DOI: 10.1111/j.1468-2249.2012.00344.x
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MEYER’S ANVIL: REVISITING
THE
SCHEMA CONCEPT
[U]t ceteras artis, experientia docuit.
[E]xperience has taught this as it has all other arts.
– Tacitus, Histories, V.6, (109 A.D.)
Experientia does it – as papa used to say.
– Charles Dickens, David Copperfield (1850)
Origins: Meyer’s Anvil
The entire research output of Leonard Meyer may be summarised by an age-old
Latin proverb: ‘Experientia docet’. In the dissertation that later became Meyer’s
first and highly influential monograph, Emotion and Meaning in Music (1956),
musical knowledge – whether conceived in its compositional, listening or performative dimensions – is said to derive from one’s transactional encounter with
music as a fundamentally cultural product. There, Meyer attributed the ‘life
stream of musical perception and communication’ to the intersubjective category
of ‘habit responses’ (1956, p. 62) – a term widely used in philosophical and
psychological circles during the first half of the twentieth century, and increasingly in the decade after the Second World War, when Meyer was writing Emotion
and Meaning in Music at the University of Chicago under the auspices of its
Committee on the History of Culture.1
Habit responses, as the very essence of musical knowledge, are learned ‘online’ – that is, directly from one’s socially conditioned experience with music:
Musical meaning and significance, like other kinds of significant gestures and
symbols, arise out of and presuppose the social processes of experience which
constitute the musical universes of discourse ... . The response to music as well as
its perception depend [sic] upon learned habit responses ... . These dispositions
and habits are learned by constant practice in listening and performing ... .
Understanding music is not a matter of dictionary definitions, of knowing this,
that, or the other rule of musical syntax and grammar, rather it is a matter of
habits correctly acquired in one’s self and properly presumed ... in others. (Meyer
1956, pp. 60–2)
These predications from the 1950s mark the earliest occasions of a lifelong
research programme that argued unswervingly for the cultural and historical
determinacy of musical structure, style and cognition (Meyer 1956, 1967
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Fig. 1 The development of the schema concept in Meyer’s writings, 1956–89
[1994], 1973, 1980, 1989 and 2000). To be sure, Meyer’s several monographs
and articles may exhibit distinctive foci at the surface: meaning and affect in
Emotion and Meaning in Music; communication, information theory and art
reception in Music, the Arts, and Ideas (1967); analysis and criticism in Explaining
Music (1973); and style change and its motivations in Style and Music (1989).
And yet, each argument was built on the same foundation. In a manner of
speaking, all of Meyer’s works were forged on the same ‘anvil’. Throughout his
writings, ‘habits’, ‘habit responses’, ‘behaviors’ and the highly replicated style
forms that give rise to these habits (such as ‘ideal types’, ‘norms’, ‘classes’, ‘class
concepts’ and ‘class patterns’) – these categories and their sociocultural resonances all gradually came to be represented by a single predicate: ‘schema’.
Fig. 1 graphically illustrates this development by tracing Meyer’s usage of
several terms over the course of three decades, from 1956 to 1989. It shows,
among other things, the gradual replacement of ‘habit’ or ‘habit responses’ by the
term ‘schema’ or ‘schemata’. Whereas ‘habit’ and ‘schema’ occur 59 and 0 times,
respectively, in Emotion and Meaning in Music, the relationship is largely reversed
by 1989, with respective occurrences of 15 and 84 in Meyer’s magnum opus,
Style and Music.2 ‘Schema’ eventually subsumed every other category and its
meaning both quantitatively and qualitatively, as seen in Fig. 1.3 The lexical
variations abstracted in the figure illustrate not a change in research agenda but
rather something of a groping for the proper terminology to express an invariant
idea – namely, that historically and socially affected experience is the basis of
applied musical knowledge. Notice the similarity of the following argument from
Style and Music to that above from Emotion and Meaning in Music:
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[W]e perceive and pattern the world ... in terms of ingrained habits
[that] ... affect our understanding of and response to human behavior, including
works of art ... . [K]nowledge of style is ‘tacit’: that is, a matter of habits properly
acquired (internalized) and appropriately brought into play ... . [A]n experienced
listener brings into play the stylistically appropriate habit responses ... that make
sensitive understanding possible. (1989, pp. 5, 10, 83)
This underlying theme or foundation of Meyer’s work – that is, Meyer’s anvil –
is what might be called the ‘schema concept’.
In the course of elaborating the concept, while refining his terminology, Meyer
moved from the markedly reflective nature of his earlier writings to a more
explicitly analytic orientation. Emotion and Meaning in Music was, in essence, a
philosophical treatise, an interdisciplinary meditation on the procedural basis of
musical knowledge – a style of exposition which he largely sustained in Music, the
Arts, and Ideas. It was only with Explaining Music (1973), and in a series of later
articles subsequently reprinted in The Spheres of Music (2000), that his work
engaged the kind of declarative knowledge encountered in more ‘traditional’
strains of music theory. Although this change in orientation was also accompanied by a change in vocabulary,4 the concrete theoretical categories Meyer
advanced in his later writings were extensions of the habit-response epistemology
of the 1950s and the evolving schema concept that permeates each of his
writings. Style and Music was both a culmination and a synthesis of Meyer’s two
research phases, philosophical and analytical, represented by changes in terminology around 1973: although ‘schema’ dominates by 1989, important terms
from the earlier philosophical treatises return in a more balanced equation,
indicating that the later analytical categories were attempts to objectify procedural musical knowledge (shaped by cultural context) in declarative form (see
again Fig. 1).
The most familiar among Meyer’s analytic contributions to the discipline is a
series of so-called changing-note schemata – scale-degree configurations based
on a I–V, V–I harmonic progression that feature characteristic scale-degree
‘rhymes’ in the top voice – e.g. 1–7, 4–3; 1–7, 2–1; and 3–2, 4–3. The first of
these is perhaps the most well-known among the changing-note paradigms,
having become the focal object of Robert Gjerdingen’s A Classic Turn of Phrase
(1988), and later renamed the Meyer in Gjerdingen’s Music in the Galant Style
(2007).The pattern (Ex. 1a), featured in the oft-cited opening to Mozart’s Piano
Sonata in G major, K. 283, consists of a tightly knit pair of sub-phrases that
express a metrically segmented tonic–dominant, dominant–tonic parallelism,
articulated by the 1–7, 4–3 rhyme in the top voice – the structure’s most
characteristic feature. Meyer viewed patterns such as the 1–7, 4–3 not merely as
theoretical categories, however; rather, schemata were deemed socially ‘ingrained
habits’, categories of mind fundamentally shaped by the mind’s interaction with
a particular cultural environment. Meyer saw in these style forms the holistic
convergence of history, culture and cognition – documentations of the ‘culturally
qualified behavior of human beings in specific historical/cultural circumstances’
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Ex. 1 (a) Wolfgang Amadeus Mozart, Piano Sonata in G major, K. 283, first
movement, Allegro, bars 1–4 (1774): the 1–7, 4–3 schema (after Meyer 1980)
Ex. 1 (b) The 1–7, 4–3 schema: abstract representation (from Gjerdingen 1988,
p. 64)
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Fig. 2 Historical population distribution of the 1–7, 4–3 schema (from Gjerdingen
1988)
50
45
40
35
30
25
20
15
10
5
0
1720
1740
1760
1780
1800
1820
1840
1860
1880
1900
(1989, p. x).5 The analytic objectification of ‘habits’ and ‘behaviors’ in
Meyer’s later writings provided the cornerstone for a listener-orientated music
theory in which music analysis became synonymous with the explication of a
situated psychology of hearing, one predicated on the ‘social processes of
experience’.
This theory was extended in important directions by Gjerdingen’s galant style
project – a product of the Penn School (Juslin and Sloboda 2010, p. 586; and
Gjerdingen 2002, p. 976, and 2010, pp. 61–3), and therefore similarly forged on
Meyer’s anvil. In its first instalment, A Classic Turn of Phrase,6 analysis of a
sizeable corpus brought statistical evidence illustrating the historical situatedness
of the 1–7, 4–3 as a style form. Fig. 2 graphs the distribution of the schema
across nearly two centuries, from 1720 to 1900. Usage of the Meyer peaked
sharply in the 1770s, with a period of generally increased activity between 1760
and 1790. The pattern, it turns out, followed a ‘life cycle’, seen in the schema’s
‘historical outline’, which ‘approximates a normal distribution’ (Gjerdingen
1988, pp. 100 and 262).7 This research brought statistical evidence suggesting
that, as categories of mind, schemata may configure a situated psychology of
listening because the musical patterns themselves are historically limited. In
other words, it advanced further evidence for the historical dimension of Meyer’s
‘social processes of experience’ and of the ‘stylistic appropriate[ness]’ of ‘habit
responses’.8 The second instalment, Music in the Galant Style, demonstrated that
such highly stereotyped musical phrases as the 1–7, 4–3 were widespread in the
eighteenth century and therefore characterise an entire galant culture of ‘schematic music-compositional thought’ (2007, p. 397). This more recent research
programme also perpetuated Meyer’s contention (1989) that musical structure,
style and processes are in themselves a reflection and symptomatic of a broader
social fabric and its underlying ideologies. Galant schemata are but another
individuation of the general custom of ‘artfully modulat[ing] all [of one’s] social
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... behaviors’ (ibid., p. 3) within the social systems of eighteenth-century European courts, which were ‘adapt[ed] to city life’ (ibid., p. 6). And, once again, the
music-analytic act is commensurate with a situated psychology of hearing: galant
schemata are proffered as a means of ‘hear[ing] this music more as a Mozart
might have’ (ibid., p. 452).
The purpose of this article is to introduce new findings that further extend the
research programme of Meyer’s anvil in several respects. More specifically, I
re-examine the schema concept with a multidimensional case study on
Beethoven’s Eroica Symphony (1803), which formed the centrepiece of my
dissertation on the culture and cognition of key in the eighteenth century (Byros
2009a), and which was conducted in the spirit of the psychologically orientated,
humanistic music theory that characterised Meyer’s lifelong research programme. Meyer’s and Gjerdingen’s previous studies have advanced the schema
concept by means of introspection and by interpreting a musical corpus as a
metaphor for experience (see the subsection ‘Schemata: Methods of Objectification’, below). Evidence for the existence of schemata as mental categories that
engender a situated psychology of hearing has largely been advanced through
music analysis – that is, the historically situated ‘replicated patternings’ (Meyer
1989, p. 4) in musical scores. For this reason, the schema concept has remained
a ‘hypothesis’ (ibid., p. 352) or is based on an ‘assump[tion]’ that ‘musical
patterns replicated in th[e] repertory correspond to ... patterns learned by its
listeners ... [and] are at once an inventory of part of their musical knowledge’
(Gjerdingen 1996, pp. 380–1). The listener, in previous schema-theoretic
studies, is a virtual construct, which occupies and is abstracted from musical
scores.
The Eroica case study I advance here brings a novel perspective to the idea
that schemata engender a historical mode of listening, by establishing a correlation between real listeners’ responses, abstracted from documents in the symphony’s reception history, and the replicated patterns unearthed by my own
analysis of several thousand compositions from the long eighteenth century
(1720–1840). By means of this correlation, the case study bears out several
theoretical predictions implicit in Meyer’s formulation of the schema concept:
(1) that replicated patternings in eighteenth-century music are commensurate
with listeners’ knowledge structures; (2) that these knowledge structures are
historically contingent and therefore engender a situated psychology of hearing;
(3) that these situated psychologies are affected by style change; and (4) that
schemata provide access to historical modes of listening today. In what follows,
I first sketch the main themes of the schema concept in works by the Penn School
(picking up on the preceding discussion), as a preamble to a five-part consideration of the Eroica case study. The first of these five subsections deals with
competing responses to the Eroica’s opening theme throughout two centuries of
reception. The latter four variously employ a particular schema, which I call
the le–sol–fi–sol, to raise a mirror to the schema concept from several interrelated
angles.
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The Penn School
Schemata as a Situated Psychology of Hearing
Meyer’s implementation of the schema concept was uniquely both cognitivist
and anthropological: he viewed the ‘culturally qualified behavior’ that mental
abstractions embody as playing out on a distinctly cultural-historical stage. The
degree and type of replicated patterning in a given style were viewed as important
constituents in the way listeners negotiated – that is, formed habits about – that
style. Schemata were deemed responsible for configuring a historical mode of
listening, or a historically situated psychology of hearing, on account of their
stylistic specificity.
To exercise this notion, consider the opening theme of Mozart’s Violin Sonata
in G major, K. 301, shown in Ex. 2. The construction of this theme is largely
based on two stereotyped eighteenth-century phrases. The first is the familiar
1–7, 4–3, which occurs here on two levels that correspond to the underlying
sentential design of the phrase. The schema, here presented in its variant,
root-position form (cf. Exs 2a and 1b), frames the entire presentation as well as
the repetition of the basic idea, whereby the opening G, scale degree 1, is
regained as an appoggiatura at bar 5. The second schema is a variant of what
Gjerdingen has named the Prinner (1992, 1996 and 2007). The most characteristic feature of this prototype is a la–sol–fa–mi top voice over a bass that
descends in parallel tenths, fa–mi–re–do, thereby forming the harmonic progres4
sion IV–I6–ii7–vii°6 (or V 3 )–I, as seen in Ex. 2b. The Violin Sonata example is
a root-position variant featuring IV–I, V–I. Root-position harmony is a common
feature in a frequently encountered ‘paired’ variant of the schema, where the
la–sol and fa–mi dyads in the top voice of the Prinner are rhetorically articulated
as pairs:9 this occurs in the Sonata via the presentational design of its theme,
where the fa–mi of the basic idea’s varied repetition (bars 7–8) serves as an
answer to the preceding la–sol (bars 3–4). The combination of the two schemata
is enabled by this fa–mi ending, which is common to the second halves of both
patterns and results in an elaborate display of eighteenth-century ars combinatoria that nests a Prinner within a 1–7, 4–3.10 To bring out the combination,
Mozart highlights the structural tones of these patterns with rhetorical markers:
not only are they positioned at the beginnings and endings of phrases, but each
scale degree is thrown into sharper relief by means of appoggiaturas and trills.
For Meyer, a stylistically appropriate response to this theme presupposes the
activation of a referential mental template that operates as a top-down influence
on the ‘sound stimulus’ (Meyer 1956, p. 46). This mental model results from
the internalisation of prototypical features encountered in the past experience of
numerous instances of other passages that make use of the 1–7, 4–3 and Prinner
paradigms. Repeated active listening and exposure to a given stylistic idiom will
give rise to mental abstractions.11 The ‘ideal type’ (ibid., p. 57) that is abstracted
from these memories later operates as a cognitive context for interpretation
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Ex. 2 (a) Wolfgang Amadeus Mozart, Violin Sonata in G major, K. 301 (1778) first
movement, Allegro con spirito, bars 1–8: 1–7, 4–3 and Prinner schemata
(see Gjerdingen 1988) when new instances are encountered. Most generally,
‘schema’ refers to a mentally abstracted prototype of a statistical regularity in a
particular musical style which forms the basis for apprehending future phenomena. At bottom, schema theory is a theory of experience and memory as applied
knowledge.12 For example, a ‘stylistically appropriate habit response’ to Mozart’s
theme would understand the fa–mi and dominant–tonic riposte in bars 7–8 as a
highly probable consequence of the preceding music, owing to the confluent
fa–mi endings of these two schemata. But the significance of the schema concept
does not lie in the expectation embodied by the habit response per se. Expectation
here is effect rather than cause. The schema concept refers foremost to the
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Ex. 2 (b) Prinner schema, abstract representation (from Gjerdingen 2007)
psychological setting up of a stylistically appropriate interpretative context for
the whole of Mozart’s opening theme. The psychological activation of this
interpretative context is what Meyer intended by ‘an experienced listener bring[ing] into play stylistically appropriate habit responses’ (emphasis added). The
fa–mi expectation arises as a by-product of the schema that has been set up in the
mind during the act of listening. In other words, expectation is an indication or
sign of a top-down, schema-driven hearing. To experience a prediction or anticipation, the mind must have first established an interpretative context, and it is
this frame of reference that is causally responsible for the expectation. Expectation presupposes the recognition of some familiar, previously experienced
context – ‘we recognize ... in the sense of bringing appropriate habit responses
into play’ (Meyer 1956, p. 59). For Meyer and Gjerdingen, musical meaning,
understanding and communication arise from and are firmly predicated on this
re-cognition process of establishing an external, extra-opus, psychological
context as an evaluative frame of reference.
The Penn School assigned this re-cognition process a decidedly historical
dimension. Because the notion of stylistic appropriateness operates on a historical axis, Meyer and Gjerdingen would also maintain that to hear the opening
theme of Mozart’s Violin Sonata through the lens of the 1–7, 4–3 and Prinner
schemata is a historically and culturally conditioned activity. Both of these
patterns underlying the construction of Mozart’s theme, which was composed in
1778, had their greatest currency in the 1770s. Use of the Meyer, as already seen
above, peaked in the 1770s; and the Prinner, as Gjerdingen tells us, was especially prevalent from 1720 through the 1770s (2007, p. 455). The cognitive
activity of setting up the Meyer and Prinner as appropriate interpretative contexts is historically and culturally situated because these ‘replicated patternings’
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(Meyer 1989, p. 4) are particular to a specific culture and historical period. To
hear Mozart’s theme against these patterns as interpretative frames is therefore
to be situated in Mozart’s historically contingent musical culture – ‘to hear this
music as a Mozart might have’. The idea is that the replicated patternings of a
musical style have a direct consequence on the formation of mental categories.
Because the patternings of style differ in time and place, historically and culturally, mental structures and modes of listening (according to Meyer’s thesis) will
differ accordingly: within the same culture, schemata provide the basis for
successful communication; cross-culturally, listening habits at home in one style
may produce ‘cultural noise’ (Meyer [1967] 1994, p. 17) in another. For this
reason, as early as 1956, in Emotion and Meaning in Music, Meyer located the
culturally and historically circumscribed evaluative functions of schemata (‘habit
responses’) at the centre of musical experience, at the basis of music’s intellectual, aesthetic as well as emotional engagement – in short, the ‘life stream of
musical perception and communication’.13 By ascribing to schemata the power
to configure a situated psychology of hearing or a historical mode of listening
that enables ‘sensitive understanding’, Meyer anticipated what the anthropologist Clifford Geertz – who held a residency at the University of Chicago during
Meyer’s tenure – called the ‘shared symbols’ of a culture (Geertz 1973, p. 250):
‘a set of symbolic devices ... cultural patterns [and] historically created systems
of meaning ... for controlling behavior’. These symbols, as ‘abstractions from
experience’, may be ‘words ... but also gestures, drawings, musical sounds, ...
anything, in fact, that is ... used to impose meaning upon experience’ (ibid., pp.
45, 52 and 91). In this way, to speak of a ‘1–7, 4–3’ and a ‘Prinner’ in Mozart’s
Violin Sonata, for example, is to advance a theoretical objectification of the
cognitive as well as cultural-historical conditions – the shared symbols – necessary for a ‘stylistically appropriate’ hearing and ‘sensitive understanding’, which
would include, among other things, the perception and intellection of its ars
combinatoria.
Schemata: Methods of Objectification
Meyer’s entry into the schema concept was initially through introspection: one
imagines that his meditations on style and habit responses in the 1950s were
accompanied by 1–7, 4–3s sounding in his inner ear. Indeed, Eugene Narmour
maintained that stylistic knowledge was ultimately accessible by such introspection alone: ‘stylistic representations ... are introspectively accessible. Were this
not so, the study of musical style would be impossible. So would any attempt to
test the psychological reality of stylistic knowledge’ (1999, p. 441). But Narmour’s formulation touches on a methodological difficulty that is inherent to
schema-theoretic thinking. In so far as replicated patterns such as the Meyer and
Prinner are declarative objectifications of procedural or tacit knowledge, it
becomes difficult to sustain an objective interpretation of musical structures as
psychological categories of mind or as genuine abstractions from experience.
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Meyer and Gjerdingen moved beyond the potential subjectivity of an introspective, armchair approach, however, by advancing a methodological objectivism.
