I have experienced one of the most interesting
musical revelations of my life, gradually over the last several
years, in studying West African dance-drumming and in playing
jazz, hip-hop and funk. The revelation was that the simplest repetitive
musical patterns could be imbued with a universe of expression.
I have often witnessed the Ghanaian percussionist and teacher
C. K. Ladzekpo stopping the music to chide his students for playing
their parts with no emotion. One might wonder how much emotion
one can convey on a single drum whose pitch range, timbral range,
and discrete rhythmic delineations are so narrow, when the only
two elements at one's disposal are intensity and timing. Yet I
have become convinced that a great deal can be conveyed with just
those two elements. Some investigations into how this can happen
are set forth in this chapter.

Rhythmic expression in African and African-American
musics. Some of the arguments in this
chapter draw upon cultural aspects of music listening. Working
from the documented historical lineage between West African and
African-American cultures, Wilson (1974) has identified a constellation
of conceptual tendencies that exist in the musics of that vast
diversity of cultures. Among the musical preferences and principles
he enumerated were the following:


  • rhythmic contrast
  • stratification
  • antiphony (i.e. "call and response")
  • connection between music and physical body
    movement
  • percussivity
  • continuity between speech and sound
  • heterogeneous sound ideal
  • tendency to fill up musical space
  • concept of music as meaningful "in motion"
    -- as part of everyday life

These and other concepts can serve as the beginnings
of a pan-African musical aesthetic, since so many of these notions
appear so often in so many different kinds of West African and
African-American music. A great majority of this music falls in
the category of groove-based music that I have mentioned, meaning
that it features a steady, virtually isochronous pulse that is
established collectively by an interlocking composite of rhythmic
entities and is intended for or derived from dance. This somewhat
inadequate description should not be viewed as a definition
of the concept of groove; indeed, to some degree, that definition
is what we are searching for with this work. One could say that,
among other functions, groove gives rise to the perception
of a human, steady pulse in a musical performance.

In groove-based music, this steady pulse is
the chief structural element, and it may be articulated in a complex,
indirect fashion. In groove contexts, musicians display a heightened,
seemingly microscopic sensitivity to musical timing (on the order
of a few milliseconds). They are able to evoke different kinds
of rhythmic qualities, such as apparent accents or emotional mood,
by playing notes slightly late or early relative to their theoretical
metric location. While numerous studies have dissected the nuances
of expressive ritardandi and other tempo-modulating rhythmic
phenomena (Repp 1990, Todd 1989, Desain & Honing 1996), to
our knowledge there have been few careful quantitative studies
that focus on expressive timing with respect to an isochronous
pulse. In groove-based contexts, even as the tempo remains constant,
fine-scale rhythmic delivery becomes just as important a parameter
as, say, tone, pitch, or loudness. All these musical quantities
combine dynamically and holistically to form what some would call
a musician's "feel." Individual players have their own
feel, i.e. their own ways of relating to an isochronous pulse.
Musical messages can be passed at this level. A musician can pop
out of a polyphonic texture by a "deviation" from strict
metricality, or a set of such deviations. As I shall attempt to
demonstrate below, these kinds of performance variations create
an attentional give-and-take to emphasize different moments interactively.
This and similar techniques are manipulated with great skill by
experienced musicians playing together, as a kind of communication
at the "feel" level. We claim that this variety of expressive
timing against an isochronous pulse contains important information
about the inner structure of groove.

Often when the topic of musical communication
is breached, one is tempted to wonder what is being said amidst
all this communication. This raises the question of what actually
constitutes a musical message, or, for that matter, musical meaning
in general. Here, I feel, one should draw upon the processual
notion of communication, as a collective activity that harmonizes
individuals, rather than on the telegraphic model of communication
as mere conveyance of literal, verbal meanings. For example, the
musical notion of antiphony, or call and response, can function
as a kind of communication, and nothing need be "said"
at the literal level to make it so (although we need not rule
out the possibility of musically encoded symbolic meaning). What
definitely is happening is that the interactive format,
process, and feeling of conversational engagement are enacted
by the musicians. In a context like jazz, the presence of this
kind of dialogic process can be constant throughout a performance,
as sustained antiphony. I am arguing that a significant
component of such a process occurs along a musical dimension that
is non-notatable in Western terms -- namely, what I have been
calling microtiming.

