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192
Robert O. Gjerdingen
“H I S T O R I C A L L Y I N F O R M E D ” C O R P U S S T U D I E S
R O B E R T O. G J E R D I N G E N
Northwestern University
M USICIANS CAN CHOOSE BETWEEN VARIOUS
“historicist” or “presentist” ways of performing works
from the past. Music scholars who study early music
sometimes are forced to make similar choices. If one
thinks of corpus studies in music as an objective form
of counting the “elements of music,” the question of
what constitutes an “element” can involve similar historicist/presentist dilemmas. The article examines three
historically significant characteristics of European art
music—three historicist features—that are not always
recognized in presentist corpus studies. For an illustrative example, a comparison is made between how the
cadenza doppia in a Bach toccata for organ might be
represented in a corpus study as either a two-voice
framework or a series of Roman numerals in the tradition of Allen McHose (1947). Because that type of
cadence was a commonplace in Bach's time and in
Bach's compositions, a corpus analysis should be able
to detect its multiple occurrences as a core element of
the music.
Received: October 15, 2012, accepted March 14, 2013.
Key words: music theory, corpus studies, Bach, cadenza
doppia, BWV 564
“HISTORICALLY INFORMED”
can be incendiary in the world of Western classical music. To its proponents it means performing the music of the past on instruments of the past
(“period” instruments) and in the styles of the past
(“authentic” performance practice). To its opponents
it connotes a deceptive marketing ploy that pretends
to recover the irrecoverable sounds and manners of
musicians who died before the dawn of recording
(Taruskin, 1990). Over recent decades the disputes
between proponents and opponents have settled into
chilly détente, with many metropolitan centers now
having successful resident ensembles from both camps.
Yet even if one discounts some of the earlier disputes as
overblown rhetoric or a vying for commercial advantage, there still remains a significant intellectual core to
T
HE CATCHPHRASE
Music Perception, V OLU M E 31, IS S U E 3,
R IG HT S R E S E RV E D . P LEASE D IR ECT ALL
PP .
192–204,
IS S N
0730-7829,
the arguments pro and con. Intractable dilemmas can
arise from the interplay of past and present, memory
and imagination.
Living musicians, for example, play music in the present, even if the scores they play were written in the past.
From their location in the present these musicians must
make specific choices about how to reanimate those
silent texts. Some players may view current performance standards as the ideal and older practices as
evolutionary dead ends. I will term this a “presentist”
orientation. Other players may view various historical
styles as worlds unto themselves, each a perfection in its
own time and for its own purposes—a “historicist” orientation. The same dilemmas are often forced upon
music scholars. In the course of their work they may
need to make clear choices between historicist and presentist alternatives, even if the underlying issues are far
from clear or easily resolvable. When such choices are
made in corpus studies they can have real implications
for the kind of results obtainable and for the types of
evidence that might thus be presented for or against
a particular theory of the musical mind.
In many ways corpus studies have been the subject of
musicology, music theory, and ethnomusicology since
the inception of those disciplines. Knud Jeppesen’s pioneering work in the 1920s on the style of Palestrina, for
instance, was based on a meticulous examination of the
entire corpus of Palestrina’s works (Jeppesen, 1922).
The word “corpus” has graced the titles of several scholarly editions, as for example the series titled Corpus of
Early Keyboard Music (Caldwell, 1963–) or the Corpus
mensurabilis musicae (Ranzini, 1966–). My own dissertation and the ensuing book A Classic Turn of Phrase
involved a large corpus study (Gjerdingen, 1984, 1988),
and generations of music historians have worked with
corpora of musical prints and manuscripts as part of
their daily routine. What distinguishes “corpus studies”
in the sense intended by this special issue of Music Perception is the formalization of inquiry such that it can be
accomplished through machine computation, hence as
a form of computational musicology, and further, that
the results have import for the study of music cognition.
If anything, the sharpening of concepts and categories
into algorithmic form may require one to make even
starker choices between presentism and historicism,
though the choices may not always be recognized as such.
EL ECTR ON IC I SSN
1533-8312. © 2014
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RI GHT S AND PER MIS S IO NS W EBS I TE , H TT P :// W W W . U CPRE SS J OU RNA L S . COM / REPR INT INF O . A S P .
DOI: 10.1525/ M P .2014.31.3.192
“Historically Informed” Corpus Studies
In terms framed by the musicologist Carl Dahlhaus, one
scholar may view a musical phenomenon as “natural”
while another views it as a “second nature” (Dahlhaus,
1968). A natural phenomenon may be stable over all
times and places whereas something learned as a second
nature may be limited to a specific era and social group.
A simple recipe for doing a corpus study of any type
might read as follows:
1. Define the set of elements believed to occur within
the corpus.
2. Calculate appropriate statistics on the time series of
those elements.
3. From those statistics, deduce pertinent norms or
rules for the corpus.
