benjamin - 'pour les sixtes', an analysis

8/19/2019 Benjamin - 'Pour Les Sixtes', An Analysis

1/39

Yale University Department of Music

"Pour les Sixtes": An AnalysisAuthor(s): William E. BenjaminReviewed work(s):Source: Journal of Music Theory, Vol. 22, No. 2 (Autumn, 1978), pp. 253-290Published by: Duke University Press on behalf of the Yale University Department of MusicStable URL: http://www.jstor.org/stable/843399 .

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2/39

"POUR LES SIXTES":AN ANALYSIS

William

E.

Benjamin

The

opening

notes

of

Debussy's

Etude

"pour

les

Sixtes"

can

only

be

ascribed to a

richly

historical

self-consciousness-a

sense

of

artistic

indebt-

edness

which

elicits

hommage,

and

an

awareness of one's

place

which

permits

the

open

and

confident

payment

of

hommage.

That

Debussy

was

supremely

aware of

his crucial

role

must be evident

to

any

experi-

enced

pianist

who

attempts

the

realization of

these

first

few

notes,

since

the

player

can

scarcely

have made

contact with

the

keyboard

before

being

led

back,

in

a rush of

tactile

memory,

to the

familiar

sounds

given

in

Example

1.

Debussy's

willingness

to

acknowledge

a

debt

to

the

man

whose

memory

he

apparently

intended to

honor

with these

Etudes,1

which

points

to

his

unconcern

about

being

mistaken

for

an

imitator,

is

drama-

tized

by

his choice

of

occasion

on

which to make

a

clean breast

of

it:

the

medium,

the

genre,

and the

very

title of

the work

could

hardly

fail to

quicken

an

audience's

associative

bent. The

confidence thus

bespoken

could,

of

course,

have been

misplaced,

but

does

not

appear

to have

been,

for

in

spite

of

its

thinly

veiled

allusions to

Op.

25,

No.

8

and

to

other

works

of

Chopin,

this

Etude,

when

but

loosely

scrutinized,

can

be

seen to

reveal a

world of

means and

purposes

which

lies

quite

outside

the

scope

of

those ancestor

works.2

253


3/39

Vivace

mo/rto

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mezzo voce

J"7-1

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l

Example

1

[

) b) c)

0-

vi

-

AL kv, -

VP

0|v

Example

2

a)

b) C)

I"

I

v

-06v

Example

3

254


4/39

It

is

only

upon

closer

scrutiny, however,

that

a

determinant of

"pour

les Sixtes"

emerges

which

seals

the sense

one has

of its otherness

vis

d

vis

the

many

instances

in

nineteenth-century

piano

music

where

sixths

are

used

pervasively: i.e.,

a

concept

of

tetradic

consonance

within the

diatonic scale. A mere hint (and hardly an adequate portrayal) of the

far-reaching

effects of

this

concept

is

attained

by

comparing

Example

1

with the

opening

measures

of

"pour

les

Sixtes." If

Example

2a

is

acceptable

as

a

reduction of the

content of

Example

1,

Example

2b

may

perhaps

serve

as a

comparable,

if

slightly

simpler, representation

of

mm. 1-3 of

Debussy's

Etude.

Example

2c

is an even

simpler

sketch

of

mm.

1-4.3

Chopin's

initial

sonority-a

major-minor (hereafter:

"Mm")

7th

chord -resolves

directly

to

a

triad. Since

the 7th

chord is

represented

as

a

pair

of

sixths,

this

resolution

implies

a

progression

of

one of

these

sixths, played here

by

the left

hand,

to a fifth. In the case of

"pour

les

Sixtes,"

the

initial

harmony, pitch-class-identical

to that of

Op. 25,

No.

8,

proceeds

immediately

to

another Mm 7th

chord

and

proceeds

thence,

and

at a more

remote

level,

to

a tetrad

of

type

(0,3,6,9).

By

sticking

to a

progression

of

4-pitch-class (4-PC)

sonorities

at

all

but

the

most

foreground

levels,

Debussy

maintains the

integrity,

at all

of

these

levels,

of

each

of two

streams

of

imperfect

consonances. On

the

other

hand,

the

triadicity

of

Chopin's style

implies

that

at most

one

such

stratum will

endure

beyond

the

merest

evanescence.

A

direct

result

of

this

distinction is

the

sharp

textural

contrast between

the two

works:

Op. 25,

No.

8

makes obsessive

use

of

an

ornate,

essentially

conjunct

melody

in

sixths,

set

against

an

arpeggiated

accompaniment

comprising

sixths,

fifths,

and other

simultaneities,

which

only

occasionally,

though

at

crucial

spots,

achieves an

independent

sixth-stream of

its own:

by

contrast,

"pour

les

Sixtes"

makes

flexible,

indeed

functional,

use

of

a

range

of

textures,

each of

which

derives

from a

distinctive

way

of

dif-

ferentiating

between

two

underlying

PC

streams,

each

containing

a

pair

of

PC

lines

consistently separated by

IC's

3

or

4.4

We

may

begin

our

discussion of

Debussy's

Etude with an

overview

of

systematic

constraints which

govern

its

progress.

First

among

these

is

the

notion

of

tetradic

consonance,

which

entails the

reference,

at

some

level(s),

to

a

total-piece-partitioning

succession of

4-PC

harmonies.

Tetrads

may

appropriately

be

termed

consonant

to the

extent

that

they

do

not

result

from

the

melodico-rhythmic

elaboration of a

triadic

succession.

If

they

are

said to

result

from

such

a

succession,

it is

because

a

conceptual

3+1

partitioning

seems in

order,

on

the

basis

that

special

(i.e., more highly constrained) treatment of their allegedly extra-triadic

elements

elicits

it.

In

effect,

then,

tetradic

consonance is

justifiably

in-

voked when

the

singling

out

of

one

tetradic

constituent

(e.g.,

the 7th of

a

7th

chord)

as

hierarchically

inferior

does

not

enjoy

the

support

of

the

facts. None

of

this

in

any

way

enjoins

one

from

singling

out a

tetradic

255


5/39

constitutent as

hierarchically superior, or,

in

other

words,

from

designat-

ing it,

on

some defensible

basis,

as

a

root. This sort

of

reverse

parti-

tioning

into 1+3

is

exactly

comparable

to

the 1+2

partitioning

we

customarily

inflict

upon

triads.

Consonant tetrads, therefore, are not supercharged triads. Still, they

may

be heard as

dependent

upon,

and

dissonant

to,

one

another

in

much

the

same

way

that a dominant

triad is heard in

relation

to

its

tonic

triad.

This

amounts to

saying

that there

may

be

a

hierarchy

in

the

flow of

consonant tetrads.

In

any

instance

of

tetradic

music,

our

discernment

of

this

hierarchy

and its exact

makeup

will rest on rhetorical

aspects:

that

is,

on

the

way

the music

emphasizes

certain

elements

and

downplays

others.

We

think

of

music

as more

systematic,

however,

when it

estab-

lishes some sort

of

correspondence

between

roles

rhetorically

expressed

and sonority types. In fact, it is this correspondence, however rough,

which

guides

us toward

positing

some hierarchical

organization

of

the music's elements

as

its

analysis.

Distinctions

between tetrads

can

be

made in three

stages.

