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Society for Music Theory
"Grundgestalt" as Tonal FunctionAuthor(s): Patricia CarpenterSource: Music Theory Spectrum, Vol. 5 (Spring, 1983), pp. 15-38Published by: University of California Press on behalf of the Society for Music TheoryStable URL: http://www.jstor.org/stable/746093
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rundgestalt
s
T o n a l
Funct ion
Patricia
arpenter
In this
paper
I
will
explore
one
of
the
important
unctionsof
a musical
idea-namely,
how such an "idea" functions
in a
tonal work
to
effect
a coherent
tonality
of
the
whole.
I
use "mu-
sical dea"
in a sense taken from
Schoenberg:
hat
which a
piece
of
music
is "about."
By Grundgestalt
r
"basic
shape"
I
mean
the
concrete,
technical
aspect
of the idea. I will
clarify
this no-
tion
by bringing ogether
some of
Schoenberg's
tatementscon-
cerning
the
musical idea and
by
a brief sketch
of his
theory
of
tonalityas a networkof tonalrelations. Finally,I willelaborate
the notion
of
the
Grundgestalt
y showing
it at work in an
ex-
ample
that
Schoenberg
used to demonstrate the
unity
of
the
horizontal
and vertical
implications
of
the idea-Beethoven's
"Appassionata"
Sonata,
op.
57.
I
"In
ts
most common
meaning," Schoenbergsays,
"the term
idea
is
used
as a
synonym
for
theme,
melody, phrase,
or mo-
tive. Imyselfconsiderthe totalityof apiece as the idea: the idea
'The
following
works will be
cited:
SFH StructuralFunctions
of Harmony
(New
York,
1954)
FMC
Fundamentals
of
Musical
Composition,
ed.
G.
Strang
and
L.
Stein
(Oxford,
1967)
SI
Style
and Idea:
Selected
Writings
f
Arnold
Schoenberg,
ed.
L.
Stein
(New
York,
1975)
HL
The
Theoryof Harmony,
tr. R. Carter
Berkeley, 1978)
which
ts
creatorwanted to
present."2
But he too uses the term
in its narrower
raditional
meanings
of
theme,
melody,
or mo-
tive.
By
themeor
melody
he means a
complete
musical
hought;
by
motive,
ts
smallest
segment:
"The
featuresof
the motive are
intervals
and
rhythms,
with
harmonic
mplications
which com-
bine
to
produce
a
memorable
shape
or
contour."3
That
memo-
rable
shape
is
the
Grundgestalt;
he harmonic
mplications
are
its tonal function.
Schoenberg truggled hroughouthislifewith the conceptof
the musical
dea,
which served
as center for the
notions of co-
herence,
unity,
and
logic
that
pervade
his
thought
about
music.
His use
of the term took on
a
range
of
meanings
as his
concept
changed
and
deepened,
developing
from
the traditionalmean-
ing
of themeor
motive,
of
which there
were
many
in a
piece,
to
that of a
singleunifying germ.
In
1939 he wrote
of
a
previous
article:
"Then I
spoke
of
'new
motives,'
while
now I
believe in
the
availability
of
only
a
single
motive."4
And,
more
expan-
sively, in Fundamentals f MusicalComposition,a productof
his lifetime of
teaching
and the
most
explicit
publishedpresen-
tation
of
his
technique
of
motivic
development:
"Inasmuch
as
2SI,
p.
122f.
3FMC,
p.
8.
4Quoted
by
Bryan
Simms
n
"New
Documents
in
the
Schoenberg/Schenker
Polemic,"
Perspectives f
New
Music 16
(1977),
p.
122.
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16
Music
Theory
Spectrum
almost
every figure
within a
piece
reveals some
relationship
o
it, the basic motive is often consideredthe 'germ'of the idea.
Since
t
includes
elements,
at
least,
of
every
subsequent
musical
figure,
one
could
consider
it
the 'smallest
common
multiple.'
And since it is included in
every
subsequent figure,
it could
be
considered
he
'greatest
common
factor.'
"5
Ultimately
this se-
mantic
range
for
the term dea-from
the
totality
of the work to
its smallest
segment-designates
for
Schoenberg
a
single
con-
cept:
the
source of coherence
in
a work and the
subject
of
the
musical discourse.
I will
demonstrate
in
this
paper
how these
two, elementandwhole, are two forms inwhich the Grundges-
talt s made
manifest.
I will
explicate
three technical
features
of
the
Grundgestalt:
motive,
harmony,
and
tonality.
Motive,
although
analyzable
into
its
elements of
interval,
rhythm,
andharmonic
unction,
is
a
unity
of all three:
"A
musical
dea,
though consisting
of mel-
ody, rhythm,
and
harmony,
is neither the one nor the other
alone,
but
all three
together.
The elements of
a musical
dea are
partly
incorporated
in
the horizontal
plane
as successive
sounds, and partly in the vertical plane as simultaneous
sounds."6
Harmony, Schoenbergsays,
is the
logic
of music without its
"motor,"
or motive.7The motive is
the motor because
it "vital-
izes" the
appropriate
voice of a
progression
or modulation.A
good
musician,
he
says,
will make
a
progression
ucid
by
vitaliz-
ing
the crucial
ine,
thereby illuminating
he harmonic unction
it carries.
A
theme,
then,
is not so much a
figure
against
an har-
monic
background
as the surface of the
underlying
harmonic
progression.Theme and harmonicprogressionaretwo sidesof
the same
idea;
therefore the
developing
Grundgestalt
s
made
manifest
n
its
harmonicas well
as
its melodic function.
The
logic
of
the harmonic
progression
s the
expression
of a
5FMC,
p.
8.
6SI,
p.
220.
7HL,
p.
34.
tonality.
Each work makes
manifest
a
tonality
in a
particular
way. In a tonalpiece, Schoenbergsays, the idea has to do with
tonal resolution
and closure:
"Every
tone which is
added
to a
beginning
tone
makes
the
meaning
of that
tone
doubt-
ful. ...
In this manner there is
produced
a state of
unrest,
of
imbalance
which
growsthroughout
most of the
piece,
and
is en-
forced
further
by
similar unctions of the
rhythm.
The method
by
which balance
is restored seems
to
me the real
idea
of the
composition."8
And the same
means,
it seems to
me,
are those
by
which
mbalance
s
produced.
The functionof the Grundgestaltn effectinga coherentto-
nality
n
a work s to make
manifest
hat
process by
which
nsta-
bility
is
brought
about in a work and
stability
finally
restored.
When
we
comprehend
the
work,
we
understand
hat
process,
following
t
in
the
developing
harmonic,
as well as
thematic,
as-
pects
of the
Grundgestalt.
