Berry Metric Rhythmic Articulation

8/11/2019 Berry Metric Rhythmic Articulation

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2/28

e t r i c

n d

hythmic

Articulation

in

M u s i c

Wallace

Berry

Thisdiscussion s ordered n three

parts:

irst,

I shall

dentify

certain

preconceptions

which

I

take as

points

of

departure,

hus

exposing

undamental ssues thatrecur

problematically

n stud-

ies

of

rhythm

and

meter;

a second

segment

brings

ome

of these

issues

into focus

by

analysis

of

two

pieces,

both

widely

treated

in

analytical

studies;

and

finally

I

shall list in

summary

certain

propositions

o which

I

am led.

Underlyingassumptions.

I

conceive

rhythm

as the articula-

tion

of time

by

events of a

particular

class.

In

thus

suggesting

that there

are

many interacting

or

cohering

streams

of

rhythm

in

any

ndividual

tructure,

one

acknowledges

as well some ulti-

mate

rhythmic omposite

of all events in all

operable

elements,

one

that

must

typically

be,

in

interesting

pieces,

a

rhythm

of be-

wilderingcomplexity.

Meter I

regard

as such

a

punctuation

of

time

by

events of

the

classification"accent."

Without

going

further

in this

prelimi-

nary

context,

I refer to a few bars from

Haydn

(Ex.

1)

in illus-

tration

of

a

patently

unequivocal

series of

accents,

points

of ar-

ticulative

exposure

at a

particular

evel of

structure,

by

virtueof

intrinsiccontextual

properties.

Later

I

shall refer to a further

aspect

of

meter,

one to which I ascribe

mperative

ignificance:

the interactiveassociation

of

disparateyet functionally

nterde-

pendent

impulses.

The

problem of

accent.

With

respect

to

bar-line

meter,

that

palpable

recurrent

articulation,

what

specific

actors

determine

a sense of

grouping?

n

Example

2,

we can observe

that

the

first

Example

1.

Haydn,

Sonata

n D

Major,

H.XVI, 37,

Finale

A..

Presto, ma non troppo

pa

r^^J

I

M?

r

A

F

It

9

U-1 * *ri

L^

1-

A

6:

.

*

W,

4 i

-

n

-

,-

I

'I

Accents

f

pitch,

duration,

issonance,

nacrusis

measure

s marked

by

a melodic

impulse

underscored

by

tex-

ture,

relatively

high

pitch,

duration,

and also

by

its

approach

through

a

leaped

anacrusis.

The

upbeat

substantiates he bar-

line

accent,

as we

might

demonstrate

by

the reverse conse-

quence

of

leaving

t

out.)

I

shall

argue

that

harmonic

rhythm

s,

like

motivic

and other

rhythms,

often concurrentwith

meter,

yet

a distinctmode

of

articulationat

times

subtly opposed,

as

here

at

mm.

5-6.

The

question

of accent

can

furtherbe stated:

In

the metric

unit,

what

does "one"-the

"one" of

counting-signify?

(Riemann's

term

Hervortreten,

a

"stepping

forth,"

is

sugges-

tive.

Moreover,

merged

arrival

and

departure,

n fulfillmentof

anacrusis

nd

the

thrustof

downbeat

mpetus,

is an

apt

conceit

by

whichto characterize

many

notated

measure

beginnings.)

If

"one" in the metric unit is to be

defined as

a

relativelystrong

impulse,

there follows

of

course the

difficult ssue of criteria

of


3/28

8

Music

Theory

Spectrum

Example

2.

Chopin,

Prelude

in

E

Minor,

op.

28,

no.

4,

mm.

1-6

Accents

of durationand anacrusis

throughout]

and

pitch [m. 1];

bass

changes usually complementary

and

corroborative

[but

see mm.

4-5]. At right, meter in its periodic aspect as a levelled systemof

beats

and

amplified

beats

(four

levels functional

n

this

context); rep-

resented are

superficial

and

deeper

units of

analogous

strong-weak

determinantsand content.

0o o0

r r r

r

rr

*

WII

*The east articulate

grouping

as

to accent

accentual

projection:

presumably

these criteria

have to do with

such

properties

as

longer, higher,

more

this,

more

that.'

The question of accent returns in this study, and I do not pur-

sue

it here

except

to note the

obvious

factors of its

importance

and

complexity,

while

drawing

attention

to

a

few

patently

evi-

dent criteria.

Clearly

we need to

know

more about the

experi-

ence of accent as a determinant

of

grouping.

Tonal

function

and accent.

Does I in tonal

music

denote

"weight"-accent

in some

sense,

as

often assumed?

My

view

is

that the obvious

primacy

of I in

tonal

structures must not be

confused

with

its variable metric

import.

Theoretical consider-

ation of this issue has been, I believe, much influenced by early

studies

of Edward T. Cone

and

Roger

Sessions,

who view the

cadence

as an accent of some kind.

Both

discuss

a

number of

types

of "accent" or

"downbeat,"

including

for

Sessions

an

'See

the author's

Structural

unctions

n

Music

New

York:

Dover

Publica-

tions,

in

press), chap.

3;

see also William

Benjamin,

"A

Theory

of

Musical

Me-

ter,"

Music

Perception

1,

no.

4

(1984):355-413,

which

includes

a

substantial

and

mportant

discussion

of

criteria or

accent

(especiallypp. 358-71).

"accent

of

weight"

characterized as "the

principal rhythmic

accent

[emphasis

added],

which

corresponds

with the

end

of a

musical 'phrase,'

"2

and for Cone a comparable phenomenon:

"By

structural

downbeat,.

. . I

mean ...

phenomena

like

the

articulation

by

which the

cadential chord of a

phrase

is iden-

tified,

the

weight by

which the second

phrase

of a

period

is felt

as

resolving

the first."

(Here

the

association of

"weight"

and

tonic is

explicit.)

And later

in

the

same

paper,

"the cadence is

the

point

in

the

phrase

at which

rhythmic emphasis

[again,

my

italics]

and harmonic function

coincide."3 I

acknowledge

that

2HarmonicPractice

New

York:

Harcourt,

Brace&

Co.,

1951),

83.

3"AnalysisToday,"

Musical

Quarterly

46,

no. 2

(1960):182-83.

In this

early,

seminal

study,

Cone

notes

(p.

185)

in connection with his characteriza-

tion

of

Stravinsky

s

a

"downbeat"

omposer

hat an

exception

can

be found

n

the

end-of-phrase

accent

(by

mode

change

and

orchestration)

on

the word

Dominum at

the

beginning

of

the final

movement of the

Symphony

of

Psalms.

This seems to me

significantly

o

qualify

the viewof accentual

weight

nherent

in the

cadential action

itself,

since

here Cone is

citing specific properties

of

a

particular

adential

event

independent

of

its tonal function.


4/28

Metric nd

Rhythmic

rticulationn Music 9

Cone and

Sessions,

in these

distant and

tentative

studies,

are

thinkingof accent n senses different romthat of mymetric ni-

tiative,

yet

terms such

as

Cone's

"rhythmic mphasis"

presum-

ably

denote

something

of metric

consequence.

Example

3 makes the

point

thateither

barring

s

plausible,

depending

on

properties

of

events

other

than their

tonal

posi-

tions and functions. It is

notable

that the

version

having

agogic

accents

on

dissonances s in

general

effect

more "active."

