Motion in Musical Time and Rhythm
Music is an art of time: hence, it needs to be heard in order to be adequately experienced. In a sense, a composer deals with time as a sculptor or an architect fills space. In this sense, time is like space with at least two (horizontal and vertical) and possibly three (depth) dimensions. An image which demonstrates the three dimensions is a flowing river (horizontal) with fluctuating width (vertical) and depth. Width and depth influence the perception of the speed of the flow. The wider and deeper the river, the slower the flow seems; the narrower and shallower the river, the faster the flow seems. Depth may also refer to the density of the musical texture. We, the listeners, do not hear time just as we do not see space. It is for this reason that our perception of time is an integral part of musical experience. Once our attention is directed to that aspect, we can make comments about our perception of the way time-space has been filled.
What factors contribute to our perception of time? One answer would be through the experience of rhythm. But what is rhythm? At this point, rhythm is difficult to define. Perhaps through a discussion of contributions to the definition of rhythmic experience, we can arrive at a satisfactory definition of rhythm itself.
Several authors have provided stimulus for a synthesis of their ideas regarding musical time.1 This synthesis is the essence of this article, which is organized to begin with very broad generalizations about motion and rhythm and lead to more and more specific aspects of the rhythmic experience.
The broadest generalization which can be made about the rhythmic experience is that it provides for the listener a sense of motion and direction. The nature of the motion shapes the listener's perception of the passage of time, just as a person's state of mind can alter his perception of a specific block of time. If one is eager or in a state of anticipation, he will perceive time as passing slowly. Paradoxically, if one is bored, he again perceives time as passing slowly! However, if a person wants to savor every moment, chances are he will perceive its passage as fleeting. Time examined passes slowly, while time forgotten passes quickly.
Jan LaRue states that musical shape is the memory of movement.2 The implications of this statement are formidable. The memory of movement allows for a synoptic view of a composition. It is comparable to an air passenger observing the progression of a car on a highway. The air passenger sees the movement and is aware of the direction in which the car proceeds. Since the car is on the highway, its goal is somewhat predictable—at least on a short term basis. Any side roads along the way offer alternatives for the car to follow. The observer sees where the car goes, whence it has come, and the alternative directions available to it.
What are some of the properties of motion which contribute to a satisfying musical experience? Fluctuating tensions and resolutions are what fill musical time, be they kinetic, emotional, or intellectual. The musical texture is a dense fabric of counterpointing tensions and releases which, although each is a measure of time, does not always coincide with the others. So our temporal experience tends to correspond with the visual experience of a mosaic. If each piece, or even each color, is taken by itself, it then detracts from our perception of a whole entity. It forces the other elements to be perceived as "irrational," unfocused, or lacking shape. Focus and the perception of shape come with a synoptic view. Tensions fluctuate in duration as well as in importance: driving or dragging, emerging in the foreground, or sinking into the background. They give quality to the passage of time which unfolds in the tempo of the basic pulse which the listener perceives.
The concept of motion assumes more shape with the addition of tension-release considered as a type of counterpointing. It is important to recognize the interdependence of musical elements in order to achieve a more comprehensive understanding of a composition. To separate these elements runs the risk of rendering our observations invalid.
How is tension created as a result of motion? What moves? How does (do) it (they) move? Is this movement organized in any way?
Since we are discussing music, we must logically say that the smallest unit of music is the musical tone. But do tones move? Victor Zuckerkandl has made a study of this question; in his view, tones do not really move but contain an inherent kinetic energy which allows them to point toward other tones. I find Zuckerkandl's theory only applicable within the limits of traditional music which exhibits harmonic relationships as a basis for composition. Zuckerkandl explains his theories on the basis of scale degrees manifested both vertically and horizontally in a musical texture. I disagree with his idea that tendency is an inherent quality of tone. Among other things, tonality expresses a hierarchy of tones rather than the equality of tones. So a tone's importance within a tonality does not correspond to its order of appearance in a scale. Rather, the musical context reveals the relationship between tones which the composer has created in order for the listener to perceive tonality. Ultimately then, the scale is a derivative from a musical context, not a determinant of tonality as Zuckerkandl might lead us to believe.
