Swinging Impulse Coordination as a Source for Swing Rhythms

John Ito, Columbia University

IntroductionFeelings of swing, characteristic of some jazz performances, are both perceptually salient and definitionally elusive. Put less formally, you recognize a swing feel when you hear it, but it's not at all clear just what "it" is. One of the initial problems in studying swing is that the word is used to describe a wide variety of phenomena. It can describe a style of music popular in the 30's and 40's, a feel of performance (e.g. as an alternative to funk or Latin), or an ineffable quality which a performance can possess to varying degree. (Swing as a quality is ineffable in part because, though most centrally describing music in the swing feel, some jazz musicians feel that it is also found in music in other feels. This paper's hypotheses about hierarchical impulse coordination may offer a partial explanation of this.) For the purposes of this paper, 'swing' will be understood as characterizing a competent performance in the swing feel; such a performance should be identifiably in the swing feel and should possess a basic minimum of the quality of swing. Thus to ask of a performance in the swing feel, "Does it swing?" will be taken as the equivalent of asking of an utterance, "Was this utterance produced by a native English speaker?" To answer 'yes' to either question is to identify the object as being acceptable and competently produced; it indicates membership in a category and says nothing about location within that category.

The analogy with native English speakers can be pushed further. Just as an individual speaker will have both a regional accent and unique individual characteristics, so swing feels vary both according to stylistic currents within jazz and with the personal stamp of individual musicians. Both domains also offer research problems of comparable complexity. When we recognize a specific person's voice, we do this on the basis of so many individual but mutually-interacting parameters that a complete understanding of our mental processing is a practical impossibility (Handel 1989). Accent recognition (here native vs. non-native speaker) requires an abstraction out of those already complex factors, and thus poses an even greater research challenge. The problem of characterizing swing requires a comparable abstraction out of already complex objects, so we should not expect to find more than very incomplete conditions for swing, conditions which are certainly not sufficient and often not even necessary.

Discussions of the sources of swing often focus on phenomenal accentuation of weak beats at the tactus level and delay of weak beats at the first subtactus level, with particular attention given to the latter condition. It is well known among musicians who do computer synthesis of jazz, however, that these conditions do not suffice to produce a feeling of swing. Merely delaying weak eighths will not make music swing. (In notating jazz, the quarter-note level is almost always the tactus level. This practice will be assumed in much of this paper, and references to specific note values will always assume a quarter-note tactus. This will simplify the discussion of different metric levels.) Furthermore, there is no archetypal rhythmic proportion of the swung eighth to the quarter-note span in which it is embedded (hereafter "swing ratio"). This fact is a commonplace among jazz musicians, and empirical verification of this was the subject of Experiment 1.

Experiment 1In Experiment 1 recordings by eminent jazz drummers were studied for the relative durations of the swung eighths played on the ride cymbals. Ride cymbals were chosen because they are extremely salient on a sonogram, extending well above the frequency ceiling of the other instruments. Furthermore, the typical swing pattern on the ride cymbals (all quarters plus offbeat eighths of beats two and four) provided plenty of swung eighths to study. Drummers Art Blakey and Max Roach were chosen because they are particularly flexible rhythmically. Because they are both ranked among the greatest jazz drummers, two important assumptions may safely be made: that this flexibility is the product of intent and not of lack of control; and that their performances fall within the bounds of acceptable practice.

Multiple portions of four tracks from two albums were imported as .aiff files and subjected to sonogram analysis using the program AudioSculpt. In many cases markers corresponding to ride-cymbal hits were placed algorithmically by AudioSculpt; in some cases they needed to be placed by hand. For each sample the markers were exported as a list of timings. This list was analyzed by a PatchWork patch which calculated the swing ratios, their average, minimum, and maximum, and their standard deviation. The results are tabulated as Appendix 1. Swing ratios were found to range from 14% to 48%; this strongly confirmed the belief that there is no archetypal swing ratio, and thus that rhythmic alteration is not a sufficient condition for swing. Similar methods were used by Friberg and Sundström (1999), and similar results were obtained.

The Role of the Performer's BodyWhile the results of Experiment 1 are important for demonstrating the non-existence of an archetypal swing ratio, it should be stressed that such an archetype would not sufficiently explain the phenomenon of swing even if it did exist. For example, melodic lines that contain no eighth notes can be perceived to swing. In the shout chorus of a swing-feel big-band chart the band is often in rhythmic unison, and there may be no consecutive eighth notes for lengthy stretches; in a good performance these passages will nonetheless be perceived as swinging.

In looking for sources of swing that go beyond the rhythmic structure of consecutive eighths, a number of researchers have focused on the role of structured asynchronicity among performers. Another issue commonly discussed among jazz musicians, it has been most prominently discussed in the academic literature by Keil (1987), and has been studied analytically by Prögler (1995), synthetically by Friberg (1999), and using both approaches by Iyer (1999). While the importance of structured asynchronicity has been demonstrated by the success of these studies, there are plenty of other factors which contribute to swing, and some of them do not involve synchronization . For example, it is possible for a solo line without accompaniment to swing, in which case there are of course no issues of synchronization.