The

first

stage

is

to

distinguish

different

tetrad

types,

or

4-PC

sets;

the second is

to

distinguish

transpositionally equivalent

tetrads;

the third

is

to dis-

tinguish

different

registral

orderings

of

the same tetrad. At

the

first

stage

one

distinguishes

between

the

tetrads

represented

in

Example

3a

(m.

13,

beat

1);

at the

second,

between those

represented

in

Example

3b (mm. 18-19); and, at the third, between the tetrads of Example 3c

(m.

12 and m.

19,

respectively).

Distinctions

among

tetrad

types

are

fundamental,

and,

in

this

music,

form the basis

for

choosing

an

underlying vocabulary.

Tetrads

which

may

be

partitioned

into two

IC3's,

two

IC4's,

or an

IC3

and an

IC4

figure

as

items

in

the

vocabulary;

others

do

not.

Any

tetrad

containing

still

another

IC3

or

IC4

in addition to those

which

partition

it

enjoys

a

privileged

status: it

may

be used as

a

harmony.

The

highest-level

har-

mony,

or

tonic

tetrad,

is

a

special

case

and will

be discussed

later.

Except

for the

tonic

tetrad,

the

harmonies

of

the

highest

middleground

level

are all

global

or

local dominants and are PC

sets of

types

(0,3,

6,8,)

and

(0,3,6,9).

Constituents

at the next

lower

level serve to

facili-

tate

the

progress

from dominant to dominant and are chosen

from

set-

classes

(0,2,5,8)

and

(0,3,5,8).s

The

latter,

in

turn,

are elaborated

by

harmonies

of what

may

be

called the lowest

middleground

tier(s);

i.e.,

those

of

types

(0,1,5,8)

and

(0,1,4,8).

At

the

foreground,

a

variety

of non-harmonies-tetrads

which

can be

partitioned

in the manner

described

above,

but

which

contain no additional

IC3

or

IC4-make

their

appearances.

Most

frequently

used

among

sonorities

of this last-

mentioned

sort are

those

from

set-class

(0,2,3,5)-m.

12,

10th

i-and

set-class

(0,1,3,5)-m.

26,

beat

3,

2nd

?,

and m.

28,

6th

1.

The

assignment

of

transpositionally

equivalent

tetrads to

various

256


6/39

levels

of

a

hierarchy,

the

choice

of one

as

being

"more

in the

back-

ground"

than another

is an

exceedingly complex

matter.

Only

one

circumstance which

helps

to

clarify

this choice

will be

discussed

here;

namely,

when

it

is

simplified by considering

the PC

voice-leading

implied in a surface progression of parts.6 Example 13a presents a

PC

model

of

mm.

1-6 which

comprises

three

voice-leading

strata.

Each

of

the two

top

strata contains two

PC

voices or

lines,

while

the lowest stratum

presents

a bass PC

line

(not

to

be confused with

the lowest

part

in

the

music).

The

registral

representation

of

these

lines

is

essentially arbitrary,

but

it

has the virtue

of

displaying

PC

connections

as

pitch adjacencies.

The

distinguishing

feature

of

each

upper

stratum

in

Example

13a is that at a

middleground

level

(repre-

sented

by

white

noteheads)

its two lines are

PC-conjunct

and are

consistently separated

by

IC's 3 or 4.

If, however,

we restrict our con-

cern

to

the first

part

of

the

example (up

to and

including

the

harmony

labelled

D-flat:

IV),

we

observe the

use

of

black noteheads. Like

the

preceding

V,

this

IV is a "Mm

7th

chord,"

but

unlike

the

V,

it

is

parti-

tioned

by

voice-leading

into an

IC3

(middle stratum)

and

anIC2

(top

stra-

tum).

The

general principle

here

is this:

assuming

that

this sort of

model

of

PC

voice-leading

can be

produced,

any

tetrad

which

is

partitioned

so

as

to

generate

IC's other than 3 or 4

in either of

the

top

two strata is "more

in

the

foreground"

than a

transpositionally

equivalent

tetrad which

is

partitioned

into a

pair

of

3's,

a

pair

of

4's,

or a 3

and

a

4.

On the basis

of

this

principle

D-flat:

IV

is here

accorded

a

relatively

low-level

status.

In

triadic

tonal

music it is

customary

to

distinguish

the three

inversions

of

the triad

with

respect

to the

role

and

hierarchic

status

of

each.

It

would

also

be

possible

to

distinguish

the

registrally

partially

ordered

represen-

tations

of

tetrads

and to

speak

about

root-positions,

first

inversions,

and

so on.

If,

however,

tetrads

at

virtually

all

levels

are

obtained as

aggre-

gates

of

pairs

of

"sixths,"

as

seems

to be the

case

here,

only

two inver-

sions of the

primary tetrads, quasi-7th-chords,

are

accessible,

the

?

and

the

1.

It

appears

that

no

systematic

functional distinction between

these

registral arrangements

is

applied

in

"pour

les Sixtes". Root-

positions

of

"7th chords" are

accessible

under

the conditions which

apply

in

this

work

only

when

the

fifth PC

voice,

the structural

bass,

doubles

the root.

This sort

of

doubling

is sometimes

used to

signal

the

relatively

high-level

status of

a

tetrad

(as

in

mm. 5-6

and,

of

course,

in

mm.

57-58),

but

other

uses

are found

for

it as well. For

example,

the

fact that

the "D Mm

7th

chord" at m.

28,

beat 3 is in

root-position

heightens the interruptive effect of the G-flat root which follows it,

with the

result that

m.

29

sounds as

if

it

were

interrupting

the

progress

from

m. 28

to m.

30.

In the

world of

"pour

les

Sixtes,"

where five PC

lines-a

bass

and four

upper

voices-are

frequently

in

operation,

5-PC

sonorities

come

in

257


7/39

handy

because

they

allow the

bass

PC's

of

its

own. When such

allowance

is

made,

telling

effects can

result,

such as those of mm.

46-50.

Occuring

at various

levels,

5-PC

sonorities result

from the melodic elaboration

of

tetrads of

type

(0,3,6,8)-normally,

dominants-through

the

replace-

ment in some octave of their individual roots (their 8's) by upper

diatonic

neighbors:

i.e., by

9's

or 10's. The net

results are

pentads

of

type

(0,3,6,8,9)-m.

45,

beat 3-or

of

type

(0,3,6,8,10)-mm.

49-50.

In a tetradic

system

pentads

can

justly

be

termed

"dissonant".

The role of

triads in this

system

is

manifold

and

particularly

interest-

ing.

These

figure

in

a

profusion

of

foreground

elaborations of harmonic

tetrads.

In this

connection

Example

4

(which

abstracts the

content

of

m.

35,

beats

1

and

2)

will

prove

instructive. The

underlying sonority

during

these

beats is

(D-flat,

F-flat, A-flat,

C-flat),

which

prepares,

and,

after prolonged interruption, resolves to (G-flat, B-flat, D-flat, F-flat)

in m. 37.

The latter

sonority

acts

as

an altered

dominant-of

the sort

popularized

as

a German

6th-leading

to F.

Example

4a shows the

fundamental

progression

(the

bass

line is

left

out)

in which a

sonority

of

type

(0,3,5,8)

is

used

to

prepare

one

of

type

(0,3,6,8).