Both interpreted the replicated patternings directly observable in musical scores
as instances of human behaviour and knowledge with regard to composition and
listening. The tacit knowledge of schemata is equally the province of composers’
and listeners’ minds: ‘It is the goal of music theorists and style analysts to explain
what the composer, performer, and listener know in this tacit way ... . This can be done
only by making inferences from observable data – the replicated patternings present
in works of art – to general principles’ (Meyer 1989, p. 10; emphasis added).14
This methodologically objective standpoint was advanced in the earliest stages
of Meyer’s thinking:
[I]n musical experience the same stimulus, the music, activates tendencies, inhibits them, and provides meaningful and relevant resolutions for them. This is of
particular importance from a methodological standpoint. For it means that,
granted listeners who have developed reaction patterns appropriate to the work in
question, the structure of the affective response to a piece of music can be studied
by examining the music itself ... . The importance of this ‘objective’ point of
view of musical experience is clear. It means that once the norms of a style have
been ascertained, the study and analysis of the affective content of a particular
work in that style can be made without continual and explicit reference to the
responses of the listener or critic. That is, subjective content can be discussed
objectively. (Meyer 1956, pp. 31–2)15
In ‘Courtly Behaviors’ (1996), Gjerdingen outlines a similar methodological
objectivism and further suggests that the analytic processes of pattern recognition may even serve to reconstruct ‘native’, historical modes of listening that
compete with more modern modes of cognition:
Because their prior musical experiences differ substantially, ... ‘[n]ative listeners’
of eighteenth-century court music ... [and] modern listeners ... will have different
musical perceptions of the same piece. Charting the exact musical knowledge of
modern listeners would be a daunting task. Musics from popular culture, musics
from the near and distant past, and musics from various ethnic regions coexist
today in a vast commercial marketplace of sound. The musical knowledge of
eighteenth-century aristocratic listeners, by contrast, stemmed from relatively
homogeneous compositions of similar ethnic, geographic, social, and chronological derivation. If we assume that the musical patterns replicated in this repertory
correspond to the patterns learned by its listeners, then an inventory of those
replicated patterns is at once an inventory of part of their musical knowledge.
(Gjerdingen 1996, pp. 380–1)
The idea is that a corpus study of musical works – ‘an inventory of those
replicated patterns’ – can serve as a metaphor for eighteenth-century musical
experience and knowledge.
Implicit in this argument is that the tacit behaviours and choices of composers
(Meyer 1989) are equivalent to those of listeners. This stance recalls an epistemMusic Analysis, 31/iii (2012)
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ological position central to reader-response theories of communication, in which
the categories of author and reader collapse into a single supracategory of style.
By way of example, Umberto Eco has postulated that both author and reader
occupy the literary text.The author ‘is textually manifested only as a recognizable
style ... [which] distinguishes not an individual but a genre, a social group, a
historical period’ (Eco 1979, p. 10). The reader – what Eco called the ‘Model
Reader’ – occupies the text as its ‘structural strategy’ (ibid., p. 9). That is, the
reader (or listener) is the work’s structural strategy.16 Meyer anticipated the same
argument with a communicative interpretation of the musical act:
Communication ... takes place only where the gesture made has the same
meaning for the individual who makes it that it has for the individual who
responds to it ... . It is because the composer is also a listener[,] ... because he is
continually taking the attitude of the listener[,] that the composer becomes aware
and conscious of his own self, his ego, in the process of creation. In this process
of differentiation between himself as composer and himself as audience, the
composer becomes self-conscious and objective ... . [W]ithout a set of gestures
common to the social group, and without common habit responses to those
gestures, no communication whatsoever would be possible. Communication
depends upon, presupposes, and arises out of the universe of discourse which in
the aesthetics of music is called style. (Meyer 1956, pp. 40–2)
In light of this communicative reading of the musical act, to move the underlying argument of the schema concept beyond the level of a ‘hypothesis’ (Meyer
1989, p. 352, and Gjerdingen, personal communication),17 or ‘assum[ption]’
(Gjerdingen 1996, p. 380), would require evidence that such a style-based,
communicative transaction has taken place – evidence of a correlation between
stylistic knowledge reconstructed from musical scores and listeners’ responses
that correspond to the details of that knowledge. To establish such a correlation
would require a demonstration that the responses of a Model Listener, as they
are predicted by corpus analysis, are corroborated by the responses of a real
listener. In reader-response studies, such ‘real readers’, as the literary theorist
Wolfgang Iser explains, are ‘invoked mainly in studies of the history of responses,
i.e., when attention is focused on the way in which a literary work has been
received by a specific reading public’ (1978, p. 28). To that end, ‘observable data’
are also available in the form of the reception history of musical works, in so far
as it may provide documents which illustrate habit responses at play. Documents
in a work’s reception history may betray or preserve traces of a given time
period’s schemata.
Beethoven’s Eroica: Case Study
Reception History and Listener Response
In 1807 the editor of the Leipzig Allgemeine musikalische Zeitung, Friedrich
Rochlitz, published a review of Beethoven’s Eroica Symphony (Ex. 3) that
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Ex. 3 Ludwig van Beethoven, Symphony No. 3 in E major, Op. 55, Eroica (1803),
first movement, Allegro con brio, bars 1–11
documents a rather provocative hearing of the work’s opening theme. Rochlitz,
quite matter-of-factly, describes bars 6–9 of the theme as having modulated
formally (förmlich) to G minor:
The symphony begins with an Allegro con brio in three-quarter time in
E major ... . Already in bar 7, where the diminished seventh appears over C in the
bass, and in bar 9, where the 64 chord appears over D, the composer prepares the
listener to be often agreeably deceived in the succession of harmonies. And even
this preludising deviation [präludirende Abweichung], where one expects to be led
formally to G minor [wo man förmlich nach g moll glaubt geleitet zu werden] but, in
place of the resolution of the 64 chord, finds the fourth led upward to a fifth, and so,
by means of the 65 chord, finds oneself unexpectedly [unvermuthet] back at home in
E major – even this is interesting and pleasing. (Rochlitz 1807, p. 321; modified
translation from Senner, Wallace and Meredith 2001, p. 21; emphasis added)18
The details of Rochlitz’s description suggest that this G minor hearing of the
theme resulted from the ‘appropriate br[inging] into play’ of some habit. To
begin with, in calling this moment a ‘preludising deviation’, Rochlitz situates bars
7–9 within the eighteenth-century context of fantasy and improvisation. The
description normalises this problematic moment in the Symphony, in some
measure, by justifying the deviation according to the aesthetic and generic
expectations of improvisatory genres such as the fantasy or prelude. More
important, Rochlitz’s language suggests that the modulation itself is the result of
some conventional procedure: ‘one expects to be led förmlich to G minor’.
Contemporary dictionaries at the turn of the nineteenth century translate this
term as ‘properly’, ‘formally’ or ‘explicitly’; and a related expression, in der
eigentlichen Form, translates as ‘in due or proper form’ or ‘according to rule’.19
The förmlich qualification may also be an explicit or implicit reference to Heinrich Christoph Koch’s notion of förmliche Ausweichung, or ‘formal modulation’,
which specifies a closed modulation by way of a cadence and phrase ending
(Koch 1782–93, vol. 2, p. 188).Whatever habit response may have been in force,
Rochlitz’s language also implies that the expectation of its completion has been
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denied: ‘instead of the resolution of the 64 chord’ at bar 9, the ‘ 65 chord’ in bar 10
prompts an ‘unexpected’ return to E major – one ‘finds oneself unexpectedly
back at home in E major’ – which indicates that Rochlitz’s ear was firmly in G
minor by bar 9. The listener is therefore ‘agreeably deceived’ not by the theme’s
celebrated C, but by the unexpected return from this G minor tonality which it
precipitates to the opening E major.
Nearly two centuries later, Rochlitz’s provocative review figured into a discussion of the Eroica Symphony by Brian Hyer:
For the reviewer, ... the 64 above D suggests a cadential arrival on the tonic G
minor in the following measure. It thus surprises him when G in m. 7 ascends in
the violins to A in m. 10, forming a 65 above D that returns ‘home’ to a 53 above
E at the end of m. 11. I must admit to finding the reviewer’s hearing of the 64 above
D unpersuasive: I believe our memories of E are too recent for us to hear D as anything
but a leading tone to E. But few of us will have difficulties hearing a deceptive
continuation from C to D. (Hyer 1996, p. 81; emphasis added)
Whatever past experience may have influenced Rochlitz, a very different habit
response seems to have conditioned Hyer’s interpretation: the G minor hearing
is deemed ‘unpersuasive’.20
Now, one might simply resign this discrepancy in the Eroica’s reception as
evidence of some perhaps inevitable subjectivity about music perception. But
‘the philosopher’, as Wittgenstein famously put it, ‘treats a question; [sic] as an
illness’ ([1953] 2001, p. 77). That Rochlitz was writing in 1807 and Hyer in 1996
would suggest that their differing environments are causal factors in the different
ways that each assigns a key context to bars 6–9 of the Eroica’s opening theme.
Their differing historical environments suggest that some objective or intersubjective criteria might be responsible for the competing hearings. With these two
documents in the Eroica’s reception history, we may be witnessing real-life
evidence for Gjerdingen’s hypothesis that, ‘[b]ecause their prior musical experiences differ substantially, these two classes of listeners will have different musical
perceptions of the same piece.’ In other words, the dissonance between Rochlitz’s and Hyer’s hearing may be schema symptomatic.
To approach the schema hypothesis from the perspective of listener response
is, in essence, the inverse process of that adopted by the Penn School: in terms
of concrete evidence, both Meyer and Gjerdingen began from the music itself.
But the very first manifestation of modern schema theory in the twentieth
century, in the work of the British social psychologist Sir Frederic Bartlett,
resulted from his observations of the competing experiences of real-life subjects,
analogous to the Rochlitz-Hyer opposition in the Eroica’s reception history.
Writing several decades before Meyer’s dissertation was published,21 Bartlett
advanced the very first definition of a schema in modern, psychological terms,
and he did so in terms of ‘responses’ conditioned by ‘past experience’ (Bartlett
1932, p. 210).22 Both also developed the schema concept in the light of ‘cultural
anthropology and social psychology’ (Meyer 1989, p. x).23 However, unlike
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Meyer, Bartlett began from the details of readily observable differences of
experience. He conducted a genre of research known today in the social sciences
as phenomenography: ‘the object of phenomenographic research ... [is] variation in
human meaning, understanding, [and] conceptions’, or variation in ‘ways of
experiencing a particular phenomenon’ (Åkerlind 2005, p. 322). In the phenomenographic model, research inquiry begins precisely from the diversity of experience: ‘observable data’ here begin not with musical scores but with competing
experiences of the same object, event, behaviour, and so forth, which are documented in what phenomenographers call ‘transcripts’.
In Bartlett’s research on social psychology, this diversity of experience
emerged in a series of real-life case studies. For several of these, Bartlett practiced a type of experiment known as repeated and serial reproduction of a
narrative: students at the University of Cambridge were asked to read several
short stories and then reproduce the texts, in writing, as faithfully as possible
from memory. The subjects believed the experiments were only assessing
‘accuracy of recall’ (Bartlett [1932] 1995, p. 66), but Bartlett had deliberately
chosen stories that ‘belonged to a level of culture and a social environment
exceedingly different from those of [his] subjects’ in order to examine ‘what
happens when a popular story travels about from one social group to another’
and the ‘general conditions of transformation under such circumstances’ (ibid., p.
64; emphasis added). The most famous of his experiments involves a Native
American folk tale called ‘The War of the Ghosts’, an allegory about ghosts
stealing the spirits of the living. The true meaning of this tale is never made
explicit in the narrative; its supernatural significance is only alluded to, via
imagery, metaphor and cultural codes – that is, via schemata that would have
been immediately recognisable to a Native American mind.24 The reconstructed texts produced by the Cambridge students all differed from a typical
Native American reconstruction,25 as Bartlett’s subjects utterly misunderstood
the tale’s meaning. The Native American schemata on which the allegory is
based were obviously foreign to a European mindset, and as a result of their
cultural differences, the folk tale underwent significant transformation in the
students’ reconstructions. The subjects attempted to assimilate unfamiliar concepts and situations to the schemata of their own culture, a symptom of
schema absence that William F. Brewer has since called ‘transformations to the
familiar’ (2000, p. 72). The underlying phenomenographic method in Bartlett’s
programme illustrated that the ‘conditions of transformation’ in the crosscultural misinterpretation were, in effect, schemata.
If we adapt the phenomenographic model to the reception history of musical
works, we might understand Rochlitz’s and Hyer’s competing experiences of the
Eroica’s opening theme as being conditioned by cultural differences that obtain
in historical time. In his treatise on music and culture Beethoven’s Anvil (2001),
the cognitive scientist William Benzon suggested that such cultural changes
across history may give rise to cognitive plasticity: ‘The nervous system is plastic,
taking the impress of its environment. As culture molds the human environment,
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Table 1 Eroica case study ‘transcripts’: three strains of reception/cognitive response
to bars 6–9 of the opening theme, 1807–2006 (from Byros 2009)
so it molds the nervous system ... . Thus it seems quite possible that our
descendants a century or two from now will have nervous systems that differ
from ours in small but critical ways’ (2001, p. xiii). By extension, the RochlitzHyer opposition in the Eroica Symphony’s reception history may indeed be the
consequence of modern nervous systems that differ from those of two centuries
ago.
Looking at the Eroica’s reception more comprehensively, the dissonance
between the Rochlitz and Hyer transcripts is not an isolated one but rather part
of a larger set of competing categories. Typically, alternative experiences of a
given phenomenon will give rise to categories of description that are logically
related in what phenomenographers refer to as an ‘outcome space’ (Uljens 1996,
p. 84). In the Eroica case study, the reception-history transcripts fall into three
such categories or strains of reception, organised in Table 1. The most common
and best-known strain involves largely metaphorical descriptions of the C
diminished seventh chord in bars 7–8 – such as Donald Tovey’s (1935) ‘Cloud’
and Aléxandre Oulibicheff’s (1857) ‘Fog’ metaphors, which highlight some
cognitive ambiguity about bars 6–9. In Table 1, this ‘Cloud’ strain of reception is
situated at the middle of the outcome space, which may be understood as a
continuum that projects outward from this centre of ambiguity. The ‘Cloud’
strain actors acknowledge something ‘out-of-key’ (Marston 1991, p. 214) about
the phenomenon; exactly what constitutes that otherness, however, remains
indeterminate and ambiguous. The extreme categories, at the left and right of
Table 1, situate Rochlitz’s and Hyer’s hearings in larger social groups – in a G
minor and E strain, respectively. To the right, the problematic C and its surrounding bars are heard entirely within the key of E major. At the other extreme,
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Table 2 Diachronic reorganisation of Eroica reception history transcripts: perceived
key change commensurate with historical regress
1807
Rochlitz (1807)
G minor:
Parry (1880)
Marx (1859)
1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 2020
increase in perceived key change
1857
Oulibicheff (1857)
‘Cloud’:
Rumph (2004)
Sipe (1998)
Earp (1993)
Ringer (1961)
Riezler (1936)
Lockwood (1982)
Hepokoski/Darcy (2006)
Rexroth (2005)
Brinkmann (2000)
Cooper (2000)
Marston (1991)
Tovey (1945)
Heuss (1921)
Epstein (1979)
1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 2020
Schenker (1930)
Klein (2005)
Day-O’Connell (2002)
Lerdahl (2001)
Barry (2000)
Hyer (1996)
E major: 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000
1930
bars 6–9 are explicitly heard as having modulated to or even ‘settled in G minor’
(Rumph 2004, p. 90).The structure of this outcome space, then, read from right
to left, involves a gradual increase in perception of a key change.26
In studies of reception history, such intersubjective categories are said to result
from the influence of a ‘cultural code’: ‘whatever judgments may have been
passed on the work will ... reflect various attitudes and norms of that public[,
and] ... mirror the cultural code which conditions these judgments’ (Iser 1978,
p. 28). Or, as the literary and reception theorist Felix Vodička characterised it,
‘[T]he object of reception history does not lie in individual reactions but in norms
and normative systems [cf. schemata] that determine how surviving texts are perceived
within groups or strata conditioned by history, society, and ethnic origin’ (1975, cited
in Dahlhaus [1977] 1984, p. 152; emphasis added). Reception history is thus
inherently suggestive of phenomenographic inquiry, as it might reveal ‘tendencies [that] operat[e] throughout the whole of the [social] group concerned’
(Bartlett [1932] 1995, p. 125).
To that end, Table 2 reorganises the Eroica reception-history transcripts diachronically. Here, we see that the increased tendency to perceive a key change in
bars 6–9 operates on a historical axis – that is, the historical situation of each strain
appears to be a contributing factor in the variation of experience. The G minor
hearing begins in 1807 with Rochlitz’s review. The E major response, on the other
hand, originates in 1930, and its recurrences are otherwise limited to responses at
the turn of the twenty-first century. If we take the date of origin of each strain as
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surate with historical regress. In itself, the reception history of the Eroica brings
initial evidence that cognitive plasticity occurred in historical time. The G minor
hearing appears to be a historically and ‘stylistically appropriate’ one, which
gradually came to compete with new hearings in the late 1850s and the 1930s. But
in the same way that corpus analysis by itself may only advance Meyer’s schema
concept at the level of a hypothesis, so too is the evidence advanced by reception
history alone ultimately hypothetical. It remains to be determined whether or not
a correlation exists between the details of the Eroica’s reception and the regularities of a musical corpus, interpreted as a metaphor for musical experience – that
is, whether a musical schema is the ‘condition of transformation’ that gives rise to
these competing responses to the Eroica’s opening theme.
The Le–Sol–Fi–Sol Schema as Musical Structure
My dissertation involved an extensive corpus study whose main ambition was to
reconstruct the knowledge base potentially responsible for Rochlitz’s G minor
hearing of the Eroica’s opening theme.To the extent that one may read a musical
corpus as a metaphor for experience, as suggested both by Meyer and Gjerdingen,27 we should be able to reconstruct the tacit knowledge base and, hence, the
past experience and ‘ingrained habits’ of a historically situated listener such as a
Rochlitz from actual musical scores. In doing so, it ought to be said, the
orientation of such a corpus study compared to, say, that of Gjerdingen (2007)
is somewhat different: here the concern lies not in detecting and defining
replicated patternings in general, but in identifying a specific pattern that would
fit bars 1–9 of the Eroica Symphony’s opening theme. In several important
articles from the 1970s and 1980s, David Rumelhart defined schemata as
‘recognition devices whose processing is aimed at the evaluation of their goodness of fit to the data being processed’ (1980, p. 41).28 In my case study, the
details of Rochlitz’s review (and of the Eroica’s reception in general) prompted a
search for such a recognition device. The corpus study sought to isolate and
define the replicated pattern that would have caused Rochlitz to ‘re-cognise’ a G
minor context in bars 6–9 of the opening theme, and so matter-of-factly at that.
In reconstructing this recognition device, I posed several questions relating
to a comprehensive musical corpus. Most important among these is the following: if we abstract the opening figured-bass progression that occurs in bars
1–9 of the Eroica as a discrete chunk, in what tonal context(s) does this progression normally appear? More specifically, in what tonal context(s) might an
eighteenth-century listener have encountered a bass line whose intervallic
profile is defined by two descents by semitone followed by an ascent of the
same interval, and whose individual notes are specifically harmonised with a
major 53 chord, a minor 64 chord, a diminished seventh and a minor 64 ? I
applied this question to a corpus of roughly 3000 musical works composed
between 1720 and 1840.29 They covered every significant genre of the long
eighteenth century, including symphonies, quartets and quintets for strings
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and other chamber ensembles; piano trios and solo sonatas; concertos; operas;
and sacred and secular vocal works. The corpus represented works by more
than 100 composers from throughout Europe, including Italy, France, Austria,
Germany, Great Britain, Bohemia, Poland, Slovakia, Hungary, Spain, Portugal,
Sweden, Denmark and Norway.30
The details of this corpus indicate that an eighteenth-century listener would
have encountered the Eroica’s figured bass progression invariably in the following
tonal context.
6
6
⎡ VI − i 4 − iv°7 ⎤ − ⎡i 4 …⎤
⎣
⎦ ⎣
⎦
When set at the same pitch-class level as the Eroica, the progression’s key profile
is exclusively G minor. More important, the corpus reveals that Beethoven’s
setting of this pattern in the Eroica elides the final chord of the progression. In its
6
normative configuration, the pattern resolves the 4 at the end of the above
roman-numeral string to a dominant triad or seventh chord (I will return to this
below).
