Download ars combinatoria in selected works of cpe bach

ARS COMBINATORIA IN SELECTED WORKS OF C.P.E. BACH:
AN ANALYTIC INVESTIGATION
by
@
Nancy Wilson
Thesis submitted to
The Faculty of Graduate Studies and Research
in Partial Fulfillment of the Requirements
for the degree of
Master of Arts
<
Faculty of Music
McGill University
Montreal, Quebec
November 1988
Short title:
ARS C011BINATORIA IN SELECTED WORKS OF C. P. E. BACH
c
ABSTRACT
This
thesis
combinatoria,
permutation
explores
the
of
some
technique
musical
implications of ars
of
material,
eighteenth-century music, using
combination
for
ideas
and
analysis
of
of
Leonard B.
Ratner as a starting point.
Examined here
are solo
Bach: several pieces from
leichte Clavierstücke
keyboard works by C.P.E.
the two
sets of
Kurze und
(H. 193-203 and H. 228-238) and
a longer, more serious work, the Freye Fantasie
minor
(H.
300).
The
analyses
demonstrate
in F#
that
Ratner's ideas can provide analytic insight into these
contrasting works
by Bach and that the selected works
suggest extensions to these
manifestations
of
ars
ideas
as
weIl
combinatoria.
several questions worthy of further study
most
notably
relating
chroma tic-enharmonie
syotem.
(
to
as other
In addition,
are raised,
C.P.E. Bach's handling of
resources
within
the
tonal
'G
"
,1';
1
1
ABREGE
Cette
l'~
thèse
explore
combinatoria, soit la
de permuter
implications
technique de
de
combiner et
la matière musicale, pour l'analyse de la
musique du dix-huitième
nous
quelques
servirons
des
siècle.
idées
debuter
nous
"
Pour
pertinentes de Leonard B.
Ratner.
Sont revues ici quelques
solos
pour
clavier de
C.P.E. Bach: plusieurs piéces des deux sèries de Kurze
und leichte Clavierstficke (H. 193-203 and
et
une
pièce
Fantasie
en
démontrent
plus
F#
que
longue,
(H.
mineur
les
H. 228-238)
plus sérieuse, la Freye
Ces
300) .
analyses
idées de Ratner peuvent suggérer
une perception analytique de ces oeuvres contrastantes
de
Bach
et
que
les
oeuvres choisies suggèrent des
extensions de ces idées,
d'autres manifestations
quelques
questions
approfondie
fa~on
don t
sont
de
qu'elles suggèrent
d'ars combinatoria.
qui
méritent
soulevées,
C.P.E.
1\
meme
Bach
en
une
En plus,
étude
particulier
traite
des
plus
sur la
ressources
chromatiques et enharmoniques dans le système tonal.
c
TABLE OF CONTENTS
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
CHAPTER 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
INTRODUCT l ON
CHAPTER 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
A MECHANISTIC APPROACH TO WORKS FROM THE
KURZE UND LEICHTE CLAVIERSTÜCKE
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
CHAPTER 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
A DIFFERENT CONTEXT: THE FANTASIA IN F# MINOR
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Bach's Writings on the Free Fantasia ....... 40
Form in the Free Fantasia in F# Minor ...... 45
Analysis of the Sections . . . . . . . . . . . . . . . . . . . 49
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
APPEND IX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Scores of Compositions Analyzed in Chapters 2 and 3
(H. 193, 196, 228, 231, and 300)
c
t
f
PREFACE
The idea
~
for an analytic investigation involving
combinatoria originated
in
a
theory
Haydn's early keyboard music led by Dr.
McGill University.
awareness
on
This
my
part
seminar
of
seminar on
Bo Alphonce at
fueled
phenomena
a
such
growing
as
ars
combinatoria and rhetoric, both of which can be sensed
as
influential
factors
construction
and
acknowledged
in
perhaps for
design,
typical
the following
discussions
and
geared
toward
guiding analysis.
distinction in
but
which
are
rarely
classroom
theory analyses,
reasons.
Firstly, written
explanations
applications occurring
were
in eighteelh-century musical
in
of
their
musical
eighteenth-century sources
teaching composition rather than
Secondly, owing to an all-too-clear
North American music education between
the content of music history and theory classes,
phenomena may
these
be considered by theorists as belonging
to the domain of the former.
Leonard B. Ratner
crossed
concerns.
several
~s
lines
Besides applying
one scholar
dividing
aspects
whose work has
these
of
differing
rhetoric and
vi
(
other
issues
derived from eighteenth-century sources
to ana1ysis in
Form, and
his
book
Style (New
Classic
York: Schirmer Books, 1980), he
has suggested the importance
our
understanding
Music: Expression,
of
of ars
combinatoria for
eighteenth-century
short, fascinating article
to
be
music in a
discussed
in this
thesis.
The music
of Carl
Philipp Emanuel
fascinating for reasons to be discussed
and
l
have
thus
chosen
Bach is a1so
in Chapter 1,
to use several of his solo
keyboard works in the analytic portions of this study.
There
is
a
growing
interest
in
his music, as the
bibliography to sorne extent indicates, a
will no
doubt accelerate
in light
growth which
of 1988 being the
bicentennial anniversary of his death.
Given aIl of the abcve considerations,
of
this
thesis
begins
by
reminding
interesting factors surrounding
C.P.E.
music,
ars
and
then
introduces
discussing Ratner's
Chapter 2
seminal
then offers
article
Chapter 1
the reader of
Bach
and his
combinatoria
on
by
this topic.
a preliminary attempt to apply
concepts of ars combinatoria
to the
analysis of solo
keyboard works by Bach in a popu1ar idiom, after which
Chapter 3 expands the scope of the analytic inquiry to
inc1ude
(
one
serious works.
of
Bach's
A
brief
least
conventional and most
conclusion
then discusses
1
vii
several issues
arising from this study which could be
further pursued.
Concerning the edition
music,
l
have
taken
used
in
studying Bach's
advantage
of
the
recent
publication of Bach's entire solo keyboard output in a
facsimile edition of which Darrell Berg is the editor.
This edition, as weIl as
a
useful
review
of
it by
George Barth, are listed in the bibliography.
At
this
proofreading
time
and
constant support
l
wish
copying
Bo
profound
have
Alphonce,
inception.
who se
understanding
helped
examples,
and encouragement.
to express my appreciation
Dr.
to thank David Judah for
motivate
of
and
to
my
and
for
his
Finally, l
wish
thesis supervisor,
insightful
comments
eighteenth-century
and
music
guide this study from its
(
CHAPTER 1
INTRODUCTION
Not only was Carl Philipp Emanuel Bach one
of the most influential composers, authors,
teachers, and performers in the musical
world of the eighteenth ~entury.
He was, of
course,
the son--indeed, the most renowned
of the five musically active sons--of the
greatest of aIl composers.<l>
As the
above citation suggests, there is little cause
to wonder why the music of
)
should
(1714-1788)
Carl Philipp
generate
Emanuel Bach
considerable
interest
within historical and analytic music scholarship.
addition to
music,
the intrinsic
there
contextual
compose r .
exists
factors
Firstly,
an
positive qualities of this
int:iguing
relating
it
In
is
to
assortment
Bach's
weIl
known
ljfe
that
of
as
a
Bach
acknowledged his father, Johann Sebastian Bach, as his
only teacher,<2> and that
training and
the Baroque
the
roots
of
his musical
compositional craft thus may be found in
tradition of
a figured
bass approach to
<1>William
S.
Newman,
"Emanuel
Bach' s
Autobiography," Musical Quarterly 51/2 (1965): 363.
(
<2>In 1773, at age 59, Bach stated in his
Autobiography that "
• in composi tion and keyboard
playing l never had any other teacher than my father."
(Ibid. ~ p. 366.)
2
composition.<3>
upon
future
Secondly,
composition
extensive, as
is reflected
C.P.E.
and
Bach's influence
keyboard
esteem
musicians
in
as
which
Haydn,
his
is
in the wide dissemination
of his treatise on keyboard playing<4>
the
playing
music
Beethoven,
German composers of Bach's time.<5>
was
and
as weIl
held
by such
various
Thildly,
as by
North
3ach was
<3>Wri ting
to Forkel in
1775,
Emanuel Bach
summarized Sebastian Bach' s method: "Sirice he himself
had composed the most instructive pieces
for the
clavier, he brought
up his pupils on them.
In
composition he started his pupil~ right
in with what
was practical,
and omitted aIl
the dry species of
counterpoint that are given
in Fux and others.
His
pupils had to
begin
their studies by learning pure
four-part
thorough basse
From
this he went to
chorales; first
he added the basses to them himself,
and they had to invent the alto and tenor.
Then he
taught
them to
devise the
basses themselves.
He
particularly insisted on the writing
out
of the
thorough bass in [four real]
parts.
In teûching
fugues, he began with the two-part CInes, and so on."
Translated by Hans R.
David and
Arthur Mendel, ~
Bach Reader
(New York: W. W. Norton & Company, 1945),
279.
<4>Carl Philip~ Emanuel
Bach, Versuch über die
wahre l l i .ill. ClavieJ.
~ spie1en,
(Berlin, 1753 and
1762).
Facs.
reprint
ed.
Lother Hoffmann-Erbrecht
(Leipzig: Breitkopf und Harte1, 1976).
Translated and
edited by William J. Mitchell as Essay ~ the True ~
of Playing Kevboard
Instruments,
(New York: W. W.
Norton & Compdny, 1949).
<5>ln his introduction to the English translation
of Bach's Versuch (see previous note), William J.
Mitchell discusses the spread of Bach's ideas, which
occurred directly via his students, and indirectly via
widespread sale of the
treatise itself.
See "C.P.E.
Bach' s Essay; An Introduction," Musical Quarterly, 33
(1947): 460-80.
As well,
a
chapter
is devç;t:ed to
interest in Bach and his music from the eighteenth
century to the
present in Hans-Günter Ottenberg's
recent biography Carl Philipp Emanuel ~ (Leipzig:
c
3
involved in various intellectual and artistic circles-music
whic~
latter
theoretical,
were
half
literary,
philosophical, etc.--
flourishing in Northern Germany during the
of
the
eighteenth
century,
and
was
concerned with fundamental aesthetic issues pertaining
to
musical
expression.<6>
displayed a practical, pragmatic
perf ormance ,
and
pedagogy
relatively comfortable material
Nonetheless
he
also
si de in composition,
which
ensured
existence.<7>
him
a
These
Verlag Philipp Reclam jun., 1982), which is translated
by Philip J. Whitmore (London:
Oxford University
Press,
1987);
see
pp. 185-217 of the English
translation.
For an account of the influence of
Bach's style on contemporaneous composers of North
Germany see Darrell Berg, "The Keyboard Sonatas of
C.P.E. Bnch: An Expression of the Mannerist Principle"
(Ph.D. dissertation, State University of New York at
Buffalo, 1975), 66ff.
<6>Significant discussions of Bach's involvement
in theoretical, literary, and aesthetic circles appear
in the following, among others: E. Eugene Helm, "The
Hamlet Fantasy and the Literary Element in C.P.E.
Bach' s Music," Musical Quarter1.I. 58/2 (1972): 277-96;
David Schulenberg, The Instrumental Music 21 Carl
Philipp Emanuel Bach, (Ann Arbor: UMI Research Press,
1984), esp. pp. 17-29; Berg, "Keyboard Sonatas," pp.