The

elaboration

of the first of these

is what concerns us here.

Example

4b shows

how each

of the

dyads

which

partitions

(D-flat,

F-flat,

A-flat,

C-flat)

is

supplied

with an

upper

diatonic

neighbor,

the scale

of reference

being

C-flat

major.

The elaboration

results

in a

temporal

skewing-a

diagonalization

of

harmonic

(and

non-harmonic)

elements. The simultaneities which result

are

of

another

type

(0,3,5,8)

and

a diminished triad.

The

latter

is

then

further

elaborated

(Example

4c)

through neighbor

motion

in

the lower

parts

and a

borrowing

of

the

lower

dyad

(B-flat,

D-flat)

by

the

upper

voices.

This

produces

a

simultaneity

of

type

(0,1,3,5).

The

sense of

a

progression,

followed

by

a

recession,

of

dissonance

within

each

beat

of m. 35 is

unmistakeable,

and

obviously

reflects

the

foregoing

analysis.

The

correspondences

and

non-correspondences

to this wave-like

action

in

other

dimensions-those

of

density,

total

range,

and

dynamic

level-

make

for

a

highly

nuanced

composite

pattern

which seems

to demand

a

rubato for

its realization.

Example

4d summarizes

the

level

structure

of

the

fragment.

A second

foreground

role for

triads involves

their

use

"in

series" as

a

way

of

leavening

extended

passing progressions

(occasioned

by

octave-

transfers)

between

higher-level

tetrads.

Example

5

depicts

this

phenom-

enon as instanced

in

mm.

13-16,

where

(A-flat,

C,

E-flat,

G-flat)

is

connected

to

(B-flat,

D,

F,

A-flat).7

The primary means of

connection

in

Example

5

is

a

line of

I

chords

which could

have been

continued

without

a break

right up

to

the

goal

sonority.

Instead,

the

chain

is broken

at m.

14,

where

a

temporizing

impulse

generates

a

wavering

triad

series.

In

m. 15

the

chain is

resumed.

Particularly

fascinating

is

the

use

of

octave

doubling

within

these

258


8/39

L b C)

d)

m.

34

35

37

Example

4

F..____---

riads

:W

--3,

U-,

----

-

. 1 14

-

15 16 17

L).

Example

5

259


9/39

triads.

Such

doubling

is

necessary

to maintain

the continued flow of

sixths,

but

alternates between

two

pairs

of

parts, obviating

a sudden

and

unwanted sonic blandness.

Part alternation

of

octave

doubling

is

also a

feature of

the

upbeat segment

of seven 's which

precedes

beat 2 of

m. 8. In this passage there is a crescendo of sonic complexity, from

dyads through

triads to tetrads.

In

this

music,

the

primary

role

of

triads

on

a

larger

scale is

interrup-

tive. The

highest middleground

level

contains a

progression

of

tetrads;

triads introduced at the next-lower level

loosen

up

this

progression,

and,

by

filling

the

junctures

from

tetrad to

tetrad,

increase

its

temporal

extent. These triads are

obviously

not resolutions

of

the tetrads which

flow

into

them,

yet they appear

to absorb their

forerunners'

energies

and,

momentarily,

to

stay

the

forward-pressing impulse

symbolized

in

the tetrad progression. Striking examples are furnished by the G-flat

major

triads

in mm. 27

and

29. The

first

represents

the

beginning

of a

large-scale

triadic

prolongation

(mm.

27-36)

which

interrupts

the

tetradic

progress

of

the

middle section as a whole. From

m.

27 to

m. 34

the

PC

syntax

is

turned

inside-out,

in a

sense,

with

tetrads

engaged

in

the

melodic

expansion

of

the

G-flat triad. These tetrads are

organized

in an

energetic

wave which

spans

mm.

28-33,

reaching

a crest

in m.

32.

M.

29 acts

as a

pocket

of

placidity

within this

wave, mirroring

the

larger

effect of mm. 27-36 as a whole.

Ultimately, then, the whole middle section of "pour les Sixtes,"-

mm.

21-45-can be heard as an

interrupted

tetrad stream

which

bridges

(F, A, C,

E-flat)-mm.

21-22-

to

(B-flat,

E

double-flat,

F,

A-flat,

C-flat)

-m.

45.

The

whole

section, therefore,

is

spanned

by

a

quasi

V-I

progres-

sion.

The

interruption

of the

stream

is filled

by

a G-flat triad

prolon-

tion,

but is

really brought

about

by

a

discontinuity

which is inherent

in

the stream itself.

This

is

made clear in

Example

7 where the

connection

between the B-flat and

G-flat tetrads

(mm.

23

and

37, respectively)

is

seen to

be

suddenly

disjunct.

In

each

stratum

the

pair

of voices folds

over from bottom to

top:

hence,

in the middle stratum, the F-flat in the

harmony

at

m. 37 continues from the

F

in the

harmony

at

m.

23,

but

the D-flat

(m.

37,

middle

stratum,

upper

voice)

appears

to

emerge

from

nowhere.

The

same sort of

thing happens

in

the

upper

stratum.

Example

6

shows how this

problem

is dealt with at the

next-lower

level.

By

means of

a

chromatic

modification

(D-D-flat)

and a characteristic

shift

(indicative

of

transition

to a lower-level

event)

from

a

sixth to a

seventh,

a dominant of G-flat is

reached at

m.

26.

The

PC

counterpoint

then

enters a

triadic

pocket

with the "dissolution"

(rather

than the

"resolu-

tion")

of the middle stratum's sixth to an octave. The tonicization of

the

G-flat

triad,

which is re-executed

with

greater

care at

m.

33,

promotes

it

to a kind

of

free

zone

in

which

constraints

regulating

the

tetradic

mid-

dleground

are

temporarily

relaxed.

In

this tolerant

setting,

arpeggiations

260


10/39

which

lead the

PC

lines

to their

new

points

of

departure

in

m.

37 are

easily

accomplished.

(See

Example

6).

Let us look

more

closely

at

Example

7

to

uncover further

conditions

which

shape

its

course.

Two of these conditions

are

particularly

obvious:

in the upper strata there is 1) uniformity of PC-conjunct motion, with

the

exception

of

the much-discussed

interruption

and of the final

anomalous

progression,

to be

discussed

below;

2)

a descent

without

reversal

in all

voices

(except

at the

point

of

discontinuity,

where the

question

of direction is

moot).

We have

already

alluded to a third condi-

tion-i.e.,

that

each

upper

stratum

uses

only

IC's

3

and

4 as

verticalities

-and we can

now

make

the observation

that the contents

of verticalities

directly

under

one another are

mutually

exclusive. In other

words,

the

upper

strata

never double

each

other and each successive tetrad is

partitioned by them without the aid of the bass. The bass, then, serves

to double

PC's or to

add

elements

of

its

own.

All of

the

above seems

simple enough

until

we realize that

we

have

left the term

"PC-conjunct" essentially

undefined. Its definition

is

implicit,

however,

in a condition which is

pertinent

to

our

inquiry

and

which we

have

tacitly

assumed

from the

start,

as evidenced

by

our use

of the

terms "tonic" and "dominant".