6
6
⎡ VI − i 4 − iv°7 ⎤ − ⎡i 4 − V (7) ⎤
⎣
⎦ ⎣
⎦
This is precisely the harmonic context and expectation suggested by Rochlitz’s
1807 description, where he speaks of the 64 chord in bar 9 being denied resolution by the 65 at bar 10. Ex. 4a displays an excerpt from the ‘Et lux
perpetua’section of Mozart’s Requiem (K. 626 [1791]). Here, the same
figured-bass progression employed in the opening of the Eroica functions as
6
6
VI − i 4 #iv°7 − i 4 . But in the Mozart, the final 64 chord resolves to a dominant
triad, and the entire progression serves to punctuate a large half cadence at bar
46 (North American terminology is used for cadences throughout; British
equivalents have been provided in the legend of Fig. 4). The same pattern
appears in a piano sonata by the Bohemian composer Jan Ladislav Dussek (Op.
45 No. 1, in B major [1800]), shown in Ex. 4b. The key context here is G
minor, and the pattern once again resolves the final 64 to a dominant triad,
producing a half cadence.
My corpus returned 550 examples of this pattern, with only five insignificant
harmonic variables obtaining in all of these instances.
1. The second 64 (chord no. 4 in the pattern) is optional: as is the case with any
cadential progression, the cadential 64 is not required. The iv°7 chord
(chord no. 3) resolves directly to a V or V7 65.3% of the time (the 64
therefore already represents the dominant).
2. The last chord may be either a dominant triad or a dominant seventh.
3. The diminished seventh chord on 4̂ may or may not have a third in the
chord (in the Mozart example the third is present; in the Dussek it is
absent).31
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Ex. 4 (a) Wolfgang Amadeus Mozart, Requiem in D minor, K. 626 (1791), ‘Introit:
Et lux perpetua’, bars 43–46 (1791): le–sol–fi–sol schema
4. The passing
6
4
chord may sometimes be a passing
6
4
2
chord (in these cases,
scale degree 6 is suspended from the first chord of the pattern into the
second chord in one of the upper voices).
5. The second, cadential 64 chord may introduce a change of mode to major.
The most characteristic feature of this pattern is its ‘chromatic turn of phrase’
(Byros 2009a, p. 137) in the bass: a chromatic trichord that folds inwardly onto
scale degree 5 ( 6̂ , 5̂ , 4̂ , 5̂ ). Hence, I have named this replicated patterning the
le–sol–fi–sol schema.32 The key-defining character of the le–sol–fi–sol operates by
way of two stages consisting of four events that correspond to the scale-degree
progression of the bass. In the annotations of Exs 4a and 4b, as well as in the
abstract representation of the pattern in Fig. 3, the events of the schema are
represented by scale-degree nodes. Simple lines without arrows between nodes
group events within a stage. Bold lines with arrows indicate a higher-level
syntactic articulation between the two different stages of the schema. The first
stage is a chromatically intensified subdominant expansion that composes out an
augmented sixth as a diminished third in the bass,33 thereby creating a highly
‘dominantising’ orientation. The first stage of the le–sol–fi–sol communicates an
attraction to the dominant which mirrors that of an augmented sixth chord.
The aggregate effect of the three events in the first (le–sol–fi) stage is a sense of
lingering that is also characteristic of what Gjerdingen calls the Indugio schema:
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Ex. 4 (b) Jan Ladislav Dussek, Piano Sonata in B major, Op. 45 No. 1 (1800), first
movement, bars 116–125: le–sol–fi–sol schema
Fig. 3 The le–sol–fi–sol schema: abstract representation (from Byros 2009)
6
an expansion of ii 5 or IV.34 In the le–sol–fi–sol, this lingering occurs on a
chromatically intensified and therefore even more dominant-orientated augmented sixth chord, with scale degrees one and three reiterated in the upper
voices. The first stage of the schema may be understood as an unravelling of
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Ex. 5 Joseph Haydn, String Quartet in C major, Op. 54 No. 2 (1788), first movement, bars 49–54: le–sol–fi–sol schema
the two dominant-orientated tendencies of scale degrees 6 and 4 that appear
synchronically in the augmented sixth. In the le–sol–fi–sol, these tendencies are
composed out, positioned in a diachronic setting and harmonised by the VI
chord in event 1 and the iv°7 chord in event 3, respectively. In this context, the
6
6
4 of event 2 functions as an unaccented passing chord. The Eroica’s 4 in bar 6 is
35
paradigmatic in this regard. Composers would often emphasise the passing
quality of the chord by assigning longer durations to events 1 and 3 of the
pattern. The first movement of Haydn’s String Quartet in C, Op. 54 No. 2
(1788), shown in Ex. 5, is an exemplar of this strategy: the 64 chord is positioned
on a metrically weak beat, and the framing submediant and diminished seventh
chords are given significantly longer rhythmic durations. The Eroica is also
exemplary in this respect. Instances that feature a slower harmonic rhythm,
however, where each event of the le–sol–fi–sol occupies one or more bars, will
situate the passing 64 chord in a hypermetrically weak bar, as seen in Beethoven’s
Triple Concerto (Ex. 6). Beyond metric considerations, other grouping mechanisms may be used to highlight the subdominant expansion underlying the
schema’s first stage, such as the microsentential structure (1 + 1 + 2) in the Triple
Concerto’s le–sol–fi stage, as well as thematic differentiation. The latter can be
seen in Haydn’s Keyboard Sonata in D major, Hob. XVI:19 (Ex. 7), where the
first stage of the schema serves to create a metric dissonance that resolves only
with the arrival of the cadential 64 on beat 3 of bar 56. These features of the
schema’s le–sol–fi stage served to dramatise the arrival of the dominant, which
occurs with the second stage of the pattern: a simple expression of dominant
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Ex. 6 Beethoven, Triple Concerto, Op. 56 (1804), i, bars 460–464: le–sol–fi–sol
schema
harmony, its arrival often highlighted by a cadential 64 (compare Fig. 3 and Exs
4–7).
The strong key-defining profile of the le–sol–fi–sol is also evidenced by its
normative closing usage in my corpus. That is, the schema consistently effects a
cadence or exhibits cadential function (Caplin 1998). Out of 550 instances of the
le–sol–fi–sol, 456, or 83%, lead to an authentic or half close. The half cadence is
by far the most frequent of the three primary cadence types, occurring roughly
62% of the time with 343 instances, while the perfect and imperfect authentic
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Ex. 7 Haydn, Keyboard Sonata in D major, Hob. XVI: 19 (1767), first movement,
bars 55–57: le–sol–fi–sol schema (figuration/motivic material as grouping mechanism)
Fig. 4 Cadential probabilities of the le–sol–fi–sol
1% (DC) 2% (DE)
14% (EC)
3% (IAC)
18% (PAC)
PAC
IAC
HC
EC
DC
DE
:
:
:
:
:
:
62% (HC)
perfect cadence/perfect authentic cadence
imperfect authentic cadence
imperfect cadence/half cadence
evaded cadence
deceptive cadence
dominant expanding/post-cadential
cadences follow, with frequencies of 18% and 3% respectively (Fig. 4).36 Because
of its cadential function, the le–sol–fi–sol schema is frequently encountered at the
main architectural seams of sonata form, where it serves to articulate important
moments of punctuation in its layout with respect to authentic as well as half
cadences. Regarding the former, the le–sol–fi–sol is often used to articulate the
perfect authentic cadence that structurally closes an exposition and recapitulation – what James Hepokoski and Warren Darcy (2006, p. 18) call the moment
of ‘essential expositional closure’ and ‘essential structural closure’ respectively.
Domenico Cimarosa applies this strategy in his Sonata in C major, C. 88
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Ex. 8 Domenico Cimarosa, Keyboard Sonata in C major, C. 88 (c. 1770s), bars
78–83: le–sol–fi–sol schema and essential expositional closure (Hepokoski and Darcy
2006)
(composed around the 1770s). The excerpt in Ex. 8 is from the Sonata’s
exposition, where the le–sol–fi–sol leads to a PAC in bar 83 (the recapitulation
restates the same music in C minor/major). But the most characteristic use of the
le–sol–fi–sol is in highly charged, dominant-orientated situations, corresponding
to the frequency with which the schema advances a half cadence. The majority
of the half cadences are encountered at ‘medial caesuras’ (Hepokoski and Darcy
2006, p. 24), cadenzas, retransitions and symphonic introductions, all locations
calling for powerfully articulated half cadences that are sustained by passages
that, in William Caplin’s terms, ‘stand on the dominant’ (1998) – what Hepokoski and Darcy call a ‘dominant lock’ (2006, p. 30), or what Gjerdingen, following
Joseph Riepel (1752–68), calls a Ponte schema (2007, pp. 197–215), which acts
as a bridge between large formal sections.37 Ex. 9 reproduces two excerpts from
Johann Baptist Vanhal’s Symphony in G minor (g2, 1764–7), where the le–sol–
fi–sol is used to punctuate both the half cadence of the medial caesura in the
exposition and the retransitional dominant at the end of the development.38 Both
Vanhal examples also feature syncopated upper voices, a Sturm und Drang
characteristic of several le–sol–fi–sol exemplars also featured in the Eroica.
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Ex. 9 (a) Johann Baptist Vanhal, Symphony in G minor, g2 (1764–67), fourth
movement, bars 10–18: le–sol–fi–sol medial caesura half cadence
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Ex. 9 (b) Vanhal, Symphony in G minor, g2 (1764–67), fourth movement, bars
73–78: le–sol–fi–sol retransitional dominant half cadence
Telling as these details may be, perhaps the most significant aspect in the
history of the le–sol–fi–sol, with regard to the Eroica, is the existence of a modulating variant. Because the schema begins with a major triad – the minor-mode
submediant – it affords the opportunity to reinterpret any tonic major triad as a
submediant by means of the le–sol–fi–sol progression in order to modulate up by
a major third. This is precisely the modulation documented in Rochlitz’s review.
6
6
⎡I ∼ VI − i 4 − iv°7 ⎤ − ⎡i 4 − V (7) ⎤
⎣
⎦ ⎣
⎦
Indeed, 118 of the 550 instances of the schema in my corpus, or 22%, appear in
this modulating context whereby a tonic major triad is reinterpreted as a submediant. Ex. 10 displays a more complete picture of the le–sol–fi–sol schema from
Beethoven’s Triple Concerto, discussed above with respect to Ex. 6. The phrase,
as has already been seen, closes with a half cadence in C minor, but it actually
begins in A, as shown in Ex. 10. Bars 456–460 feature a prolongation of A major
via tonic and dominant exchanges. But in bar 460, A major is – retrospectively39
– reinterpreted as a submediant when incorporated into the window of the
dominantising stage of the le–sol–fi–sol.40
This modulating variant also appears at the main architectural seams of sonata
form as a way of dramatising important moments of punctuation. Ex. 11 displays
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Ex. 10 Beethoven, Triple Concerto, Op. 56 (1804), first movement, bars 456–464:
le–sol–fi–sol modulating variant (cf. Example 6)
an instance from the first movement of Haydn’s String Quartet in D major, Op.
50 No. 6 (1787). The context here is the anticipated structural cadence of the
recapitulation. The perfect authentic cadence expected at bar 139 is denied by a
deceptive close on VI, B major. Bars 139–143 proceed to sustain B as a new
tonic via tonic and dominant reiterations. In bars 144–145, B is then reinterpreted as a submediant through the le–sol–fi–sol, which leads to a perfect authentic cadence in bar 149.41 The same strategy was used to dramatise important
half-cadential punctuations: in the first movement of Beethoven’s Sonata in E,
Op. 14 No. 1 (1798), the retransitional dominant of the development is
approached from the key of the minor-mode submediant (C major), which gives
way to E minor/major for the recapitulation when assimilated into the modulating window of the le–sol–fi–sol in bars 75–81 (not shown).42
Much like other highly stereotyped eighteenth-century phrases, the le–sol–fi–
sol is readily found in pedagogical artefacts of the period. In terms of Italian
partimenti (Gjerdingen 2007), the schema typically appears in advanced exercises, such as, for example, in Books III–VI of Fedele Fenaroli ([c. 1800] 1975).
But perhaps its most important instructional reference is a prominent modulating variant that appears in another highly influential and German pedagogical
context of the eighteenth century: the second movement from the fourth sonata
among six that Emanuel Bach appended to his Versuch über die wahre Art das
Clavier zu spielen from 1753 (see Ex. 12). This movement is the eleventh of
eighteen Probestücke or instruction pieces, each of which served a musical as well
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Ex. 11 Haydn, String Quartet in D major, Op. 50 No. 6 (1787), first movement, bars
138–150: le–sol–fi–sol modulating variant (deceptive-cadence-to-perfect-authenticcadence strategy)
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Ex. 12 Carl Philipp Emanuel Bach, Achtzehn Probestücke zu demVersuch über die wahre
Art das Clavier zu spielen, Sonata no. 4 in B minor (1753), second movement, Largo
maestoso, Probestück no. 11, bars 22–24: le–sol–fi–sol schema, modulating variant
as a pedagogical function. Bars 23–24 show the same replicated patterning, now
prompting a modulation from D major to F minor. The underlying pedagogical
context is especially relevant in this connection: the Probestück illustrates the
schema’s use not merely as a means of modulating up by a major third, but as the
means of doing so – the modulation is highlighted as a signature move of the
schema. This Largo maestoso begins in and returns to D major at bar 15,
following modulations to the dominant (in bars 5–12) and relative minor (bars
13–14). The modulation to F minor in bars 23–24 that is induced by the
le–sol–fi–sol causes the movement to end in a different key than its opening D
major: F minor is sustained via extemporisation and confirmed by a perfect
authentic cadence at bar 26 to close the movement. The Probestück thereby
spotlights the modulating variant of the le–sol–fi–sol, objectifying it as a customary means for modulating up by a major third.
Bach probably also intended that the schema serve as a more general pedagogical exercise in modulation, as evidenced by his decision to employ a particular le–sol–fi–sol modulating exemplar: when a structural or otherwise
significant modulation was needed in a composition, composers often preceded
the le–sol–fi stage of the progression with a longer ‘standing on the tonic’ passage
in the previous key, which may consist of either tonic reiterations or arpeggiation,
as in the Probestück and Eroica examples, or tonic-dominant exchanges, as in Op.
50 No. 6 (see again Ex. 11 as well as Ex. 13 below). These modulating exemplars
feature a consistent asymmetry in duration between the ‘standing on the tonic’
passage and the trichordal le–sol–fi descent. Table 3 registers the comparative
length of the ‘standing on the tonic’ and le–sol–fi stages of the schema from
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Ex. 13 Haydn, Symphony in D major, No. 86 (1786), first movement, bars 117–124:
le–sol–fi–sol modulating variant exemplar with Fenaroli (Gjerdingen 2007) as ‘standing on the tonic’ cue
recorded performances for several of these exemplars, including the opening of
the Eroica.43 The ratio between the ‘standing on the tonic’ and le–sol–fi stages is,
on average, 64:36. In addition to their temporal durations, asymmetry also
results from differences in syntactic content. The ‘standing on the tonic’ is static,
repetitive and circular, whereas the le–sol–fi is dynamic, progressive and goal
orientated. These asymmetries are rather conspicuously visible at the end of the
‘developmental core’ (Caplin 1998, p. 140) from the first movement of Haydn’s
Symphony No. 86 in D (1786), which closes on a half cadence in vi (B minor)
(see Ex. 15). In bars 118–124, a modulating variant of the le–sol–fi–sol takes the
music from G major to B minor. For the ‘standing on the tonic’ function here,
Haydn chose to use the Fenaroli schema (Gjerdingen 2007), whose tonicdominant reiterations communicate both circular motion (canon between outer
voices) and repetition. The Fenaroli, as a modulatory cue, stands in a ratio of
67:37 to the le–sol–fi in bars 122–123. In light of these asymmetries, the ‘standing
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Table 3 Le–sol–fi–sol modulating variant exemplars: asymmetrical durations between
a static, ‘standing on the tonic’ cue and the dynamic le–sol–fi stage of the schema,
measured in samples (recordings provided in example footnotes)
Cue
(samples) ( )
le–sol–fi
(samples) ( )
Emanuel Bach, Probestück No
Wq
. [D major–F minor]a
Mozart, Grabmusik, K
elsen, spaltet euren Rachen,
major–G minor]b
Haydn, Symphony No
, “L’Ours,” iv
major–G minor]c
Haydn, Symphony No
G major–B minor]d
Beethoven, Violin Sonata in D major, Op
ii
major–D minor]e
Beethoven, Symphony No
major, Op ii
major–D minor]f
Beethoven, Symphony No
major, Eroica, Op
major–G minor]g
a. Gabor Antallfy, Classic Produktion Osnabrück
b. Nikolaus Harnoncourt, Teldec
ny
c. Bruno Weil, Vivarte (Sony
d. Bruno Weil, Vivarte (Sony
e. Jorja Fleezanis And Cyril Huvé, Cyprés Records, EU
f. Jos van Immerseel, Zig-Zag Territoires
ustria
g. Daniel Grossman, Preiser Records
y(
on the tonic’ stage in all these exemplars becomes marked, and functions as a cue
that a modulation is afoot.44 It fulfils a priming function, supplying a sign for the
impending modulation.
Robert Hatten (1994) has classified the opening of the Eroica Symphony as
one of Beethoven’s characteristically marked themes owing to the instability and
sense of a developmental component that is infused by the chromatic descent in
bars 6–9. The ‘standing on the tonic’ passage which precedes the le–sol–fi
descent, however, is also marked, precisely because of its immobility.45 The
theme features instability (bars 6–9) following an overstated stability of E major
in bars 1–6. For this reason, the opening is not a theme, at least not in the
ordinary sense of the term, but rather more of a fragmented, improvisatory
gesture, as suggested by Rochlitz’s ‘preludising deviation’ comment. Indeed,
Carl Dahlhaus placed the Eroica among several other works from the period of
Beethoven’s ‘new path’,46 whose opening gestures advance not themes but rather
‘thematic configurations’ (1991, p. 17). In the Eroica, Dahlhaus sees this playing
out in the opposition between tonic arpeggiation (in bars 1–6) and chromatic
descent (bars 6–7). This opposition and the unthematic nature of the opening
result from Beethoven’s having ‘fronted’ a process-orientated, modulatory and
cadential schema – that is, positioned it as the opening gesture of a symphony.
Meyer called this compositional strategy ‘positional migration’, defined as the
(re)positioning of process- or closure-orientated schemata at the beginning of a
work (1989, p. 124).47 To further highlight the modulation that results from this
migration, the le–sol–fi ‘window’ of the schema is aligned with a shift in topical
discourse: the fanfare of the opening triads and the ‘horn call’ of the subsequent
E major arpeggiations in the cellos (which becomes a literal horn call at the end
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of the development), are contrasted by the Sturm und Drang characteristics of the
le–sol–fi–sol. These include, aside from the chromatic trichord in the bass, the
powerfully syncopated Gs in the first violins, which are featured in several
exemplars of the schema, such as Vanhal’s G minor Symphony, above (see again
Ex. 9), and which also seem to be lifted from the opening of Mozart’s early G
minor Symphony, K. 183 – perhaps as an intertextual referencing of this tonality.48 The end result causes the le–sol–fi–sol to bear the weight of the Symphony’s
first harmonic motion, which would cause a contemporary, experienced listener
to momentarily hear the Eroica as a G minor symphony that begins in medias res,
as implied by the details of Rochlitz’s review in 1807.
The Le–Sol–Fi–Sol Schema as a Category of Mind
The earliest sketches for the Eroica in the Wielhorsky Sketchbook (1802–3)
suggest that an opposition between E major and G minor was in Beethoven’s
thinking from the Symphony’s inception. Among these sketches are drafts for a
third-movement Menuetto serioso in E major with a G minor Trio.49 Although
the movement was abandoned, its tonal problem was reworked into several
dramatic and strategically located G minor episodes throughout the Symphony.