II
In 1934
Schoenberg
wrote,
"An idea in
music
consists
prin-
cipally n the relationof tones to one another" andexplicated
tonality
as a
network
of
such
relations,
referring
"not
merely
to
the relation
of the tones with
one
another,
but much more
to
the
particular
way
in which all tones relate to a fundamental
tone,
especially
the fundamental one
of
the
scale,
whereby
to-
nality
s
alwayscomprehended
n the sense
of
a
particular
cale.
...
If,
however,
we wish to
investigate
what
the relation
of
tones to each
other
really
is,
the first
question
that arises
is:
what makes
it
possible
that a second tone should
follow
a first.
. . ? How is this logicallypossible?" Only, he says, because a
relation
already
exists
between
the
tones themselves.9
By
"tonal
function"I mean those
preexisting
relations
among
the
tones.
Tonality
or
Schoenberg
s not
merely
a certain
collection
of
8SI,
p.
123.
9SI,
p.
269f.
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Grundgestalt
s Tonal Function
17
pitches,
a
scale,
but more
importantly,
a
kind
of
centricity.
All
pitchesof a key-collectionare related to a single tonal center,
each in a
specific
way.
The
function of a
single
tone is
signified
by
the
degree
of
the
scale
it
represents.
The function of a chord
depends
upon
its
root,
which
is,
in
turn,
the
scalar
degree upon
which the chord is constructed.
Tonality,
then,
is
a
set of func-
tions
of
scalar
degrees.
If
we want to
grasp
he
idea
of a
compo-
sition that
is
"about"
F,
for
example,
we
shall
want
to
know
how each
pitch
that arises
n
the course
of the
piece
is related to
the tonic.
Schoenbergapparently aworganizationby tonal hierarchy
as an
attempt
to stave off an
ultimate
state of
disintegration.
The
centripetal
unction of a
progression
s
exerted
by stopping
the
centrifugal
tendencies,
that
is,
a
tonality
is established
through
he
conquest
of its
contradictory
lements.
Contradic-
tory
elements
(in
the
simplest
sense)
are
of
two kinds:
ambigu-
ous diatonic
pitches (those
which
a
key
has in
common with
others)
and
pitches
that
are
foreign
to
the
diatonic
pitch
collec-
tion of the
key.
The
"conquest"
of
such
elements is their assimi-
lation ntothe tonal whole in such awaythat defines the specific
functionof each.
Ultimately,
in
Schoenberg's
thought,
the
structure
of
a to-
nality may
be extended to
include
all
possible
elements and re-
lations.The diatonic
pitch
collection
may
be
enriched
by
tones
borrowed
from
other tonal
areas and
substituted for the
diatonic scalar
material. Such
substitutions
may
form
new
simultaneities
("transformations"
of the
diatonic
triad)
and
elaborations
of
new but related
key
areas.
Such elaborated
seg-
ments of the basic tonality are called "regions." Borrowed
tones,
no
matter how
far-reaching
their
span
of
influence-
single
tone,
harmony,
or
extended
area-must be related to the
scalar
degrees
for which
they
are substituted n
order to be as-
similated
nto
the
hierarchic
structureof the
tonality, thereby
enlarging
and
extending
it but
preserving
ts
integrity
as well.
Schoenberg's
concept
of
tonality
as
(ultimately)
monotonal-
ity provides
for a
technical
explication
of the
nature
of
tonal
musical
space.
His
conception
of a musical
space
which is
shapedand unified hroughoutbythe idea iswell-known:"The
two-or-moredimensional
space
in which musical deas are
pre-
sented is a
unity.
Though
the elements of these ideas
appear
separate
and
independent
to the
eye
and
ear,
they
reveal their
true
meaning
only
through
heir
cooperation,
even as no
single
word
alone can
express
a
thought
without relation to other
words."10
Although
this was formulated in
regard
to
his
methodfor
composing
with twelve tones "related
only
to one
another,"
t
can
be seen
to
apply
as well to tonal music. Tonal
musicalspaceis a network of all possibletonal relations. Such
relations
n
tonal
music
constitute the
preexisting
structureof
the musical
space, by
means of which a
particular
work takes
shape
and is
comprehended.
As
early
as the Harmonielehre
Schoenberg
uses the
analogy
of a
space
in which the tonal
conflict takes
place: tonality
is the
large region
in whose
outlying
districts less
dependent
forces
resist
domination
by
the
central
power.
If thiscentral
power
en-
dures, however,
it then forces
the rebels to
stay
within the circle
of its sovereignty,and all activity s for its benefit.
We can assume hat
tonality
s a function
f the fundamental
one;
that
s,
everything
hat
makes
up tonality
manates
rom hat tone
and
refersback
o
it.
But,
even
though
t
does refer
back,
hatwhich
emanates rom the tone has a life of
its
own
... it
is
dependent,
but to
a certain
egree
also
ndependent.
What
s
closest o the
fundamental
has he most
affinity
with
t,
what s
more
remote,
ess
affinity.
If,
roaming
ver he domain f the
fundamental,
e
follow he
traces
of its
nfluence,
wesoonreach hoseboundaries here he attraction
ofthetonalcenter sweaker,where hepowerofthe rulergivesway
and the
right
of
self-determination
of
the half-free can
. . .
provoke
upheavals
nd
changes
n
the
constitution f the
entire
tructure.11
How
is
relationship
determined
n this
space?
In the
Harmo-
nielehre
Schoenberg
says
that
the
circle
of fifths
expresses
the
l?SI,
.
223.
"HL, p.
151.
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18
Music
Theory
Spectrum
relationship
of two
keys
only
to
a certain
extent;
hence he will
not use the circle exclusively for determining the relationship of
two
keys,
but
rather
for
measuring
their distance one from
the
other.12
In Structural
Functions
of Harmony
he
elaborates this
notion,
constructing
a
chart
of
regions
that indicates their dis-
tance from
and relation
to the tonic
(Figure
1).13
In
the chart
two relations are at work-the fifth
relation and the
major/
minor relation. In the
regions
representing
the core of the
chart
these basic relations are
presented:
vertical relations are
by
fifth
(upper
clockwise,
lower
counterclockwise);
horizontal re-
Figure
1
CHART
OF THE REGIONS
m
dor
Np
ABBREVIATIONS
tonic
Np
means
dominant
dor
subdominant
S/T
tonic minor
M
"
subdominant
minor
'SM
five-minor
,MD
"
submediant
minor
m
"
mediant
minor
,sm
submediant
major ,mv
mediant
major
b'mvM
'mvm
v 6MD 6mv
6mvSM
6mvsm
ImM
ti
M 6m
6mm
h?I bm
bmSMbm
6msm
'smM
6smm
sd
6SM
bsm 6smSM
6smsm
Neapolitan
Dorian
supertonic
flat mediant
major
flat
submediant
major
flat mediant
major's
dominant
flat mediant
minor
flat submediant
minor
flat mediant minor's
five
lations
are
alternately
by
parallel
major/minor
(based
on a
common dominant) and relative major/minor (based on a com-
mon
pitch
content).