The

reference here is to the

"diatonic

condition,"

one

in

which each of the

12

PC's is

given

a

range

of

a

priori

significance by being

identified with

appropriate

members

of

appropriate "disposition-pairs" in selected major, major-minor, or

"modal" diatonic

scales.

Disposition-pairs

are ordered

pairs

of

adjacent

diatonic

scale-degrees

in

each

of which

the

first element

is

thought

of

as

disposed towards,

or

as

tending toward,

the second.

Questions

as to the

possible

bases

for

asserting

disposition-pairs

require

more

detailed answers than could

possibly

be

given

here,8

but it

should be

clear

that

the

model

of

Example

7

can

have

no

validity

unless

we

accept

their assertion as

legitimate.

Why

not?

Simply

because

there

is

no

reason to

place

our

trust

in

a

conjunction

of

two

PC's

whose

representations

in

the

music

may

be

separated

by

considerable stretches

of

foreground,

and to

say

that

one

"goes"

to the

other,

unless we

think

of

them in terms

of

their

prior

relationship

in

the diatonic

scale

or some

comparable

prior

construct.

We

should remember that

the

smooth

lines

of

Example

7

in

no

way

reflect the

registral

complexity

of

"pour

les

Sixtes".

They

are

not meant to

represent simplifications

of

an actual

pitch-counterpoint

into an

ideal

species-like pitch-counter-

point; instead,

they

are meant to

portray

the

underlying

PC counter-

point

we

call

harmony.

There

is

very

likely

no

line in

"pour

les

Sixtes"

which

"goes,"

as

does the

upper

line of

the

upper

stratum

in

Example

7,

from

some

E-flat

to the

E-flat

an

octave

lower.

We

should also

recall

that

in

conceiving

of

the tetrads

of

Example

7 as

consonant,

we

lose

any

basis

for

relying

on

an

obligatory

resolution

of dissonant

261


11/39

2

rd

m. 23 26 27 35 37

--

•i7c

•

Example

6

-

sequence

pottern

'foldlng

o

v(-.r"

pattern

rEStrtement

m

1

4

5 51 23

37

38

44

47

54

57

Db: V

(I)

v

IV

II I

C

(7)

I

CV

V

(1)

F: II

I

B

1

)

I

6I

IEI

(I)

Example

7

262


12/39

elements-7ths,

for

example-as

a

determinant

of

PC

succession.

Before

returning

to

Example 7,

let us see what

disposition-pairing

tells us

about

the

behavior

of

IC's

3

and

4 in

diatonic

contexts. The

major

scale is the

simplest,

but

what

follows

can be

adapted

to

other

instances of diatony. In what was apparently Debussy's concept of the

major

scale

(disposition-pairs

are

not

fixed for all

time),

the

primary

pairs

are 7

---

i 4

--

3,

and 2

--

i.

Three

other

pairs,

6 -+

5,

2

---

3,

and

5

-+6,

are

generally

secondary.

These

come

into

play

as

parallel

associates of

primary

pairs,

The

disposition

of

"sixths,"

therefore,

are as

given

in Table

I.

In

Table

1

a sixth is labelled

"inert" if

neither

of its

scale-degrees

is

the

first member of a

primary

pair.

If

one of its

scale-degrees

is the first

member

of a

primary pair

it

is

called

"weakly disposed," although 4/6

is regarded as stronger than 5/7 and 7/2. The pair 2/4, in which both

degrees

are

first members of

primary pairs,

has

the

strongest disposition

of

any

sixth.

The sixth

7/2

has

as its ultimate

disposition

the

identity

1/1.

To

maintain

the

fragile

world

of

"pour

les Sixtes"

1/1

is

simply

avoided at

higher

levels.

Table 2

reproduces

the

upper

strata

of

the

first

half of

Example

7 in

terms of

disposition

pairs.

What

emerges

from Table

2 is that

disposition-pairs

are not

used

in

the

purest

fashion;

indeed,

a

simple

diatonicism would be

incompatible

with the

goals

of

maintaining

a flow

of sixths and

keeping

the

upper

strata

separate

as to content. In addition to

following

their

dispositions,

the first members of

the

pairs

1)

may

be retained from one

tetrad

to the

next;

2)

may

be

chromatically

modified,

thus

entering

into

a new

scale

and

dispositional

relationship;

3)

may

progress

to

a

chromatic

modifica-

tion of the

scale-degree they

are

disposed

towards,

in which

case the

latter

may

be

thought

of

as

having

been elided

(it

is

possible,

for

example,

to

imagine

a D-flat

between the

E-flat

and the D-natural

at

the

beginning

of the

top

stratum's

upper

voice);

and

4)

may

be

enharmonically

reinterpreted.

Having

taken

pains

to

show

the

ultimate diatonic basis of this

music,

we can

now

deal with the

bass

stratum

of

Example

7 in

a

more

sum-

mary

fashion.

It

is,

au

fond,

a

diatonic-circle-of-fifths

segment:

C-F-

B-flat-E-flat-A-flat-D-flat.

In a

local

sense

the

opening

A-flat

is

a

mediant-associate

of

the

C-F

fifth;

in a

long-range

sense it is the left-

hand

jaw

of

a

dominant

vise which

grips

the

bass line

as

a

whole,

except

for the final

PC.

The G-flat which

appears

under the

tetrad

at

m.

37

is,

like the

initial

A-flat,

a mediant-associate

of the

following

(augmented)

fifth. It completes the D-flat major collection in the bass stratum and

permits

notes

5

through

8 in

that

stratum

to act as a

sequence

of

notes

1

through

4. The

strange pentad

which

appears

in m. 47-a

chromatic

substitute

for

a

more

normal

harmony

with

E-flat

as the

root-has its

263


13/39

QN

TABLE 1

strongly disposed weakly disposed

i

--7

1

2-->3

-

4--3

6 -->


14/39

TABLE

2

2

natural-1

2

---

1

4

"

3

4----

3

D-flat:

B-flat:

5

5

5

5

7

-

flat-7

7

-

flat-7

2

-+

1

4

----

3

C:

flat-6

----

5

7

flat-7

2

-----1

4

---

3

F:

5

5

7--

flat-7

Note:

the

numbers

above

represent

scale-degrees

in

spite

of

the

omission

of carats.

The

tonal

reinterpretation

of a

tetrad

is

represented

by

vertical

alignment.

265


15/39

origins

in

the

logic

of the bass

line. With

E

double-flat

substituting

for

E-flat,

three

things

are

made

possible:

1)

a

pun,

the

interval B-flat-

E

double-flat

being

both

a

fifth and an

IC4

("sixth"); 2)

an

augmented

triad,

which ties in with other results

of

whole-tone-scale

patterning

in

the bass throughout the piece; and 3) an upper-leading-tone relationship

to

the

final bass-line

tonic,

which relates

enharmonically

to

the D-flat-

D-natural

and

C

sharp-D pairings

which

are

found

in

many places

(mm.

32-33,

m.

35,

m.

42).

If we

agree

to

understand all of

Example

7

(except

its

closing

chord)

as

a massive

dominant

prolongation representable by

a

copy

of either

its first

or

its

penultimate

chord-the two

being

identical-we

may

perhaps agree

to hear the

next-higher

level,

the

background,

as consist-

ing

of

that

copy

followed

by

the

closing chord,

in

the

manner

of

Example 8a. This seems at first a curious background to entertain, since

its

PC

voices all

move

by

"leap," contradicting

the

spirit

of the middle-

ground.