58ff, and, perhaps MOSt notably, Ottenberg's biography
of Bach (see note 5), which focuses throughout on the
rich cultural and intellectual milieu surrounding the
composer.
c
<7>This practical side of Bach is revealed in the
fo1lowing excerpt from his autobiography: "Because l
have had to compose most of my works for specific
individuals and for the public, l have always been
more restrained in them than in the few pieces that l
have written merely for myself. At times l even have
had to follow ridiculous instructions, although it
could be that such not exactly pleasant conditions
have led my talents to certain discoveries that l
might not otherwise have come upon.
4
and
other
facets
of
Bach's musical personality and
activities make his life a fascinating topic of study.
There is a correspondjng
be
sensed
in
his
keyboard music,
light, popular pieces
limits
of
musical
subsequent
analyses
to
those
several
of
of
the
of
Bach's
diversity to
which ranges from
tbat
expression
chapters
of
degree of
chal1enged the
his
present
era.<8>
study
The
offer
solo keyboard works
exemplifying this diversity.
A
approaches are
the analysis of Bach's
music,
analysis
well-suited to
approaches
of
form
such
and
investigation of various
to
one
or
more
as
number
Schenkerian
phrase
structure,
stylistic
genres.<9>
of ana1ytic
reduction,
and
the
issues pertaining
In the present study,
Since l have never liked excessive uniformity in
composi tion and taste,
since
l
have heard such a
quantity and
variety of
good [things], since l have
always been of the opinion that one could derive sorne
good, whatever it may be, even if it is on1y a matter
of minute detai1s
in a piece,
probably from such
[considerations] and my natural,
God-given ability
arises
the
variety that has
been observed
in my
works." Newman, "Autobiography," p. 371.
<8>This diversity i5 reflected
in the following
set of
distinctions suggested by William S. Newman
wi th respect to Bach' s solo keyboard music:
"
music written to
order as against music written to
taste," and works written "in
the
interest of sure
sales" as against
those other works, again, wri tten
for his own artistic satisfaction.
See William S.
Newm~n, The
Sonata in the C1assic Era, 2nd ed., (New
York: W.~ N~;;-&-Compa;y, 1972),~3.
<9>See for example
Darrell
Berg,
"Keyboard
Sonatas;" Suzanne C1erx, "La forme du rondo chez Carl
Philipp Emanuel Bach," Revue de Musicologie 19 (1935):
c
5
however,
the
focus
which, because
these
other
of
is
on a different point of view
its
flexible
approaches
while
perspective on certain issues.
nature, complements
offering
This
a
point
unique
of view
will now be introduced.
*
In
a
broad
*
sense,
*
dll
western
music
can be
considered to be constructed from various combinations
and permutations
century,
eighteenth
and
combin'ation
expli,:i tl y used
technique
may
seem
the
has
little
the
were
teaching
come
While its
pre-designed
combinatoria
c
however,
permutation
in
which
combinatoria.
various
of the twelve pitch classes.
to
of
be
nonetheless
notions
of
quite
often
composition, a
known
as
~
most trivial manifestations,
compositional
more
In the
than
quaint
games of chance,
pastimes,
ars
reflects broader scientific
148-67; Pamela Ruth Fox, "Melodie Nonconstancy in the
Keyboard Works of C.P.E. Bach," (Ph. D. dissertation,
University of Cincinnati, 1983); Nancy Barnes Hager,
"Rhythm and
Voice-Leading as a Facet of Style:
Keyboard Works of J.S. Bach, C.P.E. Bach, and Mozart,"
(Ph.D. dissertation, City University of New York,
1978); Heinrich Schenker, "Ph. Em. Bach: Kurze und
leichte Klavierstückc mit verànderten Reprisen (176~
Nr. 1, Allegro," in Der Tonwille 4 (1923): 10-11
(translated by Steve -rBrson in lu Theory Only 10:4
(1987): 5-10); David Schulenberg, Instrumental Music,
esp. pp. 147-60.
~----------
-------------------------
6
and
philosophical
views
of
the
which may be subsumed under the
eighteenth century
concept of mechanism.
Briefly, mechanism is a doctrine of eighteenth-century
thought which states that aIl phenomena,
both animate
and inanimate, may be explained in terms of principles
by which
machines
derived from
operate,
that
is,
by principles
the ordering and arranging of components
according ta physics and chemistry.<lO>
Many
of
the
combinatoria and
composition
together
in
in
an
basic
issues
mechanism as
the
by
Combinatoria: Chance and Choice
in
ars
they relate ta musical
eighteenth
article
in vol ved
century
are brought
Leonard B. Ratner, "Ars
in Eighteenth-Century
<10>Based on the definition provided by the
Concise ùxford Dictionarv of Current English, 6th ed.,
s.v. "mechanism."
Discussion of this biologicalphilosophical concept appears in various standard
sources on philosophy and ideas; see e.g. Morton O.
Beckner, "Mechp-nism in Biology," in lli Encyclopedia
of Philosoph y (vol. 5). In mus il" , as is the case wi th
science and philosophy, mechanism may be understood as
being antithetical to the concept of organicism, which
is currently receiving attention in light of the
widespread influence of HeInrich Schenker's theory of
music.
The following
recent sources address the
topics of organicism and, more implicitly, mechanism:
Jamie Croy Kassler, "Heinrich Schenker's Epistemology
and Philosophy of Music: An Essay on the Relations
Between Evolutionary Theory and Music Theory," in The
Wider Domain of Evolutionary Thought, eds. D. Oldroyd
éind K.
Langham. (Australia: D. Reidel Publishing
Company, 1983), 221-60; William A. Pastille, "Heinrich
Schenker, Anti-Organicist," 19th Century MUb_c 7/1
(Summer 1984): 29-36; Ruth A. Solie, "The Living WC'rk:
Organicism and Musical Analysis," 19th Cent ury Music
4/2 (Fall 1980): 147-56.
c
7
Music. "(11)
For this
reason a
contents is presented in
article focuses
the
brief summary of its
following
pages.
The
on the various discrete components of
composition which are susceptible
to combinations and
orderings,
short
components
rhythmic figures,
such
as
melodic
and
phrases, key schemes, and even whole
movements.
Ratner
begins
aforementioned
short
the
article
by referring to the
eighteenth-century
movements,
primarily
pastimes
dance
in which
types,
were
'composed' by randomly selecting the components from a
pre-determined
reservoir
of
appropriate
musical
figures, using such means as throwing dice to make the
selec tions.
He then
suggests that
such games are a
clue to more serious compositional issues of the time:
The amusement afforded by these musical
games of chance bespeaks pure dilettantism
and, perhaps, decadence.
Yet, the proces5
by which
the games
were put together
reflects a substantial view
of musical
construction,
one
that
permeates
the
seventeenth and eighteenth centurj es.
In
this view,
the play of musical elements is
controlled 50 as to achieve a coherent and
persuasive flow of rhetoric.
At this time
in musical history, it was possible to
codify the mechanical elements of musical
composition more clearly than at any other
time.
Arrangements of such elements, though
uncountable in practice, were intelligible
(
<11>Found in Studies in Eighteenth-Century Music:
A rribute ~ Karl Geiringer.
H. C. Robbins Landon,
ed., in collaboration with R. E. Chapman (London:
Oxford University Press, 1970), 343-63.
8
and limited.<12>
Ratner
subsequently
serious issues
in
turn.
goes
on
into four
These
to organize these more
categories, discussing each
discussions
form
the bulk of the
article.
Ratner
uses
reference to
according to
alone,
term
of objects
a fixed
are
may be
set of
determined
in
arranged or placed
conditions."<13>
by
whether
These
combination
permutation alone, or both together are invoked
in a given situation.
The
permutations,
Ratner
as
mathematics.<14>
Taking
starting
we
point,
can
unordered selection of r
r
combinatoria
"the number of different ways in which a
given quantity
conditions
the
n.
phrases,
For
we
a
combinations and
notes,
set
of
define
belongs
n
objects
to
as a
a combination as an
objects from
this set where
example, given a set of four muslcal
can
containing from
topic of
select
one to
the
fol10wing combinations
four of these phrases without
regard to order:
[1]
[3,4]
[2]
[3]
[1,2,3]
A permutation,
..,..
, .
....
,
[4 ]
[ 1 , 2]
[1,2,4]
[1,3]
[1,3.4]
[1,4]
[2,3.4]
[2,3]
[2,4]
[1,2,3,4]
conversely. is an ordered selection of
<12>Ibid., p. 345 •
1
<13>Ibid., p. 345 .
<14>Ibid., p. 345.
(
9
r objects from a set of
n objects
!: n.
where r
In
other words, whereas [1,2,3,4] is the same combination
as [4,3,2,1], the two represent different permutations
of this combination of four phrases.
In
some
aspects
permutation is fixed
of
while
For example,
possible.
composition
several
a
single
combinations are
given two phrases we can fix
tha following permutation in
keeping
with
tonal and
formaI function
closing phrase
opening phrase
and
then
provide
n
Where, for example, n
optional realizations for each.
= 2,
the following combinat ions
would then be possible:
opening phrase
closing phrase
C-l
0-1
0-1
0-2
0-2
C-2
C-l
C-2
Conversely, some
aspects of
composition consist of a
single combination
and the
possibility for different
permutations--for
example,
arrangements
vertical
of
a
major
arrangements
the
triad,
of
three
possible
or
the
lines
linear
possible
in
triple
counterpoint with each other.
Each of the four
wide-ranging
categories into
discussion
of
the
which Ratner's
influence
of
ars
-
10
combinatoria is divided concerns a different
The
musical construction.
the most
basic units
A
figures.
compositional
Galeazzi
both
permutation
generate
the
by
the
of
by
that
and
rhythmic
conditions
line.<15>
of
treatises
indicate
first of these deals with
of musical
variety
a
design, motives and
different
examples
from
Ziegler,
Riepel,
either
and
permutation alone or
combination
and
level of
may
be
used
to
diastematic motives which fit
given
'slot'
melodic
in
a
From these, one possibility may be selected
student.
As
an
aid
to
composition this
procedure can generate short ideas and phrases which a
student or even professional composer might use as the
basis for a composition.
Ratner places this procedure
in a broader perspective:
AlI
the
theorists
who
treat of
permutation, from Mersenne to Galeazzi, do
so for a practical reason--to unlock the
imagination of the student.
The method is
mechanical; the materials
are
few and
simple;
but
the
possibi1ities
are
unthinkably vast. If we think of the device
as a way of obtaining a 'prius factus,' then
it does not diffcr essential1y from taking
an ostinato, a cantus firmus, a motto, or a
known melody as a point of departure for
composition. As such it need not be spurned
even by the experienced composer.<16>
The second level of musical construction to which
Ratr.er
suggests
the
possibility
<15>Ibid., pp. 346-50.
<16>Ibid., p. 350.
of
applying
ars
(
11
combinatoria
is
that
Combinat ion alone
of
is the
phrase
basic source
this level since permutation,
phrases or
the
periods, is
syntactical
and
or
the
pe riod.(17)
of options at
re-ordering of
not especially relevant given
constraints
phrases
governing
in
combination; for example, a 4-measure cadential phrase
and a 4-measure sequential
places
within
the
temporal
Ratner cites examp1es
applications of
per-:ods.