The issue of relation

between

accentual

weight

and tonal

function s the

subject

of a

recent

study

by

William

Caplin

enti-

tled "TonalFunction and MetricalAccent: A Historical Per-

spective."4

n an

interesting

observation,

Caplin

ndicates

that

Hugo

Riemann

appears

o

depart

from

the view of

tonic

as im-

plying

metricaccent n

citing

examples

nwhich

dynamic

accent

on

harmonic

dissonance

seemingly

contradicts he bar

line,

al-

Example

3

i)

I

J

I

:r:

r

r

?

y-

r

f

rIt(l

f

though

as

Caplin

points

out Riemann

doesnot follow this

to the

conclusion hatmeter is thusdisrupted.Caplin'sreferencehere

is to

Riemann's

treatise Musikalische

Dynamik

und

Agogik,

fromwhichI

quote

(in

my translation);

Riemann s

commenting

on

performance

requirements

rather than

meter,

but I

shall

want to extend

the

import

of his

commentary

oncerning

his ci-

tationfrom

Beethoven's

Op.

31,

No.

1,

my

Example

4:

The

progression

ut of a

consonant hord nto

a dissonant

ne re-

quires stronger

xecution f

the

atter,

while

he resolutionf a dis-

sonance

s

always

a

negative

ormulation,

he releaseof

conflict,

a

turning ack,andtherefore asclaim o a diminuendonperform-

ance.

Comparemy

uses,

n

comparable

ircumstances,

f theterms

"progression"rom

I and

"recession"o

I.]

When n the next-last

timeunit n less

emphasized

motivesor

phrases

dissonance

ccurs

whichs resolvedn the

ultimateime

unit,

he

dynamic igh

point

will

almost

lways

e

displaced

rom he latter o the

former.5

The

sforzando

(Ex.

4)

is

Beethoven's,

the

clearly

nevitable

crescendo-decrescendo

arkings

Riemann's.

Riemann

appears

quitecontentthat the natural onic"accent" ntowhichthe dis-

sonance resolves

(in

his

"negative"

formulation)

is

unmo-

lested. But I

should

argue

that,

while it

would be

absurd o

sug-

gest

that at

this 57th

measure of the

movement

the

firmly

preconditioned

bar line

is

displaced,

something "metrically"

Example

.

Beethoven,

Sonata n G

Major,

p.

31,

no.

1,

2

5Musikalische

ynamik

undAgogik

(Hamburg:

D.

Rahter,

1884),

187-88.

InMusic

Theory

Spectrum

5

(1983):1

14.


5/28

10

Music

Theory

Spectrum

active

happens:

he bar

line

"wobbles"a

bit in a

circumstance,

to which s accountablemuch of the vitalityof classicalrhetoric

at

even the

most

explicit

mensural

evels,

of

subtle,

veiled coun-

teraction

to

the

prevailing

meter,

the tonic

notwithstanding.

The fluctuant

accent

is one of

loudness,

pitch, supportive

ana-

crusis,

and

dissonance;

it is

independent

of tonal function

as

such.

(It

is notable

that,

in

the Beethoven

example, implica-

tionsof

duple

grouping

ollow the

quoted

bars.)

Internal

tructure

of

the

metric

unit.

The

periodic aspect

of

metric

structure

s best

conceived

as an inflated

pulsation,

and

what is especiallyinterestingabout meter is the associationof

interactive

mpulses

within a

dynamic,

articulate

metric unit

structured

as

an

integrated pattern

of

organically

nterfunc-

tional

endencies.

This is

the

aspect

of meter

which s extensible

hierarchically,

and which

is

vitally

functional

and not

merely

referential.

Music's

animate

substance s accountable

n

signifi-

cant

part

to this

property

of

meter,

in contrast o

that

aspect

of

meter

which

is a

rigidly

inanimate,

referential,

periodicity

of

levelled

pulsation.

Elsewhere, I have discussed what I refer to as the "func-

tions"

of

interdependent

mpulses

which

comprise

the metric

unit,

in an interrelation

of actions

to and

from

whichaccounts

for what

is

organic

and

dynamic

n metric structure.6These

in-

terrelations,

ike

those

of tonal

functions,

are a

necessary

ele-

ment

in

what we sense as

flow,

surge,

and ebb

in

music,

as is the

often

applicable

directed

stream of

broadening

or

declining,

thus

processive,

temporal

ntervals

of metric articulation.

Figure

1 is

a

portrayal

of the internalstructure

of

the metric

unit, viewed as an abstraction.Of the characteristicmpulses

only

the

initiative,

or

downbeat,

is a

point

of action-

Riemann's

Hervortreten,

n accentual

hrust,

a

discharge

of

en-

ergy,

so

to

speak.

The other functional

mpulses

are

currents,

typically

comprised

of

lower-level

attacks:the

anticipative

o,

the

reactive

rom,

and

the conclusive

final

dispersal

of the

ini-

6Structural

unctions,

326-34.

Figure

1

(a)

(b)

>(

(a)

metric

nitiative

ccent;

downbeat

(b)

reactive

mpulse

rom;

afterbeat(s)

(c) anticipative

mpulse

o; anacrusis,

pbeat(s)

(d)

conclusive

final

eactive)

mpulse

tiative

accentwith

which the metric unit

begins.

Metricunits

n

course,

at

a

particular

evel,

typically

conclude

with renewed

tendency

towardthe

subsequent

accent,

as we know

so well

from

experience.

Essential

for

me, then,

is the metric

gestalt

(pattern, shape,

image)

as a

central

actor

of

definition,

as a

compelling

ocus

of

interest,

and as a

conditionerof

grouping

distinguishable

rom

all others.

Carl Schachter'sstipulationsabout meter do not substan-

tially

intersect

with

mine,

but he does

discuss tonal

rhythms

both as

to

durational

partitioning

nd as to animate

tendencies

(akin presumably

o Riemann's

"positive"

and

"negative")

of

tonal

functions-in

a

system

of

organic

content

comparable

o,

but

different

rom,

meter. As Iunderstand

him,

Schachter

ees,

in addition

o

"rhythmic

mplications

of tonal

repetition

and

as-

sociation,"

a further

rhythmicaspect

"in the tonal

system,

the


6/28

Metricnd

Rhythmic

rticulationn Music

11

turning point

[i.e.,

where motion from becomes motion

to-

ward]"ashaving "rhythmicmplications" f one kind.7

Further

o

my

point,

I

like

Schachter's ater

qualification

f

meter

as two

things:

"When

we

speak

of

'meter' we

normally

mean

something

more than the divisionof time into

equal (or

equivalent)

segments;

we mean a

pattern

composed

of

strong

and weak

impulses

n some kind of

regular

alternation."8

The two

aspects

of

meter

which I deem

definitive are thus

pertinent

also to other

rhythmic

groupings-manifestly

to those

of tonal

harmony;

and

they

tell

us

something

about ancient

per-

ceptionsof music asbothcontinuousandpunctuatedby contig-

uous events.9

Periodicity

and

luctuation

n

foreground

(bar-line)

meters.

I

have

questioned

he

assumption

hatmeter's

aspect

of

temporal

punctuation-for

me,

accent to

accent-is

necessarily

one of

regularity

ven at the level of the barline. I return o

Chopin's

Op.

28,

No.

4,

where metric

periodicity

s in

this sense a series of

"amplified

beats" at

a

numberof

levels-an inflationof funda-

mental

periodic

pulsation,

imperatively

eferential,

yet

in itself

powerfullyuninteresting. nExample2, I listsomeapparentac-

centual conditions

by

which

the notated meter is

articulated,

and a

representation

f

levels of

pulsation

n

a scale

of

operative

beats

discernible n the

piece,

the

bar-linemeter

simply

one

of

these.

(That

of

whole-note

beats,

expressing

meter at the level

of the

phrase,

comes

uplater.)

Example

4,

on

the

other

hand,

suggests

luctuations n a kind

7"Rhythm

nd Linear

Analysis:

A

PreliminaryStudy,"

TheMusicForum

4

(1976):314.