This includes a grand perfect authentic cadence in G minor as the goal of the
fugal episode in the Funeral March (Ex. 14); the cadence is articulated by a
combination of a le–sol–fi–sol (German sixth variant)50 and what Gjerdingen has
called a Stabat Mater Prinner (2007, Ch. 30) – a dominant pedal with braided
2–3 suspensions beginning on scale degrees 5 and 6, and a 1–2, 7–1, 6–7, 1
countermelody.51 The music that immediately follows the cadence (Ex. 14)
references the same A5 (bar 155) in the first violins from bar 10 of the first
movement, where it ‘corrected’ the G minor modulation by denying the resolution of G to F. The tables now turn, however, as A is absorbed into a C minor
context, the (local) subdominant of G minor. The plot resumes dramatically in
the finale, which of course features a G minor Turkish dance as one of its
variations (bars 213–258), where A becomes the Neapolitan, II of G minor,
made to resolve to F in the bass of bars 233–234, 241–242 and 244–246. But it
is the very end of the Finale that contains perhaps the most important G minor
episode of all: an imposing perfect authentic cadence in G minor at bar 422,
extended via a coda in bars 422–433 before it gives way to a second, fanfarebased coda in E major (Ex. 15). The last of these G minor episodes creates an
impression of two independent tonal endings for the Symphony. G minor is not
resolved into the following E major music so much as merged with or confronted
by it: the abrupt changes in tempo (to Presto) and dynamics (to ff) enforce a
nearly direct modulation in bars 434–436 that transforms the G octaves of bar
433 from scale degree 1 to scale degree 3 (Ex. 15). The result is a ‘bifocal’ G
minor–E major ending that mirrors the symphony’s similarly bifocal opening: E
(bars 1–6) followed by G minor (bars 6–9). And the tonal opposition is once
more highlighted by a discrete change of topic. The E fanfare is preceded by a
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Ex. 14 Beethoven, Eroica Symphony, Funeral March, bars 143–158: G minor perfect
cadence
G minor cadence cast in the Sturm und Drang style yet again, as bars 419–422
revisit the same pulsating triplet semiquavers and tremolo violins from the G
minor cadence in the Funeral March before giving way to its march-like, processional rhythms in bars 422–432 (cf. Exs 14 and 15).52
In light of the sketch evidence and of Beethoven’s exploration of a G minor
tonal problem throughout the Symphony, the details of the le–sol–fi–sol schema in
my corpus indicate that Beethoven anticipated a G minor response to bars 6–9
of the opening theme from his listeners. And the earliest documented response
to the Symphony’s opening theme in Rochlitz’s review brings evidence that such
a communicative transaction did indeed take place.53 More significant for our
purposes here, the communication brings evidence that the le–sol–fi–sol as a
replicated pattern in the music was also operative as a culturally and historically
determined category of mind. Rochlitz’s review indicates that the declarative
music-theoretic category I have defined as the le–sol–fi–sol schema operated as an
instance of procedural knowledge shaped by cultural context (Ex. 16), thereby
supplying evidence for Meyer’s and Gjerdingen’s hypothesis that patterns in the
music are equivalent to the knowledge structures of listeners. It supports the
idea, advanced by the psychologist John Anderson, that ‘categorization behavior
can be predicted from the structure of the environment at least as well as it can
from the structure of the mind’ (1991, p. 427). Specifically, Rochlitz’s review
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Ex. 15 Beethoven, Eroica Symphony, Finale: G minor perfect cadence and coda, bars
417–432
evinces the psychological basis of the le–sol–fi–sol by demonstrating signs of two
of the most significant features of a schema-driven process – recognition and
expectation.
‘In terms of cognition, style is simply repetition ... . [W]e recognize when we
are hearing something learned elsewhere’ (Narmour 1999, p. 441).54 The details
of the corpus study suggest that Rochlitz perceived a G minor tonality in bars
6–9 of the theme because he tacitly recognised many, if not all, of the features of
the le–sol–fi–sol; in other words, the pattern served as a ‘recognition device’
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Ex. 15 continued: a second, E major coda and fanfare, bars 433–439
Ex. 16 Beethoven, Eroica Symphony, Allegro con brio, bars 1–11: le–sol–fi–sol
schema, modulating variant
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(Rumelhart 1980, p. 41) in the Eroica Symphony’s opening bars, including such
characteristics as the dominantising attributes of the schema’s first stage, its
cadential orientation, the priming effect of the marked cue in the exemplars of
the modulating variant, and so on. The schema-as-recognition-device argument
suggests that an eighteenth-century listener tacitly knew the key-defining profile
and normative usage of the schema (both in its non-modulating and modulating
guises) through extensive exposure to its regular occurrence in the corpus. I have
elsewhere (Byros 2009a and 2011) suggested that style-specific knowledge of
this kind is (largely) gained through statistical learning, the idea that abstract
structure or category formation may originate from the mind’s internalisation
and exploitation of statistical regularities encountered in the musical environment.55 Meyer anticipated this view as early as the 1960s, by suggesting that
statistical redundancies in a musical corpus correspond to perceptual redundancies in the mind of the listener, regularities which give rise to mental representations: as he put it, ‘the perceived regularities become “coded” as schemata’
(Meyer [1967] 1994, p. 277). The statistical-learning component implicit in
schema theory strongly resonates with the ‘embedding thesis’ in situated cognition, which holds that ‘cognitive activity routinely exploits structure in the
natural and social environment’ (Robins and Aydede 2009, p. 3). Although
Gibson (1986) first advanced this ecological view of psychology in the context of
visual perception and the natural world, its many extensions in the situatedcognition movement that he influenced have broadened the concept to all
varieties of cognition in the social and cultural domains (see, for example, Heft
2001 and Robins and Aydede 2009). Along similar lines, Meyer’s analysis of style
was implicitly Gibsonian in letter and spirit: Gibson advanced ‘stochastically
regular’ repetition and ‘probabilistic’ regularity (Gibson 1986, p. 10) as features
that define an environment; and Meyer similarly defined style as a ‘replication of
patterning’ (1989, p. 3), ‘stochastic process’ ([1967] 1994, p. 14) and ‘probability
system’ (ibid., p. 47 ). By treating a musical corpus as a metaphor for experience,
as a metaphor for the real-life musico-cultural environment of a listener, its
probabilistic structure (that is, style) can be interrogated as a causal influence on
a listener’s cognitive behaviour in order to examine whether the probabilistic
structure of the musical environment is causally responsible for some listener
response.
From these perspectives of statistical learning and situated cognition, Rochlitz’s G minor hearing amounts to a cognitive prediction – which, as stated above,
is caused by the activation of some underlying mental representation – prompted
by the probabilistic structure of the corpus as environment. Acquiring the
le–sol–fi–sol schema would likely derive from the internalisation of a third-order
probability. Because the first stage of the pattern contains three events, one may
understand the le–sol–fi–sol category as the internalisation of the regularity with
which the first three events of the schema lead to a dominant triad (or seventh
chord). In his work on statistical learning, probability and expectation, David
Huron has suggested that ‘contingent probabilities can be influenced by the
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number of events that combine to influence a particular ensuing event’ (2006, p.
361). That is, increasing the number of events in the antecedent state of a
probability matrix or Markov chain may cause an increase in the probability of
transition to a given consequent state. In the case of the le–sol–fi–sol, the probability that a dominant triad or seventh chord will follow from the third-order
6
progression VI − i 4 –iv°7 is 85.94% in the analysed corpus. Learning the schema
is, at the most basic level, a matter of internalising this regularity as a culturally
constructed affordance56 of the musical environment. Probability, or stochastically regular repetition, affords listeners a means of negotiating the environment,
of actively making predictions and therefore navigating the musical landscape.57
The stylistic information contained in the schema as a ‘packet of knowledge’
(Gjerdingen 2007, p. 11), once internalised, is ‘appropriately brought into play’
when features in the musical environment (bars 1–9 of the Eroica) are recognised
as constituents of the learned category. The AmZ review evidences such a
schematic mapping – what situated cognition researchers would refer to as a
‘causal coupling’ between subject (Rochlitz) and environment (style).58
Besides assigning a G minor key context to bars 7–9, further evidence of
schematic mapping is Rochlitz’s perceived denial of an expectation. Expectation,
as suggested above, is an indication of a schema-based process: ‘Knowledge of
style enables listeners to recognize similarity between percept [‘sound stimulus’,
in Meyer’s terms (1956)] and memory[,] and thus to map learned, top-down
expectations ... . Listeners [therefore] construct stylistic expectations that are
remarkably specific, surprisingly complex, and incredibly detailed’ (Narmour
1999, p. 441). Meyer anticipated this argument in Emotion and Meaning in Music,
by proposing that we form expectations because we organise new musical experiences according to past experience: ‘we organize our experience and hence our
expectations ... in terms of our memories of earlier relevant musical experiences’
(Meyer 1956, p. 88). Expectation results from the activation of a schema as an
evaluative recognition device. Here too, Rochlitz’s review brings evidence that
the le–sol–fi–sol schema operated in a psychological capacity: the expectation of a
G minor dominant to sound in bar 10 is highlighted by his description of the 64
chord in bar 9 being denied resolution by the subsequent 65. Thus, recognition of
the le–sol–fi–sol precipitates a G minor tonality in bars 6–9 of the theme, and the
G minor context, along with the syntactic parameters of the le–sol–fi–sol, conditions the specific expectation for the 64 chord in bar 9 to resolve normatively to
a G minor dominant. Perhaps the most remarkable feature of Rochlitz’s G minor
hearing, aside from the explicit description of a modulation, is its complete
recontextualisation of the anomaly in Beethoven’s theme, which turns a dominant strain of Eroica reception on its head. The deceptive move is situated not in
the C but in Beethoven’s not fulfilling the stylistic expectations generated by the
le–sol–fi–sol after having fronted it to the opening of a symphony – in not
completing the schema. Whereas the G minor modulation is said to occur
‘formally’, or ‘according to rule’ (förmlich) – which presumably refers to the
normative modulating function of the schema – the return to E major does so
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‘unexpectedly’ (unvermuthet), seemingly because of the violation of the schema’s
structure by the elision of the G minor dominant. The ‘diminished-seventh ...
over C in the bass, and ... the 64 chord ... over D’ (Rochlitz 1807, p. 321) in bars
7–9 serve as preparation for the deviation. Through them, ‘the composer prepares
the listener to be agreeably deceived in the succession of harmonies’ (ibid., p.
321).The ‘agreeable harmonic deception’ (‘angenehmen harmonischen Täuschung’; ibid., p. 322) comes later, with the unexpected return to E major caused by
6
the V 5 chord of bar 10: ‘one expects to be led predictably to G minor ... but in
place of the resolution of the 64 chord, finds the fourth led upward to a fifth, and
so, by means of the 65 chord, finds oneself unexpectedly [unvermuthet] back at
home in E major’ (ibid., p. 321). The sketch evidence and important G minor
music throughout the Symphony suggest that Beethoven not only intended his
listeners to cognise a G minor modulation but, as a consequence of the modulation, to focus their attention on this deception at bar 10 – the unexpected
return – as a main feature of the opening theme. The le–sol–fi–sol appears to have
functioned as a shared symbol in communicating not only the modulation to G
minor, but also the opposition between E major and G minor that will continue
to play out in the course of the Symphony’s tonal drama.
The Le–Sol–Fi–Sol Schema as a Situated Psychology of Hearing
In short, hearing G minor in bars 6–9 of the Eroica is a consequence of the
le–sol–fi–sol having been set up in the mind as a context for interpretation during
the act of listening. But for Meyer and Gjerdingen, as seen above, such schemadriven listening amounts not simply to a general psychology of hearing, but to a
situated mode of cognition. Details in the Eroica case study suggest that the G
minor hearing motivated by the le–sol–fi–sol is a historically and culturally situated interpretation. The most important among these details is the historical
population distribution of the schema. As part of the corpus analysis I conducted
a historical survey of the le–sol–fi–sol similar to Gjerdingen’s chronicle of the 1–7,
4–3. Fig. 5a gives a population distribution of the 550 instances of the schema in
the analysed corpus. Usage of this chromatic turn of phrase peaks dramatically
in the 1790s, with generally increased activity between 1760 and 1810. In
Fig. 5b, Gjerdingen’s statistics on the 1–7, 4–3 are adapted to the same criteria
of representation by distributing the population at ten-year intervals. The two
corpora generated population distributions illustrating that these schemata both
followed a life cycle, of sorts, with peaks in the 1790s (le–sol–fi–sol) and 1770s
(1–7, 4–3), respectively – decades that represent the heyday of the Classical style.
The le–sol–fi–sol schema gradually falls into disuse from the 1820s onwards,
and somewhat rapidly at that, whereas the peak is reached much more gradually
(cf. 1–7, 4–3). This can be seen in the schema population’s deviation from a
normal distribution in Fig. 5a – skewed to the left.59 In this context, I should like
to revisit Benzon’s submission (discussed above) that ‘culture ... molds the
nervous system’ – the latter being an ‘impress of the environment’ (2001, p. xiii).
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Fig. 5 (a) Historical distribution of the le–sol–fi–sol population, 1720–1840: from a
corpus of roughly 3,000 musical works, representing all genres, throughout all
Europe (from Byros 2009)
1790s
150
135
120
105
90
75
60
45
88.4%
30
15
0
1720 1730 1740 1750 1760 1770 1780 1790 1800 1810 1820 1830
Fig. 5 (b) Historical distribution of the 1–7, 4–3 population, 1720–1840 (after
Gjerdingen 1988)
150
135
1770s
120
105
90
75
60
45
30
90.4%
15
0
1720 1730 1740 1750 1760 1770 1780 1790 1800 1810 1820 1830
Insofar as the le–sol–fi–sol is a part of late eighteenth-century culture, a shared
symbol that occupies the musical environment, its gradual fall into disuse during
the nineteenth century is equivalent to a cultural and environmental change.
This change brought on by the gradual disappearance of the le–sol–fi–sol should
introduce different modes of listening that are moulded by the new musical
environment. It is precisely this type of evidence that is provided by the larger
reception history of the Eroica’s opening theme. Fig. 6 maps the date of origin of
the Eroica’s three strains of reception (Tables 1 and 2) onto a timeline that also
displays the historical population distribution of the le–sol–fi–sol. As shown in the
figure, the first G minor response, dating from 1807, and Beethoven’s composition of the Symphony in 1803 occur immediately after the schema’s peak in the
1790s, and well within the period when the schema flourished in general –
indicating that the statistical regularities reconstructed by my corpus study were
of cognitive significance for a historically situated listener. That is to say, the
statistical frequency and replicated features of the le–sol–fi–sol schema discussed
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Fig. 6 Competing musical environments and cognitive plasticity: the le–sol–fi–sol
schema as a ‘condition of [cognitive] transformation’ (Bartlett 1932)
1790s: le – sol – – sol peak
150
135
120
105
90
schema absence
75
60
“Cloud” strain
E-flat strain
45
1857
1930
30
15
0
1720 1730 1740 1750 1760 1770 1780 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930
(Eroica date of composition) 1803
1807 (Rochlitz’s review)
above would have given rise to a mental representation (as an ‘impress of the
environment’, or, in Aristotle’s [1906, p. 107] terms, a ‘copy’ of the environment),60 which was responsible for Rochlitz’s G minor hearing in 1807. The
AmZ review provides a correlation, a causal coupling between a contemporary
listener’s response and the structural details of the musical environment (i.e. the
corpus). In the nineteenth century, an inverse correlation materialises, whereby
new hearings of the Symphony’s opening theme appear with the Cloud and E
strains in the 1850s and 1930s, respectively, after the le–sol–fi–sol schema’s
population had declined, resulting in a decoupling of later generations of listeners from an eighteenth-century stylistic environment.
The presence or absence of the le–sol–fi–sol in the musical environments of the
eighteenth and nineteenth centuries seems to be causally responsible for the
competing ways in which listeners from different historical periods construct a
key context for bars 6–9 of the Eroica’s opening theme. The presence and
absence of the schema appear to be the ‘conditions of transformation’, in
Bartlett’s terms. The underlying argument of Meyer’s anvil would predict such
an outcome, owing to the problems of ‘cultural noise’ that arise with extensive
historical and anthropological distance: ‘the more ... historically or anthropologically ... distant a culture is from our present set of habit responses, the greater
the amount of cultural noise involved in communication’ (Meyer [1967] 1994,
p. 16). Meyer treats historical context as equivalent to cultural context, in as
much as the contrasting musical environments of historical periods configure
different modes of listening. In Style and Music, he sustained this argument
through a social-ideological interpretation of style change, arguing that
eighteenth-century musical style is nurture driven, while the nineteenth century’s aesthetically and ideologically motivated repudiation of convention orientated musical practice more towards ‘natural’, innate or universal gestalt
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principles of organisation. In the transition from the eighteenth to the nineteenth
century, the musical environment changed both structurally and ideologically
(Meyer 1989).
In light of this argument, we may read the decline of the le–sol–fi–sol schema’s usage in the nineteenth century (as well as that of the 1–7, 4–3) not only
as the falling into disuse of a single pattern, but also as a metaphor for this
more general stylistic trend. In particular, my dissertation suggested that schemata in the eighteenth century had strong key-defining profiles. Replicated
patternings such as the le–sol–fi–sol operated within a larger culture of tonal
stamping, which is also evident in various pedagogical, analytical and critical
writings from the period.61 In the early part of the eighteenth century, both
Johann David Heinichen ([1711] 2000 and [1728] 1994) and David Kellner
([1732] 1979), who penned one of the most widely circulated thoroughbass
manuals in the eighteenth century, used the Latin transliteration (of the original
Greek) ‘schema’ to characterise the Rule of the Octave paradigm. In Heinichen’s case, the term was generalised to describe any figured-bass progression
at the phrase level that defined a key (see e.g. Heinichen [1728] 1994, p. 905;
and Byros 2009a, Ch. 2). Towards the other end of the long eighteenth century,
Gottfried Weber’s Versuch einer geordneten Theorie der Tonsetzkunst of 1817–21
(revised and expanded in 1830–2) contains a long meditation on the ‘Habits of
the Ear’ (‘Gewohnheiten des Gehöres’). These ‘habits’ may well be the first
discussion of the schema concept in any music-theoretic literature, and, importantly, it appears in a chapter on ‘Tonality’ (‘Modulation’). In a section entitled
‘Attunement of the Ear to a Key’ (‘Stimmung des Gehöres in eineTonart’),
Weber defines modulation in the traditional twofold eighteenth-century
manner, which specified both the process of defining a key and movement from
one key to another: ‘Modulation in the Key – Modulation out of the Key’
(‘Leitergleiche, – ausweichende Modulation’). In this context, the third among
five habits that Weber discusses is the phenomenon of ‘Customary Modulation’
(‘Gewohnte Modulation’): ‘[I]t is natural also that the ear should be accustomed to many modes of modulation [i.e. harmonic progression] in the most
common use, and should become thereby much inclined to understand an
harmonic succession in the customary sense’ (Weber [1817–21] 1830–32, vol.
2, p. 137 and 1851, vol. 1, p. 355). The implication is that a schema, replicated
patterning or ‘modulation ... in common use’ is ‘stamped’ with its tonal signification. The details of the Eroica case study resonate with such contemporary
discussions, suggesting that eighteenth-century key perception was significantly
coextensive with schema recognition. Such a view is further supported by Ian
Quinn’s recent key-finding study, based on the chorales of J.S. Bach, which
indicates that ‘chord progressions ... are sufficient as windows for key-finding ...
and ... that the encapsulated identity of a chord progression is sufficient’ (2010,
p. 151). The strong key-defining profiles of schemata suggested by the Eroica
case study were an important aspect of communicative context in the eighteenth century. The regulative power of schemata afforded an efficient and
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Ex. 17 Franz Schubert, String Quartet No. 15 in G major, Op. 161 (1826), third
movement, bars 118–146: le–sol–fi–sol deformation and decontextualisation
systematic means for communicating the phenomenon of key through a kind of
tonal ‘code’. In light of the le–sol–fi–sol, Rochlitz’s G minor hearing also supplies correlating evidence of this more general practice: that experienced
eighteenth-century listeners grasped a tonal orientation by way of the tonal
windows constructed by schemata.