While stages 2 and 3 may be amenable to numerical
methods and explicit algorithms, stage 1 may not. It is
thus often at stage 1 that the researcher makes decisions
that reveal a presentist or historicist bias.
Take, for example, how a Medieval narrator, author of
the Latin tale of Vergil and Lucinius, conceptualized the
domain of literacy as a tidy hierarchical system with
a presentist bias (Johannes, ca. 1200).
Vergil, on account of his respect for and friendship
with the king, took the boy [Lucinius] and taught
him the elements of letters [i.e., the alphabet]. Then,
gently and with enticements, as is the custom of
teachers, he rapidly taught him how to construct
syllables out of letters, and how to form sentences
out of syllables, and then how to complete an
oration out of sentences.
[At Virgilius, ob reverentiam et amicitiam regis
puerum recipiens, primo quidem ei litterarum tradidit elementa ac deinde blandiendo leniendoque, ut
moris est magistrorum syllabam ex litteris conficere
et ex syllabis formare dictionem et ex dictionibus
vero perficere orationem in angustia temporis
perdocuit.]
The narrator was describing Hellenistic methods of
education (Marrou, 1948) which, though of great
authority in ancient times, have limited relevance to
a modern understanding of literacy. Today we know
that literacy depends heavily on a remembered lexicon
of words and a learned phrasicon of multi-word constructions, all stored with culturally and historically
contingent meanings attached (Langenberg, 2000). In
the act of reading, many such domains of knowledge
interact in complex ways. The relative ease with which
readers can understand texts in which the internal letters of every word have been scrambled (Rawlinson,
193
1976) shows how little the art of literacy relies on a strict
hierarchy of letters-to-syllables-to-words-to-sentencesto-orations, however useful such a scheme may have
been pedagogically. The Medieval narrator recognized
a systematic notational hierarchy in the corpus of Latin
texts, but took for granted all the situated, real-world
knowledge needed to give meaning to those texts.
If one were to replace Vergil with perhaps the Abbé
Vogler (1749–1814), one of the first music teachers to
adopt Roman numerals as proxies for musical elements
(Grave & Grave, 1988), the story of Lucinius might read
as follows:
Vogler, on account of his innovations for teaching
nonmusicians, took the boy [Lucinius] and taught
him the elements of scales [i.e., the notes]. Then,
gently and with enticements, as is the custom of
teachers, he rapidly taught him how to construct
intervals out of notes, and how to form chords out of
intervals, and then how to complete a composition
out of chords.
Vogler’s imagined outline would be as limiting as that of
the Medieval narrator—the systematics of notation do
not give an accurate picture of the cognitive structure of
music literacy. Of course the advantage of such a presentist account is its broad applicability—the notational
hierarchy would be much the same for Bach or Stravinsky. But this generality comes at the price of excluding any explicit role for knowledge specific to a given
time and place. In the following discussion I hope to
show not only that including historically contingent
elements in stage 1 of a corpus analysis can improve
the results but also, more generally, that three methodologically convenient assumptions adopted in many
computer-assisted corpus studies of past styles are
insufficiently sensitive to historically significant characteristics of European art music. These assumptions are:
(1) a single auditory stream, (2) event contiguity, and
(3) unlimited scope for statistics.
THE ASSUMPTION OF A SINGLE AUDITORY STREAM
Modern corpus studies originated in studies of language
(Firth, 1957; Sinclair, 1992; Quirk, 1960;), and the working hypotheses of those studies continue to influence
corpus studies in music. If one thinks of language comprehension as involving a type of auditory scene analysis
(Bregman, 1990), one sees that studies of verbal corpora
have made the quite reasonable and often methodologically necessary simplification that language constitutes
a single auditory stream, one represented either as transcribed speech or as written text to be heard internally
by a reader. A corpus of transcribed conversations or
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Robert O. Gjerdingen
literary dialogues requires that speakers “wait their turn,”
and transcribers will customarily edit out or regularize
instances where speakers overlap or cut into another
speaker’s utterance. In musical parlance one might say
that while corpora of speech allow for antiphony, they do
not welcome polyphony.
The story of Vergil and Lucinius dates from the time
of the first preserved examples of European art-music.
The churches and monasteries of Medieval Europe daily
performed incantations selected from a large repertory
of melodies mythologized as originating with Pope
Gregory (c. 570), hence the term Gregorian chant
(Hiley, 1993). Its notation was frequently described in
Latin as a series of “points” (puncta), after the black dots
or small squares used to mark the musical notes. For the
most sacred ceremonies, skilled singers would embellish
the chant with one or more additional auditory streams.
This was sometimes described as setting “a point against
a point” (puncta contra punctum [Petrus, ca. 1300s]),
and it is from the latter two words of this Latin phrase
that we get our word counterpoint. The European artmusic tradition from its inception thus assumed at least
two auditory streams. In particular, two streams typically formed a dynamic scaffold to which still other
streams could be added. One voice of the scaffold was
the “holder” (tenor) of the chant while the other formed
the “second song” (discant), hence functioning as what
music historians term a “discant-tenor framework”
(Cyrus, 2000).