Harmonie
form,
both
f10w of a musical work.
harmonie
combinp.tion,
the three
for how a composer
binary
of
not exehange
and melodie
combination applLed to phrases and/or
exemp1ified by
J
phrase eould
of
aIl, is
options set forth by Riepe1
might begin
name1y,
first
the second
half of a
an aseending sequential phrase
(monte), a phrase emphasizing the dominant (ponte), or
a
deseending
sequential
phrase (fonte).(18>
me10die options in phrases and periods,
discussed
by
Ratner:
given two-bar idea
aIte~native
and
alternative
As for
two types are
continuations to a
melodies
over a
fixed bass line.(19)
(17)Ibid., pp.350-53.
(18)Joseph Riepel, Grundregeln ~ Tonordnung
insgemein, (Frankfurt,
1755),
45-47.
Riepel's
theories are diseussed in Nola Reed, "The Theories of
Joseph Riepel as Expressed in his Anfangsgründe ~
musikalischen
Setzkunst,"
(Ph.
D.
dissertation,
University of Rochester, 1983).
( 1 9 >Rat n e r,
,~ Ars
Co mb i na t 0 ria," pp. 35 2 - 5 3 .
12
Moving to
yet larger
the third category
emphasis
concerns
Despite
keys.<20>
on
dominant in
components of composition,
the
overall
the
increasingly
relationship
the tonal
arrangements of
widespread
between
scheme of
tonic
and
compositions as the
eighteenth-century progressed,
other combinat ions and
permutations of
from modal influences,
keys, derived
never became entirely obsolete.<2l>
Riepel's
discussion
of
the
Here Ratner cites
options
in
tonal
a
fixed
relationships
which
combination of
keys being ordered according to any of
its
permutations.
arrangement must
can
The
result
restrictions
begin and
derived
must
from
present study
category to
As
discusses
those
kcys
The third chapter
and permutations of
related keys.
the
four th
ways
compositioual
of
broadens the discussion of this
include combinations
chromati~ally
that the
which permutations
comprised
be
diatonically related to the tonic.
of the
3re
end with the home key and
that intervening combination
are
from
in
and
final
which
procedures
as
category,
several
they
apply
Ratner
important
to
entire
<20>Ibid., pp. 343-44.
<21>A genre that continued to exploit numerous
key relationships was the free fantasy, an example of
which by C.P.E. Bach is discussed in the present study
(see Chapter 3).
c
13
movements cou1d
a
broad
conceivably be understood in terms of
notion
explains, many
variation,
century
of
~
when
music,
are
used
in
usually
thus
combinatoria
techniques
variable
compatible
many
interesting
perspective
numerous actual
thinking
that
in
and texture,
aspects
of
variation
have
composers
the
gave
been
over
the
lending
an
construction
of
facet
rise
of
to
the
the
mechanistic
games
of
~
Types of paraphrase and variation which
associates
parody,
counterpoint.
with
~
rescoring,
and
In addition to these
combinat6r~
adaptation,
multiple
also hints at the applicability of
invertible
techniques Ratner
~
combinatoria to
formaI designs:
c
~
Since
discussed.
effect,
to
:::ranscription,
pasticcio,
eighteenth-
works by suggesting that they reflect
loosely
include
and
is,
serious,
comb~natoria.
Ratner
with
respected
Ratner
to
melody
being
centuries,
more
reference
paraphrase
by
another,
he
r.onsist of a fixed harmonic-
presently
of
practised
As
procedures involving paraphrase and/or
rhythmic structure and
and
combinatoria.<22>
There is no way to assess the extent co
which ~ combinatoria might have el. tared
into the
composition of
music in the
eighteenth
century.
Dice
games and
instructions from music theory are specific;
<22>Ratner, "Ars Combinatoria," pp. 354-57.
14
we can follow the process, step by step.
But this is not the case with the composer's
imagination •.. who is
to
say
that the
principal structural layout in classic
music, the I~V, X-I
plan, which shapes the
two-reprise dance form
and
its larger
sibling, the sonata form, is not a framework
within which
composers
were constantly
creating fresh music by means of melodic
combinatorial play?<23>
In summary,
1) the
then, Ratner's
generation and
four categories are:
combination of musical motives
and figures, (2) melodic and harmonic variables within
a
fixed
ord~ring
phrase
structure,
of keys, and
movements based
(4) the
on sorne
Ratn~r
which
that
approach
pedagogy
which
arrangement of
of the
to
permutations in the
substitution of en tire
sort of common procedure, or
basic scheme, or form, etc.
from
(3)
derives
In general,
these four categories is
eighteenth-century
emphasizes
the
musical components
time.<24>
the context
Because the
compositional
construction
and
into popular forms
goal of this approach
<23>Ibid., pp. 358-359.
<24>It is for this reason that Riepel figures so
prominently in
Ratner's discussion, for Riepel's
approach to compositton,
innovative in its time,
avoids emphasizing
iigured bass and harmony
and
foc uses instead on a style-conscious handling of
phrase structure, rhythm, melody, and forme
Ratner's
sources for Riepel are the Grundregeln ~ Tonordnung
insgemein
(Frankfur~
1755)
and
the GrUndliche
Erklàrung ~
Tonordnung insbesondere (Frankfurt,
1757), which form the second and third chapters in
Riepel's magnum opus Anfangsgründe ~ musikalischen
Setzkunst. Ratner's other sources are too numerous to
Tist in entirety, but include the following: Christian
Gottlob
Ziegler,
Anleitung
zur
musikalischen
---~~
~~~~~-
(
15
was presumably to rely less and less on pre-determined
formulas and
clichés and increasingly on original and
subtle handling of musical materials, it
to
detect
the
consciously
modern
extent
practised
scholars
we
to which ars combinatoria was
by
advanced
cannot
phenomenon to the finest
in the
was
to
)
model
scholars.
However,
this
compositions written
students
and
lesser
was compositional pedagogy in the
eighteenth century does not
anal y tic
link
As
simply on the basis of how
taught
composers--for what
composers.
conclusively
of the
eighteenth century
composition
is difficult
necessarily constitute an
available
the
to
twentieth
organization
of
century
this topic
into four clear categories by Ratner may weIl serve as
a workable
involving
The
starting
~
point
analytic inqujry
~n
combinatoria.
following
two
chapters
analytic inquiry undertaken
keyboard compositions
(
for
with
represent
respect
by C.P.E. Bach.
in the present chapter,
Bach's
gifts
encompassed
ability
to
both
the
su ch an
to several
As noted early
as
a composer
compose
deeply
Composi t ion
(Quedl inbur g,
MS.
1739) ;
Francesco
Galeazzi, ~lementi teorico-pratici di musica (Rome:
Puccinelli, 1791-6); Honore F. Langl~, Traité de la
basse ~ le chant, precedé de toutes ~ r~glëS
la composition (Paris:
Naderman,
1798); William
Crotch, Elements
Qi Musical Composition (London:
Longmans, 1812).
E
16
artistic works and the
to
lighter,
more
publication.(25)
Chapter Two,
~
popular
turn his attention
styles
for court use and
The wQrks to be examined include, in
short pieces
from the two sets of Kurze
leichte Clavierstùcka ~ verandE~ Reprisen (H.
193-203
and
H.
228-238),<26> and, in Chapter Three,
FR
the Free Fantasia in
different
works:
reasons
led
Kurze
und
the
intended for
a
pragmatic
intended to
minor
to
the
leichte
(H.
300).(27)
Very
composition of these
Clavierstficke
were
students at the early stages of keyboard
studies; in contrast,
with
ability to
ex~ress
using Ratner's
the
function
Fantasia
was
not written
in mind, and was instead
Bach's most personal
:~elings.
In
four categories as a basis of inquiry,
we shall be interested in (1) whether they can provide
(25)Bach
himself
even
indulged
in
the
aforementioned
games
of ~
comb!natoria.
His
"Einfall" is discussed on pp. 357-58 of the article by
Ratner in question. As weIl, E. Eugene Helm provides a
translation of it along with commentary in nSix Random
Measures of C.P.E. Bach," Journal .2i Music Theory 10:1
(1966): 139-51.
(26)The Helm numbers for Bach's w0rks are found
in various recent sources including New Grove (s.v.
"Bach, Carl
Philipp Emanuel")
and
the Whitmore
translation of Ottenberg,
Carl Philip Emanuel Bach,
pp. 225-43 and 245-48. These numbers will be used in
the present study.
For reference, the older Wotquenne
numbers for the Kurze und leichte Clavierstücke are as
follows: for the' firstSet (H. 193:'203): Wq. 113 #1-11
and for the second set (H. 228-238): Wq. 114 #1-11.
(27)Wq.
67.
Background information regarding
this work is provided on pp. 38-39 of the present stuny.
17
analytic insight into these contrasting works by Bach,
and
(2)
whether
the
to
these
extensions
manifestations
encompass~ng
questions
than the
simply to
selected works by Bach suggest
categories
of
combinatoria.
and comprehensive
would
require
one presently
provide a
with which
to
century music.
answers
to
other
Since
these two
a much more extensive study
undertaken, the
sample,
Bach's keyboard output and
ars combinatoria
and/or
goal here is
both of the diversity in
of the
potential value of
as one of a number of analytic tools
approach
this
and
other eighteenth-
CHAPTER 2
A MECHANISTIC APPROACH TO WORKS FROM THE
,
KJRZE UND LEICHTE CLAVIERSTUCKE
Bach's
two
sets
of
leichte
Kurze
Clavierstücke mit veranderten Reprisen und beygefügter
Fingersetzung
für
Anfanger
Berlin in 1766 and
indicates,
were
f.irst published in
As
1768 respectively.
fingerjngs
as
weIl as varied repeats are
provided for the beginner, the varied
as
introductory
and
diminution
student of
master.
models
which
for
in
the keyboard
assorted pieces,
repeats serving
the art of ornamentation
the
eighteenth
would have
Each of the t*o
The design
each of
the two
-
phrases.
first work in
'Allegro di Molto' in F major, H. 228.
of H.
228 is
a binary form in which
sections con tains
followed by its varied repetition.
8-measure units
eleven short,
the sever al to be considered
in this chapter we shall begin with the
the second set,
century a
been expected to
sets contains
and of
the title
consists
In terms
in
of issues
turn
an 8-measure unit
Each of these four
of
two 4-measure
raised in the previous
chapter we can view this formaI design as
a series of
-------
--------.----~-~-------
C
19
phrase slots
whose specifie permutation is determined
by
within
function
establishes
the
the
tonie
overall
by
1
work:
phrase
to
authentic
moving
an
cadence,
phrase 2 moves to the dominant, phrases 3 and
4 repeat
1 and 2 with variations, phrase 5 focuses on
the dominant with a ponte,<l> phrase 6 returns
tonie
and
closes
with
the
strongest
to the
cadence, and
phrases 7 and 8 repeat 5 and 6 wita variations.
The
following diagram summarizes this view of the work:<2>
\~~ SQ.c:t'~
,.-
lM .•
1 lM.$'
r t.
X"c:.
1:
-.........
1 1_.1\
1 1H\. '3
X
1:
"t.
'Io.C"\d. ",~\s." ~
M • \~
1"va.'
%
t·t'· .....")
•
'r
.~~
a
1M. 1.,\
ft\. '\S
"V:.
1
galant
1
)
1:
p~~
~ .. ~~"eQ.•• )
conven tional,
"1.t,.
........
"..
""'"' 1 1
1
%4-1
1:,,<-
~c.