Previous microtiming studies.
Miniscule timing deviations from metronomicity are
frequently miscast as "discrepancies" (Keil 1995), "motor
noise," or "inaccuracies" (Rasch 1988). But there
has been a small thread of research dedicated to the uncovering
of structure in these so-called inaccuracies. It turns out that
these deviations both convey information about musical structure
and provide a window onto internal cognitive representations of
music. One of the most compelling examples of this direction in
research is provided by Drake & Palmer (1993). They proposed
three types of accent structure:

 


  • rhythmic grouping accents,
    in which a longer note tends to end a rhythmic group and is perceived
    as accented (a.k.a. the "gap" principle), as indicated
    by the accent mark:

[inline-center:Image20.gif]


  • melodic contour accents
    (turns or leaps in pitch contour), as in:

[inline-center:Image21.gif]


  • metric accents
    (so-called strong beats), such as:

[inline-center:Image22.gif]

In studies of timing of numerous skilled classical
pianists, they found systematic deviations from strict regularity
that correlated with these accent structures. Their qualitative
findings are summarized below (table adapted from Drake &
Palmer 1993).

[inline-center:Image1.gif]

In these results, it is clear that small performance
variations in timing, intensity, and duration enhance aspects
of musical structure. Drake and Palmer concluded that these performance
variations facilitate listeners' segmentation of musical sequences,
since the accent structures serve to break up a musical sequence
into smaller, more tractable chunks. Furthermore, Drake and Palmer
found that the expressive effects that stemmed from rhythmic grouping
tend to dominate melodic-accent or metric-accent effects; the
former tended to override the latter two when the music yielded
conflicting accent interpretations. That the metric accents would
tend to be overridden is unsurprising, since one would expect
expressive timing to break up the regularity of repetitive metric
accents. But the fact that rhythmic grouping effects dominate
melodic-accent effects suggests a more general primacy of rhythm
over melody, in both production and perception. Also worth noting
is that these expressive variations allow graduated change
-- flexible, continuous variability. A moderate amount of
expression is the norm, and performances that are low or high
in expressivity will stand out as extreme.

In his studies of microtiming variation in
small chamber groups, Rasch (1988) conducted statistical analyses
of inter-musician differences in note onsets from recorded ensemble
performances. Although he averaged out all musical structure,
including metric accents and tempo variation, he found that generally,
in a string trio, the violin's lead voice tends to lead by 5 to
10 milliseconds, the cello tends to follow, and the viola's middle
voice tends to lag by another 5 to 10 milliseconds. It is unclear
how accurate these findings are, however, because the standard
deviation for each of the instruments was around 35 milliseconds.
But at any rate, Rasch's hypothesis that there might be systematic
variation in ensemble performance is a valuable one.

The above studies focused on European classical-music
performance, which would not fall into the realm of groove-based
music because of its reliance on tempo variation for expressive
purposes. Indeed, the above results indicate that beats are frequently
lengthened or shortened by the performer. Also, as discussed in
the previous chapter, the treatment of metric organization as
implying a series of weak and strong beats does not apply particularly
well to West African or African-American musics; in these contexts
there is no such thing as a metric accent, in terms of performance
variation. Although the above studies are valuable, their stylistic
scope does not coincide with ours.