The illusion of tonal motion is the result of the dynamic or tendential quality which tones acquire when they express certain relationships in tonal music. Tonal motion, then, is directed motion toward a goal. As an aspect of the more general musical motion, tonal motion demonstrates that rhythm is a consequence of the interplay of various components of the musical texture.
Curt Sachs attributes the fluency of rhythm to "ever renewed impulses" which act to organize rhythm as well as to grant it life and ease. The word "flow" seems to imply not only motion, but also a continuum that can either give motion direction or provide it with momentum. What, then, is the nature of the aforementioned "impulse" possessing "orderliness"?
To approach the question historically, impulse derives from the concept of the tactus, it simply means "beat" but more importantly implies an undifferentiated beat. A tactus4 is a regularly recurring basic pulse underlying the rhythmic motion of a musical line. Its psychological functions are to govern the sensing of tempo and to give the listener a point of reference which allows for the mental grouping of the rhythms he perceives. The basic pulse must be experienced kinetically, visually, or aurally by the performer and the listener. Its perception is not dependent upon the number of notes, nor on the number of accents, but on the sensing of a steady flow of even pulsations underlying and permeating the rhythms. It is an ordering device for rhythmic shaping. It therefore can be either coordinated with the rhythms, or not coordinated with them. When not coordinated with the rhythms, the basic pulse makes the conflict perceptible.
The concept of basic pulse was in operation well into the eighteenth century. E.T. Cone observes that in Baroque music this specific phenomenon operates on the beat level. The framework seems prefabricated and independent of the musical events it controls. It is as if the beats were placed and regularly divided into the appropriate sub-units, combined into measures and then the music composed upon this framework. Sometimes the music fits the framework exactly, sometimes not, as in the case of fugue subjects in stretto. But the common denominator is the beat. Perhaps the framework is prefabricated in some cases, but the performer's and listener's sense of meter arises from the music itself, as we shall see later.
This is not to deny any sense of accent-release in music before the Baroque period. The two concepts of barline and accent were not originally associated. The presence of the tactus was to facilitate reading and ensemble in complex polyphonic textures.
Meter has been incorporated into the discussion of basic pulse. Each can be more easily understood in contrast to the other. Although "basic pulse" and "meter" are related, they are not the same thing. The underlying regularity of the basic pulse allowed for a wide variety of rhythmic play in music in the Renaissance and Baroque periods. As it became more associated with meter in the Classic period, a different organizing force replaced the basic pulse even though pulse remained an important element in the musical texture. This means of organization was the measure. Regularity remained, but the sense of return in the cycle went to a higher architectonic level. Where the impulse was formerly felt on every beat, a new quality was perceptible—that of accent. Beats following the accented one now acquired the quality of "unaccent." What had been perceptible on a lower level became perceptible on a higher one. This generalization does not exclude the possibility of an even higher architectonic level having priority over the measure level in Classical compositions.
What was formerly a tenuous association became a conventional fact of musical life. The barline became the signpost for the primary accent of the measure. Although the relationship of unaccented to accented beat is not fixed, we must sense accent and release to experience meter at all.
E.T. Cone has drawn a clearer distinction: the Baroque measure is to be heard as a multiplication of the pulse which is primary. The displacement in Baroque subjects is not so "disturbing" because its position in the measure is not as strongly influenced by "accent." Classical themes, however, are more firmly tied to their metrical position because of the accent-release phenomenon on the higher architectonic levels. For the most part the musical context agrees with the framework. Classical syncopations and cross rhythms seem more striking than Baroque ones because they represent a conflict between the rhythmic surface and the notated measure. Elisions and extensions may shift Classical themes to the "wrong" half of the measure. Today, such passages would be clarified by notating a temporary meter change. Such a change was not conventionally allowable until the mid-nineteenth century, and only became common toward the end of that century. We must then concur with E.T. Cone in the statement that ". . . the true measure is always there to be determined, and primary once it is."5
Just as the shift to higher architectonic levels occurs in the Classical period, a similar shift to higher levels occurs again in the Romantic period. Whereas the measure is the largest metrical unit in Classical music, the four-bar phrase of Romantic music is itself metrically conceived and demands to be counted as a "measure." Cone refers to these regular four-bar phrases as "hypermeasures." The tendency for the measure to behave as a beat is already evident in very fast Beethoven scherzos.