In the nineteenth century, this custom gradually collapsed, owing to an
exponential growth of possibilities for novel harmonic successions. Liberal
chord usage dissolved the system of codified configurations for expressing a
key, so that harmonic progressions became increasingly less scripted in so far as
their key-defining attributes were concerned, which inevitably led to a retrospective negative influence on the key-defining significance of eighteenthcentury schemata. Ex. 17 provides a telling example from the history of the
le–sol–fi–sol of the kind of nineteenth-century behaviours that recontextualised
and de-signified eighteenth-century patterns. In the Scherzo of Schubert’s late
String Quartet in G major, Op. 161, D. 887 (1826), we find an unprecedented
transformation of the schema. Although the situation is identifiable as le–sol–
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tualisation and transformation of the pattern. The key context in bars 118–146
is an unrelenting B minor. Twice within this context (in bars 131 and 141) we
hear the following progression: E 53 –G minor 64 –C°7. Out of context, the progression fits the first stage of the le–sol–fi–sol. But in the Schubert, the diminished seventh is resolved to a B minor triad in first inversion (i6) instead of the
normative G minor dominant. That, in addition to the oppressive and unrelenting B minor which surrounds bars 131 and 141, recontextualises what in
6
the eighteenth century would have been an unequivocal
VI6 − i 4 –iv°7 progres6
sion in G minor to sound as a rather bizarre III– vi 4 – vii° 4 progression in B
minor. Schubert’s Quartet was written in 1826, well within the period when the
le–sol–fi–sol was undergoing a rather marked decline in usage (see again
Fig. 5a). In respect to the 1–7, 4–3, ‘on the descending or late slope [of the
historical population] the schema is already in a process of transformation’
(Gjerdingen 1986, p. 36). Indeed, the Schubert example is more an echo of the
le–sol–fi–sol than a bona fide instance of the schema. In light of Meyer’s overarching argument in Style and Music, this transformation of the schema emerges
as a representative instance of the larger stylistic changes that transpired in the
transition from the eighteenth to the nineteenth century. More specifically, the
schema’s ‘deformation’ (Gjerdingen 1986, p. 36) fits neatly within Meyer’s
‘sketch-history’ (1989, p. 161) of the nineteenth century, which maintains that
the ‘gradual weakening of syntactic relationships ... was perhaps the single most
important trend in the history of nineteenth-century music’, ‘coupled with a
correlative turning toward more natural compositional means’ (1989, p. 272).
Nineteenth-century aesthetics, as Gjerdingen has similarly argued, shattered
eighteenth-century schemata, which have lain ‘in the musical rubble of the
ancien régime for almost two centuries’ in the form of musical ‘potsherds’ (2007,
p. 436). We can see this metaphor playing out in the historical moment that is
sedimented in Schubert’s Quartet and its deformation of the le–sol–fi–sol. The
schema, as discussed above, is based on a third-order probability that a dominant will follow from a three-chord progression consisting of a major triad, a
minor triad in second inversion and a diminished seventh over a descending
chromatic trichord in the bass; the probability for this transition, as we have
seen, is 85.94%. The ideologically motivated expansion in the nineteenth
century of the harmonic-syntactic gamut represented by Schubert’s Quartet
fragmented this high-level probability and, in the process, the le–sol–fi–sol itself.
In Schubert’s Quartet, one can see the le–sol–fi–sol fall to the ground and
shatter, leaving only a fragmentary trace of an older, forgotten or otherwise
contested practice.62
For Meyer, the significance of these stylistic changes moves well beyond
music historiography. They affect modes of hearing by altering the kinds
of habit responses listeners form: ‘[s]tyle changes have, of course, almost
always presented problems for listeners’ (Meyer [1967] 1994, p. 292). Today
the most relevant consequence is that styles are learned in an ahistorical
capacity.
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Fig. 7 Inverse proportionality between information and probability as style change
metric (after Meyer [1967] 1994 and 1989)
1.0
probability
0.8
0.6
0.4
0.2
0.0
0.2
0.4
0.6
information
0.8
1.0
[E]ach musical experience ... modifies, though perhaps only slightly, the internalized probability system (the habit responses) upon which prediction depends
... . [T]his process of modification is ahistorical. Not only does hearing or
rehearing a work, say, by Schubert, by modifying our internalized probability
system, change our experience of the work of later composers (say, Stravinsky); it
also changes our experience of the music of earlier composers – for instance,
Bach. (Ibid., p. 47)
The statistical basis of schema acquisition is especially apposite here. By Meyer’s
estimation, the ‘weakening of tonal syntax’ (1989, p. 102) in the nineteenth
century resulted less from the novelty of nineteenth-century progressions than
from the impact of those progressions on listeners’ perceptions of eighteenthcentury probabilities: ‘making more use of progressions that have previously
been rarely chosen changed the probability relationships among all progressions,
including those that defined tonal centers’ (Meyer 1989, p. 299; emphasis in
original). Part of Meyer’s thesis regarding the stylistic changes that obtained
from the eighteenth to the twentieth century involves a gradual increase in
entropy (or information). The more information-laden styles of the nineteenth
century complicated the information-poor probabilities of eighteenth-century
music (Meyer [1967] 1994, pp. 116–22, and 1989). An increase in the degree of
probability relationships is directly correlated with a decrease in ‘statistical
redundancy’ (Meyer [1967] 1994, p. 277) or regularity. That is, probability and
information are inversely related, as shown in Fig. 7; and, as ‘perceptual redundancies’ (ibid., p. 227), these statistical regularities are the very affordances for
schema acquisition in eighteenth-century music. Gjerdingen describes this as
follows:
The concept of affordance may ... describe a cognitive resonance between an
object in the environment and a perceiver’s memories of past actions or ideas. If
we admit sonic objects to the class of things permitting affordances, leading to
truly ‘musical’ affordances, then listening itself becomes a type of interaction with
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an aural environment. Several types of listener-oriented music theory could be
described as frameworks for recognizing and evaluating affordances. The
implication-realization model of Leonard B. Meyer (1973) and Eugene Narmour
(1990) would be an obvious case, and, with respect to larger objects, the formalfunctions work of William Caplin (1998). Similarly, my own work (2007) with the
stock phrases of eighteenth-century music could be described as creating an
inventory of historically perceived affordances. (Gjerdingen 2009b, p. 124)
The later expansion of progressions and liberal chord usage in the nineteenth
century problematised the regularities of eighteenth-century music as
affordances for schema acquisition: ‘new learning is contingent upon the possibility of discovering – of perceiving – some sort of manifest order and regularity
in experience ... . [T]he perceived regularities become “coded” as schemata’
(Meyer [1967] 1994, pp. 276–7). It stands to reason that musical environments
with higher levels of information or lower levels of regularity or redundancy
are unfavourable ones for schema acquisition.63 The gradual deformation of
eighteenth-century conventions, along with the greatly expanded harmonic
lexicon and probability system of the nineteenth century, dulls the affordances
and meanings of eighteenth-century schemata for subsequent generations of
listeners, because they will experience eighteenth-century patterns with more
modern and pluralistic ears – that is, through the larger or broader probability
system internalised from exposure to nineteenth- and twentieth-century music,
idioms from non-Western and popular cultures, and so forth. Even when, or if,
still present in the nineteenth century, eighteenth-century schemata were defamiliarised by this more loose-knit stylistic environment.
The British musicologist Charles L. Cudworth was among the first to suggest
that eighteenth-century patterns are less accessible to present-day listeners. He
maintained that music of the galant half-century (1730–80) ‘made use of many
mannerisms’, such as the eponymous ‘cadence galante’, which were ‘so markedly
of [their] period’ but, having been ‘battered by the heavier musical artillery of the
Romantic composers’, ‘the[ir] effect ... is largely lost on modern ears’ (1949, p.
176). Indeed, Cudworth argued that the cadence galante was ‘hitherto unnoticed’
(ibid., p. 178). The same argument underlies Gjerdingen’s Music in the Galant
Style, although on a magnified scale: the breaking down of eighteenth-century
syntactic regularities has led modern listeners to, as he put it, ‘become deaf to’
(2007, p. 59) eighteenth-century schemata such as the Prinner: ‘habits of listening became transformed in the nineteenth century’, resulting in a more ‘black
and white’ hearing of eighteenth-century music (2007, pp. 59 and 4). The
Eroica’s reception history brings evidence that the similar deformation of the
le–sol–fi–sol in the nineteenth century gave rise to cultural noise in subsequent
responses to its opening gesture.
Recall that for Rochlitz, writing in 1807, the G minor 64 harmony in bar 9 is
the moment richest in G minor significance in the opening theme. The E
transcripts, on the6 other hand, all uniformly interpret this chord as an incidental
harmony. The ‘ iii 4 ’ in bar 9 is ‘functionally extraneous’ (Barry 2000, p. 109), an
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‘apparent chord’ (Klein 2005, p. 83), an ‘unheimlich apparition’ (ibid., p. 82) and
a so-called neighbour to a neighbour (Schenker [1930] 1997). The rationale for
hearing this chord as an incidental harmony is a perceived syntactic relationship
6
between the diminished seventh chord in bars 7–8 and the V 5 at bar 10: ‘the
diminished seventh chord of C could be resolved onto the first inversion dominant seventh in m. 10, so retaining the upper-line appoggiatura, G–A, and also
the inner line, G–F, thus bypassing m. 9’ (Barry 2000, pp. 109–10). Hyer voices
the same interpretation, stating that at bar 9 ‘we ... expect G to move to F above
an A, forming a dissonant 65 above D in m. 10’ (1996, p. 88). Likewise, Klein
describes ‘the underlying harmonic progression [as] mov[ing] directly from the
chord with the C in the bass to the dominant [of E] with D in the bass [bar 10]
– the G minor harmony of m. 9 is an apparent chord that results from the
staggered motion of the upper and lower voices’ (2005, p. 83).64 This attention
given to the unfamiliar G minor object (‘unheimlich apparition’) is an indication
of cultural noise: ‘uncertainty arises when the probabilities are not known ...
because the listeners’ habit responses are not relevant to the style (cultural
noise)’ (Meyer [1967] 1994, p. 17). Typically, ‘uncertain’ or ambiguous stimuli
invite greater attention from subjects, as seen in several studies of visual perception, where subjects were found to direct their eye movements more often to
schema-inconsistent than to schema-relevant information (Friedman 1979; and
Loftus and Mackworth 1978). Moreover, the E major descriptions exhibit the
kinds of rationalisation techniques that have been characterised as symptomatic
of schema absence (Bartlett [1932] 1995) – what Brewer, following Bartlett, calls
‘transformations to the familiar’ (discussed above). The familiar object here, it
would seem, is a common nineteenth- and twentieth-century harmonic device:
the so-called common-tone diminished seventh chord (hereafter CT°7). The
CT°7 allows for an ‘underlying harmonic progression [which] moves directly
from the chord with C in the bass to the dominant with D in the bass’ (Klein
2005, p. 83). And Jeremy Day-O’Connell (2002) explicitly characterises the
C in the Eroica as a raised submediant, which forms the basis for a CT°7
interpretation.
I want to suggest that the competing G minor and E hearings are consequences not only of the relative presence and absence of the le–sol–fi–sol, but also
of the presence of a competing schema in the nineteenth century – that of the
CT°7. I would maintain, further, that these two schemata also represent competing psychologies of hearing that are characteristic of eighteenth- and
nineteenth-century modes of listening, respectively. That is, both strains in the
Eroica’s reception are schema symptomatic, but in different ways. The le–sol–fi–
sol and CT°7 are schemata of a different order:
In 1977, the psychologists Roger Schank and Robert Abelson distinguished
between different categories of schemata they called ‘scripts’ and ‘plans’. A
‘script’ is an extremely detailed knowledge ‘structure that describes appropriate
sequences of action in a particular context ... a script is a predetermined, stereotyped sequence of actions that defines a well-known situation’ (Schank and
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Ex. 18 Eroica Symphony, first movement, bars 1–11: ‘plan’-based organisation of the
opening theme: E hearing influenced by the CT°7
Abelson 1977, p. 41). A ‘plan’, on the other hand, is a more general structure, a
‘repository for general information that will connect events that cannot be connected by use of an available script or by standard causal chain expansion’ [or
when] ... ‘a script is not available’ (1977, p. 70). (Byros 2009b, p. 276)
The le–sol–fi–sol fits Schank and Abelson’s definition of a ‘script’ as a ‘stereotyped
sequence of actions’, whose harmonic and scale-degree events and stages are
both intercontingent and well defined; a script ‘is made of up slots and requirements about what can fill those slots ... . [W]hat is in one slot affects what can be
in another’ (Schank and Abelson 1977, p. 70). The ‘stereotyped sequence of
actions’ in the le–sol–fi–sol is the third-order probability that underlies the constitution of the schema. The CT°7, by contrast, is more suggestive of their
definition of a ‘plan’ – a general structure ‘that will connect events that cannot be
connected by use of an available script’. In the Eroica’s E major responses, the
CT°7 allows for the connection of otherwise disjointed harmonic moments: as
6
shown in Ex. 18, it allows for the V 5 to be connected to the diminished seventh
of bars 7–8, thereby bypassing the 64 of bar 9 (and that of bar 6). This plan-based
organisation of the Eroica’s opening results in an ‘underlying harmonic progression’ (Klein 2005, p. 83) in which G minor plays no syntactic role. In addition to
these details, scripts are also more top-down (learned), while plans are more
bottom-up (innate): ‘script-based processing is a much more top-down operation ... a process which takes precedence over plan-based processing when an
appropriate script is available’ (Schank and Abelson 1977, p. 99). Implicit in
Schank and Abelson’s definition of a plan is that less information from the sound
stimulus is interpreted in a schema-relevant capacity.This aspect of a plan relates
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to yet another distinctive feature of a learned schema’s absence – namely, the
mind’s resorting to more bottom-up or data-driven strategies to organise or
assess a situation (see e.g. Mandler 1984, pp. 106–7). Because ‘[b]ottom-up or
data-driven processes are hard-wired, [they] do not depend on learning or
context, and rely on structural perceptual features of stimuli, not the stimuli’s
meaning’ (Johnson and Hirst 1993, p. 260; emphasis added). Indications of such
a bottom-up strategy may be inferred from Hyer’s description, quoted above
(1996). The rationale offered for hearing the bass note D in bar 9 of the Eroica
as ‘anything but a leading tone to E’ is ‘our too recent memories of E’ major –
simply put, there is a larger amount of E major information presented prior to
bars 7–8, as ‘structural perceptual features of the stimul[us]’.
In Style and Music, Meyer assigned a historical dimension to the categories
of scripts and plans, arguing that eighteenth-century music is inherently scriptorientated, while nineteenth-century music is increasingly plan-based in its
organisation.65 In light of the foregoing discussion of the effects of style change
on listeners’ responses, the competing stylistic dispositions of eighteenth- and
nineteenth-century music would give rise to comparably different modes of
listening for those with extensive exposure to one or the other style system.
Eighteenth-century music affords a more top-down, schematic or script-based
mode of listening, whereas nineteenth-century music – with its breaking down
of syntactic regularities – promotes a more bottom-up, archetypal66 or planbased listening strategy. And one can see these differences playing out in the
Eroica’s reception history, between the G minor and E strains of reception.
With the G minor hearing, conditioned by the le–sol–fi–sol schema as a scripted
configuration, ‘nurture (syntactic convention) dominates nature’; in the later,
E hearing, ‘nature dominates nurture’ (Meyer 1989, p. 244). The plan-based
organisation of the opening theme engages more innate processes of perception characteristic of gestalt psychology.67 Most noticeably, the E major
responses reduce bars 1–10 to a simpler form (see again Ex. 18) in a way that
is reminiscent of gestalt psychology’s basic law of Prägnanz. As already suggested by Schank and Abelson’s description of the underlying differences
between scripts and plans, the latter are activated when a script is not recognised: Meyer himself argued that the absence of recognition of a known syntactic context (script) will activate a plan – ‘general gestalt-like cognitive
dispositions, [and] not ... learned conventions’ (1989, p. 329). ‘For the human
mind, operating under the aegis of the law of Prägnanz, will go to almost any
lengths to avoid the doubts and anxieties which are created by ambiguity [cf.
the G minor 64 chord of bar 9]. That is, the mind will tend to apprehend a
group of stimuli as a pattern or shape if there is any possible way of relating
the stimuli to one another’ (Meyer 1956, p. 162). The plan-based, CT°7
organisation of the Eroica’s opening theme allows the stimuli of bars 7–8 and
10 to be related and thereby to give rise to a more coherent E major ‘pattern
or shape’ (Meyer 1956, p. 162). In sum, the G minor and E hearings appear
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ences, hearings that are representative of a more general binarism between a
script- and a plan-based strategy of listening. Following Meyer’s thesis on style
change, this more general opposition plays out on a historical stage. Scripts
and plans are characteristic of eighteenth- and nineteenth-century psychologies
of listening, respectively – an argument borne out by the Eroica case study,
where changes in listeners’ responses appear alongside historical changes in
musical style.
The Le–Sol–Fi–Sol Schema and the Paradox of ‘Convergence’
In 1832–3 Robert Schumann composed an unfinished G minor Symphony that
several commentators have suggested took Beethoven’s Eroica as a model (e.g.
Marston 2007; Daverio 1997; and Mayeda 1992). These scholars have noted
several features in common between the two symphonies, such as the triplemetre Allegro, motivic correspondences and the Beethovenian design of Schumann’s opening theme, which, ‘like many of those in Beethoven’s middle-period
compositions, is less a theme than a thematic configuration’ (Daverio 1997, p.
100). But perhaps the most significant association lies in bars 15–16 of Schumann’s opening, where we hear a prototypical instance of a le–sol–fi–sol in a G
minor context (Ex. 19). That Schumann employed this schema in a G minor
symphony modelled on the Eroica is no coincidence, for the schema is the central
feature of Beethoven’s theme. Nor is it coincidental that Schumann resolves the
le–sol–fi–sol deceptively onto an E major triad, although now as VI in G minor:
a local deceptive cadence in bar 18 that features a melodic profile similar to that
of the Eroica. The G–A–G progression in the Eroica (bars 6–10) is ‘corrected’ to
G–A–G. The G minor Symphony thereby brings intertextual evidence for
Schumann’s own G minor hearing of the Eroica: with this gesture, it is as if
Schumann is clarifying the events that transpire in Beethoven’s opening from
three decades prior.
The G minor Symphony was composed just a few short years after Schubert’s
G major Quartet (discussed above), which significantly deformed the le–sol–fi–
sol. Schumann, however, uses the schema in a prototypical fashion, and at a time
when he was deeply immersed in the study of eighteenth-century music: besides
Beethoven, the music of J.S. Bach and Friedrich Wilhelm Marpurg’s Abhandlung
von der Fuge (1753–54).68 The differences between Schumann’s and Schubert’s
contemporary uses of the le–sol–fi–sol speak to perhaps the most characteristic
aspect of nineteenth-century music, one that would become more and more
pronounced in later centuries: pluralism. Not only did self-proclamations of
artistic freedom give rise to new musical discourses, but the rise of nationalism
also played a fundamental role in fragmenting and diversifying style in the
nineteenth century. The eighteenth century, by contrast, was a more coherent
and thoroughly international style; as Daniel Heartz has argued: ‘[w]hat resulted
ultimately was an international style that merged French and Italian currents,
along with German ones’ (2003, p. 23). Map 1 plots the geographical distribu© 2013 The Author.
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Ex. 19 Robert Schumann, Symphony in G minor, ‘Unfinished’ (1832–33), first
movement, bars 13–20: prototypical le–sol–fi–sol schema ‘convergence’ in the 1830s
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Map 1 Geographical distribution of the le–sol–fi–sol population, 1720–1840, showing
cities and towns that either featured at least one instance in a composition known to
have been composed or performed there or otherwise were residences of composers
whose works employ the schema
tion of the 550 instances of the le–sol–fi–sol from 1720 to 1840; it shows cities and
towns that featured at least one instance of the schema in a composition known
to have been composed, performed or published there, or that were the residence
of a composer whose works employ the pattern. Using this ‘chromatic turn of
phrase’ once more in a representative capacity, we see in this map that
eighteenth-century music exhibits a tightly knit social fabric. The eighteenthcentury court system of patronages bore and sustained a musical culture that
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flourished in central and western Europe and extended as far north as Trondheim, Norway, as far southwest as Lisbon, Portugal, and as far east as St
Petersburg, Russia.