8"Rhythm

nd Linear

Analysis:

Durational

Reduction,"

TheMusic Forum

5

(1980):231.

9See

Lewis

Rowell,

"The

Subconscious

Language

of Musical

Time,"

Music

Theory

Spectrum

1

(1979):96-106.

In this

study

Rowell

observes that "one

central

problem

s this: how

can we

reconcile musical

continuity, perceived

as

motion,

with

music's

pulsating

tructure

of

beats

.. ?"

He

refers

n this

regard

to

ancient Chinese

views

of

experienced

time as

both "continuous and com-

partmentalized" p.

98).

of

half-relief.

More extreme situationsreveal accent-delineated

groups n mobile contextsdeliberatelyopposedto the notated

bar

ine,

commonly

with a

subsequent

process

of

resolutive

en-

dency

toward reclarification

f an

establishedorder.

In

Exam-

ple

5 there

s such

opposition

at the

beginning,

ollowed

by

fluc-

tuation

towardaffirmation

f the

notated

bar

line and meter at

m. 5.

My reading nterprets

mm. 1-3 as

periodic

n

meter,

not in

accord

with the

signature,

with

a

slightly

extended

grouping

n

m. 4

"modulating"

oward he bar-line

accent

of

m. 5.

(There

s

immediate fluctuation again.) Through much of the piece,

Example

5.

Chopin,

Prelude

in D

Major,

op.

28,

no.

5,

mm.

1-5

Allegro

molto

A Li

I

II

I

1 1

Ir1j'

I I I I

-

-

A-

t

I

;\

',

',

s

2

Accents

f

duration,

pitch),

articulative

tress,dissonance;

orrobo-

rative

motive

grouping.

*Decelerative

ffect

of 5-unit.

Ij

I.

I

j_

-

ii~_


7/28

12

Music

Theory

Spectrum

counteractive

accents-the initial

2-grouping

and

subsequent

fluctuations-prevailso generally hat it maybe doubted there

is

any appreciable

metricstandard

at

all,

although

here is a de-

cisive,

finally

resolutive

accordwith the notated bar line four

bars

before

the end.

I have come

to

believe

that circumstances

of this

kind,

often

having

a dimmer

experiencedreality

n rela-

tion to a

determinate

preconditioning

meter

(as

in Ex.

4),

are

common,

and

often a basis

for animate

structure,

vitally mpor-

tantto understand

n

performance.

Since I take accent

o be the

defining

metric

determinant,

do not consider hat meter

s sus-

pendedorinterruptedn such mobile contexts.

Processive

metric

fluctuation;

metric

dissonance. Where the

bar-linemeter s

fluctuant,

what can

we

hypothesizeconcerning

resultant

unctional,

expressive processes?

By processive

fluc-

tuationI mean that of deliberate directedness:units getting

longer

or

shorter,

n

palpable

effects of

retardation nd acceler-

ation,

the former

or

example

as an

aspect

of

cadential

endency

and the latter

of

development,

at

whatever evel and on what-

everscale. Let us consider

Example

6,

often cited in studies of

meter.

If Mozart's

sforzato, "dynamic"

accents

project

an

ap-

preciable

countermeter,

n

half-relief,

and if

my reading

can be

taken as

legitimate,

the fluctuation s

processive

n that the 6-

unit,

following

two

asymmetrical

-units,

is cadential-that

is,

retardativemetrically-and supportiveof cadential unctionex-

pressedtonally by approach

o the

Bb:V

and

thematicallyby

subsequent esumption

of

the fluctuantmotive.

By

the same to-

Example

6.

Mozart,

Piano

Quartet

n

G

Minor,

K.

478,

1

54

-

-_

___ '______

RFp~

bb

e

11

}

P J -

ipw

JI

)- L

.

-

I

I I

I

I

jj

I

I

-

Area

of metric fluctuation

against preconditioned

basis:

accents

of

pitch,

sforzato

ar-

ticulation,

duration.

LU4~4~~

~

~rr-

V1

{f

PP

K4rNJIr

2

*

4. rJJJjJJ

-

If-

r

(f P

dP

(f

p-

P

sf

p

,f

p

If

ipf//

sf'

jp

(>J>S J- ?.:

~2

c tJ'-

-~

A

r..-

a.

MM_~_~6iL-r;

'

(6-unit

of

5-5-6

fluctuation

is functional

in

ten-

tative

m. 61

cadence,

complementing upper-

voice

descent.)

IF

'ri

'ir-

li

5

r

I I

6

5

I

5


8/28

Metric

nd

Rhythmic

rticulationn

Music

13

ken,

that

resumption

restores

developmental

process

n the re-

verse

juxtaposition

6-5,

an

acceleration. I

believe that

music,

even of

apparent

metric

uniformity,

s

replete

with such condi-

tions

of

comparably

ordered

processive

tendency

to and from

relatively

active or

resolutive

states.

Such

mobility

in the bar-

line

meter

comprises

a

factor

of,

so to

speak,

"dissonance"

within the metric

element,

an

aspect

of

development

comple-

mentary

o that

of tonal

fluctuation,

and

subject

to

appreciable

tendenciesof resolution.

(See

Exx.

4, 5, 7,

and

9.)

The true nat-

ure of metric luctuation

ommonly

depends

on

subtletiesof in-

flection

n

performance.

Preconditioning

n the

experience

of

metric

luctuation.

How

decisive

might

preconditioning

be with

respect

to

metric fluc-

tuations n a

particular

ontext?In

Example

5,

referentialmeter

is itself of some

uncertainty.Example

7

is,

on

the other

hand,

like

Examples

4

and

6,

more

characteristic f

tonal

music:met-

ric

anomaly

n a

perspective

of

well-preconditioned

grouping,

noncongruent

meter in

half-relief,

experienced

against

a clear

preconditioned

standard,

subtly

expressive

of

mobility

if the

performer

does not

extinguish

t

by

overtresistance.These

ex-

amples

hus

pose

no real

questions

of

fundamentalmetric

orien-

tation;

events

momentarily"tug"

at

the bar

line one

way

or an-

other

and it is

promptly

reaffirmed.

Example

7.

Bach[?],

Prelude n

C

Major

for

Organ,

BWV567

r

m. 10

Yet there

are times

when

compositional

ntent is an

expres-

sion of

metric

ambiguity,

as

in

Example

5,

or in

the Beethoven

theme

quoted

in

part

as

Example

8 and

occurring

n Der

freie

Satz as an

instance of

Schenker's "antimetric

rhythmic

situa-

tions"

(the

Oster

translation).

Schenkercomments:"The form

of the

opening

is

boldly

maintained

throughout

the

entire

theme

and even in the variations.

Hence,

performers

nd isten-

ers alike tend to confuse the

upbeats

with

downbeats."10

The meter's

2-grouping

s

resolutely

clear,

but its

placement

as to the bar line is confused

by

the motive's

descending

hird

against

unmoving

ower voices. I should

differ with Schenker's

commentthat this state

prevailsthroughout,

or as the motive

1?Free

omposition,

rans. Ernst

Oster

(New

York:

Longman, 1979),

123,

concerning ig.

146,

ex.

4.

Example

8.

Beethoven,

Quartet

n

E-flat

Major,

op.

74,

4

Allegretto

con

variazioni

3

,,

r

5

T

._ ..,

10

N-

^

_ V

cresc.

/

-AY.

li

"-

-?

L 1

--

-

PH

cresc.

17 _ --

-

I I

If

I

I

I

I

p

f

cresc.


9/28


10/28

Metric

and

Rhythmic

Articulation

n Music 15

Example

10.

Haydn,

Sonata in C

Major,

H.

XVI,

35,

2

Adagio

-i

7

S^~

.e-1t

----r

r

entire

first

phrase

(mm.