We must be careful not to equate meter with regularity, and especially with regularly recurring accents. Meter is produced from the grouping of accented and weak beats. But regularity of accentuation is not a prerequisite of meter. Evidence of this can be found in Gregorian chant, music of the late fourteenth century French Mannerists, and in some twentieth century music where variable meters are present. This music cannot really be called ametric, and certainly not arhythmic. Accent and release are present, and therefore meter is produced, but regularity on the metric level is not present. The regularity that is present is on the level of the basic duration. We can therefore concur with H.E. Smither in his observation that "meter . . . means either regular or irregular grouping of a constant unit of measurement, rather than regularity of accentuation."6 Of particular significance is the "constant unit of measurement"—the basic duration or undifferentiated beat—which transcends stylistic boundaries. Meter in the sense of regular groupings over long space, on the other hand, reveals a stylistic identity of a more limiting nature. The reaction to the "tyranny of the barline" in the nineteenth century attests to these limitations felt by reacting composers.
Jan LaRue observes that regularity quickly develops cyclic responses that are confined to lower architectonic levels and are incapable of producing the basic direction that an effective composition requires.7 But the regularity of recurring pulses and of an underlying meter can produce an overwhelming effect. Rather than destroying rhythm, the regularity of Classic and Romantic meters evolved into a completely new rhythm which proved to be full of subtlety and power—rhythm bound to the law of the meter, rhythm fed by the forces dammed up in meter. Meter is not an accentuation imposed on music from the "outside." It is not in the beats. It is the result of the events between the beats where time merely elapses. The way the music moves from one beat to the next gives quality to the sense of meter. According to Victor Zuckerkandl, it is experienced as a wave. As tones fall on a particular phase of the wave, they acquire a direction which is communicated to the listener. It is not because "one" is assigned to a tone or because the tone is accented that one knows that he is at the beginning of a measure; it is because he has been carried to the wave crest, and simultaneously, beyond it into a new wave cycle. Each tone, and each rest, is characterized for perception by a quality peculiar to its position in the measure. One knows from this quality of the tone where he is in the measure. So the experience of meter, and rhythm as well, is kinetic. It is organic. We experience flow if we allow ourselves to focus on the kinetic aspect of the musical experience.
Going one step further, tones speak easily when they are freed from the constraints of strict metrical accentuation. This allows for the placement of accents as musical declamation. This important qualification of the application of accentuation now frees the interpreter from a blind allegiance to both the barline and the metric wave. The music, and hence, the rhythm is not controlled by the wave. Rather, it is the rhythm that determines the shape of the wave.
Some important questions linger. How is the wave initiated? Who or what is the initiator of the wave? If the performer is the initiator of the wave, does he then give up control of the wave and allow himself to be carried by the momentum of the wave—like a surfer? Or does he maintain full control of the wave as a driver controls his car? One would think that the previous discussion attributes control of the wave's momentum to the rhythm itself, but that would seem to apply to the ideal performance. In actuality, the performer activates the wave which the composer has initiated by establishing rhythmic relationships within the composition.