".".
Isolating
",....,.
OZ'-.1 l:
'l1\~ s.u.'t:'o~
I",.,~
'1."". n.,,",~ ~ ..n.\-' ......
1
style formaI
<l>This term is discussed on page Il.
<2>1n the following
example and throughout the
remainder of
this study, HC, PAC, and lAC refer to
half cadence, perfect authentic cadence, and imperfect
authentic cadence respectively.
These labels are used
here in accordance with Edward Aldwell and
Carl
Schachter, Harmony ~ Voice
Leading l (New York:
Harcourt Brece Jovanovich, Inc., 1978), 76.
20
design such
permits
as
this
from
clearer
a
other
view
The
also
model
a
comparison
of
structure
is
relevant
successi ve
phrase
determined
by
the
functions
of
thus many works created.
to
fill
each
imagination
composer s,
accepted
slot
in
the
or
musical
composers.
Before
we shall
put this
each
options is
slot.
Many
phrases fulfilling
the
the
in
the
of
a
lively
most
inventive
of
currently
body
case
of
lesser
the music of a composer
former
turning
handling of the indi vi dual
for
reservoirs of phrases
of
When considering
applicable.
that
consist
of
the
of
phrase
slats may be generated, and
might
clichés
it, and
to
regard:
actual
case
of C.P.E. Bach's rank
of
These
perhaps
on
apr lied
reservoir
a
these
based
this
function
of
individual
between several such works.
in
slot
different combinations
the
work
combinatoria
~
the
of
idiosync racies of any single
thus
musical parameters
to
is
certainly more
Bach's
imaginative
idiosyncracies of
H.
228,
concept of different options for a
phrase slot to work in the following comparison.
Of the eleven pieces contained in each of the sets
of
Kur?~
fourth
und
derive
leichte
from
namely that which was
.......
(see page 19).
Clavierstücke,
the
first and
a common formaI-harmonie design,
illustrated
These works are:
above
for
H. 228
................ _ ;
~
=11
«0::1111""4. zœXll 53 _
c
kU;;,
21
No. 1
No. 4
1766:
Allegro in G
H.193
Minuet in F
H. 196
1768:
Allegro di Molto in F
H. 228
Minuet in G
H. 231
There are several minor differences such as the use of
PACs in
H.
193
interpolation in
into the
rather
these individual
The
each of
aspects is
the se works come
the manner
and
of each
work influences
function
of
the
half.
recall
page
the
chart
on
the
8.<3>
leading
These
repetition in
tone
goals
in
are
In
19
ponte
f
is
to
tonicize
<3>The music for
reproduced on page 31.
H.
ponte
228, we
that an lAC is
with an arrivaI
the upper voice in measure
reiterated
in
measures 9 through 16.
the specifie option which
the exact
respective
reached in measure 4 followed by a HC
on
in which the
specifie progressions and cadential goals
phrase beginning each second
from
general design,
case in point regarding comparison of
in the first half
realization
a 2-measure
the same, and provides a backdrop against
A
strength of
and
H. 231; the se will enter
shortly.
which individual aspects of
into focus.
lACs
the minuet
discussion
however, is
than
Bach
uses
the
varied
Following this,
to
realize the
the dominant for two measures
the se
eight
measures
is
=
n
LA.
22
before reverting to V7 of the home key.
1
M.\ ~
. - . :1!:
•
J"\
..
w
1:
f
~
y~
.....
1..-
~,
.....
'"Z~
~
~
_
..
'(
--
x:
The two lACs, with melodic 4-3 suspensions (measures 4
and 8), result in reiatively inconclusive
scale degrees
3 and
7 respectively, with the move to
dominant harmony in measure
half
cadence
tonicizing
therefore,
in
the
is
arrivaIs on
the
8
home
dominant
in
being
expressed
key.
The
the
subsequent
as a
effect
of
ponte,
to strengthen the role of the dominant,
providing more
tonal
contrast
before
the
Lonic is
reconfirmed in the final phrase.
By
contrast,
following:
(2)
a
H.
193
in
G
major con tains the
(1) a PAC in measure 4 rather
correspondingly
strong
than an lAC;
tonicization
of
the
dominant with a PAC in V in measure 8 rather than just
a HC
in I;
and (3)
tonicizing V as in H.
th~
home
measures.
key and
a ponte which,
228,
rather than first
moves immediately
back to
simply states V7-1 throughout its 4
c
23
'"'-
..... 1
.::--
-
;.j
....
+
""
-
/l
,
•
.
-'
..,O'l\~··
1
M.I':\-
"
I~
==bl±:·: I~·
•
J
~'-r
•
:bQ
l
-f:-
A
:Ét=
...
-
.
f-f
--
-F
r
Given the tonicization of
function
~t"-=
:E::= :r
r
tne
--
./"\
of
the
in mea&~re 8,
the dominant
ponte,
therefore,
rather than
being to further strengthen and intensif y the dominant
as
in
the
above
case,
i3
to
direction by immediately turning
home
key,
ensuring
that
the
stabilize the tonal
back
to
dominant
V7
of the
area is
n~t
overly prominent in such a short work.
A further case is
the
G
major
Minuet
H. 231;
-
24
.
r
weIl, the components cohere in a unique way.
here, as
A slightly more extravagant
of the
two works
ii chord and a
tonal palette
than those
just mentioned includes a tonicized
chromatic bass
motiorr into
the
He
in
measure 8:
-M.
f
oJ
..
,...
•
. :a
.
.fA.
. ..
.
,.
-
1
,
IJ
..
!: .
r.T
,...-~
.
"
.
...:
"
..
yS" ~'I
Seemingly
as
a
result,
the ponte is that much more
adventuresome as weIl, remaining
four measures.
Subsequently,
in V
the concluding phrase is
expanded from four to six measures:
---..
, ~,
throughout aIl
25
-
-'on.+t."
ri------------~~~------------~Ir___-------
m.'~
,J
~
.....
~
"
...
-
..
.
.
~
!~
..
•
":!
-=
..
..J
-.
y-
This playful alteration of the 32-measure norm clearly
destabilizes the regular phrase structure; at the same
time, though,
it balances
the strong emphasis placed
upon the dominant a few measures
earlier by providing
extra breadth to the return of the home tonic.
The
196)
reader
would
find
in the other minuet (H.
another interesting example to considere
In aIl
four cases, the specific weight of cadences (IAC, PAC,
HC) and strength of harmonic direction (whether or not
a
tonicization
occurs)
in the first section imposes
conditions for the specific content of
(
for what
function it
tonal coherence of
the
the ponte, and
will fulfill within the overall
work.
Thus
the
choice of
26
content for
eaeh phrase slot in these pieees fulfills
not only general requirements
of style
and form
as
19,
but
also specifie
desire for
coherence and
were
diseussed
on
page
conditions arising from the
~dch
correspondenee of aIl material within each work.
Of
the
mentioned
four
ie
categories
previous
the
discussion relates
to the
and periods, and, by
movements based
of
the
above
second, options in phrases
extension, to
the fourth, whole
on a common design.
combinatoria
combinatoria
chapter,
drawing attention to component
~
~
lends an
By isolating and
phrases
in
the form,
analytic framework derived
from a meehanistic perspective to what might be termed
a 'generie'
approaeh to phrase and form analysis.
may weIl
be, though,
practice
~rs
eombinatoria
ubiquitous to the
isolated models;
language
and
point
~
construction
in
of
phrase
preeluding
compositional
structure
is
clearcut and
proeess
may
weIl
be
Ratner hints at this when he notes
combinatoria
characteristic
terms of compositional
the whole eighteenth-eentury musical
saturated with it.
that
that in
It
of
often
at
this
level
"points
eighteenth-century
practised
by
to a
musical
eomposers
and
frequently sensed by listeners--the interchangeability
of melodie components."<4>
<4>Ratner, "Ars Combinatoria," p. 353.
c
27
We turn
first
now to
work
rather
generic analysis,
thorough analysis of the
H.
discussed,
combinatoria,
on the
a more
than
offers
228,
simply
its own
musical construction.
in
which
amplifying
!!.!.§.
more
ur.ique perspective
The lively contours and
rhythms of this piece derive from
four basic motives,
two of which are melodic and two rhythmic:
x
;~
1+
~
-4
1-
J'J
The way
'/
• •
J: i • • •
%
are built out
~f
mechanistic procedures
JJ/J JjJ J
-41.
phrases in
these
both halves of the work
motives
calls
to
mind the
of!!.!.§. combinatoria.
AlI four
combinations of rhythm and melody, X+S,
Y+R
(see
above)
are
..
R
dl J J'
in which
•
X+R, Y+S, and
systematically explored in the
upper line at the entrance of the respective 4-measure
phrases.
The
following
chart
summarizes
(omitting the 8-measure repeats in each half):
this
....".
28
~
Upper Line
Measur.e
~
1-4
X+S
5-8
Y+R
17-20
Y+S
21-24
X+R
thus
combinatoria
generating
plays
contrasting
yet
an
important
related
role
melodic
in
ideas for
different phrases.
Since
this
work
texture throughout,
combinatorial
we
in
can
In
X+S,
X+R,
doing
two-voice contrapuntal
consider
what the
are
for
two
contrapuntal
Y+S,
and
Y+R
as composite
we
find
that
there
are ten
combinations, including those
four
which
use
the same
composite motive
so
a
further
possibilities
lines involving
motives.
is
in both
combinations which
use
voices.
For each
of the six
different
composite
motives in
each voice, there are two vertical permutations depending
upon which material is
which in the lower.
possibilities.
If
placed
in
the
upper
voice and
In aIl, therefore, there are sixteen
one
wished
to
consider
melodie or
rhythmic components alone, they are embedded within these
possibilities as
S
) R
R S
for rhythm and
v..
y
'1 ,) X
for melody.
-.....
With these
possible motivic combinations in mind we
r 1.
can
expand
the
------~----------------
formaI
------
diagram
shown
on
page
19
to
(
29
incorpora te those
Bach uses
in this
work.
Some of the
more 'creative' and less 'systematic' details, which will
be
discussed
later,
are
not taken into account by the
following diagramj it does, however, provide
of
how
rhythmic
and
diastematic
an overview
figures
interact
systematically with the phrase structure and form:
's.,\" "C.~'Of\
IM
I~.~
.\
R"
X+,.
\.M
~+.
",.--
'M&.'
y'."
~+&
1:
1:
~.~
1:
~
1:"(,
"'"
\.M
"t+R
"-+S
1:
'J:
1:
,,<.
1 I~.U'
.'1.\
~""tt
'-'c:.
.., .....
'11:
)
\,. tcw\~")
T
~~c..
~.\~-1.4
CIÇ.
l ""'.
"'f'~"
~~s
'E4 - J
l:
,...
........
l "'"
..., .. ft.
..,'.R
'lA"'• ...-..n-
~
...,.~~
1M.\!.
'Ii. +
'-'(.
'1~ su.~O~
"~.\~
"""."'IQ. CIÇ. M. '-Il.......,.
'JG."'~
-...
",,-
'1,
........
1
"'...s
lC.+.s.
'te
• J:
~" .. o~.. )
In this diagram, y' indicates that leaps are
~"c:.
embedded in
the overall stepwise linear motion derived from Y for the
purpose of
gaining a
higher register.
Sever al of these
instances are discussed further along.
Bach
(
also
plays
direction of the individual
general possibilities
with
long-range
lines
in
this
contour
and
work.