1-4),

and it is the

essential basis for

mm.

1-13,

after

which hethemeresumes.While thedissonantdominantcan of course unction

accentually,

t

is not

tonal function tself that effects metric

mpulse

n the ambi-

guity

of the

foreground.

The

displaced

accent that we sense from the outset

is

attributable

o

other

factors. I

agree

with the

analysis

of

this

passageby

Ben-

jamin (op.

cit.,

370),

whom

I

quote:

"If one

were to think

of

the first three

measures...

in terms of

group

[i.e.,

motivicjstructure,

and

without

regard

o

accent,

one

might

hear the terminalsilence of each measureas an

independent

'null'

group

and ... end

up

with

6

meter.

That one is little inclined o

do

this

is

the result

of two

factors:

The first is another kind

of

grouping,

the so-called

harmonic

hythm,

which

pulls together

events

across he terminal ilences

...;

and

the

second,

and

more

important,

s the

succession

of

time-spans

between

attackswhich, disregarding he sixteenth note in m. 2, is 1,2,1,2,1,2, etc.,

which

puts

an

(unrealized)

accent

of length

on

the

second beats of notated mea-

sures. Taken

together,

these factors

substantiate

a

3

meter the measures

of

which

begin

on the

second

beats

of those

actually

notated."

(Italics mine.)

I

should

put

this

only slightlydifferently,

to

say

that the

"displaced"

meter

of

agogic

accents

(and

of

dissonance,

and

initially

of

pitch)

happens

here to coin-

cide with

harmonic

hythm

and

is fortified

hereby.

The

consequent

phrase

s

a

resolution

in which notated first beats

are

accented:

points

of

exposure

are

placed

clarifyingly

t the bar ines.

Example

11.

Beethoven,

Sonata

in

E-flat

Major,

op.

7,

2

Largo,

con

gran

espressione

r

F

,

, :

,

I

-

'-'

r

r


11/28

16 Music

TheorySpectrum

The critical ssue

of

tonal structureas a

rhythmic

determi-

nant comesupin extensobelow, especiallyas to theproblemof

deep

tonal structure

and

durational

partitioning,

and

the fre-

quent

misconstruction

f such broad

structureas a

background

"meter."

Metric tructure

t

underlying

evels. Does

meter

have mani-

festationsover

larger spans,

at

more basic levels?

And,

if

so,

must

not the

properties

by

which such

encompassing

units are

articulated

be

analogous

to those of

relatively

superficial

ev-

els?

Most

theorists,

I

believe,

would

acknowledge grouping

analogous o that of the shallow mensuralunitextending o the

phrase;beyond

that

things

become

increasinglyproblematic.

Example

2 is a suitable

passing

llustration:

he first

mpulse

is

putatively

he

point

of

primary

accent

(the

accentual

nitiator)

for

each four-measure

unit,

and this

principleapplies

also to the

overalltwelve-measure

phrase.

How far

might

the

principle

extend in a

hierarchy

of accen-

tual values?

Might

that further

aspect

of meter which

I have re-

ferred

to

as an

integrative

metric

gestalt apply

to

broad,

even

comprehensive,unitsof structure?One hang-up n the consid-

eration

of meter

at

deeper

levels is the

assumption

hat meter

is,

by

definition,

periodic,

a bias that

is,

I

have

argued,

of

doubtful

usefulness

in

characterizing many

surface metric

structures,

and

increasingly

questionable

at

phrase-

and,

to be

sure,

at

deeper

levels.

My

sense of meter as to

commonly

fluc-

tuant

attributesat all

levels,

and as to an internal tructural sso-

ciation

of impulse-tendencies,

ismisses

the

bindingconcept

of

meter

as

merely

an

amplified

beat,

a referential

pulsation

appli-

cableto relativelyshallow evels of metric

unction.12

I

shall

not labor the

issue of

deep-level

accentual

implica-

tion,

sinceit comes

up

in both of the

subjects

of

detailed

analy-

'2While

he termsof reference

are

of

course his

own,

Benjamin's

discussion

(op.

cit.,

410)

of the

first21 measures

of the second movementof Mozart'sSo-

nata

K. 330 is

pertinent

here:

as to meter

in

relation to other

grouping

modes,

and as

to accentual

grouping

unctions

at

underlying

evels of structure.

sis which

I shall take

up

presently.13

t is

perhaps

sufficient

o

note herethatmyview of encompassingmetricstructureneces-

sarily

ascribes

particular mportance

to the

organic aspect

of

meter

as an association

of

interfunctional vents.

Indeed,

the

issue

of

periodicity

obviously

loses all

relevance as one

pene-

trates a structure

to

regard increasingly

few units

and,

ulti-

mately,

a

single encompassinggestalt.

Conceiving

meter as an

organic

array

of interactive events within the metric unit at

whatever

evel,

and

not

merely

as

a

stream of marked

pulsa-

tions

(periodic

or

otherwise),

I find

altogether plausible

the

conceptof a totallyoverreachingmetricgroupingdescribinga

broad course of

directed,

dynamic

organization.

I shall draw

this

point

further

n

analysis

of the two

major

examples

which

follow.

I now turn

to two

C-majorkeyboard

preludes

n

analysis

di-

rected

to a number

of the concernsdetailed above. These

prel-

udes are the

firstof Bach's

Well-

Tempered

Clavier

and of

Chop-

in's

Op.

28,

both

endlessly

revealing

of subtleties

and

perplexitiesof structuredespitetheirguileless appearances.

Some

of

the

rhythms f

the

Chopin

Prelude.Of the

Chopin,

I

ask

by way

of introduction

what its

rhythms

are,

considering

that its

rhythmicanalysis

s a

quest

for

understanding

f those

articulations

and

consequent

groupings by

which the

piece's

time is

partitioned

withineach

functioning

element.

A

rhyth-

mic

partition

might

be:

of

one

thing

(e.g.,

tonic

prevalence,

a

particular

egistralplacement,

a

phrase);

or

an

area

offluctua-

tion

from

one

state to

another,

unified in a

binding

processive

tendency(say, a crescendo,or graduatedchange n tempo).

Seeking

to

identify

such

cofunctioningrhythms,

one sees

at

once what an

intricate

paradigm

s a

piece's

inclusive

hythm:

f

the absolute

surface,

the

composite

of all

foreground

attacks;

13A

pertinent

supplementary

eference

s

my analysis

of

Bach's

Little

Prel-

ude

in D

Minor,

in

"Dialogue

and

Monologue

in the Professional

Commu-

nity,"

College

Music

Symposium

21,

no. 2

(1981):92-97.


12/28

Metric

and

Rhythmic

Articulation

n

Music

17

Example

12.

Chopin,

Prelude

in

C

Major,

op.

28,

no. 1

Agitato

nA --

3

___C_

~

C

j1S

u

L

L

q

L

UFL

.

5

-t3 r

-

g

r

'1A

(n

-

=-

-E

--

-

_

I^

r

4t 1

IlII

i

0 O -

Pt

*

='

'7

*

a.

*

U%.

*

,

*

q>.

*

I(

i

i

J

It

-

=-

r,5

.J

?-

.

'.-

-

- -

-

.

-

-? - --

stretto-

3

.....

*

.

*

',e'b.

*

*

.

*

.

..

e.

*

te.

?


13/28

18 Music

TheorySpectrum

of individual

lines

or

voices;

of

tempo

and modulationsof

tempo;of unitiesand fluctuations ndynamic ntensity;of fore-

ground

harmonic

changes;

of

underlying

harmonic

content;

of

broad

registral

unities

(for

example,

that

linking

the

e2

of

m.

7

to that

of m.