As one factor behind the phenomenon of swing which is more general than structured asynchronicity, I propose that there are characters of movement of the performer's body which leave sonic traces in the articulations and timings of the notes, and that these characters of movement are important in generating feelings of swing. The music swings because the performers' bodies swing. This fits well with Gunther Schuller's (1989) frequently quoted definition of swing: "in its simplest physical manifestation swing has occurred when, for example, a listener inadvertently starts tapping his foot, snapping his fingers, moving his body or head to the beat of the music." (p. 223) Iyer (1999) also roots his methodology in the physicality of performance; his account of structured asynchronicity is based on physical aspects of some African and African-American cultural practices and values.

My proposal differs from previous work in its emphasis on the role of articulation. I believe that amount and uses of muscular tension in the performer's body make a difference in the quality of the sound, that a note played as a rebound sounds different from a note played as a main impulse. If our bodies tend to respond physically to music,

it seems plausible that they do so because of recognizing the character of motion of the bodies that made the music. (The possibility that physical participation may affect perception will be discussed briefly below.)

A substantive description of swinging characters of movement is well beyond the scope of this study. While some characterization will be offered, for the moment it will suffice to argue for the plausibility the concept. First of all, it must be possible for subtle differences in muscular control to make a qualitative difference in the sound produced. Iyer, for example, states that in playing certain drums "the only two elements at one's disposal are intensity and timing." (1998, p. 105) In general I am skeptical about claims that any instrument in which the performer's body is not entirely mechanically distanced from means of production of the sound (i.e. any instrument not like the pipe organ) does not respond to subtle differences in the way the performer moves when playing. To stay with the ride cymbal example, this may seem initially to be too simple an instrument to produce such shadings of sound; it might be argued that the location on the plate of contact with the stick and the forcefulness of that contact are the only variables. But this neglects the fact that the stick and the plate have a complex interaction. They are in physical contact for a finite period of time, and during this time they will behave to some extent as coupled oscillators. The firmness with which the stick is held, the angle with which it contacts the plate, and the degree to which the stick is controlled or allowed to bounce freely will all affect the interaction of stick and plate, and thus affect the vibration of the plate. Secondly it must be established that the listener can in fact reconstruct information about the performer's body from the sonic traces thereof. This is intuitively plausible based on the extremely detailed knowledge inferred from environmental sounds; more direct verification was the purpose of Experiment 2.

Experiment 2In Experiment 2, computer-altered versions of ride cymbal patterns recorded by a jazz drummer were played for subjects. In each of two example groups, the swung eighth note was be moved in time but had its spectral envelope preserved; the two groups were based on originals with differing swing ratios (.285 and .196). The initial hypothesis was that when asked which version swung the best, subjects would choose the original timing of the swung eighth based on articulation cues.

Experimental Method

Examples were based on recordings made of Dave Gluck, a nationally touring jazz drummer who is based in New York. Dave played a 20" Zildjian Custom Dark Ride cymbal, and was recorded on DAT with sampling rate 44.1 kHz using a stereo microphone placed between three and six inches from the cymbal. He was asked to play typical ride patterns (all quarter-note beats plus offbeat eighths of beats two and four) with three different feels; one in which the swung eighth was approximately equal to a triplet eighth, a snappier feel which was more like a sixteenth, and a straighter one which was closer to a straight eighth. The feels were recorded in that order, and before each a metronome was played at 130 beats per minute in order to have the different feels have approximately equal tempo. Within each feel, after recording several measures I had him play the same feel again twice, this time interrupting him by knocking his stick away in the middle of the pattern. This was done after beat 2 and after the eighth that follows beat 2. The idea was that when moving the swung eighth, either the off-beat eighth or the on-beat eighth that preceded it would have to be made longer, and that it would be helpful to be able to copy the decay that would have occurred had the next note not been played. The stick was knocked away, rather than simply asking Dave to stop the pattern, in order that the physical motions which produced the note in question would be exactly those that would have been used if the next note were going to be played.

The recordings made were imported as .aiff files and processed using BIAS Peak v. 2.0. Within each feel, one half-measure excerpt was selected which seemed to swing particularly well. When it came to processing the examples, however, problems arose due to my having underestimated the complexity of the sound of the ride cymbal. Although I was explicitly testing its capacity to carry subtle articulation cues, I had not observed its low-frequency behavior. In many musical settings the lower frequency components are not particularly salient relative to other sounds in the same spectral region, and the envelope of these lower components evolves relatively slowly. I had therefore not realized that they would present problems. What I found was that hits with the same metrical position within the same feel were perceived as differing in overall pitch; it was therefore not possible (with one exception) to mix the decay of one hit convincingly with the attack of another. It was then necessary to find another way of extending the decay of some of the hits. After trying a few different methods, I ended up simply copying the last few milliseconds of the hit and pasting them in at the end. This usually involved only a few milliseconds (at most 23.5 ms pasted four times, but that was extreme). I did not perceive this as causing any distortion of the sound. The only other method used was in lengthening the swung eighth of the version with swing ratio .196.