And

yet,

to

have

continued

in

that

spirit

by

allowing

the

dominant's tones to reach their

dispositional consequents

would

have

been

impossible:

we would have lost our final

tetrad

(Example

8b).

Nor

would

Example

8c

do;

its

upper

stratum

is

anti-dispositional.

It

might

occur to

someone

that

Example

8c is

"really" Example

8a with

a

content

exchange

between

strata,

as shown in

Example 8d,

but

it

seems

more

than

a little

forced to

"explain"

an

allegedly

basic

progres-

sion (8a) as a distortion (8d) of an incorrect one (8c).

What then are we to make

of

Example

8a?

At the risk of

appearing

to

be

resurrecting

and

trotting

into view much

nineteenth-century

theory,

grown

musty

with

neglect,

let us

try

out the notion

of the final

tetrad

as

neither

a

7th

chord

nor a

pair

of

sixths,

but as an

interlocking

of

D-flat

major

and

B-flat minor triads.

This

explanation

is

perhaps

not

entirely

removed from the

notion of

an

added-6th

chord,

but

is,

unlike

the

latter,

made to bear

the

weight

of

more

than a bit

of

foreground

fluff.

What we are

claiming,

in

effect,

is

that the

principles

which

govern

the

background differ essentially from those which determine the next-lower

level.

We

regard

the

tonic tetrad

as

having

two

potential

roots and as

being,

in

this

crucial

sense,

unlike

equivalent

tetrads

of

the

middle-

ground.

At

middleground

levels,

tetrads

of

type

(0,3,5,8)

have 5

as

their

only

possible

root

and act to

prepare

dominants

(e.g.,

the

principal

sonority

of mm.

10-11).

At the

background

level this tetrad

has two

possible

roots-the

5

and

the 8-and

it

falls to the

bass stratum

to

focus

on one of

these.

Consideration

of

Example

9 and of the

following

table

will

help

to

clarify

matters.

Example

9a

interprets

the

voice-leading

of

Example

8a as

deriving

from a

voice-leading

in which

there

are

no

leaps

(whole-note-

heads in

Example

9a).

This same

voice-leading

is

represented

in

letter

notation in the two

left

columns

of

Table 3.

There

are

two

aspects

of

266


16/39

a)

b)

c)

d)

--

-1

Example

8

G)

b) C)

-p4

--i

c)-------

_

_

_,,0

I

,

;OS LP; IF.

a

. Lr

E

_93

Example

9

267


17/39

TABLE

3

E

•-Rotation--

E-flat-

D-flat

B-flat

G-flat-

F

IC4

D-flat

)C3

B-flat scale-

-D-flat scale

A-flat-

A-flat

F

-

IC

)

IC2

IC3

-

C

B-flat

A-flat

268


18/39

this

proto-voice-leading

which

require

clarification.

In the

first

place,

it

is

inherently

bimodal: the

upper

voice

of

the

lower stratum

of

Example

9a

implies

D-flat

major

while

the lower voice

represents

a

disposition-

pair

in B-flat

minor;

the

voices of the

upper

stratum

correspond

to

disposition-pairs in either D-flat major or B-flat minor. The result is that

the

progression

as a whole

can

be

decomposed

into

two

sub-progressions,

one

of

which leads to a D-flat

major

triad and the

other,

to a B-flat minor

triad.

This

decomposition

is shown in both

Example

9a and

Table

3.

The

addition of a

bass-stratum

A-flat-D-flat,

(as

in

Example

8a)

to

Example

9a

supports

the

D-flat

voice-leading

and causes

it

to dominate

the

progression

as a whole. The

second

aspect

of

Example

9a

which

deserves our attention

is

its failure to

maintain sixths in both

strata. In

the

second chord of the

example

there is

a seventh

in the

lower stratum.

In view of our earlier discussion it would seem that this result is

appropriate

to a

foreground

progression

and

not to the

highest

level. As

a

way

of

getting

around

this

problem,

the

background

transforms the

second chord of

Example

9a

by

vertical

rotation. This

will be

readily

observed

in

Table 3.

The

third

column in the

table

is

simply

the

second

column

rotated down one

position. Example

8a is the result of

this

rotation,

and,

as is

evident,

the

sixths

of

both strata are maintained.

Examples

9b

and 9c show what

happens

when

the

bass

underlying

the

upper

strata of

Example

8a

is

changed.

In

each case

one

of

the

upper

tones is

chromatically

modified. The

results in

both

cases

are

tonicizations

of

B-flat

triads

with

undertones

of

D-flat

major.

The

effect is

less

unitary

in

Examples

b and c than

it

is

in

Example

a,

which

is

to

say

that the

secondary

scale

(D-flat)

is

less

well

accommodated in

the

coupling.

The 7ths

against

the

B-flats

in the

bass

(Examples

b

and

c)

are

undoubtedly

largely

responsible

for

this,

but one

must also

consider

the

cross-relation

in

Example

b and the

weaker

bass motion in

Example

c.

So

far

we

have

only

a

hypothetical

explanation

of

Example

8a

in

Example 9a,

and two

contrived

examples

in 9b and

9c. Does the

music

somehow

validate our

understanding

of

Example 8a,

and

does it cor-

roborate this

validation

by

incorporating

tonicizations which

are the

possibilities

implied

in

that

understanding,

those

represented

in

Exam-

ples

9b and

9c? The answer to both

questions

is

yes.

The

background

progression

makes its surface

appearance

as the work's final

cadence

in

mm.

54-59,

where

it is

elaborated in a

singular

way.

As shown in

Exam-

ple

10,

the

component

sixths

of

the

dominant tetrad are

once

again

temporally

skewed and

presented

in

conjunction

with elements

"more

in the foreground." The bimodal implications of the remarkable bell-

chord in

mm.

55-56 are

especially

evident.

It is clear

that

A-natural acts

as

a

leading

tone

to

B-flat;

its

presence

supplies

the

context

of

the final

cadence

with the

only

disposition-pair

of

B-flat minor

missing

from

Example

8a.

269


19/39

MI10

of

Bb

bO

Example

10

a)

b)

c)

mm.8-9

(V[)V.

VI

11

Example

11

-I-

p

Example

12

270


20/39

The

tonicizations

of

B-flat

triads

corresponding

to

Examples

9b

and

9c occur in

the

music

at

mm.

8-9 and

13-16,

respectively.

These

tonicizations are of

only

local

significance,

as befits

the

inconclusive

nature of these

progressions.

In

the

first

case the tonicized

B-flat

root

(m. 9) yields immediately to one a fifth lower, and is thus absorbed in

the

prevailing

D-flat context.

Example

11

accounts in three

stages

for

the

way

in which

the content of

Example

9b

is elaborated in

these

measures. The

relationship

between

Example

9c and mm. 13-16

is

not

as

clear,

but

only

because the

music uses a

foreground

voice-leading

(without

rotation)

like

that

of

Example

9a.