This underlying presumption of a guiding twostream structure remained central to music education
and composition in the Renaissance (Schubert, 2002)
and continued without interruption into the 17th and
18th centuries. Italian composers, for example, were
still called contrapuntisti in the days of Bach and Handel (Pitoni, ca. 1713), and the music centers of Bologna, Rome, and Naples all required apprentice
musicians to become fluent in the extemporized creation of two-voice counterpoint (Sanguinetti, 2012).
Further north, the Langloz manuscript (Renwick,
2001) shows how fugal partimenti were used to aid
training in extemporized counterpoint within Bach’s
circle. The historically important duet of the discanttenor framework or the bass-melody framework might
be likened to a pas-de-deux in classical ballet. One
FIGURE 1. J. S. Bach, Prelude (BWV 1007, i), mm. 1—2.
could try to reduce the dancers’ interactions to a single
numerical “stream,” computing perhaps the time series
of a distance-vector. But would knowing that the male
dancer is 0.76 meters from the female dancer really tell
us anything of significance about the art of dance? It
seems more likely that one would need to know what
both dancers were doing and how they interacted in
terms of the established categories of ballet in order to
model a human understanding of a pas-de-deux. By
the same token, trying to “iron out” the inherent twoness of a two-voice framework risks ignoring a fundamental feature of this musical art of coordinated
human actions.
THE ASSUMPTION OF EVENT CONTIGUITY
Some of the obvious statistics to compute on any corpus
would be the distribution of event frequencies and the
transitional probabilities between events. In studies of
language, Zipf’s law (Zipf, 1935) emerged from the ranking of word frequencies, and important concepts in information theory were first exemplified by the transitional
probabilities of letters of the English alphabet (Shannon,
1951). Whereas studies of corpora of English texts can
confidently assume the significance of contiguous strings
of characters, or of the explicit cues (white space) that
demarcate direct successions of words, the question of
what to count is considerably more complex in music.
Take, for instance, the opening measures of J. S. Bach’s
G-major Suite for Cello (BWV 1007; see Figure 1).
It is a true statement that the opening G2 is followed
immediately by D3 and then by B3. But as the prelude
continues a listener begins to recognize that those three
pitches are less the contiguous elements in a melody and
more the subsequently discontiguous events in a threevoice chorale (i.e., three auditory streams; Cambouropoulos, 2008; Davis, 2001). In this latter sense the B3 of
measure 1 “goes to” the C4 of measure 2, even though
those tones are separated by (depending on how one
counts) three to seven intervening tones. Perceptually
relevant events in a musical corpus may thus occur in
multiple streams where perceived contiguities—and
hence computable transitions—occur at multiple time
spans.
Implied polyphony is a known trait of Bach’s works for
solo cello or violin. Yet even when separate instruments
“Historically Informed” Corpus Studies
195
FIGURE 2. Joseph Haydn, String Quartet in F Minor (Op. 20, no. 5; Hob. III:35), mm. 1—3.
are available to perform each auditory stream, discontiguous events remain important. Take, for example, the
opening bars of Haydn’s string quartet Op. 20, no. 5
(Hob. III:35; see Figure 2), where the composer lays out
a stock 18th-century “opening gambit” (Gjerdingen,
2007, Chapter 6).
The stock melody, aurally highlighted by long tones
on the downbeats of each measure, ascends the first
three steps of the F-minor scale (➊-❷-❸, as marked
on Figure 2); the default bass for this opening gambit
would sound scale degrees ➀-➆-➀, which is exactly
what Haydn presented. In Haydn’s world, such moves
were as common as the chord progressions (the
“changes”) of a Gershwin song might be to a jazz musician today. Note, however, that while the melodic transition ➊-❷ does involve contiguous tones (F4–G4), the
❷-❸ transition does not. Haydn’s art depended for its
effect on his listeners’ ability to hear discontiguous
events as focal points in the syntax of his theme.
In his Studies on the Origin of Harmonic Tonality,
Carl Dahlhaus (1968/1988) singled out a clearly perceptible metrical hierarchy as one of the contributing factors in the transition from the looser tonal organization
of the 16th century to the more modern tonal organization of the 18th. In the sacred works of Palestrina, for
example, many if not most of the important relationships between tones involve contiguous pitches. With
Vivaldi, by contrast, an understanding of many of his
long sequences depends on a listener being able to relate
discontiguous pitches that occur at corresponding
moments within successive metrical units. If this recognition of discontiguous but fundamentally important
events is central to a listener’s experience of Vivaldi,
Bach, Haydn, and practically every composer who came
later, then it is a questionable methodological shortcut
to limit the computation of event frequencies and transition probabilities to directly adjacent tones.