16);

of

form-motives,

phrases, periods;

of low-

level

metric

units;

of

such

higher

metric orders

as

may

be

in-

ferred;

of areas

of acceleration

and deceleration

(other

than

of

metronomic

empo)-as,

for

example,

in harmonic

rhythm;

of

formal

processes-for

example,

cadential

or

developmental;

of

paths

of

melodic descent

and

ascent

as

opposed

to areas of

actionmore-or-less n place (as in the piece's beginningthree

bars,

or

its

conclusion).

I am sure that these are

only

some

of

the

rhythms

of

the

Prelude-segments

identifiable

as to actions

of

particular

inds-which can

be adduced n

theory

and

appre-

hended in

experience.

Surface

meter.

I wish to

consider a

few

of

these

rhythms

which

are

especially

interesting

and

problematic,

beginning

with surface

meter,

that of the notated

measure.

One

agitato

as-

pect

of

foreground

rhythmic

grouping

s

the

apparent

displace-

mentof the upper-voicemelody in relation to the barline and

initiating

bass

articulation,

and in relation to surfaceharmonic

rhythm.

That

melody, momentarily

table

on

g

(or

g ),

can be

interpreted

as in the

register

of the

right-hand

humb

or,

on the

other

hand,

n the

uppermost

register.

Insistingagain

on distinc-

tion between

harmonic

rhythm

and

(accentually

articulated)

meter as two

rhythms,

however

they

may

coact or

interact,

one

can see

that there are conflictsbetween harmonic

rhythm14

nd

metric

structure

n either melodic

placement,

the latter

dis-

placed by a half bar or tripletsixteenth note. The performer

who stressesthe

initiating

bass note of

each measure

n

the

in-

terest

of

"clarifying"

he situationmisses the

point.

14Conventional

armonic

rhythm

n the Prelude

might

be

represented

as to

changes

in bass

pitch

classes,

where

it is a

regular

rhythm

held back

only

at

points

of cadential

retardation,

or as to

changes

in bass

pitches,

where

it has

perfect

regularity

up

to the

concluding

pedal.

Either

is

largely

a

referential,

periodic, amplifiedpulsation

which

coincides

with the bar

ine.

In

the

activity

of the

right-hand

humb,

there is functional

contrast between occurrences at the bar line (mm. 18-20,

where the

placement

compensates

or

tempo

acceleration,

and

25-26,

expressing

elative

stability

over

the tonic

pedal),

and on

the other

hand the usual

displacement,responsible

or much of

the

piece's

drivingenergy.

Chopin's

notation,

indicating

a sus-

taining

of "tenor"

attacks,

is

suggestive

of

this

interpretation

(Ex. 13),

while a

mid-bar

accent

of

pitch

and duration

appears

explicit

in the notation of mm. 29-32. The

latter maintainsa

duple

meter,

enhanced

by

the

accompanimental "ripple"

which,butfor its finalretardation,rises to and descendsfrom

exactly

this

point.

Yet that

interpretation

which

represents

he

shortest nterval

of

displacement

s

manifestly

agitato,

articulat-

ing

a

triple

meter of

invigorating,

counteractive

mplication

(Ex. 13).15

Example

13

Agitato

i

jconteractive

counteractive

harmonic

rhythm

t5Interesting

o

compare

as

to

placement

of the

upper-voice

melody

and

consequent

metric effect are recorded

performances

by

Vladimir

Ashkenazy

(Decca

CS

7101,

1978)

and

Rafael Orozco

(Seraphim

S-60093,

1969).

The

formerat first

projects

a mid-bar

placement

of melodic

attacks,

shifting

his to

the

right-hand

humbas

the

piece

develops;

the latter

concentratesmore

on

the

right-hand

humb

placement,

n

a

relatively

overt

interpretation

bringing

out a

fairly

consistent

3

meter associatedwith that

placement

of the

melody.

i.e.,

11


14/28


15/28

20 Music

TheorySpectrum

responding

n

point

of IV

occurrence

(Ex.

15a),

this IV a basis

for

expansion

n

the

second

phrase,

and

the

I

havingprecisely

thesame

presentation

n mm.9-12 as in 1-4. To summarizeall

of this in a

special way,

m.

16

(with

its

counterpart

at m.

14)

elaborates

the structuralIV

surrounding

t,

anticipating

and

overreaching

o the cadentialV at m.

24--one

point

of the har-

monic

repetition,

thus of

emphasis,

of mm. 14-15 in mm.

16-

17.

Moreover,

if

there is a

(rhythmically

mplicative)

nitiating

sixteen-measure

segment expressing

the

Ursatz

I,

its critical

completion

the occurrence

of

scale

degree

3 at m.

16,

in

what

sense

might

such a

rhythmic

segment

include the

subsequent

upper

neighbor

of

3,

embellished

by rising

sixthchords n mm.

17-22,

where

these elaborativechords

also

"express"

he

pre-

dominant

V?

What

is crucialand

profoundly

nteresting

s that such vari-

ant

implications

of harmonicarticulations

oint

to

putative

un-

derlying

durational

hythmic

tructures

nherently

ndistinct

by

virtue

of

overreaching

(elsewhere

I

use the term "multi-

lateral")

and

overlapping

onal functions-a factor seen even

more

palpably

n

the

Bach

Prelude whose

analysis

ollows.

In

consideration f

underlying

"tonal

rhythm"

ntheBach

piece,

I

ian

Analysis

(New

York: W. W.

Norton,

1982),

191-94,

m. 16 s viewed as ca-

dential,

the end of the second

phrase,

as a

"point

of

rest,"

on thisbasisof

pri-

mary

onic

prolongation.

shall

return to the

suggestion

that the

enigma

of

durational

rhythmic

implications

of

basic

tonal

elements

appears

to

deepen

with

deeper penetration

of the tonal structure.

Broad metric

tructure.

revert now to

the issues of

accent-

to-accentmetric

grouping,

seeking

an

approach

o

questions

of

broadermetricstructure

n

the

Prelude,

and

defining

hat struc-

ture as to accents of

encompassing pans

of

implication.

In a first

step,

I

reduce the scale of

the

piece by

discounting

segments

of

"parenthetical"

unction,

aiming

o

get

at

the Prel-

ude's basiccourse

of

action.

For

instance,

the

upper-voice

mel-

ody

is

in

place

in

the first hree

barswhile

the tonic is

clearly

set,

and nthis sensem. 1

points

to m.

4,

and

analogously

m. 5 to m.

8.

This is

suggested

in

Example

16,

which

overlooks the rich-

ness of surfacedetail to

grasp

essential

content and action.

Another listener

might

well differ as

to the

gist

of the

piece;

but to

get

to

my

central

point

about broad

meter,

I

infer that

this exercise

would assess as

parenthetical

mm.

6-7,

10-11,

16-17,

25-28,

and

30-34,

the residual

elements

traversing

all

essentialmelodic and harmonic

ground.17

Seventeen

measures

are

in

this

sense deemed

auxiliary

o

the

overriding

action-

17Note

hat I have done

away

with m.

16,

a focus of

earlier discussionof

tonal

structure,

egarding

t as a "redundant"

xtension

of m. 14

because t is a

reiteration,

as I hear

it,

and

also

because

I

shall ascribe o m. 15

particular

c-

centual

significance.

Example

16


16/28

Metric nd

Rhythmic

rticulationn Music

21

exactly

half of the

piece,

just

as,

with reference to

Example

16,

we

deleted

half of the first

phrase.

I

give

the

consequent

contraction as

Example

17,

whose

chief

purpose

is

to

portray

accents of

deep

implication.