It

is

important

to

under-

stand

Example

12,

which

shows this

voice-leading,

as a

tonicization of

a

B-flat

triad

against

the

sustained fifth of

a

D-flat

triad,

and

not as

a

pitch-contrapuntal

elaboration of the V4

of

E-flat

minor such

as one

might find in Mozart. The fact that B-flat is to be heard as a local tonic,

and

not

(except

in

retrospect

at

m.

19)

as a dominant

of

E-flat,

emerges

most

clearly

from its

prolongation

in mm.

16-18,

where

the

diatonic

content

is

best

described as B-flat

quasi-Mixolydian.

This

wavering

between

a

prevailing

D-flat

tonality

and a

potentially

emergent

B-flat

tonality

conditions

the

first 20

measures of

"pour

les

Sixtes" in

so

obvious a manner

that

it

would

have been

tempting

to

dismiss it

as a

conventional

opposition

of

"relative"

keys.

Its source

is

not

convention,

however,

and

must be

located at the

very

background

of the work itself.

There

is a

symmetry

to the

thematic

plan

of

"pour

les

Sixtes"

which

is

perhaps

better

described

as a

concentricity.

The

larger

scheme

is

obviously tripartite,

with

an

expository

section

(mm.

1-20),

a

digres-

sion

(mm.

21-45),

and a

reprise

(mm.

46-59).

Moving

inwards,

one

can

see

that

the

digression

follows

a

ternary

plan:

A

(mm.

21-26),

B

(mm.

27-37),

A'

(mm.

38-45).

The

middle

section

exhibits a

similar

design:

a

(mm.

27-30),

b

(mm.

31-33),

a'

(mm.

34-37).

To the

extent

that one

perceives

"the

form"

as

just

presented,

m. 32

becomes

its

very

center. Two

possible

observations then

gain

in

significance:

1)

that a

fairly

straightforward

case

can

be

made for

performing

the

downbeat of

m. 32

as

the

dynamic

(or

accentual)

climax of

the middle

section

and,

perhaps,

of

the

whole

piece;

and

2)

that

the

harmony

of

m.

32,

a

polar

(tritone)

substitute for the

dominant

of

D-flat,

while

unique

to

the mid-

dle

section,

points

back

to

the

beginning

dominant and

forward

to

mm.

48-50,

where it

reappears

as

a

quasi-domninant-9th

over

flat-II

before

proceeding

to

the'closing

dominant.

There

is,

however,

something

which

opposes

the

neat

3-partness

of

the

middle

section: the

music

at m. 37 seems

to want

to return

to

the

beginning,

a

beginning

which,

to

be

sure,

would find

itself

a whole-tone

lower.

This

"urge"

is

signalled

by

the

not-quite-obvious

reappearance

of

the

opening

motive on

the

last

eighth

of m.

37.

(A

pronounced

271


21/39

ritard would create an

unmistakable

reference

to

m.

1.)

But this

is

only

the

tip

of an

iceberg

of

formal

ambiguity,

the true dimensions

of

which

are revealed

only

upon

further

study

of

Example

7. It shows that the

highest

middleground

level

progression underlying

mm. 37-54

is,

roughly speaking, a sequence of that which is the skeleton of mm. 1-23.

So the sense we

have

of

a

possible

thematic

return

at

m. 37 is the

result,

in

part,

of

an

extremely

deep

parallel

between

two

points

in the

music

(m.

1

and

m.

37).

A. The

Expository

Section

(mm.

1-20)

This section

is in

two

parts.

The

first

(mm. 1-6)

seems to

be

all of

a

piece;

in the

second

(mm.

7-20),

obvious and

not-so-obvious

features

conspire

to

suggest

a

major

division on the downbeat

of m.

16.

Example 13a is a model of PC counterpoint in mm. 1-6, which has

been alluded

to

previously.

The

symbols

used should now

be

familiar,

with

curved

arrows

signifying

disposition-pairing,

and

straight lines,

chro-

matic

modification.

Both notions are

applicable

at

various

levels.

These

various

levels are

indicated,

in the

simplest

possible way, by

a

hierarchy

of

note

values.

There

are

no

beams

or

slurs,

and

much

of

the other

paraphe-

nalia associated

with

Schenker-analysis

is

likewise

missing

for

the

reason

that

these

are

more

appropriate

to

a

model

of

multi-levelled

pitch-coun-

terpoint,

something

that

does not

concern

us

at the

moment.9

The bases for level-determination in a PC counterpoint, such as that

in

Example

13a,

should be

recalled

from the

previous

discussion:

the

primacy

of

tetrads

over

triads,

of "sixths" over

"sevenths,"

and of ascent

over

descent are

important

here.

Particularly

interesting

is

the

gradual

"loss of

depth"

in mm.

1-3,

after

which

there is a sudden

plunge

beneath

the surface.10

In

a conventional

D-flat

major context,

the

arrival

of the first

root-position

tonic

triad-considerably

delayed

and

harmonically

prepared-would

constitute

the

focal

point

of an initial

phrase.

Here

it

is the

last

outpost

on

a

cul-de-sac,

as

is evidenced

by

its

occurring on the "extra" beat of the only

I

measure in the immediate

environment.

Example

13b

shows

the actual

registral

disposition

of

the

upper

strata of

13a. It

suggests

that

this

disposition

may

have,

at

least,

three

functions:

one

is the establishment

of

long-range

identities

and

adja-

cencies

of

pitch;

the second

is the creation

of

large-scale

contours

which,

in

addition

to

establishing

their

own

dialect,

also

articulate,

at their

crests and

troughs

and other

junctures,

major

goals

along

the

music's

harmonic

path;

and

the third is

the

fashioning

of

correspondences

between the realms of

pitch

and

pitch-class,

so that

relatively

low-level

PC

connections

are

distinguished

in

yet

another

way

from those

at

higher

levels. Whereas

the

middle stratum

of

Example

13a

is

registrally

confined

in

Example

13b so

that its PC

voice-leading

is

interpreted

as a

272


22/39

m. 1 2 3 4 5

D

V

IV

V

I

(I)

F:

m

C:

w)

I

b)

.1

.

.

v..

9,-,01

Example

13

273


23/39

series of

pitch

adjacencies,

the

upper

stratum of 13a

migrates

through

much of

the

piano's range, executing

a

large

curve. Thus

the main

purpose

behind the

interpretation

of the middle

stratum seems

to

be

the establishment of

an

"obligatory

register"

in

which future

progress

on that stratum can be monitored (the first function mentioned above).

The

upper

stratum,

on

the

other

hand,

seems to

emphasize

the C in

m.

5,

this

being

the first time that a tetrad

root

has

appeared

in the

bass

part

(the

second

function).

A

particularly

fine

detail

is

the

registral

inter-

pretation

of

the

V-I

progression

in m. 3.

The simultaneous

appearances

of octave

shifts

in

both

strata,

which

give

the music

a

wayward

and

palpably problematic

quality

(enclosed

segment

in

Example

13b),

underline

the

atypical foreground

status of

this

progression

(the

third

function).

Other issues of interest in the first "phrase" are: 1) the motivic

independence

of

the

bass

part,

1)

the use

of

melodic

sequence

to articu-

late the succession

of

highest-middleground-level

tetrads,

and

3)

the

use

of diminution as a

summarizing technique.

The bass

part,

until it reaches the C

in m.

