basic Musical
Structures. Cambridge, Massachusetts: AVEC Presse.
Thompson, W. F., and M. Stainton. 1996. ‘‘Using Hum-

drum to Analyze Melodic Structure: An Assessment of
Narmour’s Implication-Realization Model.’’ Comput-
ing in Musicology 10:24–33.

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