Further
regions
are
related
by "propor-
tional"
relations,
e.g.,
as submediant
(a)
is to tonic
(C),
so tonic
minor
(c)
is to flat
mediant
(Eb),
and so on. When
I
speak
in
Part
V of this
paper
of
"analogy
of tonal
function,"
I
draw
on
this
kind of
relationship.
Schoenberg
did
not
consider
tonality
to
be
an
end
in
itself
but rather
a means
to an end: it is one
of the technical
resources
facilitating unity
in the
comprehension
of
tone-progressions.
Its function begins to exist if the phenomena that appear can
without
exception
be related
immediately
to a tonic. Its effect
lies
in the result
that
everything
that
occurs
in the
harmony
is
accessible
from the
tonic,
so
its internal
relationships
are
given
suitable
cohesion.14 How does the
Grundgestalt
work to
clarify
the
manifested
tonality?
III
Let us turn to the
example,
Beethoven's
piano
sonata,
op.
57, the "Appassionata."
In
Figure
2,
I have constructed a circle of fifths from the
tonic
of the
sonata,
F
minor,
incorporating
the relative
minor
relations.
This results in a two-track
circle,
which I use for both
minor
and
major
tonalities,
rather than
Schoenberg's
some-
what awkward
chart of
regions
in minor. There are certain dis-
crepancies
between
the relations
to
the tonic
laid
out
by
the
cir-
cle
and the chart of
regions,
which we will see as
we follow the
tonal "adventures"
of the
Grundgestalt.
Here
the circle
will
serve as a map of the musical space of the sonata.
Example
1. The
basic
tonality:
tonic minor/mediant
major
The
Grundgestalt
can be
expressed
in
its most
essential
form
as
a
major
third
(A/bC)
with its
upper
semitonal
neighbor
(Db)
'2HL,
p.
154.
3SF,
p.
20.
Reprinted
by
permission.
M
S/r
MM
Mm
MSM
Msm
SMM
SMm
SMSM
SMsm
S/TM
S/Tm
S/TSM
S/Tsm
/Tsm
T
means
D
SD
t
sd
v
sm
m
SM
"
M
14SI,
p.
261.
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Grundgestalt
s
Tonal
Function 19
Figure
2. The
tonality
of
Beethoven's
op.
57,
first
movement
(Example
la).
Now the
interesting
hing
abouta
single
third,
in
triadic
onality,
is
its
ambiguity.
And one
of
Beethoven's
games
in this
piece
is a
play
with
thirds.
The basic
tonal
contrastof this
first
movement
involves a
reinterpretation
of
the
Ab/C
third: t
is made to represent3-5 in F minor in the firstsection of the
exposition
and
1-3
in
Ab
major
in
the
second.
The
initial the-
matic
materialof
these two
sections
presents
those
two
possibil-
ities,
first
placing
that
third
within
the
F
octave and
relating
t
then to
Eb
(Example lb).
In
this
example
I
have
designated
he
main
themes
of
the
two
sections
of the
exposition
A
and
B,
and
the
intervallic
motives
as
T
(the
ambiguous hird)
and
T
(the
defining
ifth or
fourth).
The
two
intervallic
elements of
the
Grundgestalt,
he third
and its neighboringsemitone, can each define the tonal func-
tion of the
other.
Given that
third as
established n F
minoror
Ab
major,
the
semitone
functions as
either
b6-5 or
4-3.
Con-
versely,
the semitone
b6-5
can
serveto
relate such a
third
to its
tonic,
and
in an
essential
way:
as one
of the
operative
pitches
of
the
diminished eventh
chord.
Schoenberg,
following
his
Vien-
nese
tradition
n the
theory
of
harmony,
considersthe
dimin-
ished
seventh
to be an
incomplete
dominant
ninth
chord. I
spoke
of
the
defining
function of
the b6-5
semitone
as
"essen-
tial" because the necessary resolution of the ninth-that is,
66--completes
the
dominant,
thus
establishing
the
triad to
which the
ambiguous
third is
to
belong
(Example lc).
Beethoven
strongly
emphasizes
this function
in the
striking
three-note
figure
of the
first
theme,
Db/C.
I take
this
procedure-the
reinterpretation
f a
major
third
by
means
of the
reinterpretation
of a
diminished
seventh
chord-to be
the
primary
harmonic
implication
of the
Grundgestalt.
By
means of it
the
basictonal
contrast,
tonic mi-
norandmediantmajor,is achieved.
The
difference
between these
two
tonal
areas,
F
minor
and
Ab
major,
consists of
two
cross-related
pitches:
Dtlb
and
Etb.
The
reinterpretation
of the third
involves
the
latter,
requiring
the
enharmonic
change
of
Et
to
FlS,
he
b6
of the mediant
Ab
(Example ld).
Beethoven
placed
the
enharmonic
change
at
that
point
in the
bridge
where
he lets
go
of the
thematic
mate-
rial of
the first
heme and
introduces
he
bridge
theme,
exhibit-
ing
in an
instant
both the
transformation
of the
function of
the
semitone D6/C fromb6-5 to 4-3 and the transpositionof the
function16-5 to
the
mediant,
F$/Eb.
Notice
the
elegant
return
in the
recapitulation
of
this
crucial
point
(Example
le):
the re-
voicing
of the
motive
in relation
to the
harmony
places
it
a fifth
(notthird)
higher,
forcing
the
underlying
semitones to
ascend.
Here
Beethoven reminds
us that
reckoned
by
straightforward
fifth-relation,
Ab
s
affinity
s
with
Db,
not F. I shall
return o
this
implication
of the
Grundgestalt.
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20
Music
TheorySpectrum
Example
1. The basic
tonality:
tonic
minor/mediant
major
-
i
,
(a)
A
[4):j
-
1.2~
B
3
a
L
I
I
^L_
~b
1
b
6
5
7 8
4
3
2
3
a
I
a
2
*..
b
I
.
I
-*- op
rbl
a
I
I
_.
-10
-
_
4):,/b I-ir
F r
r
r
,*
rI
11
I
A
b6
-5
(c) J
J
,
. I,
,
k
I_
I
6a
WnO
lw~~I
R_11
_-
____ _
--_
_|
1
o0
o
I
?
II
0
oT
r
b6
-
5
tj
1
J
*
i^
Fbl
b6
5
.
1a
bd_
(b)
I -to
ILL
- I
1
1
(d)
(e)
Z7 0b
0
o
11
0
o
1
i
0
11
I
't
I
;
7/23/2019 Carpenter Grundgestalt
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Grundgestalt
s Tonal
Function
21
Example
2.