THE ASSUMPTION OF UNLIMITED SCOPE FOR STATISTICS
Allen McHose, longtime professor at the Eastman
School of Music and a major influence on American
music theory, was among the first to employ statistical
methods in the analysis of harmony (McHose, 1947).
He tabulated frequencies and transitional probabilities
for musical events, using Roman-numeral representations as proxies for those events. His practice of choosing an inventory of chords to represent the elements of
a musical corpus was in line with views widely held in
early 20th-century psychology. Edward B. Titchener,
for example, stated in his Outline of Psychology (1902,
p. 85) that, “Since the first task of the psychologist is to
analyse consciousness into its elements, he is obliged to
count up the total number of sensation qualities.”
McHose’s inventory of chordal types served as a plausible realization of Titchener’s call to establish the “total
number of sensation qualities.” Psychology, of course,
went on to largely reject Titchener’s approach. The
Gestalt psychologists in particular noted that a perceived
whole (Gestalt) was often more important than the
details of its parts.
One problem with taking chordal types as independent
actors in the world of music—that is, reifying these “sensation qualities”—is that musical relationships can be
highly dependent on context. The great pianist (and
musical conservative) Claudio Arrau once complained
that Shostakovich “has not written one good note of
piano music. No. Let me correct that. He has written one
good note, but not two” (Kahn, 1972, p. 52). Though his
assessment would be disputed by Shostakovich’s many
admirers, Arrau did understand that musical elements
out of context have little intrinsic meaning. McHose
allowed his statistics unlimited scope, assuming that local
contexts had no strong influence on the meaning of, for
example, a “IV” chord. What if, however, statistics constrained by local scope better reflected actual usage?
Take, for example, the question of whether a native
speaker of English should use the definite or indefinite
article preceding the work “stroke.” A global analysis of
the immense corpora of English currently available for
study might reveal no strong preference for either article. But if the statistics are limited in scope to particular
topics, the results are quite different. When the context
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Robert O. Gjerdingen
FIGURE 3. Jean-Marie Leclair, Sonata for Violin and Continuo, Op. 5, no. 1, mvt. 3, “Aria,” mm. 1—4 (Paris, 1734).
is personal health, native speakers almost always use
“a,” as in “She had a stroke” (Danielsson, 2003). To say
“She had the stroke” would mark the speaker as an
outsider of some sort. Yet if the context is time, native
speakers invariably say “He arrived at the stroke of
midnight.” Most native speakers could not even imagine saying “He arrived at a stroke of midnight.”
Particular linguistic constructions (form-meaning
combinations of words; Goldberg, 1995) can have
a strong effect on the probabilities of particular verbal
collocations. In the words of Stefanowitsch and Gries
(2003), experts in computational corpus analysis:
Traditionally, the lexicon and the grammar of
a language are viewed as qualitatively completely
different phenomena, with the lexicon consisting of
specific lexical items, and the grammar consisting of
abstract syntactic rules. Various expression types that
fall somewhere in between lexicon and grammar (i.e.
various types of fully or partially fixed multi-word
expressions) have been recognized but largely
ignored (or at least relegated to the periphery) by
mainstream syntactic theories (notably, the various
manifestations of Chomskyan generative grammar).
The predominance of this view may be part of the
reason why corpus linguists, until recently, have
largely refrained from detailed investigations of
many grammatical phenomena. The main focus of
interest was on collocations, i.e. (purely linear) cooccurrence preferences and restrictions pertaining
to specific lexical items. If syntax was studied systematically at all, it was studied in terms of colligations, i.e. linear co-occurrence preferences and
restrictions holding between specific lexical items
and the word-class of the items that precede or
follow them.
These authors pioneered the “collostructional analysis”
of verbal corpora, where instead of allowing global
scope, statistical calculations are designed to uncover
the internal regularities of particular constructions.
If, in McHose style, one asked, “To which chord does
a IV chord progress in ‘common-practice’ music?”
there would be an array of answers of varying probabilities representing an unknown number of different
musical contexts and constructions. If, by contrast, one
said, “To which chord does a IV chord progress in
a ‘Prinner’?” the answer would be “I6, with a probability
near 1.0.” “Prinner” (Gjerdingen, 2007, Chapter 3) is
the name given to a common riposte in opening passages of innumerable 18th-century works. The opening
of the Aria movement from a violin sonata by JeanMarie Leclair (see Figure 3) shows an initial Romanesca schema followed, as is the norm, by a Prinner
riposte. In this context, IV not progressing to I6 would
be potentially ungrammatical, regardless of the global
statistics.
It may be worth noting that recognition of the Prinner, as one of the core patterns of 18th-century musical
syntax, emerged only after an extensive corpus analysis
of the repertory, an analysis that focussed on the coordinated behaviors of voices.