This would appear to be yet more evidence for the extent to which present-day
listeners are divorced from eighteenth-century musical culture. But such a
conclusion would ultimately go against the grain of Meyer’s anvil. Perhaps the
most pervasive element in Meyer’s several formulations of the schema concept is
that stylistically appropriate responses to music of the past are indeed still
possible in later centuries. In so far as eighteenth-century affordances are still
available through the conservation of the repertoire, it is conceivable that
modern listeners may acquire knowledge structures that are analogous to those
of their ancestors from two centuries ago. Gjerdingen discussed such crosshistorical learning of schemata in terms of ‘convergence’: ‘in spite of subjects
having quite different initial music experiences, there can be a convergence upon
the same prototype when very large numbers of similar exemplars are heard’
(1991, p. 127). In as much as the formation of habit responses rests primarily on
the statistical regularities of eighteenth-century music that are still available to
us, the same statistical learning process, although complicated by a pluralistic
musical world, is nevertheless possible. Gjerdingen provided ‘anecdotal evidence
of such convergence’ (ibid., p. 132) – namely, Meyer’s own intuitive convergence
on the 1–7, 4–3 schema and the prototypical usage of the eighteenth-century
Fonte schema discussed by Riepel (1755) in popular musics of the twentieth
century. Schumann’s prototypical usage of the le–sol–fi–sol in the G minor
Symphony is evidence of a similar convergence on an eighteenth-century pattern
in the 1830s. And the Eroica’s reception history provides evidence of continued
le–sol–fi–sol convergence throughout two centuries: the G minor hearing is consistently replicated from 1807 onward and has also persisted into the present (see
again Table 2). The evidence suggests that it is still possible to be situated within
the musical landscape abstracted in and represented by Map 1: ‘“native listeners” of eighteenth-century ... music’ may be ‘deceased members of those courts
or modern listeners who have immersed themselves in the galant style to the
point of acquiring it as a second language’ (Gjerdingen 1996, p. 380).
Eighteenth-century music has continued to occupy a position within the pluralistic musical landscape of the nineteenth and later centuries. In the end, a
situated psychology of hearing that interprets historical context as cultural
context rests on a ‘paradox’ (Byros 2009b, p. 236): ‘in order to demonstrate that
historical modes of listening may exist, one must articulate some difference with
the present so as to qualify the situatedness of cognition as “historical” in some
way, while maintaining that differences are somehow mediated all the same, in
order to allow “history” a place in cognition’ (ibid.). Schema theory invites this
otherwise uncomfortable paradox. From its inception, Meyer’s anvil has sustained both a negative and a positive orientation, outlining the historical and
social conditions that give rise to competing musical experiences (1989) while
reconstructing the conditions that allow for ‘stylistically appropriate’, ‘sensitive
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understanding’. It is precisely from its paradoxical nature that the schema
concept derives its substance and momentum. Musical cultures are both material and virtual constructs, established and accepted practices for shaping the
auditory stream in recognisable and meaningful shapes in a given context, but a
context that may transcend time and place. The ‘social processes of experience’
are both contingent and transferable; eighteenth-century experiences are distant
yet still possible. Schemata are responsible both for cloistering non-natives off
from a particular style and for providing access to otherwise foreign musical
languages. In the words of Niels Bohr, ‘How wonderful that we have met with a
paradox. Now we have some hope of making progress’ (Moore 1966, p. 196).
Conclusions and Implications
Yet all experience is an arch wherethro’
Gleams that untravell’d world, whose margin fades
For ever and for ever when I move.
The words are Tennyson’s (Ulysses, lines 19–21), and for the American philosopher John Dewey, they became something of a mantra, cited, as they are, in both
Experience and Education ([1938] 1997) and Art as Experience ([1934] 2005).
Dewey makes a cameo in several works of Meyer, who was heavily influenced by
the pragmatist philosopher in ideas, style and method. To place Meyer’s work in
the context of his own influences is perhaps the most fitting conclusion for the
preceding exposition. That is, the significance of experience in learning and the
arts can be so intuitive as to appear self-evident, and perhaps no reader would
object to it as a condition for knowledge. But at the same time, as soon as one
enters into that ‘untravell’d world’, the situation becomes far more complex.
Dewey, for example, argued that experience was necessary for true education, by
assimilating the phenomenon or subject matter in question to the life of a
subject. But to implement an experience-minded educational system is no easy
matter: suddenly a theory of experience is necessary. Dewey’s research, as an
antecedent to Meyer’s contributions, is a sobering reminder of the great work
that remains to be done.
I will therefore not pretend to have arrived at any definitive answers with
regard to either the nature or the function of experience. But in having struck
Meyer’s anvil once more, I would submit that the research introduced in this
article does advance the concept of a schema as an important instrument for a
theory of musical experience, and for that experience as a condition for musical
knowledge. The details surrounding the le–sol–fi–sol schema and the Eroica’s
reception history emerge as indications of the ‘social processes of experience’
that Meyer located at the basis of musical structure, style and cognition, and, in
the process, as evidence that supports several hypotheses basic to the research
programme of Meyer’s anvil: namely, (1) that replicated patternings in
eighteenth-century music are commensurate with the knowledge structures of
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listeners; (2) that these knowledge structures are historically contingent and
configure a situated psychology of hearing as a result; (3) that these situated
modes of listening are affected by style change; and (4) that historical modes of
listening are nonetheless still possible today. It is my hope that these advances
have outlined future paths for further investigations of the many aperçus lying in
Meyer’s workshop.
NOTES
1.
The term is ubiquitous in philosophical and psychological journals and
monographs in the first half of the twentieth century, which can now be
further investigated and verified by electronic text search. For biographical
essays on Meyer’s life and work, see e.g. Levy (1988) and McClary (2009).
2.
Tracing all of the subtleties in all of Meyer’s terms and their usage would
constitute an article in itself. But it should be noted here that Meyer had a
relatively short-lived romance with the term ‘archetype’. ‘Archetypes’ first
appear in 1973, and became the focal point of ‘Exploiting Limits: Creation,
Archetypes, and Style Change’ (1980). Archetypes are more general,
loosely constrained structures and therefore cross-cultural and transhistorical to varying degrees. But in this essay Meyer was problematically talking
about ‘schemata’ under the name of ‘archetype’, which explains the latter’s
sharp peak in use and then its decline in 1980 and 1989 (see again Fig. 1).
Meyer himself recognised and addressed the problem in Style and Music: ‘I
have discussed the nature and function of schemata in Explaining Music, pp.
213–26, “Exploiting Limits”, and (with Burton S. Rosner) “Melodic Processes”. In these studies I usually referred to such stable, replicated patterns as archetypes. I prefer the term schema, however, not only because it is
the term commonly used in cognitive psychology, but because there is a
possible confusion with Jungian psychology, which uses archetype to refer to
presumably innate universals. But as far as I can see, the schemata of, say,
tonal music are significantly a matter of learning; that is, they arise on the
levels of style rules, not cognitive universals’ (1989, p. 50, n. 31). Though
the term ‘schema’ first appears in Meyer’s writings after he had read
Gombrich’s Art and Illusion (1960), increased usage of the term was also
further influenced by Gjerdingen’s dissertation (1984), supervised by
Eugene Narmour at the University of Pennsylvania.
3.
See also Gjerdingen (2009a).
4.
The change in orientation was partly influenced by Eugene Narmour,
Meyer’s student at the University of Chicago in the early 1970s. I thank
Robert Gjerdingen for bringing this to my attention. Among other important changes in terminology (also influenced by Narmour) was the use of
‘implication’ as an alternative to ‘expectation’.
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5.
Though Meyer never advanced his own formal definition of ‘culture’, his
discussions of the concept in general are highly suggestive of Geertz’s
(1973) interpretation of culture as a ‘system of shared symbols’, and Meyer
explicitly characterised the ‘disciplinary outlook’ of Style and Music as ‘akin
to that of cultural anthropology or social psychology’ (1989, p. x). This
affinity between Meyer’s and Geertz’s ideas may be more than coincidental. Their paths crossed at the University of Chicago: Geertz was on the
anthropology faculty from 1960 to 1970, and Meyer, who was on the music
faculty from 1946 to 1975, actually completed his dissertation under the
auspices of Chicago’s Committee of the History of Culture (prior to
Geertz’s arrival); his PhD was awarded in the ‘History of Culture’. Meyer
does cite Geertz on two occasions in ‘A Universe of Universals’ (1998,
reprinted in Meyer 2000), and as early as Music, the Arts, and Ideas ([1967]
1994), he references Geertz’s ‘The Impact of the Concept of Culture on
Man’ (1965), which was written while they both were at Chicago and
which later became part of Geertz’s influential monograph The Interpretation of Cultures (1973). Both were also influenced by the American philosophers G.H. Mead and John Dewey. But whatever the historical details may
be, to interpret Meyer’s conception of ‘culture’ along Geertzian lines, is, I
maintain, a fair and accurate assessment of Meyer’s thinking and should be
understood to underlie the discussions of culture here. See also, in this
connection, the discussion below on schemata as shared symbols, and the
discussion of Meyer’s ideas in relation to Bartlett’s schema theory and
social psychology.
6.
Though the origins of Meyer (1989) date to the late 1960s, with a project
then titled ‘Music as a Model for History’ (see e.g. Meyer 1989, p. iv),
Gjerdingen’s A Classic Turn of Phrase was not only published prior to Style
and Music but also came into existence well before the latter’s publication,
as a dissertation at the University of Pennsylvania (see n. 2 above). In
consequence, Gjerdingen’s research left its influences on Style and Music,
most notably in Meyer’s use of the term ‘schema’ and of certain schematheoretic literature (e.g. Bartlett [1932] 1995; Schank and Abelson 1977;
and Rumelhart 1980).
7.
The 1–7, 4–3 population actually deviates from a normal distribution with
significance in its kurtosis (the measure of the sharpness of the distribution’s peak). The Meyer distribution is leptokurtic (sharper than a normal
distribution’s peak), with more than 4 standard errors of deviation (Kurtosis: 1.2139679; SEK: 0.297044). I thank Ric Ashley for his assistance in
analysing the formal statistical properties of the 1–7, 4–3 and of my own
population distribution discussed below.
8.
Gjerdingen (1988) also illustrated that the degree of ‘typicality’ of a schema’s instances is commensurate with its ‘prevalence’ in a given historical
period. By extension, the more constrained a particular pattern is in its
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definition, the more likely its historical population distribution will look
something like Fig. 2 – an ascent to a sharp peak, followed by a decline. See
the relevant discussions on ‘typicality’ in Gjerdingen (1986), (1988) and
(2007).
9.
Although Gjerdingen himself never discusses any examples of a ‘paired’
Prinner, he states that ‘in later decades [of the eighteenth century] it
became common to separate 6–5 from 4–3’ (2007, p. 49). Indeed, ‘paired’
Prinners are readily found in the later decades of the eighteenth century.
Mozart’s Piano Sonata in B major, K. 281 (1774), first movement, bars
3–4, is a paradigmatic example. Gjerdingen has also discussed a general
trend in which several schemata, like the do–re–mi and sol–fa–mi, were
adapted to a ‘pairing’ principle later in the eighteenth century – perhaps a
consequence of the period’s preoccupations with Classical symmetry, proportion and balance. See e.g. Gjerdingen (2007), pp. 85–6.
10.
On the practice of ars combinatoria in eighteenth-century music, see e.g.
Ratner (1980), Gjerdingen (2007) and Berkowitz (2010).
11.
The nature of this abstraction as a mental representation varies in the
psychological literature on categorisation. See n. 12.
12.
The literature on schema theory and categorisation is vast. The following
representative and seminal works have informed my thinking and understanding of the schema concept in general, beyond those by the Penn
School: Aristotle (1906); Locke ([1706] 1997); Hume ([1777] 1975);
Bartlett ([1932] 1995); Piaget ([1947] 2001); Piaget and Inhelder ([1968]
1973); Minsky (1975); Rumelhart (1975), (1977) and (1980); Neisser
(1976); Rumelhart and Ortony (1977); Schank and Abelson (1977);
Mandler (1979); Mandler (1984); and Rumelhart, McClelland and the
PDP Research Group (1986).
Beyond this important literature, more recent studies have dealt specifically with problems of categorisation – that is, with how schemata are
represented in memory. There are two primary and competing strains of
categorisation theory: the so-called prototype and exemplar theories of categorisation. Each deals with the problem of abstraction and generalisation
quite differently. In the prototype theory, a schema is viewed as a mental
abstraction of the invariant features – that is, similarities – encountered in
numerous instances of some phenomenon in a given environment. The
exemplar theory, by contrast, views a schema not as an abstraction but as
the mental registering of the total instances of the phenomenon encountered, which are classified in memory according to their invariant features.
In practice, the difference amounts to mentally ‘comparing’ a new instance
of the object or phenomenon with a ‘prototypical’ mental abstraction, or
with numerous ‘exemplary’ traces of the object or phenomenon existing in
memory as engrams. In the latter view, ‘schema’ refers not to any individual
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exemplar but to the simultaneous functioning of all the previously experienced instances of the object held in memory. This is referred to as
an ‘aggregate response’; see e.g. Johnson (2007) and Bartlett ([1932]
1995).
Prototype and exemplar views of categorisation are still part of an
ongoing debate in cognitive psychology and linguistics. But the exemplar
theory has recently gained favour from several experiments (e.g. Smith and
Minda 2002; and Dopkins and Gleason 1997), and is considered by some
to be a ‘mainstream’ approach to the modelling of memory (e.g. Baddeley
1997 and Johnson 2007). Its recent prevalence is likewise owed to important work by Nosofsky (e.g. 1986, 1988, 1991 and 1992), and to reconceptualisations of language processing as exemplar-based (Daelemans and
Van den Boesch 2005). More recently still, other studies have attempted to
reconcile the two paradigms (Verbeemen, Vanpaemel, Pattyn, Storms and
Verguts 2007; and Abbot-Smith and Tomasello 2006). Interestingly,
Meyer’s own language implies a conception of a schema that combines
prototype and exemplar views. On the one hand, our memories and past
experiences collectively provide an interpretative context in an aggregate
capacity: ‘As we listen to a particular musical work we organize our experience ... in terms of our memories of earlier relevant musical experiences’
(Meyer 1956, p. 88). But at the same time, he also spoke of schemata as
‘abstractions ... all stylistic response sequences involve abstraction’ (ibid., p.
57), in the form of ‘ideal types’, ‘class concepts’ or ‘norms’ (cf. also Meyer
1973, p. 213; ‘norms are abstractions’). Still, proponents of the exemplar
theory maintain that the generalisation and abstraction properties characteristic of the prototype view are also exhibited by exemplar models, and
thus render a separate prototype model redundant (see e.g. Johnson 2007,
pp. 34–5). Finally, for more general sources on the problem of categorisation, see Smith and Medin (1981) and Rosch (1978). Zbikowksi (2002)
remains a primary resource for music categorisation studies, and offers
an engaging history of the categorisation literature in the cognitive
sciences.
See also the discussion below on statistical learning and affordance.
13.
By no means do I wish to limit the concept of a ‘historical mode of
listening’ to the habit-forming and response-conditioning functions of
replicated patterning. But I would maintain that schemata provide a necessarily first and strong foundation for a broader, more ethnographically
minded study that investigates, along with the conventions that configure
one’s stylistic listening habits, other important communicative dimensions
grounded in these habits, such as compositional play and its aesthetic
effects, including humour, wit, irony, the serious and the sublime. This,
indeed, is the course set out in my further extensions of the schema
concept in an ongoing book project on the cognitive and communicative
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dimensions of style, tentatively titled The Act of Hearing: Style and Cognition in Music of the Late Eighteenth Century. In this connection see also n.
52.
14.
See also Meyer ([1967] 1994), p. 8: ‘Once a musical style has become part
of the habit responses of composers, performers, and practiced listeners it
may be regarded as a complex system of probabilities’.
15.
It is important to note that, while Meyer is speaking specifically about
‘affective response’ in this passage, he viewed ‘affective’ and ‘intellectual
responses’ as being predicated on the same ‘stylistic habits’. See Meyer
(1956), pp. 39–40 in particular. See also Meyer (1989), p. 12, for the same
argument.
16.
In a study on music and communication in the eighteenth century (Mirka
and Agawu 2008), Bonds (2008) has advanced a similar view, arguing that
both Kenner and Liebhaber listeners are inscribed into the ‘compositional
matrix’ of eighteenth-century music.
17.
In a personal communication, Gjerdingen described the corpus-asmetaphor-for-experience argument as a ‘hypothesis’.
18.
The review is actually anonymous. The Rochlitz attribution is from Geck
and Schleuning (1989).
19.
From Ebers ([1796] 1802).
20.
‘Persuasive’ is an interesting term here, as Rochlitz is clearly not proffering
the G minor hearing as an analysis in the modern sense – that is, as an
instruction set for a plausible hearing of which his readers are to be
persuaded. There is nothing of persuasion in Rochlitz’s rhetoric. This is a
casual description of the Symphony’s harmonic details in the context of a
review.
21.
Although Bartlett’s monograph was published in 1932, much of its
research derives from earlier work, some dating from the decade 1910–20.
See for example Bartlett (1920), also relevant to the discussion below on
the ‘War of the Ghosts’.
22.
‘“Schema” refers to an active organisation of past reactions, or of past
experiences, which must always be supposed to be operating in any welladapted organic response. That is, whenever there is any order or regularity
of behaviour, a particular response is possible only because it is related to
other similar responses which have been serially organised, yet which
operate, not simply as individual members coming one after another, but as
a unitary mass. Determination by schemata is the most fundamental of all
the ways in which we can be influenced by reactions and experiences which
occurred some time in the past. All incoming impulses [cf. Meyer’s ‘sound
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stimulus’] of a certain kind, or mode, go together to build up an active
organised setting [and] ... all the experiences connected by a common
interest: in sport, literature, art, science, philosophy, and so on, on a higher
level’ (Bartlett [1932] 1995, p. 201).
23.
Meyer characterised the ‘disciplinary outlook’ of Style and Music as being
‘akin to that of cultural anthropology or social psychology’ (1989, p. x).
24.
The folk tale is actually specific to the Chinook people, who spoke
Kathlamet.
25.
The story has in fact survived via repeated oral transmission and reconstruction. See Boas (1901).
26.
Several of these documents in the Symphony’s reception history are discussed in more detail in Byros (2009a), particularly Ch. 1.
27.
Cf. above, ‘Schemata: Methods of Objectification’.
28.
These Rumelhart sources are listed in n. 12.
29.
Another question, not treated here, involves what types of harmonisations
were most common for a -1, -1, +1 bass progression. The harmonisation in
the Eroica is the most frequent among 23 possibilities, and sits at the top of
a power-law distribution. See Byros (2009a), Appendix B.
30.
Though no formal measures were taken to normalise the corpus, the
roughly 3,000 works are fairly evenly distributed throughout the 1720–
1840 time period. For a complete inventory of the compositions and
editions consulted, see Byros (2009a), Ch. 3 and Appendix A.
31.
Eighteenth-century thoroughbass manuals classified diminished-seventh
chords without a third as bona fide diminished sevenths. In his Versuch,
Emanuel Bach ([1753, 1762] 1949, p. 133) actually discusses this species
of diminished seventh and its voice-leading details specifically in the
context of this pattern.
32.
Every one of these 550 examples of the le–sol–fi–sol schema (and several
hundred other variants) may be referenced in Appendix B of Byros
(2009a), where detailed information is provided for each instance, including the composer, work, date, movement, bar numbers, key(s) and variant
type (if a variant). The analytic component of the corpus study was done
entirely using traditional means: eyes, ears and hand. I studied the bass
lines for each composition in the corpus, searching for a -1, -1, +1 bass
progression in semitones and for descending chromatic tetrachords. The
harmonisation for each instance was analysed and then recorded in an
Excel document. In total, when including different harmonisations, topvoice variants of the le–sol–fi–sol, etc., 109 different variants of the schema
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were recorded using a coding system of my own design, in which features
of the schema (mostly involving harmony) have a unique character representation. For example, the character string ‘•(6)’ indicates a variant of the
6
schema that includes a iv 3 chord instead of a 53 for event one, while the
string ‘•(ß)’ indicates a substitution of an augmented sixth chord for event
one. None of these variants figured into the population of 550 examples of
what I call the schema’s ‘default form’ discussed in this essay. Further
instructions for reading the coding system are available in Byros (2009a),
Appendix B.
33.