Thefirst
onal extension:
major/minor nterchange
Thereis a secondprocedureexpressing he harmonic mpli-
cations
of the
Grundgestalt
which I
take to
be
also basic to this
work:the
major/minor
nterchange.
The
b6-5
relation s a func-
tion of the minor mode.
Schoenberg's
notion of
"borrowing"
allows
the substitution n the
major
mode
of
that functionof the
lowered
sixth
degree,
on the
basis
of
the
"interchangeability
f
major
and minor"
by
virtue of
their common
dominant.
By
this
means
Ab
minor s
acquired Example 2a). Again,
this relation-
ship
is
expressedby
the
thematic material: he
second theme
of
the contrasting ection(B') is indeed a reduction(in the minor
key)
of the first
(Example 2b).
I
have
designated
the minor
third
7.
To
complete
the tonal
picture
we must add the
possi-
bility
of F
major.
In the
recapitulation
onic minor and
major
are
juxtaposed
at the
beginning
of the
bridge
n lieu of a
modu-
lation;
and of course the B
theme
is
in F
major,
reaffirming
he
analogy
between tonic
and mediant.
The
major/minor
nterchange
takes us
one
quarter
of
the
circle of fifths clockwise or
counterclockwise. Notice that
this
relationof parallelminor/major,"close" in the chartof regions
and
achieved
in
a
single
step, projects
the
motion
quite
far
along
the
circle,
opening up possibilities
for
easy entry
into
more far-relatedareas.
In
regard
to
Schoenberg's
theories one
might speak
of
the
structural unction of motive as well as of
harmony,
for he
pre-
scribes
specific
procedures
for both in
the
articulationof tonal
form. Such
procedures
are
especially
clear
in
transition
pas-
sages.
A
bridge,
which
introduces a
new
tonal
area,
shows
by
motivicanalogyhowthat area s related to the old. The work of
a
bridge
is
twofold:
motivically,
it
neutralizes old
material in
preparation
or
the
new,
while
harmonically,
t
introducesthe
new
pitch
content and
transforms he
functionof the
old. Moti-
vic intervals
can be used in
straightforward
motivic
ways:
n real
and tonal
transpositions,
strict
forms
of
inversion
and retro-
grade,
and free forms of
variation.
But
because
I
aminterested
here in
working
out
the
harmonic
mplications
of
the
motive,
I
shallseparate wo aspectsof its intervalliccomponents:specific
pitch
and tonal function.
Either can be
manipulated.
The
tonal
functioncan be
maintained
and
transposed
o
another
pitch,
or
the
specificpitch
can
remainconstant
and
transformed n
func-
tion. This
bridge,
as
we have
seen,
must
accomplish
both:
the
b6-5
function
s
transposed
o the
mediantas F
/Eb;
Db/C
s
rein-
terpreted.
Exploiting
the
region
from which
the new
b6-5
function is
borrowed,
the
bridge
approaches
the
contrasting
region
through ts ownminor,firmlyestablishingFl asagainstE . The
material
of
the first
heme
(Example
2c)
is first
reducedto semi-
tones,
given
as
those
crucial o the
minor,
and
finally
iquidated
to
a
motivically
uncharacteristic
emitonal
descent,
spanning
the linear third
which will
characterize he
next
thematic sec-
tion. In the
closing
theme
(Example
2d),
the
bridge
material s
reduced
o its
simplest
form.
Example
3. The
second tonal
extension:
The
Neapolitanregion
Let me now return to the
opening
statement of the first
theme. I want to
begin
to
formulate the
problem
of this move-
ment,
which will
have to do
with how
imbalance is
produced
andhow balance s
restored.
For
Schoenberg
a theme is
an
hypothesis.
He
distinguishes
theme
from
melody
on
this
basis:
"Every
succession of
tones
produces
unrest, conflict,
problems.
One
single
tone is
not
problematic
because
the ear
defines it as a
tonic,
a
point
of re-
pose. Every
added
tone
makes this
determination
question-
able. Every musicalform can be considered as an
attempt
to
treat this
unresteither
by
halting
or
limiting
t,
or
by
solving
the
problem.
A
melody
re-establishes
repose
through
balance.
A
theme solves
the
problem by
carrying
out its
consequences.
The
unrest n a
melody
need not
reach
below the
surface,
while
the
problem
of
a
theme
may
penetrate
to the
profoundest
depths."
A
melody,
then,
can
be
compared
to an
aphorism,
7/23/2019 Carpenter Grundgestalt
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22 Music
Theory
Spectrum
Example
2.
The first extension:
major/minor
interchange
(a)
tLbb
b0o
l1 I
,
bi II
[B']
F51
(b)
Bt
V
I-
I
I
r
I I
1111
1
B
F
_.
---
_
I
=
.,L.I1
v
-
'Pv
I
h-,
'Ii II
,Iv-
b3
a3
a,
a'
i-
,
I
_:rrr-F
Ir
_
)1:
.b
F; ^
r
F
L a Im
I
a I
E
-):,.b,
/--^
I r, I
r I
f
r
r 11
a
1-n
II
O) I
p
:
--
-
I I
ff
.
p
;
,,.
,
...
A
(?5b
I
I
):
h?lM
I'
I
1
I-
-
l
*rf:rffff
rfI f
1-
f
ffMfr
II
30bI
4 t7
,
Y)
a
_,
a
I I
i
*
-F
(c)
(4bW
-f
-"
J
'
-
W
r
-
Il
X
b--
..I_
'1J,
I
l
_11
11-1'
b "
v
-
'I
I
--
-L-9- Iv
(4^X 1^
-
-YIN ^-
V
I
STr-
)
bVI
i
*
M
[I
I
i f fbwww
J n m r n r
m m m -
_=kw
mi(
7/23/2019 Carpenter Grundgestalt
http://slidepdf.com/reader/full/carpenter-grundgestalt 10/25
Grundgestalt
as
Tonal
Function
Example
2
continued
i
s
r
XbI
b
*1
j
'
'
' -
dim.
1
dim.
pp
1U
l I
I LI
I i
I
I
I I I I
I
I
I
I
L
(c)
cont'd.
pp
[30]
b6
---
5
n
I
.
L_
I
I
a'
[63]
j
b
Vb Vt
111
8
Iti
||
I
vr
b6--
5
dim.PP
4 i
d-^
"'--1
4.
-
4
sfp
.-
.-
while a theme resembles a scientific hypothesis which does not
convince without
a number of
tests,
without
presentation
of
proof.15
Schoenberg
used the
theme of
this
sonata as an
example
of a
motive
explicated
as both
linear
interval
and
harmonic
rela-
tion,
manifesting,
that
is
to
say,
both
horizontal and
vertical di-
'5FMC,
p.