Recalling the kinetic quality of rhythm, it is not the unequal lengths of beats that disturb a listener in a bad performance where the sense of time is erratic. Timing seems erratic when a performer fails to project a metric wave. The metric wave provides a point of reference for the perception of the equality and inequality of beats. The so-called equality of beats then proves to be rhythmic balance. It is their kinetic quality which allows us to perceive differences in the duration of tones. To understand the essence of rhythm we must sense the preparation of a new event in the ending of a previous one. To move rhythmically, a person's gestures must be complete so that one can sense a beginning, intent, and fulfillment, and in that fulfillment, anticipation of another gesture. It is the same in music. Erwin Stein suggests that to bring a score to life, the performer must understand and execute the composer's plan. The score indicates not only what the motions of a performer should be, but the mental action as well. Performer and listener alike should view groups of notes as latent forces waiting to be released in performance in continually fluctuating tensions and resolutions. In this way, music is felt to move. "In the visible world, movement is the only condition in which the progress of time is directly perceptible. Applied to music, the term movement signifies a continuous change of sonorities."8
Perhaps it is clear by now that rhythm is not to be experienced as a mechanical motion, but as an organic motion. Regularity as manifested in the basic pulse or meter acts as an important organizing force in a large body of music literature ranging from the twelfth century to the present. The many exceptions only seem to prove the rule. To say that man moves rhythmically implies that there is room for fluctuation in motion. Fluidity can still be observed without the necessity of an unchanging, unrelenting flow. What allows for this is that motion, just as speed, is relative. Only in relation to something else do we perceive motion as fast or slow, driving or plodding. Rhythm is a proportional phenomenon. Rhythmic grouping is a mental fact, not a physical one. In other words, the mind has a tendency to simplify and organize what it perceives. It compensates for any slight irregularities which may exist in the duration of a rhythmic group. The mind draws relationships where it can, seeking order in apparent chaos. Awareness of this gives the performer more freedom. He can then play with illusions of time based on a highly developed sense of proportion. He controls the rhythmic motion making adjustments when necessary: tempo fluctuations (rubatos, accelerandos, or ritardandos), or even compensation for a relatively inappropriate sound. Ideally, as he plays, he adjusts his sound in relation to what preceded in order to correspond to a sound image derived from a study of the composition. If he makes every effort to reveal in his performance his conception of the structure, then his chances of convincing his audience are greatly improved. "After all, one test of a good performance is the extent to which a listener knows where he is, even in a work with which he is unfamiliar."9
Any structural ambiguities in the score are left to the performer to decide upon and communicate through his sense of form and timing. And what is a performer concerned with in dealing with problems of timing if it is not the question of proportions? Through timing, his interpretation of the structure is revealed on several architectonic levels, not just one. The performer determines the pace at which he wants his listener to follow without missing the context.
We can now begin to formulate a definition of rhythm based on the previous discussion. Our information is still incomplete. Consequently, the following discussion will slightly modify the definition which will now be posed.
. . . musical rhythm is: movement in time, divided into units which are characterized by the principle of proportional values. These units, through proportion, establish a basic pulse discernible to the mind as regularly recurring beats of equal duration.10
Because we have not escaped from hearing music in our culture, we bring to every new musical experience a set of expectations. These expectations become a basis for our sense of satisfaction and fulfillment. Leonard B. Meyer deals with the subject of expectation rather extensively in his book, Emotion and Meaning in Music.
Composers of the common practice period were grappling with the notion of expectation. "Common practice" (applied long after the end of the age) indicates a conventional vocabulary—a standardized means of musical communication.
The great composers of the art music which was to survive their age with distinction balanced clichés with more original musical content. Their aim was to manipulate a listener's expectations so that the temporary delay of fulfillment could equal or surpass the anticipated fulfillment of expectations. As the common practice period progressed, and in a sense evolved (witness the fairly consistent "development" of harmony, for example, from the brand of chromaticism of the late Baroque which is the result of contrapuntal—horizontal—manipulations, to the diatonic textures and more vertical orientation with retention of the melodic dimension in the Classical period, to the increasingly "functional"—vertical as well as horizontal—chromaticism of the Romantic period), the number of clichés increased as did a basis for expectation in music.
An important facet of expectation is that of ambiguity. Ambiguity attracts the listener's attention. This clearly explains one of the main reasons why a composer would exploit it. Ambiguity can only be perceived when the listener has more than one expectation for the solution of a conflict of interests—when he can envision several potential relationships given the information at hand. Detection of ambiguity is impossible without the ingraining of habits of perception—both in the composer and his audience. Otherwise, there would be no awareness of the artist's fulfillment of and subtle departures from established conventions and forms. The esthetic pleasure derived is from the arousal and suspension of fulfillment of expectations. These expectations constantly undergo revision in light of the direction taken by the music.