This note was problematic because for some examples it needed to be lengthened considerably, and because it was interrupted by the next hit very soon into its decay, at a point at which the envelope was evolving extremely rapidly. For this set I ended up using as my model the last complete pattern from the take in which I interrupted the drummer after the swung eighth. The swung eighth which ended that take was thus played almost immediately after the swung eighth in the pattern used as a model, and they had the same overall pitch. I was therefore able to splice the decay of the final eighth onto the swung eighth from the basis pattern.

Three groups of seven examples each were produced. The first group was based on a half bar from the approximately triplet feel and had swing ratio .285. The second was based on the snappier feel that was more similar to a dotted rhythm and had swing ratio .196. The third feel was from the straighter feel and had swing ratio .35. In each group the overall duration of the pattern was kept constant, and the swung eighth placed in seven different positions, ranging from ratio .42 to ratio .18 in increments of .04. In each case the basis pattern lasted from the attack of beat one until just before the attack of beat four. The span from the attack of beat two until just before the attack of beat four was then copied and pasted in repeatedly until there were three full bars, concluding with the first beat of the fourth bar (i.e. ending just before the attack point of the second beat of bar four). Once these groups had been generated, the entire third group was discarded as sounding awkward; something about the feel of the original half bar made it not conducive to exact repetition. The first and final examples of each group were also discarded as obviously not swinging, leaving five examples in each group ranging in ratio from .38 to .22.

There were several problems intrinsic to this method of constructing examples. In order to isolate the relationship between swing ratio and articulation, it was necessary to repeat the same pattern exactly several times. (It might have been possible to use examples only a half bar long, but it would have been very difficult to judge such a short example as either swinging or not swinging.) The exact repetition, however, created a situation which is basically never heard in real jazz; even the most consistent drummers do not use such absolutely exactly repeating patterns. The second problem was that the perceived lower frequency pitch of the cymbal changed over the course of the half bar. Pasting on a repetition thus led to a completely abrupt change in the perceived main lower frequency; such abrupt changes are never heard in real cymbal playing. The result was a

strange oscillating melody of sorts in the lower frequency range. (Readers wishing to hear some of the examples should visit my website, "www.columbia.edu/~jpi9".)

Once the examples had been generated, I realized that the coding of bodily motion via articulation cues did not create such strong restrictions as I had supposed. I was correct in predicting that the same swung eighth, moved in time from its original position, would not only sound rhythmically different but also sound like it had been produced with a different character of motion. It was true that the same eighth, at first relaxed and natural, would gradually become stiff and awkward. But this did not happen as quickly as I had expected. Rather, there was a considerable range across which the character changed, but in which the examples still sounded musically viable.

In an attempt to verify the importance of articulation cues, I created a number of other examples which were identical to existing ones in temporal and peak intensity profiles but which were assembled out of hits which were not originally proximate (and which should therefore be expected to have little relation to each other in terms of structure of articulations). In making various examples I used a single on-the-beat hit, a variety of on-the-beat hits, or hits which retained their original metrical position but which came from different feels. To my ear those examples ranged in the order presented from stiff and unmusical to fairly reasonable. At the least, this indicates to me that on-the-beat hits and off-the-beat hits are, in fact, qualitatively different.

Examples were put into pairs and triplets for comparison, with sets falling in three categories. Within each of the two groups derived from one of the original feels, the five examples were divided into two overlapping triplets, with swing ratios ranging from .38 to .30 and from .30 to .22. These four sets comprised the first category. There were also five pairs, in which the examples having the same swing ratio from each of the two groups were compared. Those were the second category. Finally, the third category consisted of six pairs and one triplet in which the more synthetically generated examples were compared with the originals which they were imitating. All sets were then randomly ordered, and within each set order of presentation of the examples was also randomized. Once in sequence, the 37 examples comprising the 16 sets were burned as separate tracks onto CD-R; they were distributed over two CD-R's for ease of track control.

Jazz musicians have extremely divergent attitudes about research into the inner workings of the music. While some are eager to think about and discuss such issues, others find the attempt to explain that which is ultimately unexplainable at best futile and at worst offensive. Although I do in fact agree that the workings of swing will never be completely explained, I decided that it was safest and easiest not to indicate to the subjects that swing was the object of my investigations. They were therefore informed that the experiment looked at differences between jazz and classical musicians in how they perceive and characterize swing rhythms. Subjects were asked to rate the examples within each set numerically, and also were also asked to write a few words about how they perceived the differences in character. Subjects were allowed to use the same number more than once if they felt that there was no difference in their preference of some of the examples. Subjects were given a booklet in which to record responses; the booklet listed the tracks grouped into sets and had room for comments after each set. The subjects were allowed to control the CD player themselves and listened through headphones.