102.
mensions of the musical space. The semitone (I shall call it mo-
tiver
),
appearing
as the
three-note
figure
Db/C
to which
the
material of
the first
theme
is
ultimately
reduced,
is
given
first
as
an
immediate
tonal contrast
between the
tonic and its
Neapoli-
tan,
the
bII
(F/Gb).
The
musical
space
is
unified
here,
I
main-
tain,
not
simply by
the
appearance
of
two
semitones in two
di-
mensions or
at two hierarchical
levels; rather,
the
motivic
analogy potentially
indicates
the
preexisting
tonal relation
of
(d)
fbh
V
-
lr
#
b1lbj11
V%
+
h
O
, ||
23
-IV-W-
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24
Music
TheorySpectrum
the
foreign
Gb.
How is the
II
related
to the
tonic and
therefore
available n the
tonality
and
how will
this
relationship
be
made
clear?
According
o
Schoenberg,
the
II
is
related
through
he sub-
dominant
minor,
as its
bVI. In
example
3a I have
applied
the
two basic
procedures-the
reinterpretation
f the thirdand
the
major/minor
nterchange-to
the subdominantminor in
tonic
and
mediant,
thereby
acquiring
Gb,
and
Bbb,
analogous
to it in
the mediant. The move to the
subdominantminor
extends the
tonality
two fifths
counterclockwise
around he
circle to Dbmi-
nor. The same move from
the mediant
projects
us
seven fifths
away,
to
F,
minor,
a
region
classified in
the chart as remote.
The nondiatonic
"contradictory"
ones
acquired
from this
re-
gion
are
only
distantly
related to the
tonic;
their
assimilation
constitutesa
problem.
The constructionof
the first
theme
(Example 3b)
not
only
presents
the elements of
the
Grundgestalt
ut also illuminates
the
procedures
they
imply.
This theme
conforms to
what
Schoenberg
calls a
sentence: a
thematic model
embodying
m-
mediate
repetition
and
reduction in
its statement. Both har-
monic and motivic
procedures
work
together
to
articulate he
components
of the structure:
an initial
phrase (the
"tonic
form"),
its immediate
contrasting
repetition (the
"dominant
form"),
reductions,
and
further
reductions
leading
to
the ca-
dence. The tonic
and dominant
ormsof
the theme
(mm.
1-4,
5-
8)
present
the secondtonal
contrastof
the work. The
phrase
of
the firsttheme is in two
parts:
an
arpeggioplacing
the
ambigu-
ous third
n
its
F
octave and a diminishedseventh
interchange
expressed
as a
neighbor-noteconfiguration
around the domi-
nant. The
reductions
(beginning
in m.
9)
pick up
the second
part
of the
phrase,
reducing
t
to the
diminishedtriad and
the
defining
b6-5
function
(Db/C)
stated as
both linear
rhythmi-
cized motive
and chord
progression
Example
3c).
There is no indication
here of
the
function of the
Neapoli-
tan.
I
mean
by
this that there is
no
reference
to
itsderivationas
bVI
of the subdominant.
Rather,
the
dominant form
is
simply
juxtaposed,
a
"shadow"
following
the first
theme,
projected
from
Db,
the tonic b6.
The
work of
this
movement will
be to
clarify
he
borrowed
F/Gb
semitone
by
means of
motivic
analo-
gies
that
will make the
derivation,
the
relation
to
the
tonic,
ex-
plicit
and at the
same time
demonstrate
how the
extension of
this
relation to other
regions
allows for
the
coherent
extension
of
the
tonality.
I have
saidthere is no hint
of
the
derivationof
the bII. Per-
haps
this
is not so.
Notice that in the
tonic and
dominant
orms
the two
corresponding
neighbor-note
exchanges
are not
spelled
in a
correspondingway.
In the
dominantform
A~
does
indeed
indicate he
proper
derivationof II
from
the
subdominant
mi-
nor,
Bb
minor.In
Example
3b I
have
respelled
thatdiminished
seventh chord so
that it is
motivically
analogous,
as V of V in
the
Neapolitan
region.
As
such,
an
applied
dominantto
Db,
it
yields
Bbb,
b6
of the submediant. I
think
the
solution to
the
problem
of how the
many
relationships
presented
n
the
exposi-
tion will be
broughttogether
and
assimilated nto the
basic to-
nality
lies in
this Db and
the
functionsthat
accrue to it.
That
solutionwill
not be clear until
the
coda.
Example
4.
Theflat
submediant
with
major/minor
nterchange)
The
crux of the work
lies,
then,
in
the
flat
submediant,
the
simplest
harmonic
implication
of
the
Grundgestalt
Example
4a).
Notice
that the flat
submediant,
Db
major,
lies
only
one
fifth
counterclockwise
rom the
tonic,
but on the
"outside,"
major
track. The
effect of the basic
harmonic
procedure,
the
reinterpretation
of
the
major
third
(in
this
case, Db/F),
is to
bind these two
regions,
relative minor and
major,
into a
single
place
on the
circle. The first
fifth
counterclockwise, hen,
in
a
minor
tonality
locates not
only
the flat
submediant
major
but
also the subdominant
minor,
the
source of
the
Neapolitan.
The
exploitation
of
this
relationship
s built
into the
Grundgestalt,
so to
speak.
The derivation of
the
bII,
although suggested
in the first
7/23/2019 Carpenter Grundgestalt
http://slidepdf.com/reader/full/carpenter-grundgestalt 12/25
Grundgestalt
s
Tonal
Function
25
Example
3. Secondextension:
Neapolitan
region
b2
-1 b6--5
b2-
1
Tonic:
IV
Mediant: IV
b3
a
'
A
I
a
3:b~b
Sd
I
I
continued
theme,
is not
made
explicit
until
the
contrasting
section in the
mediant
major.
Note the first
appearance
of
Bbb
2 of the me-
diant)
n
the little link
between
major
and minor
themes
of
that
section
(Example 4b).
It is
introduced,
conforming
o
Schoen-
berg's
construction
of
the network of tonal
relations,
as
b6
of
the subdominant
minor, Db
minor,
thus
effecting
the
major/
minor
interchange
n the
mediant. In
the
recapitulation
of this
passage (Example
4e),
the II is
finally
assimilated
into the
tonic.
A curious
treatment of
Bbb
adumbrates harmonic
proce-
dures
Beethoven
will
use in
the
development;
they
are derived
motivically
rom this link
(Example
4c).