A composer can calculate the effect of ambiguous musical events by careful consideration of their position. The earlier in the musical series (e.g. phrase, period, section) the ambiguities occur, the more directions they can possibly follow toward clarification of their meaning. Whereas, later in the musical series, expectations have more specific direction, and the solution is more probable. It is late in the musical series where the most satisfying deviations occur. The greater the buildup of tension, the greater is the release upon resolution. But such an experience of suspense has no esthetic value unless the resolution is understandable and logical within the context.
It is important to understand the Romantic rhythmic heritage; the roots of basic pulse stemming from Baroque music, the influence of meter on rhythm in Classical music, and the late Classical treatment of measures as beats. From this perspective, one might sense an evolutionary progression in the development of rhythm that is comparable with that of harmonic rhythm during the same time which inflated to fill these larger units. The result was an expansiveness due to the slower harmonic rhythm and less frequent strong accents. At the same time as this turn of events, one can also see a spiraling of ideas—once again only slightly different—as seen in the return of contrapuntal textures with the added attraction of a clear chordal basis.11
We can view these occurrences as a stylistic phenomenon. We can even say that a historical viewpoint is a stylistic viewpoint. It is through the interplay of particular musical devices and elements in a fairly predictable way that a certain style emerges and becomes identifiable.
Our ability to identify and specify with any precision what we intuit concerning musical style is greatly dependent upon the consciousness with which we have developed this sense of style. The more we have listened to music with focused awareness, the broader our base of expectations; consequently, the music becomes more predictable. By previous exposure to music, a practiced listener will not only revise his expectations, but will focus his attention so as to impose groupings chosen over others in particular stylistic circumstances.
There are three elements in a rhythmic group: upbeat or anacrusis, accent, and afterbeat. Upbeat and afterbeat are types of weak beats. None feels like either of the others, nor does any one itself always feel the same. Cooper and Meyer define accent as a beat which is "marked for consciousness" by any one or more of a variety of ways. Duration, intensity, melodic contour, regularity of recurring patterns, and registral placement contribute to the creation of an impression of accent. However, none of them appears to be an invariable and necessary element of accent. Accent is a relational concept. It acts as a focal point to which weaker beats and rhythmic groups are drawn. The placement of accented beats tends to be fixed and stable, while weak beats can simultaneously belong to more than one group or accent.
We can return to Zuckerkandl's metric wave to visualize the phenomenon of the kinetic association of weak with strong beats by virtue of their proximity. Accents can be heard as temporary or intermediate goals of motion. A sense of mobility in music does not cease until the melodic motion carries to a point of relative repose—the goal of melodic movement. This goal is what we experience as cadence in its varying degrees of repose. Before we reach these points of repose, we experience the wave through the three different types of motion which accompany it (accent, upbeat, and afterbeat). These terms reflect their relationship to the accented beat with which they are grouped. The notation remains the same, but the interpretation of the grouping changes. The more a tone seems to be oriented toward a goal, the more it tends to function as an anacrusis. "Motion toward a goal" is probably the best generalization which can be made concerning the upbeat. It is a kind of kinetic energy pointing beyond itself to future goals.
Accents can occur anywhere on the metric wave and not necessarily change its basic shape. They can, however, change its character. Like rhythms, accents are a proportional phenomenon. They are subject to dynamic proportions. It is not absolute but relative loudness that is important. Otherwise, the metric wave is heard as being distorted. Too often, musicians are guilty of this kind of disproportional playing. If an accent "screams" or else is "swallowed," it can disturb the shaping of the melodic line. It is not always necessary to play a downbeat loudly. A stress on the downbeat can be achieved by phrasing toward the downbeat or by lingering on the first note or chord of the bar for a fraction of a second. A downbeat should be additionally emphasized in such circumstances as when it follows a syncopated rhythm.
Intelligent interpretation, then, takes into consideration such things as the unique shape of the melody plus the interplay of other musical elements. The shaping which a performer chooses is made apparent to an audience through his phrasing and articulation. Erwin Stein suggests that the most subtle means of phrasing is a keen sense of timing for the placement of notes, and this can replace accents as well as punctuation on a small scale. For reasons of artistic economy, the subtle means is preferable simply because accents are articulate by nature, whereas articulation itself adequately replaces accentuation.12 Schnabel, fully aware of this fact, taught that accents have an interrupting effect. When beginning a new phrase, one should accent the first note of the phrase, or at least separate it from the previous phrase. But one should avoid accents in long sustained melodies.