Two
are relevant here: contrary motion
30
(including oblique motion as a
spe~ific
type) and similar
motion (including parallel motion as a specifie type).<5>
By considering upward and downward directions separately,
four possibilities are generated:
2)
1)
3)
With these in mind, we note
measures 1
~
to 3
hands: .---,
to coyer
4)
that the
consists of contrary motion between the
This gesture is inverted
aIl of
measures 17
32) Bach
and eX1;ended
through 20.
phrase in measures 21 through 24
29 through
opening gesture in
(and its
provides contrast
In the final
repetition in
to this contrary
motion: both lin es make their way in simi1ar
to
the
cadence.
In
a1l,
three
combinations are used to provide overt
begins the
first section,
~
--..
motion down
of the above four
contrast:
-....
~
begins the second, and
:::::::: is found in the closing phrase,
as though
in answer
to the other two.
Ars combinatoria is thus used prominently in
interrelated parameters
and
variation.
In
to
provide
addition,
more
s~veral
systematic contrast
subtly
fashioned
details add vitality and finesse to the above mechanistic
features.
l
In comparing the first and second phrases, for
,t
<S>More specifie
distinctions are
not necessary in
order to capture this aspect of the work.
(
31
example, we
note not
only the
'mechanical' exchange of
the motivic material X+S and Y+R
but
also
the
changes
in
between the
melodic
two hands,
contour
material undergoes when it is transferred
which
Y+R
from the lower
part in the first phrase to the upper part in the second:
H.l.l!a
M.\-~
-
X+S
~
"..,
...
~
........
..J
•
-
-~
~
'1+4\
... ...
..
"'l
.
,-
•
-
11
......,
oJ
Besides
the
obvious
.... --overall
-.,. ...
f:
---
----'
I.J
~
~
..
~.
~
...
change
descending motion, the stepwise
from ascending to
bass line
through 4, when transferred to become
th~
in measures 1
upper part in 5
through 8, now contains a leap of a seventh from
and,
instead
of
(corresponding to
sixth to
D.
an
the bass
octave
leap
in measure
in
3), a
C to Bb
measure
7
leap of a
These changes add a more melodic character
32
to what
was originally
a simple
bass line,
as weIl as
providing embedded repetitions of materiai from the first
phrase, as shown below:
fO\."
"".S
J
Jg lb,It1r t 1tri r tir e j
t 11
'--_---', ,
1
1
--1
J..'_ _
~'--
The
varied
repetition
in
measures
follows the same procedure of exchangir.g
9
~~per
~hrough
16
and lower
parts for its second phrase and reaches the same harmonie
goals.
to
The following example shows
those
noted
above
occur
that changes similar
with
regard to these t«o
phrases:
"'. '!o-'~
Si r t
1
t
----:"1-,
11 r
1,
~
........
embedding
CT
of
X
stepwise contrary motion.
through
28
then
1
r
measures 17
In the ponte in
similar
!:
focuses
Î
t '7
1
through 20
there is a
contours within predominantely
Its repetition
in measures 25
on an arpeggio figure deri ved
(
33
from
measures
19
20.
and
The
following
example
summarizes these points:
'"'. 1. '1.8
M.
x
\1·-1.0
... r
1
...
_a
-'
'..(1
<.J
~
....
~
1
r
.
•
:.f;~~
..
~.
\
The underlying counterpoint relating aIl material in both
of
these
phrases
to
parallel tenths with a
the Y motive consists of stepwise
sixth
move to a higher register:
(
interspersed
to
effect a
34
----
-
~,
...
....
\0
\0
\0
\0
\0
\0
\0
III.
1
'"
1
\J
~
..
t
•
le)
manifestation of
last phrase,
upper part
\0
•
ta
...
lua)
\.
\0
~
The final
in the
.
-
•
measures 29
embeds Y+R within
humorous summary of the
~+S,
previous
embedded motives occurs
through 32.
Here th(
as though to provide a
combinatorial
play of
motives:
)(+s
........
This and
the preceding
type
~
of
presumably
examples of
combinatoria
because
it
is
not
~mbedding suggest
explored
by
Ratner
a
J
not related ta compositional
&
c
35
pedagogy or
main
musical games of the eighteenth century (his
sources),
embedding
one
namely
within
other.
This type
and
more
a
hierarchy--and
the
combination
the
overriding
of combination
encompassing
th us
motives by
framework of the
requires both
context--in
relates
of
to
other
a local
words,
hierarchical
a
analysis
involving concern for the interaction of middleground and
foreground motives.
Besides this,
the form
~
of Ratner's
combinatoria in H.
first category with the generation
of composite motives from a fixed set of
rhythmic
228 also takes
figures.
As
weIl,
his
diastematic and
second
category is
relevant to the extent that musical content at the phrase
level was
seen to exhibit some use of combinations.
scope here is broader
however,
because
than that
this
The
of Ratner's discussion,
content
includes
not
only
diastematic and rhythmic material, but also such features
as
the
switching
of
material between hands, different
combinations of ascending and descending lines, etc.
of these
uses of
~
combinatoria
result in an aurally
tangible motivic coherence within this work
combinatorial
listener.
c
aspects
are
readily
AlI
in which the
apparent
to
the
36
Conclusion
In
comparing
the
works
chapter we noted that Bach
model to
generate aIl
emphasis and
considered
uses
of them.
strategy, giving
balance between
the
used in
point
each work
analysis.
made
phrases and
basic formaI
its own unique
tonie and dominant areas, were discussed
different options
was
same
Differences in harmonie
as an example of how the mode! of
variety of
early in this
In this
periods
and
design with a
for filling it in might be
section of
~
that
a fixed
the chapter the
combinatoria
to
whole
as
applied to
movements (Ratner's
second and fourth categories) reiterates from a different
perspective, but does not necessarily of fer
insights into,
new analytic
a more basic or generic 3pproach to these
pieces.
Much
more
however,
before
it
investigation
could
be
would
be
determined
needed,
whether this
observation holds true in more general contexts.
We saw as weIl, in H.
constructed
to
a
large
combined and arranged
~
inter-related
parameters.
example
at
We
but
from
of
a work
systematically
gestures,
cornbinatoria
combinatione
an
extent
motives,
demonstrating
rnechanical
228,
and contours,
work in a nurnber of
considered
also
sorne
not
only
of Bach's more
artistic finishing touches involving surface details.
Within
procedures
these
of
~
short
pieces
cornbinatoria
by
Bach,
rnechanistic
can thus be considered
37
(
constructive compositional tools into which inventiveness
and artistry of detail
resource
reflecting
are
one
injected.
or
an analytic
more parameters within the
inherent structure or these
works,
flexible--capable
providing a different way of
both
of
thinking about more standard
modes
offering its own unique insights.
(~
As
~
of
combinatoria is
analysis
and of
CHAPTER 3
A DIFFERENT CONTEXT: THE FANTASIA IN F# MINOR
Introduction
In
the
previous
broad description of
relevant
to
chapter,
~
several
of
galant-style
compositional
handling
models,
Bach's
which
clarity
and
models
such
aIl
relate
to
style.
In the
examine
the
Bach's
works
inventiveness
important
~
in
factorG.
combinatoria
outside
this 1ight, popular
present chapter,
therefore, we shall
of
G~t~n~ion
conception
'mechanicé\l'
pragmatic
and balance, simple
Bach's
are
more
accessibility to
Nothing was shown, however, about how
might
of Ratner's
combinatoria were shown to be
compositions--compositions in
beginners,
aspects
of
of
mechanistic principles to
the
genres
in
most
free
and
his
oeuvre,
the
1east
free
fantasia.
The work to be
considered, Bach's
Free Fantasia
in F# minor (H. 300), was written in 1787, and had not
been pub1ished by the time of his death
-
1'
later.
The
title
commonly ascribed
"C.P.E.
to thia
just one year
Bach's Empfindungen" is
work, although
in fact it
(
39
actually appears
on the
made by Bach for
clavier and
manuscript of
manuscript of an arrangement
violin, and
the original solo clavier version which
is the subject of this chapter.<l>
differ very
little in
and thus the
William S.
vhich
we
title
may
seems
the
safely
for
applicable
two versions
to
both.
As
this is one of the few works
assume
its
product
The
essential content,<2> however,
Newman notes,
consideration
instead
not on the
was
written
without
world1y success, and which is
of
Bach's
own
inner feelings
(nEmpfindungen").<3>
In
this
considering
fantasia
the
aspects
procedure
of
~ combinatoria in
will
be
as
follows:
Firstly we shall examine mechanistic aspects of Bach's
concept of the free
fantasia genre
Versuch.
the
Secondly,
as stated
in his
overa11 form of the F# minor
Fantasia will be discussed, fol10wed thirdly by a more
detailed analysis
then
conclude
of its
with
a
sections.
summary
The chapter will
of
observations
concerning ~ combinatoria in this free fantasia.
<l>Elinor Goertz EIder,
"Carl
Philipp Emanuel
Bach's Concept of the Free Fantasia,"
CM.A. Thesis,
University of Rochester, 1980), 92.
<2>Ibid., p. 93.
<3>Newman, Sonata, 423. This relates to Chapter
l, footnote 8 (page 4) of the present study.
40
Bach's Writings on the Free Fantasia
In the
~
wahre
final chapter
das
Clavie~
of Bach's Versuch über die
~
SpieIen,<4>
the
topic of
improvisation in the free fantasia genre is addressed,
with prescriptions being given for how
diatonic and
to the former,
chromatic fantasias.
diatonie
type
may
to crea te both
Those which apply
be
summarized as
follows:(5)
1) assume 4/4 meter
2) begin with an aseending or descending major or
minor scale
3) determine (or select from options provided in
the examples)
an appropriate figured bass for
the scale
4) interpolate half steps and their
where desired
figured bass
5) arrange
the scale degrees between the upper
and lower tonie in a desired permutation;
i.e. these need not be in stepwise order
6) realize
the progression with a mixture of
arpeggiated and sustained textures
To these are added the
with a
tonie pedal
suggestion
as weIl
as to
pedal just prior to the final tonie.
these
guidelines
with
to
begin
and end
use as a dominant
Bach accompanies
a variety of exampIes--scales
(4)References in this chapter will
be to page
numbers in the English translation
by William J.
Mitchell, Essay ~ the True Art 2i Playing Keyboard
Instruments (New York: W. W. Norton & Co., 1949).
<5>The following
Essay, pp. 430-33.
summary is condensed from Bach,
(
41
with
figured
bass,
interpolated
half
figured bass, varied orderings of bass
and pedal
points with
dimension of
by selecting
~
figured bass.
may
with
scale degrees,
The pedagogical
combinatoria is clearly
in evidence:
acceptable combinations and permutations
from the options given in the
student
steps
fashion
a
examples the uninspired
reasonably
correct diatonic
fantasia of short duration.
When a greater amount of time is available to the
performer, Bach
considers a
chromatic, rather than a
diatonic, fantasia to be more appropriate.<6>
suggests, in
addit~on
Here he
to the basic instructions for a
diatonic fantasia (see above), the following:<7>
1) subject to nos. 2 and 3 below, any combination
may be selected from the twenty-four major and
minor keys and may be permuted as desired
2) one should not simply move systematically
through a cycle of fifth-related keys as part
of the basic plan but should instead use a
non-systematic permutation
3) a number of keys distantly related to the
tonic should be included
4) a minimum of two formaI cadences should occur
in the fantasia: one somewhere in the middle
and one at the end
5) for moving to closely related keys and for
brief forays to distant keys it is sufficient
merely to reach the leading tone
<6>Ibid., p. 434.