Notice how
he has al-
n,
(a)
(b)
1
I
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http://slidepdf.com/reader/full/carpenter-grundgestalt 13/25
26 Music
TheorySpectrum
Example
3 continued
-
(b)
'
- r -
?J
b
-;-
k'
6
7
i711
ta
a
'
P
x
x
tb6-
5
k8bba
It
Reductions
f,
,.
9
4
qk
I%o%l
.1---,
10
11
i: I efV
poco
ritar-
-
I .I
a Tempo
dan-
do,
^bl-bmY'
z 7-
Ii
&7jI
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I
I
'
'
'p 7
(C)
.
_
^
17
---
7/23/2019 Carpenter Grundgestalt
http://slidepdf.com/reader/full/carpenter-grundgestalt 14/25
Grundgestalt
s Tonal
Function 27
lowed us
the
illusion that he
carried
Bbb
up
to
0d,
gathering
t
into the
ascending
linear
motion,
transforming
he
ordinarily
descending 2 into an ascendingmotion.
In the event that we missed
the
ascending
b2
the first time
around,
Beethoven
gives
it to us
again
in that
second contrast-
ing
theme
(B'),
this
time condensed to
become two transforma-
tions
of
the second
degree,
preparing
he dominant
(Example
4d).
The link
to the
development
uses this
ascending
variantof
the motive to throw us into
the remote
region
of the flat subme-
diant
of
the
mediant minor
(Ft),
four fifths counterclockwise
from the tonic. This
completes
the
materialof
the
Grundgestalt
as set forthin the exposition.
IV
Example
5. Twotransitions
In the
development
I
particularly
want to
show
how
the mel-
ody
vitalizes the crucial
ine
of
an harmonic
progression,
ook-
ing especially
at the role
played by
the
variantof
the
Grundges-
talt,
a
third
plus
an
ascending
semitone. Its
simplest
harmonic
implication
s also
tonic/flat
submediant. Two
transitional
pas-
sages exploit
this variantof the
motive to achieve
harmonicmo-
tion: the first is the link
from the end of
the
exposition
to
the
beginningof the development;the second, the
liquidation
of
Example
. The flatsubmediant
with
major/minor
nterchange)
(a)
6W
pb
I
12
bo
I
t
l(lAi
Mediant
minor:
v
u
IV bII I
bVI
.
. I
-a-
(b)
(c)
b
a'
1 .1 .
_-"W.
I I
III
II
1%1%in
Jo/
,i. '
_
'-
I I
/
_P
f f
p
., i.
b
ffl ...
8-s:
i'2
l
.8-:
U
5
b-
6
b6-5
-0-
~0
)('x
/
t-
o
a2
I
I
bib
--v
b
continued
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28 Music
Theory
Spectrum
Example
continued
(:b?qb
ICCCLCCLLJLLLLLJLLLLL.J
I
-LLLL
ff
Sf
bb
60
_
3i
A-I
i-I
I I
blI II
V
)
m
m
m
bo
. o
I
ff
-1
I
.
-1
-a,h~
-
I
rio
"'
'
?i
-'I
II
X,,
-
.
v
--
the
materialof the
development
from
the
II
at
its close
to the
dominant
hat marks
he
beginning
of the
retransition.
The first
(Example 5a)
effects,
in
the
mediant,
a
motion
from that tonic minor
to its
flat
submediant
Fb)
by
applying
an
ascending
emitonalfunctionto
the
common
third,
Ab/C,.
This
was foreshadowed n
the second
contrasting
heme
(B')
by
its
pivot
on that third to
F,.
Here
Beethoven
pushes
the idea
fur-
ther,
applying
a
major/minor
nterchange,
arriving
at F-
minor.
Notice how far this twist
to the
motive has taken us:
seven
fifths
counterclockwise rom
the tonic.
Beethoven
rewrites
this
as E
minorand
condenses the
whole
procedure,
which becomes
the
firstmodel and
sequence
of
the
development.
(d)
<
-4:
6~Lj'6
L
V
t~Gi~bt
I
I I
1
I
A I
E_
I I .
I
.- -
.
'
I
L.
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Grundgestalt
s Tonal Function
29
The second
transition
(Example
5b)
is a
straightforward
model
and
sequence,utilizing
an
obvious harmonic
mplication
of the
variant,
36 ,
leading
from
bII
to
V,
GSto
C.
It seems
so
simple
Yet because of what we
now
know about the
b
I,
we see
that
Beethoven is
beginning
to
pull things together:
in
showing
us
again
the tonal functionof the
II,
he
produces
ts own Nea-
politan,
Abb.
By
an
enharmonic
change
to
G~
this
becomes
a
second transformation
f
II,
catapulting
us to the dominant.
I have summarizedboth these
procedures
(in
the
tonic)
in
Example
5c.
Example
.
Two
transitions
L
_
66
(4
?r-Q-
~
nj r
rt
i;
Jr^r' ft
r '
(
-6):
6'6
r
il
-64
t
-h
-
J
a.,)
-1
-
6 --w I-,
M
4
'-
(a)
to -h
.h,
A
, .
1 _--,k.4 .h3.
^ b
b
j ; 1
JInCg r
T
Tt
a*r
e
Mediant
minor:
I
bVI
III
bVI
b3
i ^
- -
1bV
s8
tV
Neapolitan:
I
Tonic:
bll
continued
L_ ,
7/23/2019 Carpenter Grundgestalt
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30 Music
Theory Spectrum
Example
5
continued
(b)
cont'd.
A .
I
. I
77l7
J I 7
i
7
7-
j
bib
Hbn
Jb
U
[e-R
tl
IV
b
(c)
i
__,
8
8
o a P S I L
Example
6. The
development: expansion of
the mediant as dom-
inant
of
the
flat
submediant
The
development
consists
of
two main
sections,
which sum-
marize
and
simplify
the motivic
harmonic
procedures.
The
link
and first set
of model
and
sequences
unfold an AN octave
by
means
of
descending
major
thirds: the
Ab
becomes
V of the flat
submediant,
preparing
a second
sequential
passage
(also
based
on
descending thirds)
to
GS,
which
sets off the retransition (Ex-
ample
6a).
The
model of
the
first
section is a condensation
of the
device
used
in
the
preceding
link,
utilizing
an
ascending
semitone
to
reinterpret
a common third
(G/B).
The
important
melodic
mo-
tion
(E/F)
is that
original
motif
r
,
1-'2;
the
b2
resolves
as
4
to
b3,
effecting
a
major/minor interchange (Example
6b).
The reduction of the
sequence
demonstrates that this semitone
LAbwb
t'-
d -JJ-
^-_.
bll
II
V
I I
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Grundgestalt
s Tonal
Function
31
(14-2)
is
analogous
to
5-b6,
here
presented
as
B6b/Ab
ndfunc-
tioning
to transform
Ab
into
the dominant of
the flat
subme-
diant. In this instantBeethoven reveals the connection of the
two
statements
of
the
semitone motif 7
in the
first
heme,
Db/C
and Gb/F.