The importance of articulation as a means of convincing phrasing cannot be overemphasized. When "pronounced correctly," the phrase does not call attention to itself, and the musical content can emerge as all-important. But if a phrase is "mispronounced," our attention is drawn to the "mispronunciation" and away from the musical content.
Concerning rests, Stein states that their duration is more dependent upon their function within the structure than on "exact" duration. One must decide whether the rest is meant to create tension or relaxation. A performer best communicates its function if he keenly feels, rather than exactly counts, the proper time interval.13
HIGHER ARCHITECTONIC LEVELS
Like the grouping of smaller rhythmic units, phrasing involves a larger level of grouping and separation of units. Although there are many instances in which a clear solution can be reached concerning the separation of phrases, they may overlap. Just as weak beats may belong to two rhythmic groups, so may the end of a phrase belong as well to the beginning of the following phrase. And more importantly, an entire phrase may retroactively be understood as the first part of another phrase.
As a part of proper phrasing, it is important to be able to determine the melodic center of a phrase so that it may be communicated in performance. It is not necessarily the highest, longest, or loudest of the notes but it is usually emphasized by a rhythmical stress or dynamic accent, however slight. Good phrasing consists not only in separating or connecting phrases, but also in shaping rhythms and dynamics to highlight the melodic center. A misjudgment in its determination can result in a change in character of the phrase. It is the determination of the melodic center which justifies all our dynamic nuances as well as nuance in tempo fluctuation.
Patchwork quilts of whole sections built of periods and double periods are plentiful in the Classical period where the norm became four- and eight-bar periods. Even with the danger of monotony, periodic phrasing brought with it new possibilities of ever larger structures. For composers, it was not just a matter of dashing off a longer composition in the same rhythmic mold with the beat or measure as the primary unit. It was a matter of providing the listener with something that could sustain his attention and concentration over long spans of time. The sophisticated performer must clearly stratify the various levels of activity which are functioning simultaneously so as to be easily detected by the listener. Further, he must lead the listener gradually to sense the organic unity, the "inevitability" of the composition through the elapse of time. Ultimately, the listener should be able to sense the flow and the total effect of the composition.
Structural awareness of a composition opens the door to relationships which were previously undetected—relationships and features which can exert an opposite influence on the ones previously recognized. The lower levels are neither "inferior" nor invalid. They are the surface levels. But they are not necessarily the same levels focused upon by both the performer and his audience. One must consider the whole structure to determine the appropriate movement. Not just rhythm, but the other aspects of music determine what is felt on the higher levels.
It is presumed that with a strong feeling for the norm of rhythmic behavior in a metric context, any deviation from that norm will be recognized more readily. This, in turn, will facilitate the untangling of rhythmic complexities such as those found in the works of Robert Schumann.
There are at least two possible meanings of complex passages. Each is equally plausible, but in many cases, one meaning may be more appropriate than the other by virtue of the character of the entire passage or the entire piece. On the one hand, an ambiguous passage may invite a syncopated rendering. That is, the underlying metric pulse is to be felt in conflict with the offbeat accents on the surface rhythm, whether or not there is an articulation on the stronger beats of the measure. A syncopated rendering is perceived as such if the pulse of the regular time is somehow continued, either in another part of the texture or by implication only. By the direction of our attention to different rhythmic levels, we can identify such a subtle implication because the norm of the meter builds in us a prejudice for certain kinds of rhythmic activity. Levels are recognized upon the repetition of units which can again synthesize on the next higher level. Once set up, the unit stays in force until it is replaced by another kind of unit; even then the established prejudice resists the replacement, and syncopation can continue for some time without disturbance.
On the other hand, an ambiguous passage may invite a mental rebarring which would eliminate the force of the metric continuum in order to establish a new one. This is most likely in passages where the listener is meant to feel at ease in the new rhythm, accepting it as something in its own right.