(
<7>The following
Essay, pp. 434-38.
summary is condensed from Bach,
42
6) when planning to remain in a distant key for
more than a brief time this key should be
reached via an extended harmonie progression
7) surprise changes in tonal direction are
essential but should not appear too frequently
8) options for quick motion to distant keys are
afforded by the three diminished seventh
chords and their enharmonie equivalents
In
student
addition
with
to
two
the
above,
The
aIl
minor.<8>
other
set contains
III, iv,
v,
VI, and
The second contains progressions to
keys
possess varying
first
each of the closely related keys: ii,
iii, IV, V, and vi in major, and
VII in
provides the
sets of modulating progressions in
the accompanying examples.
progressions to
Bach
which,
because
degrees of
their
tonie triads
chromatic inflection with
respect to the main tonality, are defined as distantIy
related to
it.<9>
In order to gain the facility
wit~
modulation required to improvise
a chromatic fantasia
the
select
student
is
encouraged
progressions and combine
transposing the
to
thew
one
progressions as
after
a
number of
the other,
required in or der to
move from key to key with smooth voice-leading.
These guidelines for
chromatic fantasia
somewhat more
the
harmonie
design
of a
are less directIy prescriptive and
complex
than
those
for
the diatonic
<8>Ibid.,
p.
435.
Upper and lower case Roman
numerals indicate major and minor keys respectiveIy.
<9>Ibid., p. 436-37.
(
43
fantasia, thus
requiring more taste and discretion on
the part of the performer.
teaching of
~
attitude
in the
both types, however, is clearly allied to
combinatoria--to
and
Bach's
stating
setting
available
combinations
and
basic plan,
options
This
fixed conditions
from which to select
permutations
iD this
fantasia.
forth
of
components
for a
case the figured bass plan for a
chapter
from
Bach's
Versuch could
therefore be added to Ratner's long list of sources on
compositional
pedagogy
which
demonstrate
a certain
degree of mechanistic thinking in how they explain the
manipulation
of
compositions.
category,
keys in
musical
It
~
cûmponents
furthermore
in
enhances
combinatoria applied to the
a composition,
creating
his
ordering of
since Bach discusses not only
the possibility of different permutations of
combination
Ratner,
but
combination,
of
diatonically
also
and
that
any
third
of
related
keys
choosing
permutation
a single
as
did
almost
any
thereof, from the
entire set of twenty-four major and minor keys.
These
possible
possibilities
arrangements
guidance for how to
permit
of
make
keys,
artistic
a
large
but
number of
provide little
choices regarding
such arrangements; for example, little mention is made
of the different functions
(
tonal
structure--a
topic
of keys
more
within an overal!
in
keeping
with
..
'C
N
.'
44
Schenker's
organicist
mechanistic view.
setting forth
view
Instead
of
it
than
music
a
more
is
available options,
with
a
matter of
following which the
good taste of the composer-performer must decide which
combination of
Bach selects
in
the
F#
analysis.
of
options is
best.
and arranges
minor
The means by which
chromatically related keys
fantasia will be considered in our
These means, as we shall see, include a set
inter-related
chroma tic
voice-leading operations
that determine certain combinations of keys as weIl as
their possible permutations.
linear
coherence
and
These operations provide
to
direction
sorne
of
the
modulatory sections of the work while at the same time
creating
a
sense
surprise
they
conventional
of
spontaneity
engender
harmonic
and
surprise
aesthetic
and
stylistic
which
to
sound
the
point
This
syntaXe
coherence
is
from
is
in
goal
of
because
of view of
duality
accordance
of
the
of
with the
Bach's fantasias,
improvised--to "come as close to
incoherence
as
possible,"
states.<10>
Form
is
anothar
achieving this goal, dnd it is
as
important
to this
writer
one
factor in
topic that we
turn as we begin the analysis of H. 300.
<10)Schulenberg, Instrumental Music, 161.
(
45
Form .il!.
lli
Free Fantasia i.!!.
Playing with
FI
Minor
the listener's expectation of form,
as Sehleuning notes in his study of the
free fantasia
genre, is a resource of which Baeh made increasing use
in his late fantasias.<11>
This work is no exception.
It is based on two contrasting but motivieally related
themes both of which
on.
The largest
entire work,
tonie being
are
presented
relatively early
level of tonal motion, spanning the
is i-iv
iv-i,
with the
return to the
preeeded hy what May properly be called a
development section in which both themes
are explored
in various keys, as we1l as by a loose recapitulation,
in the key of
iv,
of
much
earlier
material.
The
overall formaI effect, as the diagram below indicates,
is that of a three-part design
with both
strange and
familiar aspects:
<ll>Peter Schleuning, Die Freie Fantasie: Ein
Beitrag ~ Erforsehung ~ klassischen KlaviermusIk7
(Goppingen: Alfred Kümmerle, 1973), 264.
46
,"
P~'lT
P"'T \
1.
~~,+iA
~
r.\ob.\-
Mo4..\-
S~\&""'C4.
~
---____-r---__
~~-+
1Th,,,,,, ,
~'q.u4f1~
~"MII. 1.
I--...- _______ ...__-'.,
~~
l'A~
1ft
i
--
E",,~,o ..
CIj.
'A_"" \
A"~o.
The familiar aspects, notes Schleuning, suggest sonata
form influences<12>: two contrasting
of
free
passage
transi tions,
reflecting
and
an
work
three
themes, sections
functioning
primarily
large-seale
as
divisions
exposition-development-recapitulation
<12>Ibid., p. 263. Sehleuning ineludes a diagram
of the form similar to the one presented here, but
whereas his indicates harmonie motion within each of
the ten subsections (without distinguishing eadential
from non-eadential arrivaIs),
the present diagram
foeuses on the long-range
tonal motion of the three
main sections.
47
design.
familiar
These
coun tered by a
subordinate
aspects,
key
unconventional recapitulation
area
of
i v,
different meters
far as
the form
of
elements
of
the final
for themes 1 and 2, and
Schleuning even
by other easily discernible factors.
goes so
to suggest a three-way ambivalence in
this
a
work,
single
which,
sonata
he
notes, combines
form
movement,
movements of a sonata, and a free fantasia.<13>
such a
by an
in which theme 2 is not
heard until a brief statement just prior to
cadence, by
are
ho~ever,
large-scale application
combining aspects of different
of
~
t~o
While
combinatoria--
forms--may or
may not
have been Bach's deliberate intention, the main point,
J
it seems,
i s tha t
the use
various conventional
0
f fami liar
componen ts
0
f
forms in unfamiliar arrangements
and combinations engages and deceives the expectations
of
the
listener
as
part of the overall strategy of
projecting a sense of formaI spontaneity.
The clever design of the two themes goes
hand with
elements
this strategy.
of
the
first
contrasting,
yet
a
very
The second transforms many
so
as
a
slow
tempo.
The
to
important
intact: both themes begin with an
at
hand in
sound thoroughly
feature remains
open fifth sonority
result is that as the work
unfolds Llere are moments at which the listener is not
(
Il
<13>Ibid., p. 264.
l
48
sure wh1ch
each
has
Schleun1ng
of the
two themes
been
established
indicates
1s about
as
an
to enter, as
option.<14>
these transformed and preserved
features in an example
which
1s
reproduced
here ta
illustrate the above po1nt:<15)
AlI of
these aspects
of the form--the design of
the themes, discernible sonata form elements,
combination
of
differen t
combinatoria applied
on a
Ratner's
because
categories
the sense of an
number of
variables.
genres--reflect
broader scale
original form
and the
than any of
these aspects relate ta
emerging from
a large
In other words, Ratner's fourth
<14>When the performer recognizes this built-in
source of formaI uncertainty and reinforces it by not
rushing the beginnings of theme entries, the effect is
that much more successfully achieved.
<15>Schleuning, Freie Fantasie, 265. The heading
in this example reads: Adagio III (chosen instead of
Adagio l in order for correspondence of key with Largo
1).
.
49
category
goes
different
on!y
as
realizations
far
of
~
as
a
combinatoria in
pre-determined
forma!
design, a small sample of which we saw in the previous
chapter with the comparison
the same
binary design.
of
different
works from
In this and other fantasias,
however, the forma! design
itse!f
is
susceptible to
being changed depending upon how forma! components are
ordered and
combined.
Thus
the
listening process
includes such questions, conscious or unconscious, as:
Which of the themes is about
event be
to recur?
prolongational? Transitional? Developmental?
What kind of form is emerging?
~
Will the next
combinatoria
This
broad concept of
thus helps to explain how a sense of
1
formaI spontaneity is achieved in this work.
Analysis of the Sections
We turn now to
main
goal
resources
is
to
Bach
relationship
to
a
more
detailed
elucidate
uses
~
in
this
sorne
analysis whose
of
fantasia
f.2mbinatoria.<16>
the chromatic
and
their
Although a
<16>The reader should note that in this analysis
such terms
as 'modulation'
and 'key' will not
necessarily be reserved for more long-range events, as
in a Schenkerian analysis, since we shall be focusing
on technical voice-Ieading aspects of various passages
rather than on their function within the hierarchical
tonal structure of the work.
As is weIl known,
concepts such as modulation, tonicization, tonality,
and key tend to vary in meaning depending upon
historical era and analytic approach. These issues
are addressed in Richard Bruce Nelson, "Theories of
50
comprehensive analysis
shall
by Italian
may
through
the
work,
turn each of the ten sections indicated
tempo markings,
consider
the intention here, we
sequentially
proceed
discussing in
is not
not
only
in order
that the reader
chromatic areas but also the
broader formaI context into which they fit.<17>
Since
the
1 (as
three
opening
sections
comprising
Part
indicated by the chart on page 46) offer only a slight
introduction to later chromatic activity, the topic of
~
combinatoria
resurfaces only
discussion of
Parts 2 and 3.
in
introduce
order
to
the
in conjunction with
Part 1 is included here
first
instances
of
chromatic-enharmonic progressions in their context.
PART 1: Adagio
The
theme
opening
1,
in
respectively.
Adagio
the
presents
tonie
Unlike theme
two
and
statements of
subdominant
2 which
keys
enters later in
the work, theme 1 does not possess a regular, perioaic
phrase
structure,
being
instead
more
aptly
Harmonie Modulation in Selected German Treatises of
the
Eighteenth
Century,"
(Ph.D.
dissertation,
University of Rochester,
1983)
and in William J.
Mitchell,
"Modulation in C.P.E. Bach's Versuch," in
Studies ~ Eighteenth-Century Music: A Tribute to Karl
Geiringer,
ed.
H.C. Robbins Landon in ccllaboration
with R.E. Chapman (London: Oxford University Press,
1970),517-25.
<17)Also, in light of the fact that there exist
long spans of music without bar lines,
it will
facilitate discussion to refer in turn to each of
these ten sections.
(
51
characterized
as
a
thematic
continuation and elaboration.
receives a
with rather free
The
second statement
different continuation
moves to D minor,
P~!r
idea
from the first and
vi of the home key.
\ • A~!2 • \:.t 'l'Ig.\.;.