A MINIMAL CORPUS: ONE MOVEMENT BY J. S. BACH
For a test case of historically informed corpus analysis, I
will attempt to work backwards from known norms of
Bach’s compositional style (“historically informed”
stage 3 results) toward a defensible set of corpus elements (stage 1 presuppositions), while avoiding the
problematic assumptions detailed above. The work in
question is Bach’s toccata for organ in C major (BWV
564), probably written around 1712 (Schmieder 1950)
when he was still a journeyman organist anxious to
demonstrate his prowess. It begins with extended bravura flourishes first in the manuals and then for an
extended period on the pedals (Bach was a pioneer of
virtuoso pedal playing). Only in measures 32–34 does
“Historically Informed” Corpus Studies
197
FIGURE 4. J. S. Bach, Toccata (BWV 564), mm. 32—34, showing the brief canon in m. 32 and the five-count cadenza doppia in mm. 33—34.
FIGURE 5. The simple (a), compound (b), and double (c) cadences widely taught in Bach’s day.
Bach bring all his forces together to present what most
listeners will remember as the theme of this work (see
Figure 4):
In terms of late 17th- and early 18th-century musical
practice, measure 32 (after the downbeat chord) presents a formulaic two-voice canon (Gjerdingen, 2007,
Chapter 16). The lower voice (the “Follower” or comes
in Figure 4) is characterized by note-to-note contiguity,
while the upper voice (the “Leader” or dux) is “diminished” and thus serves as a model for the comes only
through discontiguous pitches occurring at regular time
intervals. The subsequent measure then presents a standard type of five-count cadence (here five eighth-notes)
that closes on the first beat of measure 34. This cadence,
a widely acknowledged norm of Baroque practice, was
known by Italian masters as the “double cadence”
(cadenza doppia [Fenaroli, 1775, p. 8]). It was one of
three basic cadences taught to every apprentice musician at the conservatories in Naples (see Figure 5), and
as late at the mid-1780s Mozart taught it to his student
Thomas Attwood (Gjerdingen, 2007, p. 103).
In Example 5, the numbers below the brackets indicate the “count” of each cadence. Note that the fivecount cadenza doppia has one voice moving twice from
the leading-tone to the keynote, which may partly
explain the meaning of “double” in the cadence’s name.
In Victorian times the double cadence was sometimes
termed a “consonant fourth” cadence (Smith, 1989) to
justify the seeming preparation of a dissonant fourth (in
Figure 5, the second C5 in the soprano voice of the
cadenza doppia, viewed in relation to the bass G3) by
a “consonant” fourth (the first C5). Such verbal hairsplitting is indicative of how this common tonal construction
—a partially fixed multi-note expression, to paraphrase
Stefanowitsch and Gries (2003)—was refractory to analysis by rule. The two-voice framework in the upper
voices of the cadenza doppia strictly observes all the rules
of Bach-era counterpoint, but its placement over a pedalpoint G introduces secondary effects (the emergent
“fourths” between G3 and C5) that the rules could not
cover.
To the casual listener, Bach repeats the music of measures 32–34 in measures 34–36. A glance at the score
(see Figure 6), however, reveals that the melody of measures 32–34 has become the bass of measures 34–36 and
vice versa.
The latter measures are, with some slight alterations,
inversions of the earlier measures. The two underlying
schemata, however, remain easily recognizable. In the
case of the cadenza doppia, Bach preserves a two-voice
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Robert O. Gjerdingen
FIGURE 6. J. S. Bach, Toccata (BWV 564), mm. 34—36.
FIGURE 7. A comparison of mm. 33—34 and mm. 35—36. Numbers in circles indicate scale degrees. Circled numbers within parentheses indicate
departures from the prototype.
framework even under inversion (see Figure 7). One
voice descends stepwise from F to C, sounding scale
degrees ❹–❸–❷–❷–❶ (in the Renaissance, this was
usually the tenor part). The other voice, B–C–C–B–C,
sounds scale degrees ⑦–①–①–⑦–① (the older discant part). The temporally and tonally specific collocation of these two voices was a norm that Bach
scrupulously observed, though a fuller description of his
practice would require a discussion of the other two
voices, a look at how considerations of sonority could
affect the two-voice framework, and a conspectus of
exemplars of the cadenza doppia in other meters and
tempos.
In measure 37, Bach modulates to the key of G major
and presents the two-voice framework of the cadenza
doppia on the upper manual of the organ, replacing the
implied pedal point on scale degree ⑤ heard in measure
33 with a series of root-position basses (see Figure 8a).
And in measure 60 he presents, in the key of E minor,
a fourth variant of the cadenza doppia (see Figure 8b).
Bach places the beginning of the old discant part in the
bass before completing it in the soprano voice. This is
his most free setting of the cadenza doppia in the entire
toccata and immediately precedes the return of the twomeasure module (the “theme”) first heard in measures
32–34.