Subjects were eight members of the Manhattan Jazz Orchestra and headlining vocalist Johanna Grüssner. All are professional jazz musicians based in New York. Subjects were given a small honorarium in appreciation for their help. Most of them completed the task in approximately fifteen minutes. Due a technical problem, 5 of the subjects had sound coming from only one side of the headphones; the responses of these subjects are not statistically differentiable from those of the others, however.

ResultsFrom the standpoint of verifying my hypothesis, the experiment was an almost complete failure. It was, however, instructive in other ways.

The only definitive results came in the sets which compared triplets on the basis of swing ratio. It was assumed that the effects in question would be strong, and that therefore any real difference should be virtually unanimously agreed upon. No statistically meaningful conclusions can be drawn from anything less than virtually complete agreement with such a small number of subjects. For the first feel, comparing ratios between .38 and .30, .30 was preferred by all eight subjects who expressed any preference. .34 was preferred over .38, but too weakly to be statistically meaningful (5-2). Comparing ratios between .30 and .22, .30 and .26 were tied (5-4) for first preference; all nine agreed that .22 was the worst. For the second feel, .30 was preferred over .34, which was

considered better than .38; two expressed no opinion and one each couldn't decide between the adjacent pairs, but no responses contradicted that ordering. Comparing ratios between .30 and .22, results were much more spread out. Each example got one of the rankings four times, one three times, and one twice. .30 and .26 were equally preferred, both receiving four number one rankings. .22 seemed least preferred, receiving four number three rankings, three twos, and two ones. From a statistical point of view, however, these differences are not meaningful.

It may support my hypothesis that with the group which was based on an original swing ratio of .285, a ratio of .22 was unanimously felt to be worse than either .26 or .30, whereas when the original ratio was .196, all three ratios were approximately equally preferred. For this to strongly support the theory, though, it would be expected that when the two examples with ratio .22 were compared directly, the one with original ratio of .196 would be strongly preferred over the one with original ratio .285. This was not the case; the preference for the one with .196 original ratio was far too weak to be meaningful. I don't think that this experiment succeeded in demonstrating anything at all about the role of articulation cues. I would also caution against any reductive conclusions about swing ratios based on the results of the timing comparisons. The preferences do seem quite clear, but they are in the absence of a musical context, and at one specific tempo. While, at a given tempo, some ratios may be more normative than others, in the right musical context ratios much more extreme ratios than those tested here can swing.

Of the five pairings of examples with the same swing ratio from the two example groups, none produced significant preferences. Similarly, of the sets which compared more synthetic examples with the originals which they imitated, only one pair produced significant results, and in that pair the synthetic example had an extremely noticeable pitch mismatch. Most surprisingly, the synthetic example which to my ear was the most awkward and unmusical was actually preferred over its original by 5 subjects. Results are tabulated more fully in Appendix 2.

The real value in the results of Experiment 2 lies in the focus it puts on the subjectivity of swing. In the introduction I stressed the difficulties in characterizing swing which result from the variety of music which is felt to swing. Swing is also difficult to characterize because it intersects with individual values which vary from person to person. It was not uncommon to have two subjects identify the same parameter as marking the most salient

difference between examples, but to evaluate the examples in the opposite way based on the same parameter. For example, they might agree that one example has more accentuation on beats two and four than the other, but while one will hear this as good, the other will hear it as exaggerated. Or, in the case of the synthetic example which had the extreme pitch mismatch, one subject liked the synthetic example, saying that it "has an interesting two tone thing going on." Another subject, though, complained that "He's fucking around with where he/she puts the stick on the ride in [the synthetic example]."

Another way in which responses were subjective was in the choice of parameters to give attention to. Even such simple examples offered a variety of different potential foci of attention. One subject, for example, made almost no comments other than 'too stiff;' it seems likely that he was bothered by the absolutely inflexible repetition of the patterns. Another subject (the same one quoted at the end of the previous paragraph) felt that almost all of the samples were terrible and expressed very few preferences; his one moment of enthusiasm came when he heard the most synthetic example, the one made with repetitions of just one hit. He said that that example was "the best so far because the drummer is not fooling around with stick placement and volume." He made exactly the same comment when he encountered that example in a subsequent set; it seems likely that he was disturbed by the pitch mismatch. In general, subjects frequently called attention to different parameters in their written responses.