It would be instructive to conduct a similar
microtiming analysis for a percussion ensemble, particularly in
instances of groove-based music which is much less forgiving in
the realm of tempo variation and rubati than a string trio
might be. Bilmes (1993) conducted a timing analysis of a recorded
performance of Los Muñequitos de Matanzas, an Afro-Cuban
rumba group [CD-37]. In a performance averaging
110 beats per minute (such that what would be a notated sixteenth
note lasts around 135 milliseconds), both the quinto and
the segundo (lead and middle conga drum, respectively)
tend to play about 30 milliseconds ahead, or "on top."
On the other hand, the tumbao (low conga drum) had a much
broader distribution, nearly as often late as early. It should
be noted that here the precise moment of the beat was not
determined by the norm set by these three instruments themselves,
as it was in the case of the string trio. Rather, the beat was
established by a reference instrument, in this case a clave
or a guagua. Hence it was possible for all three instruments
to be ahead of the nominal beat, which was not the case for the
string trio. In Bilmes's work, the average inter-drum asynchrony
was not calculated; indeed, such a measure would ignore any relationship
between timing and musical structure. But a frequency analysis
of the microtiming variations revealed systematic structure. For
example, the repetitive segundo part displayed a strong
peak corresponding to its frequency of repetition, showing that
the microtiming variations were not at all random.

Given this apparent systematicity of fine-scale
rhythmic expression in groove contexts, we can take cues from
the results of Drake & Palmer (1993) and Rasch (1988) discussed
above, as well as from our expanded view of cognition involving
the theory of embodiment, to make guesses about the function of
such rhythmic expression. Thus we hypothesize that microtiming
variations in groove music play any of the following roles:


  • highlight structural aspects of the musical
    material,
  • reflect specific temporal constraints imposed
    by physical embodiment, and/or
  • fulfill some aesthetic or communicative function.



I shall now address all of these possibilities via a few examples.

 

EXAMPLES OF EXPRESSIVE MICROTIMING

Asynchrony.
The asynchronous unison attacks described above support a scientifically
meaningful explanation. Rasch (1988) reports an earlier study
of asynchrony: a 1977 experiment in which he investigated the
effect of onset difference times on the perception of quasi-simultaneous
tones. The threshold for perceiving the upper of two quasi-synchronous
tones

    could be decreased drastically [from between
    zero and -20 dB to about -60 dB] by introducing an onset difference
    time of, say, 30 ms. In the latter case, the threshold was largely
    independent of factors other than temporal ones... In supra-threshold
    conditions asynchronization contributes to the apparent transparency
    of the compound sound multi-tone stimuli. (Rasch 1988: 80)

So a function of these quasi-synchronous attacks,
or flams, could be to aid in the perception of the timbral constituents
of the unison attack.

The accompanying audio example demonstrates
this tactic [CD-38, 39].
[node:3782 teaser]
[node:3783 teaser]

[inline-center:Image23.gif]

In the first version, the double stroke on
the first beat is essentially synchronous; in the second version,
a delay of 30 milliseconds is introduced between the two notes,
resulting in a small flam. This serves to enhance the perception
of the two timbral constituents.

In some musical situations in which blending
is preferred, this kind of multitimbral asynchrony may be undesirable,
but it is often a valued musical trait in groove-based music.
On Wilson's list of African and African-American aesthetic concepts
is the notion of a heterogeneous sound ideal, a tendency to value
the presence of a variety of contrasting timbres. Another important
cultural characteristic (not mentioned earlier) is a collectivist
ideal, in which music is construed as a communal activity among
groups of people. The rhythmic asynchronies described above aid
in the perception of a multiplicity of timbres, as well as, in
the ecological view of music perception (Gibson 1979, Shove &
Repp 1995), the multiplicity of human bodies behind those timbres.
That is, rhythmic asynchrony contributes both to the heterogeneous
sound ideal and to the sense of collective participation. To be
sure, exact synchrony is impossible with groups of people anyway;
but this principle applies even when different sounds are played
by one individual, as on the modern drumset. So here is an instance
in which a kind of subtle rhythmic expression fulfills both a
perceptual and an aesthetic function.