If the cadenza doppia represents a satisfactory stage 3
result of corpus analysis—“satisfactory” in the sense of
matching a known norm or ground truth of the musical
style—then how should its elements be represented at
stage 1? In other words, what element(s) should be
passed to stage 2 calculations so that at stage 3 one could
arrive at the cadenza doppia?
In the tradition of McHose, some corpus analyses have
chosen Roman numerals (with or without figured-bass
superscripts) as stage 1 elements. Roman-numeral analysis has the methodological advantage of producing
a single string of symbols—the assumption of a single
auditory stream. But as Table 1 below demonstrates,
a disadvantage is that the four variants of the same
cadenza doppia produce four very different strings of
Roman numerals. For a machine classifier to recognize
that these symbols all represent the same musical category would likely require a custom-designed parser of
considerable sophistication, and it would not be easy
to prevent such a parser from treating the instances at
“Historically Informed” Corpus Studies
a
199
b
FIGURE 8. Mm. 37—38 and mm. 60—61 show the two-voice framework (a) over a different bass or (b) partly incorporated into the bass.
TABLE 1. Four Variants of the Cadenza Doppia Create Four Very Different Strings of Roman Numerals.
m. 33
m. 35
m. 37
m. 60
count 1
1.5
count 2
2.5
count 3
3.5
count 4
4.5
count 5
freq.
V7
V 4/2
ii 7
vii 7
V7
V 4/2
V7
V6
I 6/4
I6
I
i
I 6/4
I6
I
i
V 4/3
ii 7
V 4/3
ii
V 5/4/2
ii 7
V 5/4/2
ii
V
V
V
V
V7
V7
V7
V7
I
I
I
i
x5
x5
x1
x1
TABLE 2. Four Variants of the Cadenza Doppia Retain Similar Two-voice Frameworks.
m. 33
voice 1
voice 2
m. 35
voice 1
voice 2
m. 37
voice 1
voice 2
m. 60
voice 1
voice 2
count 1
1.5
count 2
2.5
count 3
3.5
count 4
4.5
count 5
❹
⑦
❹
⑦
❸
①
❸
①
❷
①
❷
⑥
❷
⑦
❷
⑦
❶
⑤
❹
⑦
❹
⑦
❸
①
❸
①
❷
–
❷
⑥
❷
⑦
❷
⑦
❶
①
❹
①
❹
⑦
❸
①
❸
①
❷
①
❷
⑥
❷
⑦
❷
⑦
❶
⑤
❷
⑦
❷
⑦
❸
①
❸
①
❻
①
❹
①
❷
⑦
❹
⑦
❸
①
Note: Collectively, the variants first heard in mm. 33, 35, and 37 occur 11 times in the toccata. The variant first heard in m. 60 presents the same “voice 2” but has a different
“voice 1.”
measures 37 and 60 as two cadences (not the intended
meaning of “double cadence”). The methodological difficulties are augmented by the loss of information about
voices. As mentioned, Bach’s music takes as a point of
departure the coordinated actions of individual vocal or
instrumental parts, even in works for solo cello or violin. The integrity of those parts cannot be reliably reconstructed from a string of Roman numerals. Moreover,
the complexities and the extent of subjective interpretation contained in these composite symbols (e.g., “V
5/4/2”) can lead to cases where even the momentary
musical context cannot be determined without reference to the score.
The table’s rightmost column lists the frequency of
these four strings of Roman numerals in the onemovement corpus of Bach’s toccata. None of the strings
occurs more than five times.
By contrast, Table 2 shows the same four variants
represented as a two-voice framework. The numbers
in the columns indicate scale degrees (in terms of the
local key), and the measure numbers of first instances
correspond with those of Table 1 for ease of comparison.
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I believe that one can make at least three direct observations from Table 2: (1) the variants that appear initially in
measures 33, 35, and 37 are so similar, differing by only
a few notes out of the eighteen total, that they ought
to form a single category with 11 instantiations; (2) the
1–6–7 melodic ornament in voice 2 (beginning on count
3) appears to have a collostructional bias (Stefanowitsch
& Gries, 2003) toward this schema, at least in Bach’s
usage; and (3) the variant appearing in measure 60 shares
nearly the same voice 2 as the other variants but has
a different voice 1.
Almost any type of machine classifier ought to be
capable of clustering, without any special modifications,
the first eleven of the twelve cadenze doppie in Bach’s
toccata, and might weakly associate them with the
twelfth instance (m. 60). The idea of a general category—“cadenza doppia”—that comes in two subtypes
—one where “voice 1” begins on ❹ and one where it
begins on ❷—was a fact of 18th-century practice,
something implicit in a set of brief musical rules published in 1775 by the Neapolitan maestro Fedele Fenaroli (1775, p. 6). Shortly before specifying the details of
the cadenza doppia, Fenaroli noted, as an “axiom” (assiomo musicale), that when the bass moves from scale
degree ⑤ to ①, one can give a 7th to the first chord
(hence in three voices replacing the ❷ with ❹); “this
seventh [= ❹ of voice 1 in Table 2] cannot rise but must
resolve by falling to the 3rd degree of the key” (“La
settima minore si dà alla quinta del tono, che torna alla
prima; la quale settima non può salire, ma risolvere
calando alla terza del primo tono”).