Finally, responses to swing are subjective because listeners do not differ only in the evaluation and attention to their perceptions; they are able to affect their perceptions by their behavior. I first noticed this in the course of Experiment 1, listening to Max Roach's ride cymbal playing on Move. I found that when I listened hearing the half note as the tactus (an incorrect hearing to a jazz musician) I didn't hear any swing in the ride pattern at all. I noticed no delay of the off-beat eighth notes, and no accentuation of beats two and four. When I listened hearing a quarter-note tactus, however, both the very subtle delay of the swung eighths and the emphasis on two and four became audible; the line started to swing. I had a similar experience when preparing the examples for Experiment 2. I found that when I was disposed to an example swinging, when I moved my body in response to it, even the worst examples had at least some swing to them. But if I sat motionless as a detached and uninvolved listener, some of the better examples sounded sterile and completely unswinging. Iyer frequently refers to listeners as coperformers (1998); from these experiences it seems to me that swing is not simply a property of a sound signal, or even of a perception which may vary from listener to

listener but which is fixed for each signal-listener pairing. Rather, swing is, at least in part, something which the listener participates in, and which the listener has the power either to encourage or to resist.

Future DirectionsIn considering future versions of this experiment, there are some problems which could be readily solved, but many others which would remain. The most obvious area of improvement is the example materials. As manipulating sound files presents so much difficulty, it would seem desirable to precisely manipulate the performer instead; the obvious solution is to use a computer-controlled piano which can both record touch and timing data and play on the basis of touch and timing input from the computer. This would eliminate the problems such as pitch-mismatch while still allowing a note to be moved in time though remaining unchanging in character.

The problems related to subjectivity of response, however, would remain. This kind of investigation into swing presents an experimental catch-22. In order to isolate individual parameters, it is necessary to remove much of the context, as changing one parameter also changes the relationship between that parameter and the others present. But removing context only opens the door for the listener's personal responses and assumptions about context to play an even greater role. Furthermore stripped-down examples which are perceived as raw materials for music rather than as music itself invite the listener's participation much less than real, complex musical examples. It's not clear that it would be profitable to repeat this experiment with the relatively cosmetic (though necessary) change of example source; future experiments bear substantive rethinking.

Toward a Characterization of a Swinging PerformerAs noted above, this paper will not offer a thorough account of swinging motions in performance. There are, however, some observations about impulse coordination and hierarchy which can serve as the beginning of such an account.

Unless notes are significantly isolated in time, a performer will not usually execute all notes with equal impulses. Rather, there will be dominant impulses coinciding with hypermetrical beats; all other notes will group together gesturally with the notes receiving dominant impulses, joining either the dominant note that follows or the one

that precedes. Each of those notes will receive a subordinate impulse. These subordinate impulses will be less active, and have the character of a rebound.

An analogy with sawing wood may help convey the intended concept. Imaging first sawing through a piece of dense particle board. The hardness of the wood, combined with its internally conflicting grain, make it difficult to saw. Each stroke is very active and must be independently initiated. The saw comes to rest at the end of each push stroke, and the next pull must be entirely the product of a new impulse. In this case there is no hierarchy of impulses. Contrast this with sawing balsa wood. It is so easy, and the saw moves through the wood with so little resistance, that the pull feels like an easy rebound from the push. One main push may even produce the next three as subordinate rebound strokes. In this case the rebound strokes receive impulses which are subordinate to that of the main stroke. Note that these strokes are not literally rebounds; without the intention of the person sawing, one stroke would come to an end and stop, even with balsa wood. Although these strokes result from their own impulses, those impulses have less intentionality than the main impulse; it feels almost as if they were happening of their own accord. It is in this sense that impulses are hierarchized.

To return to a musical example, consider a string player or pianist playing a passage from Mozart featuring running eighths in a quick tempo. Dominant impulses would fall either every measure or every half measure, and the subordinate impulses would be relatively undifferentiated. This is necessary for the smoothness which is stylistically typical; more frequent dominant impulses would make the passage sound beaty and unmusical; they would also increase the physical tension of the performer. Note that this has the effect of deëmphasizing the quarter-note level: dominant impulses are less frequent than the quarter-note level and note changes more frequent. (Dominant impulses are usually audible, though not necessarily because of being louder.)

Contrast this now with a jazz musician playing running eighths in a swing feel. While there will still be a larger organization of four or eight notes, of which one will receive a dominant impulse, there will now be a hierarchically intermediate impulse given to each note falling on a quarter-note beat. There is a gestural, impulse hierarchized pairing of notes. (It is not universal that the strong impulses fall on the beat; at slow and moderate tempi the intermediate dominant impulses often fall on the weak eighths. At extremely fast tempi this kind of syncopation is rarely heard as it becomes extremely difficult to execute.) This will emphasize the quarter-note level, and the presence of more relatively

superordinate impulses will also increase the intensity. This hypothesis may account for those jazz musicians who swing even though they use little or no rhythmic inflection. They are perceived as swinging because of the audible results of the added middle level of impulse with its resultant strong-weak duple impulse pairs. The hypothesis may also explain how pieces of music which are not in the swing feel may nonetheless seem to swing. Again, it is important to state that the claim here is not simply that notes on the beat are louder. The claim is that the difference in impulse control makes the action different; the difference in action makes the sound different. It is a qualitative difference in sound that is being claimed as the crucial percept here.