Streaming. It
is well established that auditory stream segregation is a function
of both pitch and timbre (Bregman 1990). From our work, it appears
that microtiming can also contribute to streaming. This claim
builds on the role of asynchrony in facilitating the perception
of multiple tones. The audio examples [CD-40, 41] consist
of a steady stream of triplets on tom-toms, together with a series
of sparse tom-tom strokes at a lower volume.
[node:3791 teaser]
[node:3789 teaser]
The musical material is shown below.

[inline-center:Image24.gif]

In the first audio example, the unison strokes
are as simultaneous as is allowed by the MIDI protocol (i.e.,
within a couple of milliseconds of each other). In the second
example, the second stream is delayed by 30 milliseconds with
respect to the first, as indicated by the arrows in the figure,
but kept at its same low volume. In the former case, the different
timbres fuse into one stream, whereas in the latter case, the
second stream is clearly audible as a separate entity. This example
shows clearly how such miniscule timing variations can contribute
to streaming. This technique is especially important in a context
where the aesthetic tendency is to "fill up the musical space"
(Wilson 1974). Timing variations can allow an instrument that
is sonically buried to draw attention to itself in the auditory
scene. Thus the presence of multiple instruments of similar timbres,
as in a West African drum ensemble or a large jazz ensemble, need
not be viewed as enforcing the subordination of individual identity.
Individual musicians can improvise at this microrhythmic level
to create an attentional give-and-take. This streaming effect
also serves an aesthetic function, in that it enhances the perception
of different rhythmic groups as separate animate entities with
distinct "personalities" as Ladzekpo stresses (1995).

Spreading.
It was not until the advent of automated machinery that human ears
were ever treated to inhuman rhythmic precision. The fact is that
sonic trace of temporal constraints imposed by the body are often
perceived as aesthetically pleasing, while inhuman rhythmic regularity
often is not. These audio examples [CD-42, 43] consist
of two versions of the "same" rhythm, shown below.

[node:3788 teaser]
[node:3790 teaser]

[inline-center:Image25.gif]

The first rendition is executed as close to
the theoretical idealas the computer allows - that is, rigidly,
mathematically accurate. The second features timing inflections
designed to imitate an aspect of human performance. The difference
is not simply the injection of random temporal slop. Rather, it
involves the spreading apart of consecutive attacks played by
the same hypothetical limb or digit. An individual effector such
as a limb, hand, or digit has a time constant associated with
its motion; the nerves and muscles have a brief

The rhythmic expression added in the above
example is systematic; the first of each group of three taps is
about 30 milliseconds early, and the last is about 30 milliseconds
late, as indicated by the arrows in the figure. In addition to
enhancing perceived separation, this example depicts the encoding
of bodily movement in musical material. Nearly all listeners are
familiar with the kind of motion suggested by these synthetic
tapped rhythms, but that motion is strongly implied only by the
second, "imperfect" version. Again, this description
recalls the embodied, ecological view of musical perception, in
which the listener perceives the source of the sounds,
rather than the sounds themselves. In a music that embraces physical
body motion (Wilson 1974) and that is contiguous with everyday
experience, this sonic trace of the body is a valued aesthetic.

Coding for invariance.
The above three examples demonstrate the notion of
invariance. At the most basic level, expressive microtiming represents
a departure from regularity, so it is likely to be noticed in
relief against the more regular background. Gibson (1975) claimed
that our perceptual systems are attuned to variants and invariants
in the environment; they code for change. As an example, consider
the way that vibrato or a trill can facilitate auditory scene
analysis by drawing our attention to a particular instrument in
an otherwise blended orchestral texture [CD-44]. [node:3802 teaser] The microvariation
of a single pitch is enough to make that voice pop out in the
auditory scene.