Mani-

fest at

mid-level in this

portrayal

s a

regularity

of

2-units,

indi-

cated

by

solid and

dotted bar lines in

Example

17a. The basic

meter

is

depicted

primarily

as to

peaked objects

of

directed,

upper-voice

progressions,

criteria of

accentual value thus

mainly

of dissonance

(the

Prelude'smotivic

appoggiatura)

and

pitch.

In

conceiving

meter as

an

organic

structuremarked

by

accentsanalogousto those of the bar-line unit andits internal

pulsations,

am led

to a

derivative,

overallmetric

configuration

given

n

proportionate

reduction

as

Example

17b. While

such a

representation

s

of

course

(as

in

any reduction)

shorn of

the

richness

of contextual

elaboration,

the

encompassing

metric

order

does make sense as a

telescoping

of vital

dynamic

con-

tours.

Example

17a

concurrence

of metric

accentand

harmonic

hange

My

claim

would be

that,

in such a

representation,

we see-

and

hear-meter as meter in its vital

aspect,

its broader

mani-

festations

oriented

toward,

motivated

by,

and

finallyreceding

from,

focal accents

of

broad

spans

of

implication,

such

a

synop-

tic

meter one of

the Prelude's

palpable

rhythmic

tructures,

an

important

eature of which is

a

vitalizing

acceleration

(the

3-

unit)

toward

what is

construedas a

primary

accent.

While

peri-

odicity

is irrelevantat

the

deepest

level

(Ex. 17b),

it is

yet

an

aspect

of

meter at

the mid-level

(Ex.

17a).

In

distilling

one of

the

intrinsic,

dynamic

ines of controlled

actionto and from-an encompassingmeter of associated m-

pulses

whichare extensions of those

(anticipative,

nitiative,

re-

active)

of the metric

gestalt

experienced

more

patently

at the

surface-we

have induced a measure of

understanding

f one

thing,

a

rhythmic hing,

that

the

piece

is

about.

Surface hythms

f Bach'sfirst

WTC

Prelude.

I shall

skimthe

rhythmic

urface

of the Bach

example,

then

get

to some

deeper

accent

eplica,

subsidiary

itchpeak,

point

of

interim

escent

~-

~~-~

_

stretto.

crest.

'

(F'-

chromaticism,

concurrencef

harmonic

hange

preconditioned,

return,

low-accented

reascent,

chromatic ccurrence

preconditioned,

ow-lev

resumptions,

agogic

ccent,

formal

unctuation,

corroborative

ormal

replication

f

initial

punctuation,

tc.

low-level

ccent

,el


17/28

22

Music

TheorySpectrum

m.21

accent f

outer-voice

itch,

object

of

stretto,

resc.,

etc.

m.5

--- Ir

-.-?

rM

-'"'15

i

Ir

] ts\

r t r m

3*

crescendo,tretto, hromaticism,

accelerative

mplication

f

shorterunit

(5:3)

14

+

*The5-3

acceleration

ay

be

functionaln

approach

o the

primary

ccent

f m. 21.

questions

about its

rhythms.

There

are

obvious

factors

of

regu-

larity, including

the sixteenth

note's

incessant recurrenceand

the motivic half-measure

unit.

Harmony

does not

change

in

every

bar,

but there is some subtle modification n harmonic

content

n

every

measure,

and n that sense it

too is

expressive

of

regularity.

Elements

of surface

mobility

and

asymmetry

will be

touched

briefly

ater.)

Some stated theoretical

approaches

to

the

piece's deeper

rhythms.

A number

of

published

analyses

are

concerned

with

groupings

f notated measures

n this

piece,

often withoutartic-

ulate

criteriaof

grouping.

Riemann inds hree

phrases

of

a

nor-

mative

eight-measure ength,

the first extended

(mm. 1-11),

the finalone further xtended to sixteenbars-8 + 8

(mm.

20-

35,

divisibleas four

bars of V

preparation,

eight

of

V,

and four

of

I).18

Later,

I shall

adopt

Riemann'sview

of m.

8

as a

"con-

traction"

my word),

the basis for his

construction

of

the first

phrase

as extended.

18Analysis f

J.

S. Bach's

Well-Tempered

Clavier,

rans. J.

S.

Shedlock,

3d

ed.

(London: Augener, 1890),

1-3.

In

Schenker's

analysis

of

measure-groups,easily

available

and not

possible

to

quote,

the

initial

segment

occupies

four

bars,

an

obviously

cohesive harmonic

egment,

the notated

m.

5

a first

point

of

mobility.19

significant

point

is

Schenker's nter-

pretation

of

the cadence as

weak,

or

recessive: hose

of

mm.

12,

19,

and

35,

the

Prelude'smost

emphatic

formal

punctuations,

are all

"fours"

n

the

grouping.

Measure

24

is heard

as the

point

of articulation

of

the

background

V,

a matter

we shall

worry

about

presently.20

Accentual delineation

of

measure-grouping

s,

to

be

sure,

not

an

explicit

actor

here;

yet

it canat times

be inferredas

con-

ceivably

relevant. For

example,

the

initiating

of mm.

16-18

(uppervoice)

has

agogic

accent,

as does the e of mm. 20-21.

And the

initiatorsat

mm.

8,

12,

and

16

can

all be

construed

as

19Five

Graphic

Music

Analyses

(New

York:

Dover,

1969),

36-37.

20Presumably

chenker's

wo

4-groups

over the

dominant

pedal

would be

read

as an

8-group

more

deeply;

strongest

dissonancesoccur on the

"beats"of

the

8-group,

and

two-measure

occurrences

of

the

upper-voice

'

are

supportive

of

8-grouping,

asof

course is

the

pedal

itself.

Example

17b

5


18/28

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19/28

24 Music

TheorySpectrum

dissonance

accents,

as indeed I shall later

interpret

hem.

With

all

of

this,

Schenker'smid-level

structureof

measure-groups

could

n fact

arise roma few

simplepremises:

1)

the firstbar

as

an

ordered

"one,"

(2)

a

regularity

of

group engths

(but

allow-

ing

for

extension nferred

n the first our

measures),

and

(3)

the

normative

unctions of

duple

units. The associationof "four"

with

resolution-a

constructn whichI concur-arises

naturally

in

light

of these

assumptions.

Komar's

"large-scale

downbeats" are associated

with ca-

dencesand with

the "main

background

dominant,"

which he

sees

as that

of the

pedal,

its attack

point

at

m.

21,

where it arises

"at a

prior

evel."21(Does

m. 20 also

"represent"

V,

since

from

it we

clearly

nfer

IV,

which

mplies

V,

and is thus construed

as

the V's

basic articulation

point?)

In Komar's four-measure

groupings,

where "one"

is referredto as a "downbeat"

e.g.,

that of

m.

23),

the

suspension

chord

of m.

21,

the

point

of as-

serted

deeper

emergence

of

the

pedal

V,

is viewed as

weak in

relation

o its

"stronger"

esolutionat

m.

23.

Komar'smeasure-

groups,

not

clearly explained,

are 7-10

(especially

s m.

7,

the

precedent"one,"unsubstantiated),

11-14

(m.

11 is

cadential),

15-18,

19-22,

and

23 as a further

nitiator.In

general,

Komar's

"ones"

are Schenker's

"fours,"

he latter often terminal

of for-

mal or

harmonic

grouping.

I have

referredto these

studies of

rhythmic not

"metric")

21Arthur

Komar,

Theoryof

Suspensions:

A

Study

of

Metrical

nd Pitch

Re-

lations

n Tonal

Music

(Princeton:

Princeton

University

Press,

1971),

119-22.

Komar's

ubtitle

is "The

Location

of

Large-Scale

Metrical

Accents,"

an une-

quivocal

ndication

of the

issue.

"Large-scale

metrical

accent"

s also

referred

to as "large-scaledownbeat"; thus it is explicit that metric organization s

around

"accents"

and

"downbeats,"

assessed

however

as to tonal

function.