This claim about differences in impulse hierarchy seem difficult to verify short of wiring performers to take data about muscle use. Syllable choice in singing instrumental music, however, provides a way into these issues. It is commonly observed that jazz and classical musicians sing instrumental music very differently; classical musicians tend to vary the vowels they use less than jazz musicians. As the vowel chosen determines the position of the vocal apparatus, and as these various positions involve known relative amounts of muscular tension, analysis of syllable choice can yield patterns of relative tension and relaxation. At first glance, the expected patterns conform very well to the hypothesis of impulse hierarchy. A classical musician singing running eighths will often stay on one syllable, or change syllable infrequently, reflecting locally undifferentiated levels of tension. A jazz musician, on the other hand, will often employ a pattern of regularly alternating vowels, corresponding to a regular alternation in the level of muscular tension. Putting this oversimplified analysis on an empirical footing was the purpose of Experiment 3.

Experiment 3In Experiment 3 the same nine subjects used in Experiment 2 were recorded singing five instrumental lines taken from well-known jazz compositions. They were told that the experiment looked at differences between jazz and classical musicians in the ways that they communicate with other musicians by singing. They were told not to approach the task like a singer giving a performance, but rather like a musician communicating with another musician about how the music should go.

The examples chosen were as follows: the first alto part from the first sixteen bars of the first chorus (mm. 13-28) of "Basie - Straight Ahead" by Sammy Nestico, found in Wright (1982); the first alto part from the first 8 bars of the fourth chorus (mm. 109-116)

from the same chart; the flügelhorn part from the first 16 bars of "Three and One" by Thad Jones, also found in Wright (1982); the first alto part from the first sixteen bars of the second chorus, with the measure-long lead-in, (mm. 31-48) also from "Three and One"; and the beginning of a lead sheet of Charlie Parker's "Ornithology," up to the downbeat of measure 12. The examples each featured passages of running eighth notes in addition to other rhythms. The examples were chosen for their familiarity, in the hopes both that the singing would be as expressive as possible and that musicians would not need to concentrate on reading the music while singing; this was not intended to be a sight-singing task.

The recordings have not yet been fully transcribed; they may well contain enough interest to be the subject of a separate study. Initial processing reveals the following generalizations, however. Off-beat eighths are typically either schwa sounds or not sung with vowels at all, but rather with the nasal voiced consonant /n/. The schwa is produced with a very neutral, relaxed position of the vocal apparatus. On-beat eighths (and some off-beat eighths which are tied into the next beat, functioning as anticipations) are typically more active vowels, especially /i/ and /u/. /i/ is produced with the tongue high and in the front of the mouth, /u/ with the tongue high in the back of the mouth and with lips somewhat constricted. (Handel 1989, pp. 135-147) Not only are these both more active than the schwa, they are two of the three 'cardinal vowels', so named because they are produced in the physically most extreme positions, thus bounding the space of all vowels. (Handel 1989, p. 143) The most typical vowel patterns were based on regular alternations between two vowels, with either /i/ or /u/ on the beat and the schwa off the beat. This fits perfectly with the hypothesis of impulse hierarchy; the alternation between vowels that are maximally active and maximally passive makes sense as an alternation between dominant impulses and rebounds.

One of the subjects in Experiment 3 was remarkable for his musical knowledge and musical memory. With each example he glanced at the sheet of music to see what was wanted and then put down the music and sang from memory. He frequently sang more than had been requested, and in the case of the opening of "Three and One" he sang some of what the rest of the band does during the rests in the flügelhorn melody. His singing was therefore purely the expression of an already-formed musical conception, unencumbered by the parallel task of forming a conception based on reading music. His rendition of "Ornithology," transcribed as Example 1, demonstrates strategic musical use

of the physicality of vowel sounds. From here the paper will follow the informal vowel notation used in Example 1.

[Example 1 Here]

Rather than using mainly one of the more active vowels, he used both, exploiting the space between them. He moved from the initial doo to dee on the third beat of measure one, using dih as an intermediate point for a smooth transition. He then created an intensification into the goal of the phrase, the down beat of measure 2, by a direct alternation of the distant doo and dee. In measure three he left off the alternation in the third through fifth eighths in order to create a sense of headlong drive into the two syncopated quarter notes. In his rendition the b-flat in measure 4 is heard as a surprise, a sudden turn in the melody which receives a very different kind of accent from those that the syncopated quarters got. This was achieved through use of syllables, as the dee is brighter than the dih of the quarters; it stands out particularly saliently because of being preceded by a doo. The rest of the phrase is a relaxation, with less in the way of extreme contrasts. A nice touch is the variety of upbeat accents, the first produced by a strong plosive d in the duh at the end of measure 4, the second, on the second eighth of the second beat of measure 5, produced by use of a doo. A similar effect was achieved in the next phrase, when he created a weak accent on the second eighth of beat three by omitting the consonant on the preceding eighth. The anticipation of measure 9, which is heard as an intensified sequence of the preceding phrase, is brought out by use of the bright bee, though somewhat softened by the consonant choice. The accent on buh in measure 9 is very strong, set off by a complete stop of breath just before it. It shows that different kinds of accent don't have to correlate, as both vowel and consonant choice would make buh quite weak if not for the accent by physical intensification. The end of the phrase is punched out with the direct dee doo alternation, both on quarter-note beats. The rest of the example relaxes from that point of greater tension with more normative syllable alterations which do not juxtapose cardinal vowels. In addition to providing very strong support for the hypothesis about impulse hierarchy, this example shows that this kind of syllabic analysis could provide new analytic insights into scat singing.