We can make a similar generalization with rhythm.
That which is regular, or invariant, in an isochronous-pulse context
is the norm set by the regularity of pulsation, along with its
salient multiples and subdivisions; that which is irregular comprises
the variable rhythmic material along with its continuous expressive
variation. Microrhythmic expression signals a departure from the
implied norm, hence marking a particular sound or group of sounds
as worthy of attention or analysis by our perceptual systems.
This argument contributes to an ecological view of rhythm perception,
in which we are attuned to variations in an otherwise regular
environment.

Swing.
A kind of rhythmic expression that seems to be indigenous to African-American
culture is that found in jazz of the first half of this century.
Known as swing, this kind of structure can be thought of as modified
duple subdivisions of the main pulse, or as modified triplet subdivisions,
or both concurrently. As duple subdivisions, they divide the interval
of a pulse into two unequal portions, of which the first is slightly
longer. They are occasionally rendered in triplet notation as
a quarter note followed by an eighth note, but this exaggerates
the typical swing ratio, which is usually in the gray area between
duple and triple and is strongly tempo-dependent (typically lower
for fast tempi and higher for slow ones). An individual musician
has a particular range of preferred ratios and particular ways
of manipulating them, which together form crucial dimensions of
that individual's sound, rhythmic feel, and musical personality.

In a related experiment on rhythm, Fraisse
(1982) has studied the ability of musically trained and untrained
subjects to reproduce rhythmic patterns of varying degrees of
complexity. "Arrhythmic" sequences with arbitrary relationships
between time intervals caused the most difficulty. In more regular
rhythmic cases, subjects tended to simplify the ratios between
intervals, almost always settling on exactly two classes of time
interval: long (400-800 milliseconds) and short (200-400 ms).
People tend to understand rhythms to feature two and only two
interval lengths, roughly in the ratio of 2:1. This drive towards
rhythmic simplicity recalls some of the classical perceptual laws,
namely the principle of economy in organization (Fraisse 1982).
Usually as performed or as "preferred," the ratio is
lower -- in fact closer to swing, about 1.75:1, about 57%

However, it is not apparent why the interval
would be divided unequally in the first place. It would seem even
simpler and more economical if there were no such difference in
duration between the first and second of two consecutive swung
notes. But the point is that this difference facilitates the perception
of higher-level rhythmic structure. An immediate consequence of
the swing feel is that it suggests the next level of hierarchical
organization. In conventional terms, the swung eighth-note pairs
are perceptually grouped into the larger regular interval, that
is, the quarter note. If all subdivisions were performed with
exactly the same duration, it would be more difficult to perceive
the main beat. The lengthening of the first of two swung notes
in a pair amounts to a durational accentuation of the beat. (Often
in practice, the second note of the swung pair is given a slight
accent in intensity, as if to compensate for its shorter duration.)
Hence swing enhances the perception of the main pulse, as the
examples [CD-45, 46] demonstrate:

[node:3792 teaser]
[node:3793 teaser]

[inline-center:Image26.gif]

The first version plays all eighth notes exactly
equivalently and is therefore metrically indistinct, whereas the
second version introduces a slight swing, which immediately marks
the pulse.

In the pocket: backbeat delay.
The notion of a backbeat is indigenous to the modern
drum kit, an instrument pioneered by African-Americans in this
century. It consists of a strongly accented snare drum stroke
or handclap on beats two and four of a four-beat metric cycle,
where the beat is typically a moderate tactus rate [CD-47]. [node:3785 teaser]

[inline-center:Image27.gif]

The backbeat appears to have arisen in the
middle of this century, as the popular swing rhythm yielded to
the even more popular, more bombastic rock and roll rhythms of
artists such as Little Richard and Chuck Berry.