If one were to posit the historically informed melody
and bass patterns of the cadenza doppia as stage 1 elements, and were to do the same for the components of
the canon-like schema first seen in measure 32, a pattern
I have previously named a Fenaroli in honor of the
maestro mentioned above (Gjerdingen, 2007, Chapter
16), then a likely stage 2 processing of this single movement would result in, among other things, a statistical
validation of there being at least two significant collocations of voice pairs (the two schemata). Subsequent
stage 3 processing would likely reveal the high transitional probability of the succession “Fenaroli ⇒
cadenza doppia.” That simple collocation of schemata
accounts for approximately 40 percent of the toccata
(not counting the opening flourishes). Failure to recognize this pairing would truly be “missing the forest for
the trees.” In linguistic terms, the focus shifts from lexemes to phrasemes, as it has in construction-based or
usage-based grammars (Goldberg, 1995). Just as it could
be exceedingly hard to deduce the meaning of the common idiom “kick the bucket” (= die) from an analysis of
its three constituent words in an arbitrarily large corpus,
so a purely bottom-up analysis of a musical corpus
might struggle to identify larger patterns that have special meanings and functions within a musical culture.
With stage 2 results grounded in the types of choices
at hand in Bach’s world, stage 3 deductions of norms
can have direct musicological and psychological relevance. On the musicological side one could compare
a large corpus of Bach’s works with similar works by,
for instance, Vivaldi. The young Bach had studied
Vivaldi assiduously at the very time of composing his
Toccata. In the words of a noted Bach scholar, “Indeed,
it was Vivaldi who exercised what was probably the
most lasting and distinctive influence on Bach from
about 1712–13, when a wide range of the Italian repertory became available to the Weimar court orchestra.
Bach drew from Vivaldi his clear melodic contours, the
sharp outlines of his outer parts, his motoric and rhythmic conciseness, his unified motivic treatment and his
clearly articulated modulation schemes” (Wolff, 2001).
A comparative corpus analysis of Bach and Vivaldi
could perhaps help to pinpoint which aspects of Vivaldi’s compositional method Bach absorbed and which he
did not. On the psychological side, one sees evidence
for the central role that memory must take in recognizing and differentiating the interplay of known compositional units in a game of combinations—what many
scholars in Bach’s world named the ars combinatoria
(Leibniz, 1666; Ratner, 1970). The two schemata just
mentioned are, to be sure, historically contingent and
unknown to many musicians today. They would be
unlikely to occur in the works of Schoenberg or Steve
Reich. But there can be little question that they ought to
constitute elements in any historically informed analysis of this work by Bach. The same rationale would
apply to the entire corpus of Bach’s work, and very
likely to the much larger corpus of composers working
during Bach’s lifetime. More than a century later, echoes of such an overlearned pattern can still be found in
the works of Carl Czerny, a pupil of Beethoven. The
colorful harmonization and bravura right-hand passagework shown in Figure 9 only partially conceal the
traditional cues of the cadenza doppia. This ancient and
quite predictable five-count cadence helps Czerny bring
to a sure close the torrent of notes that make up the
opening section of this advanced exercise in “finger
dexterity.”
Discussion
As mentioned earlier, 18th-century apprentice musicians were given exercises to complete that required
“Historically Informed” Corpus Studies
201
FIGURE 9. Carl Czerny, Die Kunst der Fingerfertigkeit, Op. 740, no. 14, mm. 14—16 (ca. 1840s). The diminished-seventh chord in the second half of m. 14
is certainly colorful, but it admits the same two-voice framework seen in centuries of cadenze doppie.
FIGURE 10. Francesco Durante, partimento in D major (Gj0023), mm. 1—5. After two sequential patterns in D major, the partimento confirms
a modulation to A major with a cadenza doppia (the same bass pattern seen in Fig. 8a by Bach). Numbers in circles indicate the voice-pair needed
to complete the cadenza doppia.
FIGURE 11. Georg Frideric Handel (HWV 258), Coronation Anthem “Zadok, the Priest,” mm. 21—23 (London, 1727). The chorus enters as the cadenza
doppia reaches its conclusion.
them to commit to memory the musical schemata of
their day. Many of the instructional works known as
partimenti, for instance, end with the cadenza doppia
indicated by the bass (the other voices were added by
the student in performance). For example, a partimento
by Francesco Durante, one of Bach’s Italian contemporaries, modulates to the dominant key at the end of its
first phrase and confirms the modulation with a cadenza
doppia (see Figure 10), using in fact the same alternate
bass for a cadenza doppia that Bach used in the analogous location shown earlier in Figure 6 (m. 37). The
instructional intent of the partimento is clearly evident
in its presentation of two schematic sequences, one
ascending, one descending, prior to the cadenza doppia.