Convergence of the Visceral and the Cognitive: Fast Hard BopSo far this paper has concentrated on more visceral aspects of swing; there are of course also cognitive aspects, and in the case of fast hard bop these can combine to begin to account for important aspects of style.

Issues of beat finding are implicit in the above discussion, as the presence of hierarchically intermediate impulses coinciding with the tactus can aid the listener in finding the beat. These are not, however, the only cues. Consider a metrical grid of the sort used in Lerdahl and Jackendoff (1983). It is perfectly symmetrical between levels; any level could serve as the tactus as well as any other. Now apply this to a swing feel jazz tune, and suspend the assumption that the quarter note gets the tactus. It would be typical to find phenomenal accentuation on every weak quarter-note beat. As this would happen throughout much of the tune, it would make it unlikely for the tactus to be at the half-note level or above, as that would mean that the entire piece was syncopated. It would also be typical for each weak eight-note beat to come late. As the tactus is generally regular, this would make it unlikely for the tactus to be at the eighth-note level or below. (A similar conclusion, though on different grounds, is found in Iyer 1998, pp. 117-118). This leaves the quarter-note level as the only preferred level for the tactus.

Now consider fast hard bop tunes. These often have tempi above 200 quarter-note beats per minute. If a classical piece had such a fast tempo, it is extremely unlikely that the quarter note would be heard as the tactus. An experienced listener would likely hear a half note tactus for a classical piece with quarter-note tempo 200 or above. A fast hard bop tune can also be heard with a slower half-note tactus, but experienced listeners, aided by both the hierarchically intermediate quarter-note impulses and the cognitive cues discussed above, will cling to the quarter-note tactus. (Jazz musicians will simply know that that's where the tactus is, based on elementary grammatical cues.) Thus the visceral and the cognitive join forces to make perceivable a tactus which lies considerably outside of normal limits. The performance is likely to be intense, because of the tension involved in generating the tactus-level intermediate impulses. This is compounded by the listener, who often pulses along with the tactus physically. Musicians playing fast hard bop create intensity in many ways, but not least by this exploitation of cognitive and perceptual tendencies.

ConclusionsSwing is a phenomenon of immense complexity which arises out of the interactions of many parameters and which is in many ways subjectively perceived. This paper offers a very partial account of the causes of swing in its proposal that there are modes of bodily coordination which are in some way swinging, and which leave audible traces in articulation, timbre, rhythm, and intensity. We understand music to swing in part

because we decode the traces of swinging performers. One aspect of swinging bodily coordination, at least in the case of consecutive eighth notes, is an alternation of dominant and subordinate impulses. This theory of alternating impulses was strongly supported by analysis of spontaneous scat singing. Providing along the way a new paradigm for the analysis of scat singing, this method offers a window into the simultaneous manipulation of multiple parameters toward musically expressive ends. The explanatory value of impulse hierarchy was further demonstrated when issues of impulse hierarchy and of cognition were coordinated in the account of aspects of fast hard bop. Experiment 2, which failed to demonstrate that the mode of motion of the performer actually has audible effects, was valuable for highlighting the subjectivity of swing. In doing so it provided support for the main hypothesis. If it is true that we perceive swing more strongly when our bodies start to swing, then it plausible that the invitation to the dance might come through sonic recognition of potential partners already out on the floor.

AcknowledgmentsThis research began in classes taught by Fred Lerdahl and Thanassis Rikakis, and they have both continued their support and help throughout. Dave Gluck was extremely kind in allowing me to record his playing, and in discussing the issues with which this paper is concerned; he even gave me a first lesson in playing the ride cymbal. Johanna Grüssner and the members of the Manhattan Jazz Orchestra were also generous in putting their musicianship and expert ears at my disposal, as well as their time and patience. Vijay Iyer helped me through a fruitful conversation which included a contribution to the experimental design. Doug Abrams, the music director of the Manhattan Jazz Orchestra, contributed to this research indirectly through many conversations about music over the course of the last decade or so. Finally, Bret Horton spent a long day assisting me in carrying out experiments. He ran Experiment 3 while I ran Experiment 2 concurrently; without his help this research could not have been completed on time.

Appendix 1: Results of Experiment 1

Art Blakey, A Night at Birdland with the Art Blakey Quintet, vol. 1. Capitol Records, Inc., CDP 7 46519 2, (c) 1987.