That composers understood the le–sol–fi stage of the schema as functionally
synonymous with an augmented sixth is evident in their interchangeable use
of the le–sol–fi–sol and augmented 6–V schemata. In sonata-form movements and other rounded-binary structures, composers would substitute
one schema for the other in articulating a half cadence. This occurs, for
example, between the exposition and recapitulation in the first movement
of Beethoven’s Fourth Piano Concerto (1806).The exposition has a le–sol–
fi–sol (bars 104–111), while the recapitulation has an augmented 6–V
schema (bars 278–281). Such identifications between the two schemata
also appear in theme and variations, as in Emanuel Bach’s Sonata in D
minor for two-manual harpsichord (Sonata per il cembalo a due tastature,
Wq. 69, Helm 53, 1747). The third movement prominently features the
le–sol–fi–sol in its binary theme.Throughout its subsequent variations, Bach
uses the le–sol–fi progression of the schema interchangeably with the augmented sixth. For further le–sol–fi and augmented-sixth identifications, see
Byros (2009a), Ch. 5.
34.
See Gjerdingen (2007), pp. 273–83.
35.
A common variant of the le–sol–fi–sol is the le–fi–sol, which is identical save
for the omission of the passing harmony between the first and third events
of the schema’s first stage. Beyond the 550 examples of the le–sol–fi–sol, my
corpus returned 198 examples of the le–fi–sol. See Byros (2009a), Appendix
B.
36.
For a more extended discussion of the schema’s usage, see Byros (2009a),
Chs 3 and 5.
37.
Between transition and second theme, development and recapitulation, etc.
38.
Eighteenth-century conceptions of sonata form are largely punctuation
based. See Koch ([1782–93] 1969); Hepokoski and Darcy (2006); Spitzer
(2004), (2006) and (2007); and Berger (1996).
39.
On subsequent hearings, the modulation will occur phenomenologically
earlier. Gottfried Weber’s Versuch einer geordneten Theorie der Tonsetzkunst
([1817–21] 1830–2) offers a contemporary account of such effects of
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re-hearing on modulation. In a section called ‘Recurrence of Passages
Already Heard’ (‘Wiederkehr schon gehörter Stellen’), Weber writes on
Papageno’s ‘bird-catcher’ aria from Die Zauberflöte (1791), arguing that,
upon re-hearing the aria, the modulation to D major that first occurs at bar
6
7 with the appearance of the V 5 chord will shift and occur phenomenologically earlier in the mind: ‘Our internal sense of hearing [Unser innerer
Gehörsinn] re-attunes itself ... and thus readily apprehends the D-harmony
[that] precedes A7, as D: I’ (Weber [1817–21] 1830–32, vol. 2, p. 153 and
1851, vol. 1, p. 365) – that is, already as tonic, despite the fact that a D
major chord sounds as dominant of G major in the immediately preceding
beat in bar 6.
40.
The ‘window’ is often defined by differentiation in topic, thematic material
or figuration. In Ex. 10, the modulation is accompanied by a discrete
change of topic, where A major is presented in the ‘singing style’, while C
minor is in the style of the French overture (Ex. 10). On the relationship
between topics and schemata, see Byros (forthcoming).
41.
In the exposition of this movement, Haydn uses a modulating le–fi–sol in
the analogous ‘EEC’ location (bars 42–49). See also n. 35 on the le–fi–sol.
42.
The schema was also, albeit less frequently, used to perform other modulations – as, for example, when the major triad reinterpreted by the le–sol–fi
‘window’ is a dominant, to result in a modulation down a semitone, or a
subdominant, to result in a modulation down a minor third. These are also
enumerated in Appendix B of Byros (2009a).
43.
The recordings are given in Table 3.
44.
For discussions of ‘asymmetry’ as a criterion of ‘markedness’, see Hatten
(1994).
45.
In the Landsberg 6 sketches transcribed by Nottebohm ([1880] 1979),
bars 1–2 of the Symphony carried all dominant-seventh harmony, and the
second ‘hammer blow’ in bar 2 fell not on the downbeat but on beat 3 of
the bar. This was obviously changed for the final version, ostensibly for the
reasons outlined here. Though dominant harmony in bars 1–2 would not
negate the effect of a modulatory cue in bars 1–6 (as stated above, at times
the cue consists of tonic-dominant exchanges), E is nonetheless more
immobile and hence vulnerable to reinterpretation without it.
46.
For discussions of the ‘neue Weg’, including dates and the credibility of
Beethoven’s having reported the decision to embark on a new path, see e.g.
Dahlhaus (1991), pp. 166–80; Plantinga (1999), pp. 151–8; and Kinderman (1995), pp. 51–2, and (2009), pp. 61–2.
47.
In linguistics, ‘fronting’ – the process of shifting a ‘constituent’ (a word or
group of words) to the beginning of a sentence – is a common means of
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providing emphasis or ‘topicalising’. The concept also appears prominently
in eighteenth-century linguistic theory, discussed in terms of the ‘inversion’
of ‘word order’ (see Spitzer 2004, pp. 224–5 and 230–4). This eighteenthcentury perspective on the phenomenon was strongly tied to poetic language in particular, where ‘fronting’ is used for ‘emotional effect’ (Spitzer
2004, p. 224). On the potential hermeneutic relevance of this schema
inversion for Beethoven’s theme, see n. 52.
48.
The Sturm und Drang topic of bars 7–9 returns in full force in the development, where the horn-call arpeggiations are assimilated into the syncopated and tremolo violins texture within a D minor, G minor and C minor
context (bars 186–205).
49.
See Lockwood (1981) and Byros (2009a), Ch. 1.
50.
See n. 32 above.
51.
The potentially sacred resonances of the Stabat Mater Prinner in the
context of a funeral march are discussed in Byros (forthcoming).
52.
For a more comprehensive and detailed analysis of the tonal and hermeneutic ramifications of the Symphony’s opening push to G minor, see
Byros (forthcoming). There, I address, among other things, the ‘topical’
significance of the le–sol–fi–sol, and how that plays into contemporary
discussions of the Symphony’s ‘sublime’, ‘serious’ and ‘profound’ character, as well as how that significance is used to prefigure the ‘death of the
hero’ in the ‘Funeral March’.
53.
In this connection, see Meyer on communication above, as well as Mirka
and Agawu (2008).
54.
To be sure, a more comprehensive picture of style would include more
than the replication of patterning, but also, for example, composers’
unique engagement with that replication via compositional play (see also
n. 13 in this connection). The Penn School has focused primarily on what
Spitzer (2006), under Adorno’s influence, has called call Style 1 (convention) in a larger ternary model of style, which also includes Style 2 (the
composer’s subjective voice; in Spitzer’s inquiry, that of late Beethoven),
as well as Style 3 (natural or metaphorical schemata). Spitzer’s ternary
model of style offers a productive framework for future studies that might
explore the dialectical relationship between schemata (object) and individuality (subject). From an anthropological perspective, Geertz offers a
provocative and similarly dialectical argument towards that end: ‘Becoming human is becoming individual, and we become individual under the
guidance of cultural patterns, historically created systems of meaning in
terms of which we give form, order, point, and direction to our lives’
(1973, p. 52).
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55.
Though statistical learning remains a contested issue with regard to language acquisition (e.g. Saffran 2003a), other studies have indicated that
this learning mechanism may give rise to (semantic) categories (Brady and
Oliva 2008). In music, Huron’s recent work has suggested that statistical
learning is a ‘pervasive’ mechanism for music knowledge acquisition and
audition in general – that ‘statistical learning might form the basis for
auditory expectation’ (2006, pp. 71 and 153). And Patel’s research on the
analogies/homologies between music and language (2008) has brought
together and built on several statistical learning studies, to argue that
statistical learning is a common mechanism for music and language acquisition – a ‘common mechanism for sound category learning’. This view is
also advanced by Saffran (2003b). See also n. 57.
56.
See below on the idea of regularity as an affordance.
57.
I would not, however, be inclined to say that knowing the schema amounts
to having internalised this regularity alone. For a discussion of how the
le–sol–fi–sol schema is based on more abstract scale-degree probabilities, see
Byros (2009a), Ch. 3. For a discussion of the schema’s third-order probability and its other, less common resolutions, see ibid., Ch. 5, pp. 279–84.
That schemata may be learned by statistical learning is also supported by
several studies that examine listeners’ acquisition of adjacent and nonadjacent tone dependencies (Creel, Newport and Aslin 2004; and Gebhart,
Newport and Aslin 2009).
58.
The ‘mapping’ mechanism may be an abstracted ‘prototype’ or an aggregate response consisting of ‘exemplars’ of all the previously experienced
instances of the le–sol–fi–sol. See n. 12.
59.
In terms of its kurtosis, the deviation from a normal distribution is not
significant – that is, its kurtosis has fewer than two standard errors of
deviation (kurtosis: –.226212; SEK: 0.208893).
60.
The relevant discussion comes in Aristotle’s treatise on memory, De
memoria, translated in Aristotle (1906). Aristotle appears to be the first
philosopher to explicitly describe the schema concept. In this connection,
see Byros (2009a), Ch. 5 and also pp. 237–9.
61.
For example, the Rule of the Octave (Campion [1716] 1976) and various
‘Chord-Form Tables’ (Byros 2009a) – which situate a given figured-bass
chord onto a specific scale degree in the bass – are widespread examples of
this tonal stamping concept. The concept forms the basis for harmonising
unfigured basses, as described in Heinichen ([1711] 2000 and [1728]
1994) and elsewhere, and is central to partimento realisation (Gjerdingen
2007). The activity of harmonising an unfigured bass or partimento
requires recognising a suitable tonal context. In this way, partimento
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realisations were exercises in learning and practicing schemata as
‘recognition devices’. For further discussion see Gjerdingen (2007) and
Byros (2009a), Ch. 2.
62.
Resolving the apparent first stage of the le–sol–fi–sol to a minor triad in first
inversion deviates from every one of the probabilities for succession in my
corpus – that is, it also deviates from the other 14.6%. See Byros (2009a),
Ch. 5.
63.
This is a running theme in Meyer ([1967] 1994). For other studies that
deal with style from the perspective of information theory and entropy, see
Youngblood (1958), Knopoff and Hutchinson (1981) and (1983) and
Margulis and Beatty (2008).
64.
The interpretation originated in Schenker ([1930] 1997).
65.
See Meyer (1989), pp. 245–58; Gjerdingen (1988), pp. 8–9; and Byros
(2009b), pp. 275–92.
66.
See n. 2. above.
67.
On gestalt psychology, see e.g. Koffka ([1935] 1999) and Smith (1988).
68.
See Abraham (1951).
REFERENCES
Abbot-Smith, Kirsten and Tomasello, Michael, 2006: ‘Exemplar-Learning and
Schematization in a Usage-Based Account of Syntactic Acquisition’, Linguistic Review, 23, pp. 275–90.
Abraham, Gerland, 1951: ‘Schumann’s “Jugendsinfonie” in G Minor’, Musical
Quarterly, 37/i, pp. 45–60.
Åkerlind, Gerlese, 2005: ‘Variation and Commonality in Phenomenographic
Research Methods’, Higher Education Research & Development, 24/iv, pp.
321–34.
Anderson, John, 1991: ‘The Adaptive Nature of Human Categorization’, Psychological Review, 98/iii, pp. 409–29.
Aristotle, 1906: De sensu and De memoria, trans. G.R.T. Ross (Cambridge:
Cambridge University Press).
Bach, Carl Philipp Emanuel, [1753, 1762] 1949: Essay on the True Art of Playing
Keyboard Instruments, trans. William J. Mitchell (New York: Norton).
Baddeley, Alan, 1997: Human Memory: Theory and Practice, rev. edn (Hove, E.
Sussex: Psychology Press).
Barry, Barbara, 2000: The Philosopher’s Stone: Essays in the Transformation of
Musical Structure (Hillsdale, NY: Pendragon Press).
Music Analysis, 31/iii (2012)
© 2013 The Author.
Music Analysis © 2013 Blackwell Publishing Ltd
338
VASILI BYROS
Bartlett, Frederic, 1920: ‘Some Experiments on the Reproduction of FolkStories’, Folklore, 31/i, pp. 30–47.
______, [1932] 1995: Remembering: a Study in Social and Experimental Psychology
(Cambridge: Cambridge University Press).
Benzon, William, 2001: Beethoven’s Anvil: Music in Mind and Culture (New York:
Basic Books).
Berger, Karol, 1996: ‘The First-Movement Punctuation Form in Mozart’s
Concertos’, in Neal Zaslaw (ed.), Mozart’s Piano Concertos: Text, Context,
Interpretation (Ann Arbor, MI: University of Michigan Press), pp. 239–
59.
Berkowitz, Aaron, 2010: The Improvising Mind: Cognition and Creativity in the
Musical Moment (Oxford and New York: Oxford University Press).
Boas, Franz, 1901: Kathlamet Texts, Bureau of American Ethnology Bulletin, No.
26 (Washington, DC: Smithsonian Institution Press).
Bonds, Mark Evan, 2008: ‘Listening to Listeners’, in Danuta Mirka and Kofi
Agawu (eds), Communication in Eighteenth-Century Music (Cambridge: Cambridge University Press), pp. 34–52.
Brady, Timothy and Oliva, Aude, 2008: ‘Statistical Learning Using Real-World
Scenes: Extracting Categorical Regularities without Conscious Intent’, Psychological Science, 19/vii, pp. 678–85.
Brewer, William, 2000: ‘Bartlett’s Concept of the Schema and its Impact on
Theories of Knowledge Representation in Contemporary Cognitive Psychology’, in Akiko Saito (ed.), Bartlett, Culture and Cognition (London:
Psychology Press), pp. 69–89.
Brinkmann, Reinhold, 2000: ‘In the Time of the Eroica’, in Scott Burnham and
Michael Steinberg (eds), Beethoven and His World (Princeton, NJ: Princeton
University Press), pp. 1–26.
Byros, Vasili, 2009a: ‘Foundations of Tonality as Situated Cognition: an Enquiry
into the Culture and Cognition of Tonality, with Beethoven’s Eroica Symphony as Case Study’ (PhD diss., Yale University).
______, 2009b: ‘Towards an “Archaeology” of Hearing: Schemata and
Eighteenth-Century Consciousness’, Musica Humana, 1/ii, pp. 235–306.
______, 2011: ‘Quo vadis corpus?’, paper presented at the Annual Meeting of the
Society for Music Theory, Music Cognition Interest Group Panel on Corpus
Studies, Minneapolis, MN.
______, forthcoming: ‘Topics and Harmonic Schemata’, in Danuta Mirka (ed.),
The Oxford Handbook of Topic Theory (Oxford and New York: Oxford University Press).
Campion, François, [1716] 1976: Traité d’accompagnement et de composition, selon
la règle des octaves de musique (Geneva: Minkoff).
Caplin, William, 1998: Classical Form: a Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven (New York: Oxford University
Press).
Cooper, Barry, 2000: Beethoven (New York: Oxford University Press).
© 2013 The Author.
Music Analysis © 2013 Blackwell Publishing Ltd
Music Analysis, 31/iii (2012)
MEYER’S ANVIL: REVISITING
THE
SCHEMA CONCEPT
339
Creel, Sarah; Newport, Elissa; and Aslin, Richard, 2004: ‘Distant Melodies:
Statistical Learning of Nonadjacent Dependencies in Tone Sequences’,
Journal of Experimental Psychology: Learning, Memory, and Cognition, 30/v, pp.
1119–30.
Cudworth, Charles, 1949: ‘Cadence Galante: the Story of a Cliché’, Monthly
Musical Record, 79, pp. 176–8.
Daelemans, Walter and Van den Boesch, Antal, 2005: Memory-Based Language
Processing (Cambridge: Cambridge University Press).
Dahlhaus, Carl, [1977] 1984: Foundations of Music History, trans. J. Bradford
Robinson (Cambridge: Cambridge University Press).
______, 1991: Ludwig van Beethoven: Approaches to His Music, trans. Mary Whittall (Oxford: Clarendon Press).
Daverio, John, 1997: Robert Schumann: Herald of a ‘New Poetic Age’ (New York:
Oxford University Press).
Day-O’Connell, Jeremy, 2002: ‘The Rise of 6̂ in the Nineteenth Century’, Music
Theory Spectrum, 24/i, pp. 35–67.
Dewey, John, [1934] 2005: Art as Experience (New York: Perigee Books).
______, [1938] 1997: Experience and Education (New York: Touchstone).
Dopkins, Stephen and Gleason, Theresa, 1997: ‘Comparing Exemplar and
Prototype Models of Categorization’, Canadian Journal of Experimental Psychology, 51/iii, pp. 212–30.
Earp, Lawrence, 1993: ‘Tovey’s “Cloud” in the First Movement of the Eroica: an
Analysis Based on Sketches for the Development and Coda’, Beethoven
Forum, 2, pp. 55–84.
Ebers, Johannes, [1796] 1802: A New Hand-Dictionary of the German Language
for Englishmen and of the English Language for the Germans (Leipzig: Halle).
Eco, Umberto, 1979: The Role of the Reader: Explorations in the Semiotics of Texts
(Bloomington, IN: Indiana University Press).
Epstein, David, 1979: Beyond Orpheus: Studies in Musical Structure (Cambridge,
MA: The MIT Press).
Fenaroli, Fedele, [c. 1800] 1975: Partimenti, ossia basso numerato (Milan: Arnaldo
Forni Editore).
Friedman, Alinda, 1979: ‘Framing Pictures: the Role of Knowledge in Automatized Encoding and Memory for Gist’, Journal of Experimental Psychology:
General, 108/iii, pp. 316–55.
Gebhart, Andrea; Newport, Elissa; and Aslin, Richard, 2009: ‘Statistical Learning of Adjacent and Nonadjacent Dependencies among Nonlinguistic
Sounds’, Psychonomic Bulletin & Review, 16/iii, pp. 486–90.
Geck, Martin and Schleuning, Peter, 1989: ‘Geschrieben auf Bonaparte’:
Beethovens ‘Eroica’: Revolution, Reaktion, Rezeption (Reinbeck bei Hamburg:
Rowohlt).
Geertz, Clifford, 1973: The Interpretation of Cultures (New York: Basic Books).
Gibson, James J., 1986: The Ecological Approach to Visual Perception (New York:
Psychology Press).
Music Analysis, 31/iii (2012)
© 2013 The Author.
Music Analysis © 2013 Blackwell Publishing Ltd
340
VASILI BYROS
Gjerdingen, Robert O., 1984: ‘A Musical Schema: Structure and Style Change,
1720–1900’ (PhD diss., University of Pennsylvania).
______, 1986: ‘The Formation and Deformation of Classic/Romantic Phrase
Schemata: a Theoretical Model and Historical Study’, Music Theory Spectrum, 8, pp. 25–43.
______, 1988: A Classic Turn of Phrase: Music and the Psychology of Convention
(Philadelphia, PA: University of Pennsylvania Press).
______, 1991: ‘Defining a Prototypical Utterance’, Psychomusicology, 10, pp.
127–139.
______, 1992: ‘Revisiting Meyer’s ‘Grammatical Simplicity and Relational Richness’, in Mari Riess Jones and Susan Holleran (eds), Cognitive Bases of
Musical Communication (Washington, DC: American Psychological Association), pp. 225–43.
______, 1996: ‘Courtly Behaviors’, Music Perception, 13/iii, pp. 365–82.
______, 2002: ‘The Psychology of Music’, in Thomas Christensen (ed.), The
Cambridge History of Western Music Theory (Cambridge: Cambridge University Press), pp. 956–81.
______, 2007: Music in the Galant Style: Being an Essay on Various Schemata
Characteristic of Eighteenth-Century Music (New York: Oxford University
Press).
______, 2009a: ‘Meyer and “Music Usage” ’, Musica Humana, 1/ii, pp. 197–224.
______, 2009b: ‘The Price of (Perceived) Affordance: Commentary for Huron
and Berec’, Empirical Musicology Review, 4/iii, pp. 123–5.
______, 2010: ‘Mozart’s Obviously Corrupt Minuet’, Music Analysis 29/i–ii–iii,
pp. 61–82.
Gombrich, Ernst Hans, [1960] 2000: Art and Illusion: a Study in the Psychology of
Pictorial Representation (Princeton, NJ and Oxford: Princeton University
Press).
Hatten, Robert, 1994: Musical Meaning in Beethoven: Markedness, Correlation, and
Interpretation (Bloomington, IN: Indiana University Press).