In his musical interpretation of Stuckey's
(1987) study of the culture of enslaved Africans and its influence
on modern African-American culture, Floyd (1995) discusses the
the important African diasporic cultural ritual known as the ring
shout as a distinctive space in which, among other things,
music and dance were fused. This activity "helped preserve
... what we have come to know as the characterizing and foundational
elements of African-American music," including "constant
repetition of rhythmic and melodic figures and phrases,"
"hand clapping, foot patting, and approximations thereof,"
and "the metronomic pulse that underlies all music."
(Floyd 1995: 6) As a cultural model, the ring shout serves for
Stuckey as a hermeneutical point of departure in the study of
African-American art forms. It provides an alternative lens through
which to view these later practices, a lens that is grounded on
African, rather than European, concepts and aesthetics. (See Rosenbaum
1998 for more documentation of the ring shout.)

The backbeat that is so prevalent in postwar
African-American popular music seems to reference the role of
the body in the ring shout -- the bass drum (struck with a foot
pedal in the modern drumset) and snare drum (struck manually with
a stick) replacing the stomp and clap, respectively. In fact,
a real or synthetic handclap sound is often superimposed on the
backbeat's snare drum sound in popular urban dance music. The
hard-edged repetitiveness of the backbeat embodies the cyclic,
earthy atmosphere of the ring-shout ritual. Though sometimes dismissed
as dull and monotonous, the backbeat taps into the hypnotic, functional
role of repetition in such rituals, in which steady, moderate
tempo, rhythmic ostinati, and physical body motion (stomping and
clapping) were combined in a collective setting to create a shared
multisensory experience. It seems plausible that the earliest
musical activities of humankind possessed many of these qualities.
The backbeat is best understood as a contemporary, popular remnant
of what is probably some very ancient human musical behavior,
filtered through a sophisticated, stylized African ritual and
through centuries of African-American musical development.

The curious point about the backbeat in practice
is that when performed, it displays a microscopic lopsidedness.
If we consider the downbeat to be exactly when the bass drum is
struck, then the snare drum is very often played ever so slightly
later than the midpoint between two consecutive pulses
[CD-48].[node:3786 teaser] Often musicians are aware of this to some degree,
and they have a term for it: the drummer is said to play "in
the pocket." While perhaps unaware of the exact temporal
details of this effect, a skilled musician or listener in this
genre hears this kind of expressive microdelay as "relaxed"
or "laid back" as opposed to "stiff" or "on
top." This effect is much subtler than the salient rhythmic
categorization of the long and short durations of swing. It is
a miniscule adjustment at the level of the tactus, rather than
the substantial fractional shift of rhythmic subdivisions in swing.

What function does this delay structure have?
Perhaps the delay functions as a kind of accent, since it involves
the postponement of an expected consequent (Meyer 1956). It seems
plausible that the optimum snare-drum offset that we call the
"pocket" is that precise rhythmic position that maximizes
the accentual effect of a delay without upsetting the ongoing
sense of pulse. This involves the balance of two opposing forces:
the force of regularity that resists delay, and the backbeat accentuation
that demands delay.

Note that the concept of a backbeat, and the
slight delay associated with it, does not pertain if a single
voice is used for both the downbeat and the backbeat. (As an example,
the urban dance-music genre known as "house" features
an isochronous bass drum on all four beats, with the snare-drum
backbeat occasionally dropping out.) The effect seems tied to
the difference between the two sounds, and perhaps also to the
actual sounds themselves and the imagined bodily activity that
gives rise to it. In a related study, Fraisse (1982) reports,

    In speaking of synchronization, it is necessary
    to specify what is synchronized with what. In effect, if one
    measures the temporal separation between a tap of the forefinger
    and the sound, one finds that the tap slightly anticipates the
    sound by about 30 msec. The subject does not perceive this error
    systematically... Moreover, this error is greater if the sound
    is synchronized with the foot. The difference between hand and
    foot permits us to think that the subject's criterion for synchronization
    is the coincidence of the auditory and of the tactile-kinesthetic
    information at the cortical level. For this coincidence to be
    as precise as possible, the movement of tapping should slightly
    precede the sound in order to make allowance for the length of
    the transmission of peripheral information. This length is all
    the greater when the distance is longer. (Fraisse 1982)