"Once in a While"final phrase of partial return of head, 4:01-4:2328 markers tempo = 71.6 bpmave(swing ratio) = .189 (swing ratio) = .038 [swing ratio] = [.142, .253]

"Split Kick"head, 1:05-1:4849 markers tempo = 217.2 bpmave(swing ratio) = .362 (swing ratio) = .027 [swing ratio] = [.308, .403]

return to head, 8:42-9:2346 markers tempo = 217.1 bpmave(swing ratio) = .372 (swing ratio) = .034 [swing ratio] = [.329, .479*]

*Note in the distribution of swing ratios for the return to the head of "Split Kick," the second largest value is .391; .479 is anomalous.

Kenny Clarke, Birth of the Cool. Capitol Records, Inc., CDP 7 92862 2

"Rouge"first half of head, 0:05-0:2928 markers, tempo = 181.1 bpmave(swing ratio) = .256 (swing ratio) = .014 [swing ratio] = [.241, .283]

solo chorus, 1:31-2:1922 markers tempo = 177.4 bpmave(swing ratio) = .285 (swing ratio) = .079 [swing ratio] = [.186, .375]

Max Roach, Birth of the Cool. Capitol Records, Inc., CDP 7 92862 2

"Budo"8 bar intro and first half of head, 0:00-0:2797 markers, tempo = 237.6 bpmave(swing ratio) = .369 (swing ratio) = .020 [swing ratio] = [.326, .406]

trombone solo, final A of mixed solo chorus, last part of: 1:10-1:4631 markers tempo = 240.8 bpmave(swing ratio) = .380 (swing ratio) = .017 [swing ratio] = [.354, .416]

"Move"head, 0:00-0:3834 markers, tempo = 267.9 bpm

ave(swing ratio) = .356 (swing ratio) = .071 [swing ratio] = [.264, .480]

trumpet, then sax solos, 0:33-1:06; these data from sax solo52 markers tempo = 284.4 bpmave(swing ratio) = .40.5 (swing ratio) = .031 [swing ratio] = [.356, .465]

Appendix 2: Results of Experiment 2

Guide:

Numbers 1 and 2 represent the feel of the original sample on which the example is based. Feel 1 had original swing ratio .285, feel 2 had original swing ratio .196.

Letters b through f represent swing ratios of examples. B represents ratio .38, f represents ration .22, and the intermediate letters increment by .04.

Thus 2c indicates an example with ratio .34 which was altered from a sample with ratio .196.

fake 2d: 2d imitated in timing, intensity with one on-the-beat hit

fake 2e: 2e imitated in timing and intensity; all 4 hits used are different, but each are

on-the-beat hits.

fake 2d2: 2d imitated in timing, intensity with hits all taken from different files, but with same original metrical position

compa:a feel1 version with swing ratio .24

compb: a feel2 version with swing ratio .24

(.24 is average of original ratios of feels 1 and 2)

compc:an imitation of 1d in timing and intensity using corresponding hits from feel2

compd: an imitation of 2d in timing and intensity using corresponding hits from feel1

Timing results:

1b-d: 1d preferred by all expressing pref (8), 1c next (of 7, 5 to 2 over 1b)

1d-f: 1d and 1e in dead heat for first/second (5-4); all 9 agree 1f is worst

2b-d: 2d best, then 2c, then 2b. Two expressed no preferences, one each couldn't decide between adjacent pairs, none contradicted that order.

2d-f: virtually a dead heat; 2f does seem to be somewhat less preferred than 2d and 2e

1 & 2 pairings:

1b, 2b: no result

1c, 2c: no result

1d, 2d: no result (v. weak (5-3) pref for 1d)

1e, 2e: no result

1f, 2f: no result (v. weak (5-3) pref for 2f)

Synthetics:

fake2d, 2d: no result (weak (5-2) preference for fake2d, but see below)

fake 2e, 2e: 2e preferred (8-1) (1=int 2tone)

fake2d2, 2d: no result (weak (6-2) preference for fake2d2, but see below)

fake2d, fake2d2, 2d: no result - see below

compa, compb: no result

compc, 1d: 1d preferred (7-2)

compd, 2d: compd preferred (6-2)

Comparison of different fake2d, fake2d2, 2d choices:

In set 13, 10=fake2d, 11= 2d

fake2d chosen by 2, 4, 5, 6, 7

2d chosen by 8, 9

In set 10, 3=fake2d2, 4=2d, 5=fake2d

fake2d over 2d by 1, 3, 4, 5, 8 (overlap 2)

2d over fake2d by 2, 7, 9 (overlap 1)

In set 5, 10=fake2d2, 11=2d

fake2d2 over 2d by 1, 3, 5, 6, 7, 8

2d over fake2d2 by 2, 9

In set 10, 3=fake2d2, 4=2d, 5=fake2d

fake2d2 over 2d by 5, 7, 8, 9 (overlap 3)

2d over fake2d2 by 1, 2, 3 (overlap 1)

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