Underlying

vents

at

mm.

1,

21,

and 32 are Komar's

primary

metrical

accents,

that

of m.

21

subsidiary

o the

other

two,

which are

"boundary ime-points"

of

the

piece's

"structural

time-span."

Moreover,

m. 21

is asserted

to be

"stronger"

han mm.

19

(cadential)

and

23

(actual

foreground

V),

the criterion

presumably

hat of

inferred

deeper

significance.

n a

single paragraph,

Komar

uses

the terms

"strong,"

"stronger,"

and

"relativelystrong,"

as well

as "sub-

sidiary"

n

the evaluation

of

"metric"

ignificance

of events

in the

piece.

partitioning

s

part

of a

perspective

or

examination

of the

per-

plexing

ssuesof

underlying

onal elements as

rhythmic

rticula-

tors,

and

to advance

my

argument

hat

the

deeper

one

pene-

trates the tonal

structure,

the fuzzier

any

lines of

rhythmic

articulation

o be inferred.

My

concern

has to do with the broad

question

of

rhythmic mplication

n an Ursatz or other

tonal

background,

but also

with

interpretedmiddlegrounds,

onsid-

ering

"rhythmic"

s to

specificities

of

durational

egmentation

rather han as

to

motivating

endencies

to and

from,

a further

rhythmicaspect

whose

ascription

o tonal functions s

patently

obvious,

and not

in

question.

The

problemof deep

tonalelements s

determinants

f tempo-

ral

segmentation.

Primary

onal elements in the

Bach Prelude

are,

in

my

view,

best deemed a

complex

of

overreaching

ore-

ground

occurrences,

anticipating

and

reflecting.

Two occur-

rences

of

V,

conceivable

as one basic

manifestation,

enclosed

by

three

encompassing

ccurrencesof

I,

comprise

a fundamen-

tal

unity

of

linked,

overlapping

vents which

span

the

Prelude.

Example

19

mm.

1

11

19

24

32

a-

Represented

in

Example

19 are these

primary

onal

occur-

rences:

I of the

beginning,

V

of

the interimarrivalat

m.

11,

I

of

the

parallel

cadence at

m.

19,

then

V

of the

penultimate

and

I of

the ultimate

pedal.

These events describe

the course of the en-

tirepiece, expressingrhythmas to tonal tendenciesto be sure,

but

less

certainly

as to

durational

partitioning.22

22Iam

led to Schachter's

position

that

"progressions

on the

fundamental

structure

mbody

tonal,

but not

durational,

rhythm,"

butfor

my

own

reasons.

[Op.

cit.,

vol.

4

(1976):317.]

I find some ambivalence

n

Schachter

with

regard

to

this

critical

question;

for

example,

elsewhere

he identifies

"brief structural

dominants"

p.

296)

and

comparable

events.


20/28

Metric nd

Rhythmic

rticulation

n

Music 25

We

might say

that

a

rhythm

of

durational

partitions

is

markedby these occurrences,in that the second segmentfol-

lows

ten

bars,

the third seven

more,

the fourth

following

by

four

bars

(in

this

sense a

speeding up),

and the fifth

by

eight.

Yet

a fundamental

onal

"event,"

involving prefatory actors

by

which t

is

implied

as well as

subsequent

phases

in which

t

is

prolonged,

is more

than a

particular

urface

articulation,

em-

bracing

rather

a

preparation-implication

nd

explicit

or infer-

able

"reverberation"

n the sense

suggested

in

Example

19.

Any punctuating

hythm

of

deep

tonal

content

is

thus

an

equiv-

ocal matter-anticipative, reflexive, reverberative, marked

only

at the

foreground

by

distinctarticulations.The

underlying

tonal

image

thus induced

is,

while one

of

rhythm

as

tendency,

manifestly

not one

of

precise

durational

spans,

and

surely

not

metric.

This

may

be a

profound

factor in

our

sense of

well-

crafted

music

as

havingorganic continuity,

while its surface is

punctuated

by

contiguities

of

many

kinds.

I

suggest,

then,

an

image

of

musical

structure

ncreasingly

luctuantand

lacking

n

periodicities,

and

increasingly uzzy

n

implications

of

rhythmic

segmentation,as we penetrateitsdeepertonal levels.

Example

20 is

a further

portrayal

of tonal elements

in

the

Prelude's

irst

nineteen

measures,

suggesting egments

marked

byoverreaching

ccurrences,

prolongations,

and

processes,

in-

articulative

of

precise

temporal spans.

Particularoccurrences

and

recurrences

seeming

in the

graph

to

mark

explicit spans

should

be read as

veiled,

blinking,

fading

and

reemerging,

sig-

nals.

I include harmonic-melodic

processes

(progressions

and

recessions,

spans

defined as

to

tonal

going

and

coming)

as well

asprolongationsoccurrence,elaboration,recurrence,here re-

gistrally

displaced

n the broader

movements).

Harmonicuni-

ties and

processes

are thus traced nvarious

ways

underthe sur-

face.

In these

references,

I am confined to the

notion that "dura-

tional"

rhythms

must

involve

strictly

measurable

units of

time,

although

the

concept

of durational relations

may

well

have

significance

lso with

regard

o

longer/shorter

units

ackingpre-

cision

of

demarcation,

as we

might

in the Bach Preludesense

a

"gettingshorter,"

and then

a

"getting longer,"

in

deep

tonic

and

dominant

elements.

Meters

of

the

oreground

and

near-foreground.

A

superficial

meter,

concurrent

with

motivic

grouping,

is articulated

n the

opening

measures

by

a

"negative"

extural

actor: he

mildly

ac-

centual,

naked

exposure

of c1. There

is,

moreover,

a

pitch

accent at

the second

and

fourth

beats,

dividing

he motive. But

for

these

relatively

ubmissive

actors,

shallow

metricstructures

are

considerably

eutral,

where

grouping

s

determinately

moti-

vicandharmonic.Comparatively nassertive ccentualmeter

n

thefirst

measures

contributes, believe,

to

the

larger-scale

met-

ric

function

of

anacrusis-preparation

of

a

downbeatof

deeper

significance

t m.

5,

a

point developed

below.

I

note

in

passing

two subtle

countermetric actors

(Ex.

21),

both

enhancing

the music's

gentle

surface

motions.

One of

them

is a

consequence

of

directional

change

n

the half-bar

mo-

tive.

The

other is effected

by

the

above-noted

pitch

accent

of

even-numbered

quarters.

Both

seem submissive o cofunction-

ingregularities,yetsuggestinghazy ines of disjunctionhrough

the structure.

They

are

simply

there,

requiring

no

performance

interventions,

veiled counteractions

expressed

in

inherentele-

mentsof

exposure.23

The broad

metric

structure. n

conjectures

regarding

an in-

clusive,

deep

metric

organization,

m.

5

is

focal.

My reading

of

the Prelude

eads to the

feeling

that

groupings

are

essentially

n

fours,

an

impression

fortified

by

the

precedent

first four

bars,

which

I

regard

as

broadly

anacrustic,

unified

n thatmetric

unc-

tion as in harmoniccontent. In the broadtwo-octave descent

elaborating

he

tonic and

tonic-centered

bass

ine,

mm.

1-4

are

thus a

relativelypassive preparation

or

the

Prelude's encom-

passing,

nclusive

ine of action.

23A

performance

by

Glenn Gould

(Columbia

D

35733,

1965)

nterestingly,

and

perhaps

distractingly,

brings

out the accentual

implication

of

the

upper

pitch

extreme

on the

second

andfourthbeats

by

staccato

articulations.


21/28

26

Music

Theory

Spectrum

Example

20

?