In Handel’s great coronation anthem “Zadok the
Priest” (1727), it is a cadenza doppia that brings to
a close the extended orchestral introduction and ushers in the thundering chorus, an intentionally grand
moment captured in the recent film The Young Victoria (see Figure 11). The cadenza doppia was, of
course, not something invented in Bach and Handel’s
day. A recent article by Menke (2011) explores many
instances of the cadenza doppia in the 16th and 17th
centuries. This cadence was already a stock item in the
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Robert O. Gjerdingen
days of Palestrina, and it went on to become perhaps
the most frequently used large cadence in 17thcentury sacred music.
I mention this background to Bach’s usage because it
speaks to the close connection of music theory with
music history. When historical experts look at Bach’s
compositional technique, they often note the retention
of many 17th-century musical practices—hardly surprising since Bach was born and trained in the 17th
century. Musicians of the past were part of complex,
ongoing traditions, and the heavy use of the cadenza
doppia by composers from the 16th through the early
19th centuries is an indicator of how useful compositional constructions could persist and survive significant changes in musical style.
Two current research programs in corpus analysis
both take an historically informed approach to music
in the Renaissance. One is the ELVIS project at McGill
University and the other is the Digital Du Chemin project, which connect researchers in the U.S., Canada, and
France. “ELVIS” is an acronym for “Electronic Locator
of Vertical Interval Successions: The First Large DataDriven Research Project on Musical Style.” The ELVIS
project is not limited to music before 1600, but at least
two of its researchers, Julie Cumming and Peter Schubert, are noted scholars of that era. “Digital Du Chemin”
is part of a larger project, The Chansons of Nicholas Du
Chemin (1549–1568), hosted by the Centre d’Études
Supérieures de la Renaissance in Tours, France. Lead
researchers are the musicologist Richard Freedman
(Haverford College) and Philippe Vendrix (CESR). In
both cases, eminent music historians are collaborating
with experts in data analysis and music information
retrieval (MIR) to achieve impressive results. In the
Du Chemin project, for instance, missing voice-parts
have been reconstructed based on norms in the corpus,
and in the ELVIS project one can view comparative
statistics concerning the use of a particular type of
cadence by different composers. In both cases an analysis of the collocations of voice-pairs plays an important
role in the research. For the 18th-century repertory of
Italian-influenced music, which includes almost every
composer from Bach and Handel to Haydn and Mozart,
the work at Northwestern University by James Symons
(2012) shows considerable promise. By looking at
something as simple as melodic patterns that occur frequently at regular temporal intervals in a repertory of
two-voice solfeggi, and then by correlating those
melodic patterns with associated bass patterns, he has
been able not only to validate most of the schemata
previously claimed as norms of the Italian style but also
to identify new ones. When viewed together, these
ongoing studies suggest a remarkable continuity in the
practices of earlier musicians, practices that can be easily connected with the current practices of jazz musicians and others working in vernacular styles.
In conclusion, I would like to note that although
historically informed corpus studies can be considerably more difficult to plan and execute, in large part
because of the heterogeneous nature of a multitude of
patterns, the results are potentially more grounded and
useful. This type of heterogeneity has been a topic of
interest in the “London School” of linguistics since the
work of J. R. Firth in the 1950s. In his Dictionary of
Linguistics and Phonetics, David Crystal (2003) writes
that “Firthian” principles call for “an approach to linguistic analysis based on the view that language patterns cannot be accounted for in terms of a single
system of analytic principles and categories (monosystemic linguistics), but that different systems may need
to be set up at different places within a given level of
description.” In the sample corpus analysis of Bach
presented above, the fact that a pair of simple twovoice frameworks could account for about 40 percent
of Bach’s toccata (not counting the opening flourishes)
is reminiscent of some recent research in corpus studies of speech. Erman and Warren (2000) found that
about 55 percent of a large corpus of English texts
(both written texts and transcribed speech) was made
up of “pre-fabs,” meaning learned multi-word units.
This and similar research results are showing that the
brain likely enables the fluent “on-line” production of
speech through the recall of contextually appropriate
pre-fabs. However complicated and profound we may
find Bach’s musical art, there is little question that he
could “speak” it in the sense of improvisation and
fluent mental composition. If historically informed
corpus analyses of music can show that musicians
manage the rapid on-line production of music by
drawing upon similar repertories of pre-fabs, then
such studies can provide further support for the idea
of general cognitive abilities being at the foundation of
specialized cognitive skills.
Author Note
Correspondence concerning this article should be
addressed to Robert O. Gjerdingen, Northwestern University, 711 Elgin Rd., Evanston, IL 60208-1200. E-mail:
[email protected]
“Historically Informed” Corpus Studies
203
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