"\
"""fWL \ (f'\"u.a c:.oW\Ti f\U~~D'"~
-tc.M"I\"\f'\\ao.:t
- ----"QI'--lr-----ll
------------1
Th\.M." ,
\'1 ~
'-------------~-\-----------'-~~,~----~----=-~~~-------~-V\
It is subsequent to this
D minor
ar~ival
that we
get the first inkling of the chroma tic breadth of this
fantasia.
Here the bass
note
D is
retained
and a
fully diminished seventh chord unfolded over it:
•
•
"
This
minor
(
vii7
both
vi
promises
a
in
spelling
figuration (not
shown in
return
and
to the home key of F#
in
the
right-hand
the above reduction).
The
tonie is not reached, however, as the vii7 of F# minor
..•
52
is
treated
to
of
one
its
possible
many
reinterpretations.
In addition to reearding each note
of
a potential leading tone, the most
the
chord
as
common means of using vii7 enharmonically,
exists to
treat any
of the
the option
tones as an appoggiatura
and move it down a semitone
to become
the root
of a
dominant 7th chord:
J .....
In this
instance Bach moves the fifth, B, down to Bb,
the root of V7 in Eb minor.
~.p.
The surprise of this effect is enhanced by
transfer from
upper
part
appoggiatura
B to
Bb as
functioning
to
D.
weIl as
as
Since
a
by the
dissonant
D
the octave
Eb in the
ornamental
is the only tone not
enharmonically reinterpreted or chromatically shifted,
-
this Eb to D masks the more structural appoggiatura, B
to
Bb,
further
ohscuring
the
true
nature
of the
-------~- ~~--~------
(
53
progression.
Although spelled as V7 of Eb minor,
the Bb7 chord
in question resolves as a German augmented sixth chord
to V6/4 in D minor, reinforcing the importance of D as
a common tone through this passage.
not
resolve
but
is
This
V 6/4 does
instead followed by a series of
secondary V7 chords pointing to G minor, A
then B
minor, and
minor which moves to a weak arrivaI in E minor
at the very end of the Adagio.
Allegretto
The passage work of
the
above
E
minor
this Allegretto
arrivaI
to
C
shifts from
major
and
tonicizes F major, presenling earlier motives
the double
neighbour and
transformed setting.
to confirmation
one of the
of F
chromatic
A
then
such as
the lower appoggiatura in a
long dominant
major ls
pedal pointing
thwarted, however, as
possibilities
inherent
dominant seventh chord is suddenly realized.
in the
-
54
By chromatical1y
contracting the inter val between the
root and fifth so that C and G
dominant
seventh
realized,
with a
of
following
B
minor,
which
strong authentic
become C#
a
the
tritone
away, ls
Allegretto concludes
cadence in B minor.<18>
two chromatic voice-Ieading techniques
resolution
appoggiatura
and F#, the
in
the
The
seen thus far,
vii7
chromatic contraction in the V7 chord,
chord
and
will both play
a significant role after the next Largo section (to be
mentioned onl] briefly).
Largo
At this
were
point,
theme
2,
whose characteristics
with
those
of
theme 1 in an earlier
48),
is
compared
example
(see
page
subdominant key.
introduced
in G
second
statement
Adagio,
which
the
After a fluctuation between B minor
and its relative key D major, the head
again stated
in
minor in
1s
of theme
2 is
the ninth measure.
This
interrupted
begins
the
by
central,
the subsequent
developmental
section of the work.
PART 2: Adagio
In the development section Bach explores
the themes
both of
and as weIl plays more systematically with
<18>Although Bach introduced the subdominant key
ear ly in the work,
this is its first cadential
confirmation. The approach to this cadence through
the tritone-related key injects new interest ioto the
arrivaI of this large-scale goal.
~~----
..
':
~.
- --
-
-~
-
-~--~---------------~------------
55
chromatic
contraction
and
appoggiatura
resolution,
beginning in this Adagio with chroma tic contraction of
an interval
in a
dominant seventh
earlier, we recall,
tritone
this
substitution
the significant
those that
technique
just
theme 2 (see page 53).
chord.
prior
When used
resulted
in the
to the entrance of
To explain more fully,
aIl of
applications of this technique, i.e.,
yield
the
same
chord
type
(a dominant
seventh), are as follows:
t.."'f"QPNa.~ C. c.owft~+"Of\
Qf S"1I't\
-, 13J1tft§i
t"' ..._..
~.:c. C.D~"'C.~."
Of
these,
successive
)
contraction
between the root and fifth results
chords related
of
~ycle
the
the
in a
interval
cycle of two
by a tritone (the tritone substitution
se en earlier), successive contraction
between
00+ '!..-&
root
with roots a
of the interval
and seventh produces a four-member
minor third
apart, and successive
contraction of the interval between the root and third
produces these same four
the reverse permutation.
dominant
seventh
chorde in
-
56
Nowhere are such cycles indicated in the Versuch.
The opening
however,
model-sequence
demonstrates
section
that
successive
seventh, a
chromatic
one-measure
sequenced twice
in exact
this Adagio,
Bach is clearly aware of
them and the harmonie variety they
three
of
model
afford.<19>
contractions
based
form and
on
Using
of
theme
the
1 is
a third time in a
varied and expanded form:
<19>The author learned of
these
cycles from
Professor
Bo
Alphonce
in
the context of his
nineteenth-century
analysis
course
at
McGill
University.
To take an example from another work by
Bach, the Rondo in E minor H. 272 (Wq. 66, whose full
title
is
"Abschied
von meinem Silbermannischen
Claviere in einem Rondo" [Farewell to my Silbermann
Clavichord in a
Rondo])
contains such a cycle in
measures 57 through 59,
just
before
the final
statement of the refrain,
en route from G# minor in
measure 5S to A minor, iv of the home key,
in measure
60:
1
1
...
...
~
\
-
... ......
..
•
.. ...- \,.
•
~
..
•
•
•
...
1
As indicated,
the route is indirect from the first to
the second stages, but then direct until the fourth,
which subsequently resolves as a functional V7.
57
...."
"'.u.o.",1 ""
-
....
os. ..t:!:!:f\t."-
If
r
f
.m .=n'
11
1
p
r'T'l ---,;,.-- - -.;;-
..-. .
-
f
1
,.......
-- - - - - - - - - - - - - - - - - ,
~
~
1
1
1
-
c.ru -
.-..l~'r\oft:
ï""'1 ~
u," -
cl.
.~
~
•
p
1
..
r-------,
1
ft
--~--~--
1
.
The pattern
four th
is broken
dominant
in the fourth measure, but the
seventh
of
Stated
eventually reached.
contains
its
to
seventh,
F7,
cycle,
in root
cadential six-four, it points
arrives
the
position with a
Bb,
which
pointing
are
then
stated
in
that key.
rather
than
to
make
preceding
of
dominant
mentioned, the third chord
(
of theme
Eb minor,<20>
resolving it functionally Bach uses
this chord, Ab7,
cycle
Eb
The third measure
begins as expected, with V4/2 of vii in
but
when it
to Eb.
minor is reached, and the first two measures
1
is
a
last
reference
sevenths.
in that
to the
As was just
cycle, G#7 (=Ab7)
<20>Compare with measure 3 of the opening of the
work in which the corresponding chord is V4/2 of yii
in the home key.
\
",
;
.1,
f-
~
58
led only indirectly to the fourth, F7.
Now Bach makes
the connection explicit;
The F7 chord then Lesolves functionally
to initiate a
section in Bb minor based on theme 2.
In the
leading
above Adagio
operation,
chromatic
seventh, determines
in tae cycle and
they will
contraction
of
the
both the combinat ion of harmonies
the
occur.
it is clear that the voice-
specific
permutation
In determining
in which
why Bach began the
development with this cycle we can look to the opening
Adagio of the work for one reason, specifically to the
passage, already discussed
appoggiatura resolution
in
detail,
containing an
of an arpeggiated vii7 chord.
The four pitches of this chord,
recalling the example
on page
E# (=F), and they are
51, are
D, B,
G# and
followed by the V7 of Eb, as mentioned.
dominant seventh
concludes with
chords are
chords opening
V7 of
the same,
Eb, and
and in
The
cycle of
the development also
the roots
the same
of the four
order, as the
(
59
pitches of the earlier vii7 •
•
The underlying
•
•
linear qnfolding of these four p1tches
culminating in V7
of
Eb
(minor)
1s
thus
a common
structural feature shared by bûth sections, suggesting
that the latter madel-sequence section is an expansion
of
the
earlier
arpeggiated
diminished
seventh
chord.<21>
Largo
As vith the
based on
preceding
Adagio,
section is
madel-sequence behaviour and employs earlier
chroma tic linear motions more
choice and
this
ar~angement
of
fully ta
determine the
transitory harmonies.
The
averall direction of the sequence is a stepvise ascent
from
Bb
minor
digressions to be
to
C
minor
ta
D
minor
discu8sed,
ta
E
minor--a tritone
removed from the starting point.
a verbatim statement of the first
in Bb
minor,
and, with
After beginning with
measure of
theme 2
the second measure is altered by the use
of an arpeggio motive
ta
move
from
Bb
minor
ta C
<21>Even
the
characteristic 4-3 melodic motion
(Eb-D) in the upper voice of the earlier
instance i8
retained within the latter Bb7 chard.
-
60
minor.<22>
~1
\.A"IJ'
...
~p
iI~
~
--
r-ï
p
~
f
a~
In
~
,'" ~
"',,,...
the
second
second
and
~/..
~
li
"
measure, the relationship between the
third
appoggiatura
vi'·~
chords
reso1ution:
is
the
again
that
invo1ving
fifth of vii6/5 of iv,
Ab, moves to G, thereby creating V7 of C.
The move from C
simi1ar fashion.
different
ear1ier
is
enharmonie
chroma tic
are
used
D minor
is treated in
Once D minor is reached the pattern
changes, and E minor
circuitous
minor to
reached
changes
on1y
of
voice-1eading
here
one
after severa1
direction.
techniques
Two
seen
after the other, as tha
examp1e shows:
-
!
<22>It is interesting to note that
this same
quick arpeggio figure was first used in another
chromatic context,
namely the tritone substitution
preceding the first occurence of theme 2 (see the
examp1e on p. 53).
c.
61
-.
1""
..
J..
---
.--..
,.....,..-,
"-
..
J.J.
?
v
..
~
"
of departure
iv, G minore
of vii7
of
j
.
y
..--
,-
~
v
I~.
~
The point
-
,-
v
.. v
l
J..
J
of
".
f
1
...
r
of
.,•
in the first measure above is
Beginning in the next measure, the third
in G
minor, A,
is moved
down a semitone to
produce an Ab dominant seventh chord, thus redirecting
motion
from
Two of
the common
then
G
minor
maintained
are contracted
the span of
minor,
to
the
(=Gb) and
upper
occurs: the
to yield
two
itq
FI
tones,
in
enharmonie change
to its tritone-related key Db.
as yet another
root and
V7 of
measures
tritone
part
Eb (=D#) are
E minore
the
harmony
relation
third of Ab7
Thus within
points
to G
Db, and then up an
augmented second (minor third) to E minore
Bringing
combinatoria
discussion, we
note that
back
into
the
a remarkable aspect of this
passage is the fact that these three harmonies, G, Db,
and E,
were the
full cycle of
preceding
first three
dominant
Adagio.
seventh
Whereas
order of descending minor
(~Db»
(see
goals pointed to in the
the example on
contractions
there
thirds
~age
in the
they appeared in
(V7/G,
V7/E, V7/C#
57), here a different
,
\
....