Hence,
this is a
crucial
moment in
this
first move-
ment,
for it
assimilates the
contradictory
element
Gb
into the
basic
tonalityby
demonstrating
ts
analogy
to the
tonic
b
6. This
point
also starts he
motion
back toward
home,
taking
us to
the
first
ifth
counterclockwise.
The second section
of the
development
is a
straightforward
version of the
same cliche
progression
of
descending
thirds,
carrying
out as harmonic
progression
the
Neapolitan
"domi-
nant
form" of
the
opening
theme,
clarifying
or
us in a
simple
tonal
way
the
connection
between
Dband
Gb
through
the sub-
dominant
minor,
Bb-the
connection
that is not
made
explicit
in the initial
statement
(Example 6c).
Now let
me
summarizewhat I
take to be the
tonal
structure
of
this
particularpiece
of musical
space.
I
have
traced
the
path
through
he network of relations on the circle of fifths
(Figure
2).
I want
to show how
Beethoven
twice
reaches the same
outer
limit of the
tonality.
1. The basic
tonality
s F
minor/
Ab
major,
achieved
by
rein-
terpreting
hecommon third
Ab/C
by
transforming
hefunction
of its
adjacent
semitone
from b6-5 to
4-3.
2. A
major/minor
nterchange
acquires
Fi
and
projects
the
motion a
quarter
of the circle
counterclockwise.
3. The
b6-5
function
is
transposed
to
the
subdominantmi-
nor,
taking
us one fifth
counterclockwiseand
generating
the
second fifth as
the
Neapolitan
Gb.
This
procedure
n
the
medi-
ant
pushes
us to the
fifth fifth
counterclockwise,
Db
minor/FI
major,
generating
he sixth fifth
(Bbb
major)
as
its
Neapolitan.
Example
6.
The
development: xpansion
f
themediantas
dominant f
the flat
submediant
Dev I
(a)
Dev II Retransition
43
II
i bb
l
w
??.?o
"
II
11
10-
&I
as
0
0 ~~~~~\O
~
0
Vt
~II
Mediant minor
V
Submediant
bll
Tonic
V
Development
I
[t>^wmwm
m-[E
9
1
9
e 7
g
___
__0
_
_
_ _
r
f
i-
I
_ _
_
____
Model
J
I
-
S
*
.5
flif
A5
5_I_
-
5
continued
0
I
1
----b2
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32 Music
Theory
Spectrum
Example
6 continued
Development
I
{4
?
J
jbd
b
o
:
?
f
f'
v
b::
bbO
-
-:
1
b2
5 --
b6
-
5
NB
Development
II
jibb
2
llr'i
d
,2bo
4 4
l o
6:dp
r
r
r
f
bo
Development
II
114
lib
H
:
g^.~ ~~~~
?
jJ
JJ-ij
I-
/Q:Sib~~6
f
F ]
'~r-.~
I
cresc.
T m m
l fju
L-
I
1
I I
L
I
I I
I
hb.__
continued
(c)
I
C:
Ucit-cI
\IACUULt
lull
'
I
I
r~~~~y
btl~~~~b
H
-
17E-N
-
b'
" o --,
C
-.,.
. ..
I I
I I
_
,
o
7 _,
_
I
_-
,L
-
--
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Grundgestalt
s Tonal Function
33
Example
6
continued
I
II ?1i
IT
Ir
')bbbb
1
M
r
I
9:bib~~
~~~~
6 9
@
f]%
ti
0t
4. The
development
emphasizes
the
importance
of
the flat
submediant:First from
the
mediant
minor,
a
reinterpretation
of the AS/d? thirdcarries the motion to its flat submediantF
major.
A
major/minor
nterchangeprojects
the
motion to the
seventh
fifth counterclockwise
(FV
minor).
This is as far
as
Beethoven
wants to
go.
He
hops
around the dominant side
of
the
circle,
back to
the
top,
the mediant
major.
Next
the
development
makes
much the same
move,
elabo-
rating
the flat
submediant
of the
tonic,
taking
us,
by
means
of
applied
dominants,
two fifths
counterclockwise o the
Neapoli-
tan,
GC
major.
A
major/minor
nterchangeprojects
the motion
anotherquarter-circle ounterclockwise o Gbminor,thentwo
fifths arther o its
Neapolitan,
Abb
major.
Beethoven has
again
reached the same outer limit
of this
tonality,
the seventh
fifth
counterclockwise
from
the tonic. This time an
enharmonic
change
to
G
major
quickly
takes us back to the
tonic,
again
along
the
dominantside of
the circle.
V
Example
7.
Analogies of
tonalfunction
How was the imbalance
created?
By
pushing
the two
ele-
ments
of
the
Grundgestalt
o their
limits in this
work:
the low-
ered
fourth
degree (Bbb)
and the lowered
first
degree
(Fb
mi-
nor).
How was this done?
By
progressively
extending
the
tonality
by
means of what
I
shall call
analogies
of tonal
function-
analogies
that work
by
the
manipulation
of both
specific pitch
andtonal function(Example7).
First the semitonal motif
T was
interpreted
as
?6-5 or
4-3,
yielding
Fb
nthe mediant and
Gb
n
the subdominant.Next
Gb/
F,
acquired
n
the subdominant
minor,
functions as
b2-1
in
the
tonic and extends to
Bbb/Ab
n the mediant.
Finally,
the func-
tion of
Db/C
as
4-3
extends to
Gb/F
n
the flat submediantand
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34
Music
Theory
Spectrum
Example
7.
Analogies
of tonal
function
If in
tonic:
blb
?
b6
-
5
4-3
then
in
mediant:
If
in
subdominant:
30
b
o
^
then in tonic:
b6 - 5
bo
i,
b2 - 1
and
in
mediant:
bbo
,
b2
-
1
And
further,
if
in mediant:
bibb
?
'
then in flat submediant
4
-
3
0o
,
and the
mediant's
flat
submediant:
bbo
a
4
-
3
4
-
3
All
with
major/minor
interchange.
But
how is
the
subdominant
achieved?
At the
first
fifth
counterclockwise:
bblbo
bo
1b
1b8
I
I
b6 - 5
4
-
3
reached
through
the
mediant
as subdominant
of the
flat submediant.
bo
o
b6
-
5
- v-
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Grundgestalt
s Tonal
Function
35
Bbb/Ab
n
Ft,
flat submediantof the mediant. All these
relations
can sustain
a
major/minor
nterchange.
It seems
to
me
that
instability
n this
piece
is introduced
by
the
move to
the
subdominant,
expressed
as
II
in the initial
phrase
with
no
indication of its
relationship
in the
tonality,
made
cohesive
only
by
the formal
juxtaposition
of tonic
and
dominant
orms
of the
first
theme.
