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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.



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.



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.



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.



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.



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

;



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,



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(



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-



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



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



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

---



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



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.



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_ ,



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



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



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

-

--



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



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-



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



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



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

-J1I1

a;;;aL5 3 9

sT150f

*->

0

^^

fts~~~~~~~~

fi"

S

' 4.

L4'

R.4

IJ

':

.

d'

tj

.j

j

J'

tL

4

t

4

P5^

*r4

Jtfr

4

f

44

t

f

r

dr

' u.p

d

. . . L I. L

) . . . .. . I .

_ I i l l _

Ill~~~~~~~~~~~~~~~

oJp

s.n

p.

tM~oI

l

'6

Idu

r

33-13p Isjii p3.3;DMOi;

*6

31dwvxg

Lg

uo iounj

leuoi

se

jiesa6pun2j



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.