This delay architecture amounts to the subject's
hand coming after the foot for perceived synchronization,
since the anticipatory "error" is greater for the foot.
This seems to predict that a regularly alternating stomp-clap
pattern would contain a microscopic asymmetry similar to that
found in the modern backbeat. Given that the bass drum both references
and is played by the foot, and similarly the snare drum both points
to and involves the hand, it is possible that this resultant delay
structure was transferred to the drumset. Though these arguments
are quite speculative, it is plausible that there is an important
relationship between the backbeat and the body, informed by the
African-American cultural model of the ring shout.

 

RHYTHMIC EXPRESSION: TWO MUSICAL EXAMPLES

Thelonious Monk plays "I'm Confessin'."
[CD-49] [node:3803 teaser]One of the most fascinating skills
displayed by Monk and many other pianists of the genre is a high
degree of independence between the two hands, to the degree that
one hand can appear to perform rhythms that are ambiguously if
at all related to those performed by the other. Often, as in stride
piano, this takes the form of a steady pulse or repetitive bass
rhythm in the left hand (the "ground"), and upper-register,
rhythmically free melodies in the right hand (the "figure").
A classic example is Monk's 1963 solo recording of "I'm Confessin'
(That I Love You)" (Monk 1998). In this piece, after carrying
on in this expressive stride fashion for some time, the last two
bars of the first chorus give rise to an improvised melodic fragment
that rhythmically seems to stretch and tumble into the next bar
[CD-50]. [node:3804 teaser]

[inline-center:Image28.gif]

In this excerpt, the melodic structure in the
right hand temporarily overrides and upsets the underlying rhythmic
structure, only to be righted again. We can interpret Monk's unquestionably
gripping display here as the rhythmic equivalent of a struggle,
one that threatens the norm of established pulse regularity set
by what has come before. It seems to offer an example of a case
in which such regularity is sacrificed briefly to allow for a
case of extreme rhythmic expression. But note that the sense of
pulse is never lost; Monk leaves out a couple of quarter-note
chords in the left hand, but otherwise provides strong and accurate
pulse reinforcement in the stride style. The rhythmic underpinning
of the left hand compensates for the apparent deviation from regularity.

When I played the recording of this piece for
a roomful of cognitive science undergraduates, most of whom presumably
had no familiarity with jazz, this excerpt elicited a burst of
spontaneous laughter. Something about Monk's delivery is communicative
enough to transcend what one might expect of the traditional confines
of genre. Nearly upsetting the regular pulse, Monk takes a chance
and chooses to follow through on a melodic idea that momentarily
takes him rhythmically far afield.

The question of whether Monk "intended"
to play this in exactly this way is a pejorative one, akin to
reifying the role of "mistakes" in jazz (as in Walser
1995). From the perspective of an improvisor, the notion of a
mistake is supplanted by the concept of displaying one's interaction
with the structure suggested by the sonic environment. It is never
clear what is "supposed" to happen in improvised music,
so it makes no sense to talk about mistakes. This improvisation-friendly
framework allows for the possibility of musical exploration and
experimentation, including impromptu rhythmic variation of the
sort described here, without invoking a notion of mistakes.

Ahmad Jamal plays "But Not for Me."
[CD-51] [node:3805 teaser] A wonderfully extemporaneous,
playful spirit is captured masterfully in pianist Ahmad Jamal's
1952 trio version of the standard tune "But Not for Me."
In this piece, Jamal manipulates his relationship to the pulse
actively and voluntarily through the skillful use of microtiming
variation. Nearly every single phrase in Jamal's rendition contains
some interesting microrhythmic manipulations, but here I will
focus on one fragment, namely the end of the first chorus into
the beginning of the second chorus. In measure 31, Jamal initiates
a repeating three-beat figure in the four-beat metric context.
This additive rhythmic technique is a common one in African-American
music, and Jamal carries it out to a humorous extreme, letting
the blues-inflected figure cycle twelve full times (nine measures).
The first four measures of this passage are displayed below. I
have adhered to the convention of representing swung rhythms with
regular eighth notes, but it should be understood that there is
much more to this passage than meets the eye. In particular, Jamal
plays this figure extremely behind the beat, so much so as to
enhance the humorous effect of the repeating melodic figure by
casting it in starker relief against the more ordinary rhythmic
background [CD-52]. [node:3806 teaser]