(D

~

Harmonic

occurrence/recurrence

-

-

- - -

Area of unified harmonic

process

......

Extensions

of

anticipative/reflexive

mplication

(1) Initiating,

near-foreground

I

elaboration,

a basis of

departure

for

all

subsequent

motions

(2)

Linear

expression

of VI

(=

II

of

V),

mm.

5-9

(3) Linearexpressionof II (= V of V), mm. 6-10

(4)

Preparation

by

fifth

descent:

A-D-G)

of interim V of m. 11

(would

include the

harmony

of

mm.

1-4,

at

a middle level of

tonal function: thus IV-II-V of

V)

(5)

Area

of

retonicization

of C:

II-V-I,

in fifth

descent

(D-G-C)

paralleling

he

preceding

V-preparation

(6)

Middleground

V

expression

in

encompassing

octave descent

(overreaching

o

the

fundamental

V

of

the

subsequentpedal)

(7)

Linear

II

expression,

aspect

of

approach

o the retonicized

I

(8)

C-occurrences

heard as

anticipative-reflexive

within

the

overall,

three-register

bass elaborationof 1

(9) InterimcadentialV articulationm. 11)within broad I prolonga-

tion and

anticipating

he later

pedal

V

(10)

Broad nclusive area of I

prolongationexpressed

n c -c bass de-

scent

(11)

The mobile

phase

in

I

prolongationbroadly

heard,

principal

area

of fluctuant

development

(12)

Measures 20-31: fundamental V and

V-preparation,

followed

by

codetta,

the outer reach of an

encompassing

onic basis

0

4- ---~


22/28


23/28

28 Music

Theory

Spectrum

Example

22

*Complementary,

corroborative

groupings

of

sequence,

motive,

phrase

A K

, 7

I

I

01

a

_ r-

I' ,

I

WFiI

r- - FI r

n

S

,,v

-,'-

Before

leaving

this

infinitelyprovocative

piece,

I shall

sug-

gest

three conceivable continuationsof

basic metric

organiza-

tion

(Ex. 23).

Essential actions have run their

course,

and all of

these

in-

terpretations

onceive metric functions

n a state of

recession,

with ower-order

groupings

he

only

issue. The

preconditioning

effects of

precedent

metricunits are

important,

as are factorsof

local accentual

exposure.

And,

again,

the

questions arising

here are

germane

to

performance,

nterpretive

choice

among

these

or

comparable

constructsof

necessity

in

any

illuminating

realization.

The first continuation finds an

intermensural

"hypermet-

ric")

accent

on the

suspension

of m.

21,27

markedalso

by

deci-

sive descent

in the bass. This

grouping

makes anextended

pre-

ceding

unit,

supported

by

the bass

adherence to

c,

and

a

shortened

suspension

unit,

after which

(as

in

all three

con-

structs)4-grouping

esumes.

The second merely conceives the anomalous 3-group of

the firstas

implying

a

regular

4-group,

withm. 23 readas con-

tracting

a surface

II4

and

VII4

see

footnote

25),

in a

locally

in-

tensifying

acceleration owardthe dominant

pedal.

27Komar's

prior-level"

articulationof

the structural

V,

and

one of

his

three

primary

"downbeats."

-0-

I

p

j -'. /

I


24/28

Metric nd

Rhythmic

rticulation

n

Music 29

Example

23

'l

~I

nl

}

I

1

rmm.)

12

16

A

AI

E

r

I

V

A

'

)

nl.

21 m.

24

m. 32

(Interprets

the

3-group

as a

contraction

of

4,

an

acceleration)

ZJ

J

.

4

(implied)

P

??

4

(preconditioned)

s~

J/7


25/28


26/28

Metricand

Rhythmic

Articulation n Music

31

ble the referential low of

time,

as

an

experiential

ield

in

which

rhythms

are

grasped.

The oftenperiodicarticulationof musical ime in measures,

half-measures,

and like

units,

is

thus

a levelled

pulsation

of

beats,

the

conventional bar

line

representing

"amplified"

beats,

analogous

in

experience

to

lower-level

(intramensural)

beats

of

a

structure's normative

value.

Such

metric

units-

neutral, inanimate,

and

referential-are,

as

proposed

above,

grouped

by

expressive

actions

of

many

kinds. And

meter

is,

while often thus

periodic

at

relatively

shallow

levels,

increas-

ingly

fluctuantat

deeper

levels.

Figure

3

represents

his

attrib-

ute, whilesummarizinghe conceptionof meteras to intervals

of accentuationand as to a

complex

of

interactive

impulses

within

the

unit

initiated

by

the

accentual

downbeat,

at what-

Figure

3

METRIC SURFACE

ever

level. Meter is thus understood as a

dynamic,

organic

ele-

ment of

rhythm.31

In cognitions of grouping, a factor too little estimated is that

of

preconditioning

effect.

Once a

grouping,

metric or

other,

is

established at a

particular

level,

it tends

to

influence the sense

31Themetric

unit as an

array

of

interactive

endencies

brings

o mind com-

parable

actors

n other

rhythms.

The attributeof

qualitative endency

an in-

deed be ascribed

clearly

to some

rhythmic

articulations

e.g.,

that of

dissonant

harmony),

but

probably

not to

all,

if

by

tendency

we

mean an

implication

of

"leaning"

oward some

inferred state. Yet

tendency

as an

aspect

of

rhythmic

experience, somethingwe know little about except perhapsin explicit tonal

functioning,

may

well be a

pertinent rhythmic

attribute n

the articulationsof

elements

not

commonly

so

construed:

n textural

accrual,

for

example,

or

in

directed

changes

of loudness or even of

timbre.

Two

aspects

of meter:

(1)

relations

(lower

ordersoften

periodic)

of con-

tiguous

groupings;

(2)

internal dis-

positions

of

impulses

to and

from

downbeat.

DEEPER

LEVELS

OF METER


27/28

32

Music

TheorySpectrum

of

subsequent

groupings,

even of other

kinds.

(One

aspect

of

my

comment

concerning oncluding egments

of

the Bach

Prel-

udeis that

prevalent

our-measuremetric

groupings

can be felt

to

continue

where accent is

comparatively ndecisive.)

And we

hear

groupings

as abbreviatedor

extended

in

part

because we

construe certain events

as

contractionsor

amplifying

elabora-

tions

by

reference

to

an establishednormative

grouping.

I sus-

pect

that the

experience

of meter at

its most obvious evels com-

monly

reflects the

implications

of an

assertive accentual

grouping

after even one

or two

articulations-a matterof vital

concern

to the

performer especially

where

mobile,

variable

tendenciesof metricstructure

may

be,

while never

brutallypro-

jected,

allowed

necessary

rein

by

adroit,

sensitive understate-

ment of

preconditioning

groupings.

Hierarchies

n

rhythmic

tructure

are

important

n

that cer-

tain

events of a

particulargrouping

mode are

appreciable

as

having onger-reverberant ignificance,

or

span

of

implication,

than

others,

thus

articulating

more

comprehensive

units and

deeper

levels of

structure.In

deeper

metric

units,

principles

of

group

content and

organization by

which we understand he

most

obvious,

local metric

groupings

are evident in

amplifica-

tion.

Thus,

my

answer o the

question

"Whatdoes

'one'

denote

in a series of measures

comprising

a

deeper

metric

grouping?"

is that

it is an

accent,

analogous

to,

but of broader

mplication

than,

that

of

the

shallowerunit. An accent of such

deep import

is a

point

assessed as

unique

for the

unit

which t

initiates,

as

in

the

Chopin

Prelude heard

holistically

in

this

sense,

or more

problematically

n the Bach Prelude.

My

assumption

s that

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Berry Metric Rhythmic Articulation

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