5,

is a

mere

extraction

from the

upper

strata

of

Example

13a.

It

pursues

its own

course,

alternating

IC's 3 and

2

to

produce

a chain with

overlapping

pentatonic

segments.

This chain is

artfully

broken at

m.

5

in

a

way

which leads to

its

being

taken

up

again,

in

transposition,

as the

broadly

conceived

top

voice of mm. 7-20 (Example 14).

There is an obvious motivic conformance

to mm. 1-2 in m.

4,

and

a

possible

conformance

to both

of

these

in m.

3.

Had m.

3

been written

as

Example

15a

suggests

it

might

have

been,

an

opening sequence

would

have

resulted,

and

this

would have

destroyed

the delicate effect

of

th'e

measure

as written.

On

the other

hand,

the

very real, though

hidden,

sequence

which connects

m.

4

to m.

5

should

not

be missed

(Example

15b).

Here

the

underlying

harmonies are

on the

same

level,

a common-

ality

which the

sequence

confirms.

As the bass

part

descends to an ornamental dominant at the end of

m. 5 in

preparation

for

the

recurrence

of m.

5

as m.

6,

the

upper

parts

engage

in a

preparatory gesture

which

compresses

into

one beat

a

cycle-

of-fifths

progression

of

IC3's,

reaching

back to the

A-natural/C

in m. 2

and the

D-natural/F

in

m.

4. These are

directly

tied

to

the

G-natural/

B-flat

in

mm.

5-6

(Example

16).

The

second

part

of

this

section

(mm.

7-20)

does not

easily

let

itself

be

understood.

As

a

first

step

it is

necessary

to

put

aside much

non-

sense

about

parallelism

and

"planing"

in

Impressionistic

music.

There is

only

so much "nonfunctional"

parallelism-i.e.,

parallelism

without PC-

contrapuntal

(harmonic)

significance-in

Debussy's music,

and

very

little

in the late works.

The

key

to the

passage

is

given

in

the

realization

that what

happens

in

mm. 7-20

represents

a lower level

of

happening

274


24/39

penrato:c -

co.itinugtiorn

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_.

,

[ missing

pentato

ic

chromatic

shift

presented

oas

m.

2

3

4

?

-

~m.

5-6

-

ec7dlntoher

chromatic

-

-

m.

7

8

10 12

16

-

18

18 19

Example

14

)

m. 1

possible

m.

3

•.-II

v

n.------

4' 1

l

missing

present

b)

m4

beco

me

s

At

i11

m.5•

01

nIK

Example

15

m.

2

m.

4

m. 5

mm.5-6

L e f

Example

16

275


25/39

than that which

transpires

in mm.

1-6

or at the

beginning

of the

in

poco

agitato.

A

simple way

to

grasp

this would

be

to notice the obvious

harmonic connection between m.

6

and m. 21

and,

what

is

more

strik-

ing,

the

obligatory-registral

connection between

G-natural/B-flat

in

mm. 5-6, the G-flat/B-flat in mm. 19-20, and the F/A-natural in

mm.

21-22.

What mm.

7-20

"do,"

in

effect,

is to

transform.the

tetrad

(C, E,

G,

B-flat)

in

mm. 5-6-a dominant-into

the

lower-level

pre-

dominant

tetrad

(C, E-flat, G-flat,

B-flat)

in mm. 19-20.

The

essential

(PC)

voice-leading

of this

"phrase,"

as seen

in

Example

17,

has

nothing

to do with

parallelism

in

the

small;

instead

it is

an

example

of

paralellism

writ

large

and

very

much in

the

grand

tradition;

that

is to

say,

it

is

an

example

of

sequence

But

it

is

a PC

sequence

of

which

we

speak

and,

as

such,

is

only superficially

like the

pitch-inter-

vallic pattern-chains of tonal foregrounds. As such it may be expressed

in

pitch

relationships

which

are

quite

remote from

parallelism

of

any

sort. What makes

it a

sequence

are

the

motions of its PC

voices,

and

these

can

only

be

discerned

from

a theoretical

point

of view.

The

last

two tetrads

in

Example

17 are bracketed

because

they

actually belong

to the middle section.

They

are, however,

intimately

tied

to,

and

even

"implied"

by,

the content of mm. 7-20.

We

will con-

sider the

example

at its terminal extremes and

move inwards.

The last

two tetrads are a

high-middleground-level

sequel

to

the tetrad

at m.

5.

They execute a tonicization of B-flat major. This tonicization is pre-

pared

by

the

pair

of tetrads

at mm. 16 and

19,

the first of which

acts as

a dominant to

the second.

The

voice-leading

between

m.

16 and

m. 19

is the same as that

found in

Example 8a,

the

"voice-leading-by-rotation"

which is a feature

of

the

background progression.

Each PC

in the tetrad

at

m.

16

"goes"

to the next lower

PC in the tetrad

at

m.

19

(e.g.,

F-*E-flat,

A-flat-oG-flat, etc.;

see

Example

17).

The result

is

a

tonici-

zation

of the E-flat

minor triad within

the

tetrad

at

m.

19,

which is

what

makes

the latter sound

so different from

its

"inversion"

at m.

12.

The C in the tetrad at m. 19 is its other possible root, unrealized

here,

which

relates

the

harmony

as a

whole to its

higher-level

source,

the

tetrad at

m.

5.

An

"R" inside a curved arrow is

used in

this and

subsequent

examples

to

indicate

voice-leading by

rotation.

The

four

tetrads

beginning

with

the

one in

m. 16 constitute

a

high-

level

pattern

which

is now imitated in

its

entirety

in

the tetrads of

mm.

8, 9, 10,

and 12.

The imitation

is at an interval

of

10,

so

that

B-flat

is

approached

in

m.

23 whereas A-flat

is

approached

in m. 12. The

charm

of this

anticipatory

imitation

lies

partly

in our

changing

per-

spective

of the

harmony

in

m.

12.

At m. 12

it

sounds

like a dominant:

we

imagine

that

a

strong

motion

to D-flat

is in

prospect.

At m.

23,

however,

the

A-flat of m. 12 is

understood

in

retrospect

as

a

peaceful

quasi-Mixolydian

7 in relation

to

the

B-flat

of m.

23,

and,

perhaps,

as

276


26/39

F

V

(D

Db

()

w

vi

Sb:

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U12 V I

Mixolydian

mojor-

minor

Example

17

m.

8

9

10

12

16

19

Example

18

277


27/39

a mediant-associate

of

the

C

(m.

5)

and

implied

F

(m. 21)

of

the bass

stratum.

The

juncture

between

the

two

pattern

statements-i.e.,

be-

tween m.

12 and

m.

16-is also

realized as a

voice-leading

by

rotation.

This allows us a more direct

experience

of

the "modal"

VII-I

relation-

ship, since the tetrad at m. 16 is, remarkably, a forerunner of that at

m.

23.

The

registral

interpretation

of

the

foregoing

is sketched

out

in

Example

18. The

upper

stratum

of

Example

17 is

shown in

Example

18

with

stems

descending,

and

the lower

stratum,

with

stems

ascending.

It is

immediately- apparent

that

the

sequential qualtities

of the

PC

model are

preserved

in the

interpretation.