62
'
permutation reverses
the order
of the
latter two so
that E rather than Db is the last
arrivaI.
able
by
to
vary
the
permutation
relationship between the
techniques seen
two
thus far.
Bach was
exploiting
the
chromatic voice-leading
This
relationship may be
summarized as follows:
S:IJI
,1
;.,. Il
As the example indicates,
V7
and
appoggiatura
a
itd
chromatic contraction
resolution
in a
in its related vii7
form a limited set of operations that allow for direct
motion
from
any
given
V7
or
another V7 a minor third above,
or
a
tritone
away.
its
related vii7 to
a minor
third below,
In the above passage from the
development section, as discussed,
'third-appoggiatura'
ta
Bach first
uses a
point to the tritone-related
key and then a chromatic contraction
of the
third to
point up an augmented second (minor third).
The
move
to
E
minor
enharmonie key changes brings
that
ends
the
above
the development section
c.
63
back into
minor.
the diatonic realm of the main tonality, F#
Within a sh?rt time,
with arpeggio passage
and the
the
section
pedal point
elaborates vii7 of B minor,
~ork
following Adagio
opening
an extended
then initiates
of
a return of
the work in the subdominant
key.
Thus
far
in
the
work,
we
have
seen several
chroma tic voice-Ieading options for dominant and fully
diminished seventh chords
their possibilities
introduced
in
Part
explored in Part 2.
1 and
The examples
discussed are intriguing clues as to how weIl Bach may
have understood sorne of the more systematic properties
of the mod-12 pitch
)
underlying tonal
class world
context.
regard
beyond
relates to an
In the Versuch discussion
summarized earlier in this
this
a3 it
chapter he
citing
the
says little in
importance
of
the
diminished seventh and offering several examples whose
implications
are
Ieft
to
the reader.
Appoggiatura
motion is indeed included in these examples,<23> as is
a
strange
chromatic
progression
that
contraction
of
very nearly constitutes
the
third
(with
an
intervening chord):<24>
<23>For example,
fifth measure.
(~
<24>Bach, Essa!,
measure •
see
p.
page
438,
438,
figure
figure 476 b,
476
b,
tenth
64
1
J
.;
~
"
1
)
\J ~
..
1
\
....
t, 4Ft-.,~
1
Had the
;~
I\-i-
1
final chord
retained a C# as its seventh and
the intervening chord been omitted, as
in
paren theses ,
chromatic
this
contraction
would
of
in the version
indeed
the
third
be
in
a
single
a dominant
seventh chord.
In studying
some of
the modulatory options used
by Bach in this work, we find that the options
combinatoria
with
respect
permutations of keys have
to
gone
of
combinations
weIl
~
and
beyond Ratner's
original description as discussed in Chapter 1 of this
study.
with
Ratner's categories
the
general
are set
stylistic
forth in keeping
context
century musical language; this work by
of
eighteenth
Bach, however,
stretches these categories in ways that go weIl beyond
typical contexts.
seen
-
daring
thus
far,
chromatic
Besides
Part
the
keys
and modulations
3 of the work contains another
progression
for
which
i }
combinatoria offers an insightful explanation.
(
65
PART 3: Adagio
Whereas this
fantasia began
theme 1 (with different
respectively, the
with two entries of
continuations)
in
i
and iv
present Adagio does the reverse and
moves from an entry in iv to the beginning of an entry
in i.
The
and moves
latter entry breaks off after one ffiéasure
into
a
new
Allegretto,
interrupting the
recapitulation process.
Allegretto
Here
ornamental
scale
spell out
a descending
including
secondary
work
and
broken chords
fifths sequential progression
dominants.
The overall motion
until the resumption of the Adagio in the next section
is
from
i
in
F#
minor (at the end of the previous
Adagio) to C minor harmony, a tritone away.
This loss
of the F# minor tonalitj is due to VI7 moving not up a
tritone to ii of F# minor, but up a perfect
four th to
bII, G, and then on to C.
As
with
progressions in
interesting
harmonies.
cycle, Bach
ways
previously
this work,
discussed
the pattern
sequential
is varied in
involving colourful combinat ions of
When VI, D major, is reached in the fifths
dwells on
this harmony before adding the
seven th, C,
to make V7 /G.
fashions a
stepwise linear
in the cycle, G7, which in
Wi th C in the bass, he then
descent to the next chord
turn resolves
to C minor.
G
66
This linear
descent con tains model-sequence behaviour
and is harmonized in a daring
manner, as
the example
indicates:
ifr \~ ~ !I
i
J: fi 1
ri
;'1
~~:~
_Ip-}
.J
Co Mi f\
Recalling
evants
of
the
development
interesting light on this progression.
series of
The following
examples indicates the new combinations and
permutations of
these few
section sheds
development
chords.
The first
direct progression from D7
makes reference
material
to a
condensed into
example shows that the
cadence in
back to the Adagio of the development
section by immediately juxtaposing the first
that
cycle
of
goal, Eb minore
-
1 t,
Eb minor
dominant
sevenths
chord of
with the eventual
67
(
~
~
....
~ ba
-
li
q-
E~ """
The next
example indicates
that the two first stages
in the dominant seventh cycle of
the development form
the first two steps of the sequence of the progression
in question.
explore
It
that
is
cycle
recapitulation
as
if
again,
process
by
Bach
but
were
beginning to
instead resumes the
returning
to
Adagio
material.
Il
The final example shows that the progression which was
used to usher in the fourth chord of the cycle
development
progression:
(
is
transposed
here
in the
to become the model
68
J~
r==;=t
r"'"u.
-
(
V
i=F=
1.........,
1
1
t
s:-
1
I
~
'1.
1 •
1
3
=· ""~
In terms
"rn-
G
of harmonie syntax we could refer to the use
to
Eb
minor
and
V7
in the
goes
beyond
such
move from V7
of E to C minor;(25) an
understanding of the role played by
however,
\."i
•
of modal mixture in this passage
of
J
•
ars combinatoria,
a label to show how this
instance of modal mixture relates to other sections of
the work,
summary
i.e. that it pro vides an intense and daring
of
aspects
of
the
development
section by
recombining them.
Concerning
the
remainder
subsequent Adagio continues
of
the
opening
Adagio,
to
of
J
work,
the
recapitulate material
adding
extensions that point more and more
.......
,
the
adjustments
to the
and
home key •
(25)In
other
words,
each dominant resolves
deceptively to a minor chord on lowered scale degree
6.
(
69
This
section
concludes
on
following Allegretto which
vii7
of
i
and
arpeggiated
then
redirects
launches
motion
into
an
back to
elaborate
progression.
Just
final
and
tonic to
enter, however, Bach adds one last surprise.
Theme 2,
listener
we
cadential
V7/iv, precipitating the
expects
recall,
was
recapitulation
with
one
the
not
of
last
dominant
stated
earlier
at
aIl
material;
reference
to
this
as
during
the
the
Bach concludes
theme--its
only
appearance in the home key.
Conclusion
This chapter
of Bach's
began by
guidelines for
These facets in general
conditions
and
range
these
of
a
straightforward,
possibilities
seemingly
noting mechanistic facets
improvising free fantasias.
consisted of
variety
options
such
in
endless,
as
the
as
of different options, the
being
when
examples,
in
providing fixed
the
in
Bach
some
himself listed
and,
case
cases
in
others,
of options for
cornbinations and permutations derived from the twentyfour major and minor keys.
The detailed analysis of the Fantasia in F# minor
focused on this latter case.
one
(
set
of
voice-leading
chromatic contraction and
In doing so, it revealed
operations
consisting of
appoggiatura
resolution to
70
be
a
means
used
by
Bach to determine the possible
combinations and permutations of transitory chords and
keys
in
several
this analysis,
one
~
particularly
passages.
In the final section of
combinatoria
daring
offered insight into
progression
derived
from
earlier materials.
In order to approach
form was
this detailed
first of a11 considered.
the formaI design itself
for different
components,
Here we noted that
is variable
and thus allows
combinations and permutations of formaI
suggesting
characterizing
ana1ysis the
the
~
sense
combinatoria as a
means of
of form experienced by the
listener with respect to this work.
CONCLUSION
This
thesis
was
motivated
axploring sorne implications
ot
by
an
interest in
combinatoria for
~
analysis of eighteenth-century music and used Ratner's
exposition of the topic as a point of departure for an
examination of
several solo
Based on
Bach.
pages, a
keyboard works by C.P.E.
material presented
in the preceding
number of intriguing issues could be pursued
further.
)
Firstly,
results
of
concerning
these
the
analyses
approach could be compared
second
based
chapter,
on
the
a rnechanistic
with analyses
based on an
organicist approach such as that of Heinrich Schenker<ù
or
Rudolph
Reti ('l.) in
order
to
determine
complementary and contradictory aspects.
both
At one place
in Chapter 2 the issue of hierarchy arose with respect
to
ars
combinatoria
in
motives.~>
An
attempt ta
(1)Heinrich Schenker, Free Composition (Der freie
Satz), translated and edi~by Ernst Os ter (New York:
Longman,1979).
<~>Rudolph Reti, The Thematic Process III Music (New
York: Macmillan, 1962).
r
. _'"
..
;,
(3)
See page 35 •
72
clarify
mechanistic
organicist
and
treatment,
and
to
between
similarities
and
distinctions
of
concepts
motivic
formula te these distinctions in a
general manner, would be enlightening.
Secondly, an
third chapter
enharmonie
Some
interesting issue
is Bach's
exploration of chromatic and
possibilities
of
sense
the
within
wide
music
in
the
technique
of
dominant seventh chord,
means an
keys
of
is
system.
options
in
suggested in
order
to
grasp
the full
which he understood these options and, more
importantly, put them to
to
tonal
but it is necessary to analyse Bach's own
most expressive
extent to
the
spectrum
combination and permutation of
the Versuch,
arising from the
artistic use.
chromatic
for
uncommon practice
to contract the seventh
With respect
contraction
example,
it
was
in
a
by no
in the eighteenth century
once in
moving from
a major
key to its relative minor:
1]).-
1
Bach's use of the full cycle of such contractions, not
as
a
context
theoretical
of
one
demonstration
of
his
MOst
but
rather
in the
powerfully expressive
73
"
( .-
works, is significant.
diminished
type
of
seventh
chord
mathematical
combinatoria but
This
and
are
his
preoccupation
focused more
phrases,
preoccupation,
nineteenth
and
to
related
century,
properties in
the
is
more
with
tonal
to
~
on the future of tonal
manipulation of
formal
become
of the
indicative of another
language than on the construction and
motives,
uses
units.
This
widespread
symmetric
system.
With
and
in
the
cyclic
respect to
C.P.E. Bach's contribution, this issue forms part of a
larger
question:
enticipatp.
To
and/or
what
extent
influence
does
aspects
his
music
of nineteenth-
century composition?
Besides eliciting such questions as these,
hoped that this thesis has shown that
has a
music,
place
and
independent
in
the
that,
th~ory
analysis
al though
~
it is
combinatoria
of eighteenth-century
not
necessarily
an
in its own right, it is nonetheless
a phenomenon to which the analyst should be sensitive,
no matter in what context or style it arises.
f
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(
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f
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_ _ _-"..,....-.."....____ .
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APPENDIX
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