[inline-center:Image29.gif]

In these four measures, the quarter note averages
469 milliseconds (128 beats per minute). The note events in the
piano that are displayed as occurring on the beat tend
to begin actually around 40% of a beat later than the drummer's
rimshots, which are indicated with x's above. This places him
more than a triplet behind the beat. Furthermore, Jamal's second
eighth note in each swung pair tends to occur about 85% of the
way through the beat. This means that the swing ratio here is
effectively inverted; the first eighth note in a delayed
pair lasts about 45% of a beat (less than half), and the second
lasts about 55% (more than half). It would appear that the
perception of swing arises due to complex variations in timing,
intensity, or articulation; in this case, it is not merely a matter
of achieving the "correct" microrhythmic ratio.

How does Jamal pull off this apparent rhythmic
violation of an inverted swing? The answer seems to lie in his
40% phase shift relative to the beat established by the
accompanying instruments. If, while maintaining this phase relationship,
he were to adhere to the usual swing ratio of around 57%, then
the second note in a swung pair would be close enough to the onset
of the next beat (only a few percent early) that it would be heard
as on-the-beat. By employing a relative anticipation of the second
eighth note in each pair, Jamal avoids this problem, instead sounding
squarely "between" the beats. The 40% delay also affords
him enough rhythmic ambiguity so that the inverted swing does
not sound jarring. Also, Jamal enhances the sense of swing by
accenting the second of each pair (a common technique, as mentioned
earlier). So here is a case in which one kind of rhythmic expression
interacts with another; the usual long-short relationship of swing
is altered in order to accommodate the "laid-back" quality
of the melodic figure.

What is accomplished by playing in this laid-back,
behind-the-beat fashion? One might expect the same simple perceptual
effects (such as enhancing stream segregation) if he instead played
ahead of the beat, for example. Playing behind the beat
is definitely a cultural aesthetic in African-American music,
especially jazz. In an unpublished study, Bilmes (1996) found
that a West African drummer played equally as often ahead of as
behind the beat, whereas one might observe casually that skilled
jazz improvisors tend to play much more often behind than ahead.
From the ecological point of view, playing behind the beat might
be normally associated with a physical or mental state of relaxation,
or might suggest a causal relationship in which the musical material
is a reaction to the pulse. Such hypotheses would demand
further investigation.

In this chapter I have discussed some aspects
of rhythmic expression that are quite distinct from the common
body of European classical musical performance techniques typically
discussed. Instead of (or in addition to) expressive concepts
like rubato, ritardando, and accelerando,
we have seen deliberately asynchronous unisons, subtle separation
of rapid consecutive notes, asymmetric subdivisions of a pulse,
and microscopic delays. As further illustration, we have seen
extremely deft manipulation of fine-scale rhythmic material in
examples from the jazz idiom. I have chosen to focus on African
and African-American musics because they often feature these concepts
in isolation from the possible interference of tempo variation,
and because they tend to involve percussive timbres which facilitate
precise microrhythmic analysis. I have argued that African and
African-American musics incorporate aesthetics that value these
kinds of microrhythmic expression. However, I believe that these
techniques are found to varying degrees in all music, including
the European classical genres. In the next chapter, I present
a representation for rhythmic structure that allows for the explicit
manipulation of expressive microtiming of the variety discussed
above.

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