Balance
will be restored
by
demonstrating
how
this was a
coherent
move;
that demonstra-
tion will
be made
by
furthermotivic
and tonal
analogies.
As
you
have
seen,
all these
relationships
were
laid out in the
mediant.
The
recapitulation
of the
contrasting
section in
the
tonic
minor/major
hows us
all
those
connections
n
the
tonic.
I
will
present
two
examples
of how these motivic/harmonic
nal-
ogies
are
unraveled
n other
parts
of the
recapitulation.
Example
8.
The owered
ourth degree
The
first
analogy,
b6
and
b2,
which
produced
the lowered
fourth
degree
(Bbb),
s clarified
n
the
bridge,
where
indeed
it
was
first ntroduced.
The
bridge passage appears
hree times in
the movement.
In the
exposition
it
established
he mediant
ma-
jor, borrowing
rom its minor the
b6-5
(Example
8a).
It
is
reca-
pitulated
n
the
tonic,
establishing
he tonic
major by
the same
means
(Example
8b).
This affirms he
analogy
betweenDband
F1
as
b6.
In
the
development (Example
8c)
the
bridge
carries
out
the motion
to the submediant
Db,
again using
the
same
means,
thus
adding
a
further
analogous pitch,
B1b,
as
b6
of
the
submediant.
We have
been
acquainted
with
Bbb
as
b2
of
Ab,
the
mediant.
By
using
the
bridge
passage
as a
link in
Db,
Beethoven
connects
the
two functions of the semitonal
motive,
16-5
and
b2-1,
through
he flat submediant
region,
Db
major/minor.
He takes
timehere to restate
what
he
had
just
shown
us
in a flash in the
dominant
preparation
of
this
passage (Example
6b).
Further,
we see
Ab
in its new role as dominant of the flat
submediant,
Ds.
Example
9.
The
oweredfirst
degree
The second
analogy
is
12-1
and 4-3. What is the role of
F-
minor,
the lowered first
degree?
In
the
recapitulation
of the
second
contrasting
heme,
the tonic elaborates Db
major,
again
affirming
he
analogy
between
F-
and
Db
as flat submediant.
The
recapitulation
loses in the
tonic
with
the
descending
F
mi-
nor
arpeggio,returning
o the
original
ow
register
of
the
open-
ing
theme
(m. 204).
At this
point
in the
exposition
the link to
the
developmentprovides
a
major/minor
nterchange,
carrying
the
harmonicmotion to
F-
minor. At the same
point
in the
re-
capitulation
m. 205)
a coda
follows,
using
the same harmonic
procedure
hatserved asmodel at the
beginning
of the
develop-
ment. The formal
analogy
between
Db
major
and
F-
major,
set
up by
the
place
they
occupy
n the
course of
events,
makes man-
ifest the
analogy
of tonal function.
This
turn reveals
the most
surprising
analogy
in
the
move-
ment:
Gb
andF as 12
Further,
this
passage
brings
nto focus all
the
relationships
et
forth n the
movement:
n the firstmodel
of
the
development,
F
is
approached
as
b
2
and left as 4-,
3;
here in
the
recapitulation
he same transformation
of function occurs
on
Gb
(m. 206),
but without
the
major/minor interchange,
defining
Ab
as
a dominant.
Again
the crucialdouble function
of
Ab,
as tonic mediant
and
dominant
of the
flat
submediant,
is
demonstrated:because
the
original
semitonal motive
Gb-F
can
be
interpreted
as
4-3,
by analogy
Bbb/Ab
s 4-3 achieves
Fb,
as
flat
submediant
of the mediant. This
passage
n the
coda,
analo-
gous
to the farthest
imit
reached
n
the
development,
is assimi-
lated into the tonic as flat submediant
by
means
of an
elegant
turn based
on the condensation
of transformations f
II,
turn-
ing
the motion
to the dominant
n
preparation
or the close.
Fi-
nally,
in
the
Piui
Allegro,
the
Gb
akes its
place
in
the
dominant
ninth
applied
to the
subdominant,
ts
original
source
(mm.
244,
247).
The web of tonal
functions revealed
in
the coda
illuminates
an
earlier
question:
If the basic tonal contrast s
between tonic
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36
Music
Theory
Spectrum
Example
8. The
lowered fourth
degree
Reduced
in
closing
theme
to:
i
30
b6
5
A.[~
t)
Mediant
68
"I^
1r
Ir
bL6
5
__-.
A--
-0-
6bb
t8
'
bilz
dbt,
00S-
O
Pe8
BIU
8
I
t
|
j ji
b7F -t7i '1
.
-
(b)
<fp
^I]
dim.
|@
44i
k
1
ji L
.
_
__
dolce
r : b b b b
Z _ 7
r r
-
r
Z
n-a: -
n
m
i'""7
6
6
-8
5
t'
b3
blt
Mbd;
h
i
bo.
b
1
8
a
U
1
Tonic
___
b6 ----
5
n
LbV
.-
'
b6 5
---
-s-
--
t6
----
5
[5v,
V
r
v
"IsTbbt
qo
II
b
6--
5
(a)
(c)
Submediant
Submediant
I
I
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g:_r~
-~-
^
-
r
- m
W
t-
ZPI
S
S
p
,p
,
ml;-.6':;immhwHIWai"mwi i iq
ml
m
rTm m
rn
_,_, _, _ _ _ ^
M.
h, I
,
Id
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a;;;aL5 3 9
sT150f
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fts~~~~~~~~
fi"
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IJ
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d'
tj
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j
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r
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Ill~~~~~~~~~~~~~~~
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l
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38
Music
Theory
Spectrum
minor and
mediant,
why-or
how-is the initial move made to
the realm of the subdominant?The
answer seems
to
be: be-
cause
of,
by
means
of,
all
the tonal
functions
brought
nto
focus
by
the flat
submediant,
Db
major/minor.
By
the relative
major/
minorrelation
t
locates the subdominant
minor,
Bb,
the
source
of the
b2,
G
. As subdominant
f the mediant
Ab,
it
provides
he
analogous
b2
(Byb)
and the function
4-3 or
4-
3
which,
applied
to the
BbK,
arries hemotionto Fi
major/minor.
And
balance
s
restoredwhen
all
these
relationships
click into
place
at the end
of the movement.
I have been
especially
concerned here
with two
points:
first,
to
explicate
features of
Schoenberg's
concept
of
tonality
as a
network
of
tonal
relations;
and
second,
to
demonstratehow the
Grundgestalt
unctions on
several levels-as
motive,
theme,
span
of
bridge
or
development,
and
structural
design-to
make
manifest hat
tonality.