Under the

first

curved

bracket

in

Example

18,

there is

a

descent

of both sixth-streams which

corresponds

to the first

pattern

statement in

Example

17.

This is

followed

by

a

general and pronounced ascent to the phrase's high-point, corresponding

to

the

juncture

between

pattern

statements and the

beginning

of

the

second

higher-level

statement.

Finally

there

is a

second,

expanded

descent,

corresponding

to

the second

pattern statement,

one

which

finds

its

way

to the

obligatory register

established

in

the first

phrase.

Two

masterly

details merit

mention.

Both derive from a

curious

anomaly

in

the

registration

of

the

A-flat/C

dyad

which

appears

in

the

upper

stratum

of

Example

17 at

m.

12.

In

Example

18 this

takes the

form

of a

widely-spaced

tenth instead of

a

sixth. As a

result,

A-flat

also

sounds like an

expression

of the bass

stratum,

and is

easily

associated

with the

low

C

in

m. 5.

(In

fact,

the

connection between the C

and the

A-flat

is made

explicit

in

the recall of the events

in

mm.

5-6 at the

end

of m.

12.)

We

have

already

noted

(see

Example

14)

how

the

long

descent

of

the

top-voice

in mm.

7-20

can be heard

as

a

continuation

of

the

bass

part

in

mm.

2-6 and as

returning

to

the

latter's

point

of

origin;

i.e.,

the

closing top-voice

interval of mm.

18-19,

B

double-flat-G-flat,

which

is

equivalent

to the A-natural-G-flat with

which

the

bass

part opens

in mm.

2-3. This return

happens

when a

truly

non-PC-functional tetrad

is inserted

on

the last

eighth

of

m. 18.

This

tetrad

originates

in a

strict

parallelism

with the

immediately succeeding

tetrad

(m. 19,

beat

1).

A

more

interesting

consequence

of

inserting

this tetrad

is

its relation

to

the

registration

of

the

tetrad

at

m.

12 where it

provides

the

second

basis

for that

registration.

In

Example

18

we can see

how

the

C at

m. 12

is

lifted above

the

descending

sixths of

the other

stratum.

This

enables

one to

hear a

melody

in sixths

(circled

in the

example)

which is

especially

prominent

in the

music. This

melody

is

an

augmentation

of the

opening

notes

of

the

piece.

The

insertion

of the

tetrad

at

m. 18

enables

the

bass

parts

to

echo

this

melody

as

the

section comes to

a close.

B.

The

Middle Section

Since

a

great

deal has

already

been

said

about

this stretch

of

music,

278


28/39

the

following

remarks

are

confined to a

commentary

on a

couple

of

particulars

and

a

glance

at two

analytical

sketches.

Measure 26

poses

an

interesting

question:

why

is

the third

beat

is

not

a literal

transposition

(up

a

minor

3rd)

of

the

third beat in m.

25.

Perhaps we ought to rephrase the question and ask why the third beat

of

m. 26

is

more

interesting

than it would be as a

literal

transposition.

One

might

answer

as

follows: m.

27

is the

beginning

of the

long

triadic

interruption

which

comes to

an

end with the

definitive

resumption

of

tetradicity

in

m. 37.

This

makes m. 37 the

"real" continuation

of

m. 26.

By

giving

us the

high B-flat,

which is a

whole-tone too

high

with

respect

to m.

25,

and

by

delaying

the

appearance

of

an

exposed,

sud-

denly-leapt-to

A-flat until m.

37,

the musical surface reinforces the

deeper

link between

these measures.

If one follows the progress of the bass stratum at a high middleground

level-from

the

C

in

m.

5,

through

the A-flat

in

m.

13,

to the B-flat in

m.

23-one

notices

an

accumulation

of tones which

begins

to

suggest

one of the

whole-tone scales.

Indeed,

the

suppression

of

F,

which

seems

to be

called

for

but which is

apparently

replaced

by

G-flat

in

m.

22,

intensifies

this

suggestion. By

m. 27

it becomes clear that an

analogy

is

being

made to

the

(C,

A-flat)

dyadic

root-alternation of the first

section;

i.e.,

that the

new section is balanced

in

a

similar

way

on

(B-flat,

G-

flat).

Completion

of

the

whole-tone collection

and

proliferation

of

its

elements at the musical surface happen together in the bass part of

mm.

27-30,

where

the

arpeggiation-space

between

the

root

of

the

G-flat

triad

and

its third is filled

in with

a

scalar descent in whole-tones.

This

passage

and

the measures

which

immediately

succeed it are

summarized in

Example

19.

Unlike the

models

presented

so

far,

Example

19

is a

voice-leading graph

and uses the

concept

of

arpeggiation

to

account for

a

structural

upper

voice

(in

mm.

27-31).

We should

note

that this

passage

is

syntactically

"inside-out" and

that

tetrads serve to

elaborate a

G-flat tonic triad.

In

the

context

of

an

essential

triadicity

and over a

span

of

only

a few

measures,

arpeggiation

as the essential

content of

an

upper

voice

seems

sufficiently

non-arbitrary.

Particularly

notable

in

Example

19

is the

shift from

D-flat to D-natural in m. 28.

As

far

as the

structural

upper

voice

is

concerned,

this

is

the

hinge

on

which

the

progression

from

G-flat

harmony

(m.

27)

to

B-flat

harmony

(m. 31)

turns. This shift

is

answered

by

its

retrograde

in

mm.

32-33.

Example

20

is a

three-part

sketch of

the

transition to the

reprise

(mm.

40-46).

The

meaning

of

this

magnificent

passage

becomes clear

only

after

it is

over;

i.e.,

when the

bass reaches

E

double-flat in

m.

48

and the

goal-harmony

of

m.

46-48

is attained.

As shown

in

Example

20a,

the

high-level

progression

from

m.

45 to

m.

48,

in which a

chord

occurs

that

might

be labelled

"vii07 over

flat-II"

in

D-flat

and

is

preceded

by

a

"dominant-9th"

on

VI,

serves as a

model for an earlier

279


29/39

Ob -15-T

-

-

0

I

whole

tonte

th-3pn

m

27

28

29

30

31

32 33

34

G6:

1

I

I

Example

19

a)

m

40

-41

42 45

46-48

7

b9

7

VJT7

Db =171

4

Example

20

280


30/39

b)

5

(assuming Blbass)

4

0:

M•/

c)

Oti

-

Ob --88V

"

m.40

42 43

44

45

46

281


31/39

progression,

in m.

42.

The

latter is the crucial event of

mm.

40-45;

it

is

a tonicization

of D

major

which

follows

upon

the

heels

of the toniciza-

tions

of B-flat

(m.

23),

G-flat

(m.

27),

and B-flat

(m.

40),

in all

of

which

the

local tonic is

used

as

a

bass

pedal.

The tonicization

of

D

major

implies the subsequent bass motion to D or, as the larger context would

have

it,

E

double-flat. The

disposition-pair

B-4A

(65

in

D)

in the

upper

voice

of the

upper

stratum in

Example

20a,

serves

to

motivate

the

enharmonically

equivalent-but

far-fetched in

a

voice-leading

sense-

C-flat

to B double-flat

of the

succeeding, higher-level prog

benjamin - 'pour les sixtes', an analysis

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