Heartz, Daniel, 2003: Music in European Capitals: the Galant Style, 1729–1780
(New York and London: W.W. Norton).
Heft, Harry, 2001: Ecological Psychology in Context: James Gibson, Roger Barker,
and the Legacy of William James’s Radical Empiricism (Mahwah, NJ and
London: Lawrence Erlbaum).
Heinichen, Johann David, [1711] 2000: Neu erfundene und gründliche Anweisung
(Kassel: Bärenreiter).
______, [1728] 1994: Der Generalbaß in der Composition (Hildesheim, Zurich and
New York: Georg Olms Verlag).
Hepokoski, James and Darcy, Warren, 2006: Elements of Sonata Theory: Norms,
Types, and Deformations in the Late-Eighteenth-Century Sonata (New York:
Oxford University Press).
Heuss, Alfred, 1921: Beethoven: eine Charakteristik (Leipzig: R. Voigtländers
Verlag).
© 2013 The Author.
Music Analysis © 2013 Blackwell Publishing Ltd
Music Analysis, 31/iii (2012)
MEYER’S ANVIL: REVISITING
THE
SCHEMA CONCEPT
341
Hume, David, [1777] 1975: Enquiries Concerning Human Understanding, 3rd edn
(Oxford: Clarendon Press).
Huron, David, 2006: Sweet Anticipation: Music and the Psychology of Expectation
(Cambridge, MA: MIT Press).
Hyer, Brian, 1996: ‘Second Immediacies in the Eroica’, in Ian Bent (ed.), Music
Theory in the Age of Romanticism (Cambridge: Cambridge University Press),
pp. 77–104.
Iser, Wolfgang, 1978: The Act of Reading: a Theory of Aesthetic Response (Baltimore, MD and London: Johns Hopkins University Press).
Johnson, Keith, 2007: ‘Decisions and Mechanisms in Exemplar-Based Phonology’, in Maria-Josep Solé, Patrice Beddor and Manjari Ohala (eds), Experimental Approaches to Phonology (Oxford and New York: Oxford University
Press), pp. 25–40.
Johnson, Marcia and Hirst, William, 1993: ‘MEM: Memory Subsystems as
Processes’, in Alan Collins, Susan Gathercole, Martin Conway and Peter
Morris (eds), Theories of Memory (East Sussex: Lawrence Erlbaum), pp.
241–86.
Juslin, Patrik N. and Sloboda, John A., 2010: Handbook of Music and Emotion:
Theory, Research, Applications (Oxford and New York: Oxford University
Press).
Kellner, David, [1732] 1979: Treulicher Unterricht im General-baß (Hildesheim:
Georg Olms Verlag).
Kinderman, William, 1995: Beethoven (Oxford: Oxford University Press).
______, 2009: Beethoven, 2nd edn (Oxford: Oxford University Press).
Klein, Michael, 2005: Intertextuality in Western Art Music (Bloomington, IN:
Indiana University Press).
Knopoff, Leon and Hutchinson, William, 1981: ‘Information Theory for
Musical Continua’, Journal of Music Theory, 25/i, pp. 17–44.
______, 1983: ‘Entropy as a Measure of Style: the Influence of Sample Length’,
Journal of Music Theory, 27/i, pp. 75–97
Koch, Heinrich Christoph, [1782–93] 1969: Versuch einer Anleitung zur Composition, 3 vols (Hildesheim: Georg Olms Verlag).
Koffka, Kurt, [1935] 1999: Principles of Gestalt Psychology (London: Routledge).
Kunze, Stefan, 1987: Ludwig van Beethoven: die Werke im Spiegel seiner
Zeit: Gesammelte Konzertberichte und Rezensionen bis 1830 (Laaber:
Laaber-Verlag).
Lerdahl, Fred, 2001: Tonal Pitch Space (Oxford and NewYork: Oxford University
Press).
Lerdahl, Fred with Jackendoff, Ray, 1983: A Generative Theory of Music (Cambridge, MA: MIT Press).
Levy, Janet, 1988: ‘About Leonard B. Meyer: a Biographical Vignette’, in Eugene
Narmour and Ruth Solie (eds), Explorations in Music, the Arts, and Ideas:
Essays in Honor of Leonard B. Meyer (Stuyvesant, NY: Pendragon Press), pp.
439–52.
Music Analysis, 31/iii (2012)
© 2013 The Author.
Music Analysis © 2013 Blackwell Publishing Ltd
342
VASILI BYROS
Locke, John, [1706] 1997: An Essay Concerning Human Understanding, 5th edn,
ed. Roger Woolhouse (London: Penguin Books).
Lockwood, Lewis, 1981: ‘Beethoven’s Earliest Sketches for the Eroica Symphony’, Musical Quarterly, 67/iv, pp. 457–78.
______, 1982: ‘Eroica Perspectives: Strategy and Design in the First Movement’,
in Alan Tyson (ed.), Beethoven Studies, vol. 3 (Cambridge: Cambridge University Press), pp. 85–105.
______, 1991: ‘The Compositional Genesis of the Eroica Finale’, in William
Kinderman (ed.), Beethoven’s Compositional Process (Lincoln, NE: University
of Nebraska Press), pp. 82–101.
Loftus, Geoffrey and Mackworth, Norman, 1978: ‘Cognitive Determinants of
Fixation Location during Picture Viewing’, Journal of Experimental Psychology: Human Perception and Performance, 4/iv, pp. 565–72.
Mandler, George, 1979: ‘Organization, Memory, and Mental Structures’, in C.
Richard Puff (ed.), Memory Organization and Structure (NewYork: Academic
Press), pp. 259–99.
Mandler, Jean, 1984: Stories, Scripts, and Scenes: Aspects of Schema Theory (Hillsdale, NJ: Lawrence Erlbaum).
Margulis, Elizabeth and Beatty, Andrew, 2008: ‘Musical Style, Psychoaesthetics,
and Prospects for Entropy as an Analytic Tool’, Computer Music Journal,
32/iv, pp. 64–78.
Marpurg, Friedrich Wilhelm, 1753–4: Abhandlung von der Fuge (Berlin: A.
Haude & J.C. Spencer).
Marston, Nicholas, 1991: ‘Symphonies’, in Barry Cooper (ed.), The Beethoven
Compendium: a Guide to Beethoven’s Life and Music (Ann Arbor, MI: Borders
Press), pp. 214–17.
______, 2007: ‘Schumann’s Heroes: Schubert, Beethoven, Bach’, in Julia P.
Beate (ed.), The Cambridge Companion to Schumann (Cambridge: Cambridge University Press), pp. 48–61.
Marx, Adolph Bernhard, [1859] 1997: Ludwig van Beethoven: Leben und Schaffen,
3rd edn, ed. Gustav Behncke (Berlin: Verlag von Otto Janke). Selections
translated in 1997: Musical Form in the Age of Beethoven: Selected Writings on
Theory and Method, ed. and trans. Scott Burnham (Cambridge: Cambridge
University Press), pp. 157–88.
Mayeda, Akio, 1992: Robert Schumanns Weg zur Symphonie (Zurich: Atlantis
Verlag).
McClary, Susan, 2009: ‘Leonard B. Meyer: The Humanistic Music Theorist’,
Musica Humana, 1/ii, pp. 115–28.
Meyer, Leonard B, 1956: Emotion and Meaning in Music (Chicago: University of
Chicago Press).
______, [1967] 1994: Music,the Arts,and Ideas:Patterns and Predictions inTwentiethCentury Culture (Chicago and London: University of Chicago Press).
______, 1973: Explaining Music: Essays and Explorations (Chicago and London:
University of Chicago Press).
© 2013 The Author.
Music Analysis © 2013 Blackwell Publishing Ltd
Music Analysis, 31/iii (2012)
MEYER’S ANVIL: REVISITING
THE
SCHEMA CONCEPT
343
______, 1980: ‘Exploiting Limits: Creation, Archetypes, and Style Change’,
Daedalus, 109/ii, pp. 177–205.
______, 1989: Style and Music: Theory, History, and Ideology (Philadelphia, PA:
University of Pennsylvania Press).
______, 2000: The Spheres of Music: a Gathering of Essays (Chicago and London:
University of Chicago Press).
Minsky, Marvin, 1975: ‘A Framework for Representing Knowledge’, in Patrick
Winston (ed.), The Psychology of ComputerVision (New York: McGraw-Hill),
pp. 211–77.
Mirka, Danuta and Agawu, Kofi (eds), 2008: Communication in EighteenthCentury Music (Oxford and New York: Oxford University Press).
Moore, Ruth, 1966: Niels Bohr:The Man, His Science, & the World They Changed
(New York: Knopf).
Narmour, Eugene, 1999: ‘Hierarchical Expectation and Musical Style’, in Diana
Deutsch (ed.), The Psychology of Music, 2nd edn (San Diego, CA: Academic
Press), pp. 441–72.
Neisser, Ulrich, 1976: Cognition and Reality: Principles and Implications of Cognitive Psychology (San Francisco, CA: W.H. Freeman).
Nosofsky, Robert, 1986: ‘Attention, Similarity, and the IdentificationCategorization Relationship’, Journal of Experimental Psychology: General,
115/i, pp. 39–57.
______, 1988: ‘Similarity, Frequency, and Category Representations’, Journal
of Experimental Psychology: Learning, Memory, and Cognition, 14/i, pp. 54–65.
______, 1991: ‘Typicality in Logically Defined Categories: Exemplar-Similarity
versus Rule Instantiation’, Memory and Cognition, 19/ii, pp. 131–50.
______, 1992: ‘Exemplar-Based Approach to Relating Categorization, Identification, and Recognition’, in F. Gregory Ashby (ed.), Multidimensional Models
of Perception and Cognition (Hillsdale, NJ: Lawrence Erlbaum), pp. 363–93.
Nottebohm, Gustav, [1880] 1979: Two Beethoven Sketchbooks: a Description with
Musical Extracts, trans. Jonathan Katz (London: Victor Gollancz).
Oulibicheff, Aléxandre, 1857: Beethoven, ses critiques et ses glossateurs (Paris: Jules
Gavelot).
Parry, Charles Hubert Hastings, 1880: ‘Modulation’, in George Grove (ed.), A
Dictionary of Music and Musicians, 3 vols (London: Macmillan).
Patel, Aniruddh, 2008: Music, Language, and the Brain (Oxford and New York:
Oxford University Press).
Piaget, Jean, [1947] 2001: The Psychology of Intelligence, trans. Malcolm Piercy
and D.E. Berlyne (London and New York: Routledge Classics).
Piaget, Jean and Inhelder, Bärbel, [1968] 1973: Memory and Intelligence, trans.
Arnold Pomerans (New York: Basic Books).
Plantinga, Leon, 1999: Beethoven’s Concertos: History, Style, Performance (New
York: W.W. Norton).
Quinn, Ian, 2010: ‘Are Pitch-Class Profiles Really “Key for Key”?’, Zeitschrift der
Gesellschaft für Musiktheorie, 7/ii, pp. 151–63.
Music Analysis, 31/iii (2012)
© 2013 The Author.
Music Analysis © 2013 Blackwell Publishing Ltd
344
VASILI BYROS
Ratner, Leonard, 1980: Classic Music: Expression, Form, and Style (New York:
Schirmer Books).
Rexroth, Dieter, 2005: Beethovens Symphonien: ein musikalische Werkführer
(Munich: C.H. Beck).
Riepel, Joseph, 1752–68: Anfangsgründe zur musikalischen Setzkunst, 5 vols
(Augsburg: J.J. Lotter).
Riezler, Walter, [1936] 1938: Beethoven, trans. G.D.H. Pidcock (New York: E.P.
Dutton).
Ringer, Alexander, 1961: ‘Clementi and the Eroica’, Musical Quarterly, 47/iv, pp.
454–68.
Robins, Philip and Aydede, Murat (eds), 2009: The Cambridge Handbook of
Situated Cognition (New York: Cambridge University Press).
Rochlitz, Friedrich, 1807: ‘Review’, Allgemeine musikalische Zeitung, 9, pp. 319–
34, reprinted in Kunze (1987), trans. in Senner, Wallace and Meredith
(2001).
Rosch, Elenor, 1978: ‘Principles of Categorization’, in Elenor Rosch and Barbara
Bloom Lloyd (eds), Cognition and Categorization (Hillsdale, NJ: Lawrence
Erlbaum), pp. 89–206.
Rumelhart, David E., 1975: ‘Notes on a Schema for Stories’, in Daniel Gureasko
Bobrow and Allan Collins (eds), Representation and Understanding (New
York: Academic Press), pp. 211–36.
______, 1977: ‘Understanding and Summarizing Brief Stories’, in David
LaBerge and S. Jay Samuels (eds), Basic Processes in Reading: Perception and
Comprehension (Hillsdale, NJ: Lawrence Erlbaum), pp. 265–303.
______, 1980: ‘Schemata: the Building Blocks of Cognition’, in Rand Spiro,
Bertram Bruce and William Brewer (eds), Theoretical Issues in Reading Comprehension: Perspectives from Cognitive Psychology, Linguistics, Artificial Intelligence, and Education (Hillsdale, NJ: Lawrence Erlbaum), pp. 33–58.
Rumelhart, David E.; McClelland, James L.; and the PDP Research Group,
1986: Parallel Distributed Processing: Explorations in the Microstructure of Cognition, 2 vols (Cambridge, MA and London: MIT Press).
Rumelhart, David E. and Ortony, Andrew, 1977: ‘The Representation of Knowledge in Memory’, in Richard C. Anderson, Rand J. Spiro and William E.
Montague (eds), Schooling and the Acquisition of Knowledge (Hillsdale, NJ:
Lawrence Erlbaum), pp. 99–135.
Rumph, Stephen, 2004: Beethoven after Napoleon: Political Romanticism in the Late
Works (Berkeley and Los Angeles, CA: University of California Press).
Saffran, Jenny, 2003a: ‘Statistical Language Learning: Mechanisms and Constraints’, Current Directions in Psychological Science, 12/iv, pp. 110–4.
______, 2003b: ‘Musical Learning and Language Development’, in Giuliano
Avanzini, Carmine Faienza, Luisa Lopez, Maria Majno and Diego
Minciacchi (eds), The Neurosciences and Music: Annals of the New York
Academy of Sciences,Vol. 999 (NewYork: NewYork Academy of Sciences), pp.
397–401.
© 2013 The Author.
Music Analysis © 2013 Blackwell Publishing Ltd
Music Analysis, 31/iii (2012)
MEYER’S ANVIL: REVISITING
THE
SCHEMA CONCEPT
345
Schank, Roger and Abelson, Robert, 1977: Scripts, Plans, Goals and Understanding: an Inquiry into Human Knowledge Structures (New York and London:
Psychology Press, Taylor & Francis).
Schenker, Heinrich, [1930] 1997: The Masterwork in Music: aYearbook, vol. 3, ed.
William Drabkin, trans. Ian Bent, A. Clayton and D. Puffet (Cambridge:
Cambridge University Press).
Senner, Wayne; Wallace, Robin; and Meredith, William (eds), 2001: The Critical
Reception of Beethoven’s Compositions by His German Contemporaries, Vol. 2
(Lincoln, NE and London: University of Nebraska Press).
Sipe, Thomas, 1998: Beethoven: Eroica Symphony (Cambridge: Cambridge University Press).
Smith, Barry (ed.), 1988: Foundations of Gestalt Theory (Munich: Philosophia
Verlag).
Smith, Edward and Medin, Douglas, 1981: Categories and Concepts (Cambridge,
MA: Harvard University Press).
Smith, J. David and Minda, John Paul, 2002: ‘Distinguishing Prototype-Based
and Exemplar-Based Processes in Category Learning’, Journal of Experimental Psychology: Learning, Memory, and Cognition, 28, pp. 800–11.
Spitzer, Michael, 2004: Metaphor and Musical Thought (Chicago: University of
Chicago Press).
______, 2006: Music as Philosophy: Adorno and Beethoven’s Late Style (Bloomington and Indianapolis, IN: Indiana University Press).
______, 2007: ‘Sonata Dialogues’ [review of James Hepokoski and Warren Darcy,
Elements of Sonata Theory], Beethoven Forum, 14/ii, pp. 150–78.
Tovey, Donald Francis, 1935: Essays in Musical Analysis,Volume I: Symphonies.
(London: Oxford University Press).
——, 1945: Beethoven (London: Oxford University Press).
Uljens, Michael, 1996: ‘On the Philosophical Foundations of Phenomenography’, in Gloria Dall’Alba and Biörn Hasselgren (eds), Reflections on
Phenomenography (Goteborg: Act Universitatis Gothenburgensis), pp. 105–
30.
Verbeemen, Timothy; Vanpaemel, Wolf; Pattyn, Sven; Storms, Gert; and
Verguts, Tom, 2007: ‘Beyond Exemplars and Prototypes as Memory Representations of Natural Concepts: a Clustering Approach’, Journal of
Memory and Language, 56, pp. 537–54.
Vodička, Felix, 1975: ‘Die Konkretisation des literarischen Werks’, in Rainer
Warning (ed.), Rezeptionsästhetik:Theorie und Praxis (Munich: W. Fink), pp.
84–112.
Weber, Gottfried, [1817–21] 1830–2: Versuch einer geordneten Theorie der Tonsetzkunst, 4 vols, 3rd edn (Mainz and Paris: B. Schott’s Söhnen).Trans. James F.
Warner as The Theory of Musical Composition:Treated with aView to a Naturally
Consecutive Arrangement of Topics, 2 vols (London: Robert Cocks, 1851).
Wittgenstein, Ludwig, [1953] 2001: Philosophical Investigations, trans. G.E.M.
Anscombe, 3rd edn (Oxford: Blackwell).
Music Analysis, 31/iii (2012)
© 2013 The Author.
Music Analysis © 2013 Blackwell Publishing Ltd
346
VASILI BYROS
Youngblood, Joseph, 1958: ‘Style as Information’, Journal of Music Theory, 2/i,
pp. 24–35.
Zbikowski, Lawrence, 2002: Conceptualizing Music: Cognitive Structure, Theory,
and Analysis (Oxford and New York: Oxford University Press).
NOTE ON CONTRIBUTOR
VASILI BYROS is Assistant Professor of Music Theory and Cognition at Northwestern University. His research focuses on the cognitive dimensions of style in
music of the long eighteenth century, using corpus-driven and ethnographic
approaches as a way of reconstructing ‘native’ perspectives on the music. This
research underlies his current book project, with the working title ‘The Act of
Hearing: Style and Cognition in Music of the Late Eighteenth Century’.
ABSTRACT
This article re-examines the concept of a ‘schema’ in light of a new body of
empirical evidence regarding the culture and cognition of key in the eighteenth
century. The schema concept in music, which originated in the work of Leonard
B. Meyer, holds that social and historical experience gives rise to knowledge
structures that engender a situated psychology of hearing and a contextcontingent understanding of music. In previous studies by Meyer and Robert O.
Gjerdingen, evidence for the schema concept has been advanced largely by
interpreting a musical corpus as a metaphor for experience. That is, arguments
for the existence of schemata as mental categories that configure a situated
psychology of hearing have been presented primarily in the form of music
analysis – historically situated patterns detected in musical scores. For this
reason, the schema concept has remained, in Meyer’s and Gjerdingen’s words, a
‘hypothesis’ and ‘assum[ption]’ respectively.
The evidence I advance here derives from a case study on Beethoven’s Eroica
Symphony and what I call the le–sol–fi–sol schema. The study was conducted in
the spirit of the psychologically orientated, humanistic music theory that characterised Meyer’s lifelong research program. By establishing a correlation
between real listeners’ responses in the Symphony’s reception history and the
details of my own corpus study of music from the long eighteenth century
(1720–1840), my Eroica case study brings a novel perspective to the idea that
schemata engender a historical mode of listening. The case study bears out
several hypotheses that are basic to Meyer’s writings and perpetuated in
Gjerdingen’s galant style project: (1) that replicated patternings in eighteenthcentury works are commensurate with listeners’ knowledge structures; (2) that
these knowledge structures are historically contingent and therefore engender a
situated psychology of hearing; (3) that these situated psychologies are affected
by style change; and (4) that schemata provide access to historical modes of
listening today.
© 2013 The Author.
Music Analysis © 2013 Blackwell Publishing Ltd
Music Analysis, 31/iii (2012)