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8/11/2019 Berry Metric Rhythmic Articulation
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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
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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.
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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.
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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
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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~_
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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
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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.
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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
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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.
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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.
?
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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
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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
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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
8/11/2019 Berry Metric Rhythmic Articulation
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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
8/11/2019 Berry Metric Rhythmic Articulation
18/28
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I
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8/11/2019 Berry Metric Rhythmic Articulation
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.
8/11/2019 Berry Metric Rhythmic Articulation
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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.
8/11/2019 Berry Metric Rhythmic Articulation
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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- ---~
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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
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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
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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
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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