When the meaning of a passage is to contradict the original meter, this resistance should be perceived with the eye as well as the ear. It should be visible against the bars as well as in the performer's or the conductor's beat.
The friction which syncopated renderings create can be viewed as the "dissonances of rhythm," just as non-chord tones are the dissonances in a harmonic context. Syncopated accompaniments can lend a drive to a passage, keeping the tone alive where it might not be otherwise. The syncopated tone assumes a different quality of motion from that of the unsyncopated tones. This will usually be confirmed visually by the barring.
One should attempt to determine when there should be a contradiction between the visual and the aural—when the listener is meant to set aside the former metric continuum and assume the new one. This is what is meant by the term "metric displacement."
Often there are structural explanations for the use of metric displacement as well as for variety in rhythmic activity. One such explanation is for the establishment of what E.T. Cone calls the "structural downbeat," the important point of simultaneous harmonic and rhythmic arrival that is so strong as to retrospectively turn what precedes it into its own upbeat.
To communicate the structural downbeat in performance, greater weight (accent) can safely be given quite strongly without disturbing the flow of the melody. Because of the mind's astonishing ability to connect notes of similar weight and importance, the mind will remain undisturbed by notes of a lower architectonic level occurring between those of the higher ones.
Our experience of rhythm in music is not limited to the purely durational aspect. Just as we experience the rhythm of surface articulation, of the repetition of patterns (both pitch and rhythm), of metric rhythm, and many others resulting from the interplay of various musical elements, we also experience rhythm in what may be defined as the rhythmic quality of the rate of harmonic change. Motion remains an important component of this aspect of rhythmic experience. Dissonance is basically a contrapuntal principle in which the dissonant tones in a chord "want" to resolve to a more consonant relationship. That is why we can speak of chords as being composed of moving voices.
To find structurally important harmonic progressions, one should play just the harmonic rhythm in simple chords, rather than the surface rhythm which activates the chords into arpeggios, broken chords, or figuration. In this way one may follow the thread of a modulation more easily, locating the notes deserving of more attention or "direction-giving force" than others. It then becomes evident that harmonic tensions and metric tensions often coincide. This is an important technique in leading the listener to hear those connections better. The entire musical pattern is more likely to be perceived in the simplest and most satisfactory terms. This is why rhythmic organization is not just a matter of duration and accent, but of these elements in relation to all other aspects of the entire organization of the texture.
If the reader reflects on his musical experience, he may remember that his general impressions of the extremes of tranquility and restlessness were not solely the result of surface rhythm and pace, but also of tensions created by dissonant harmonies moving to their resolutions, and by the way in which these harmonies moved. He may have noticed that harmonic changes between beats create more restlessness than those occurring on the beat or measure. This is especially true when the harmonies themselves are more "active" (dissonant—demanding resolution). For the most part, harmonic rhythm rarely agrees with the single architectonic level of metric rhythm. It is one aspect that strongly determines not only the forward impulse of the music, but the character of that impulse.
Harmonic rhythm sometimes contributes to the temporary displacement of metric rhythm. Together with the other elements of accent and placement, it can create a metric rhythm of its own in disagreement with the notated barring.
I would like to suggest that metric displacement is accomplished by a combination of the many devices mentioned throughout this article. Metric displacement is employed for reasons ranging from variety in the surface rhythm, to arrival at the structural downbeat, to attempted relief of repetitious, relentless, monotonous periodicity. In any case, metric displacement is a deviation from the norm in a metric continuum which we have learned to mentally perpetuate when listening to traditional art music.
The ideas presented in this article are offered as possible catalysts for the reader's imagination and interpretive powers. Perhaps the reader will discover opportunities to apply these principles to music in many more instances than he previously would have considered appropriate.
1Victor Zuckerkandl, Sound and Symbol, Bollingen Series XLIV, 1956, and Bollingen Series, 1969 (Princeton, N.J.: Princeton University Press); Edward T. Cone, Musical Form and Musical Performance (New York: W.W. Norton & Co., Inc., 1968); Leonard B. Meyer, Emotion and Meaning in Music (Chicago and London: University of Chicago Press, 1956); Grosvenor Cooper and Leonard B. Meyer, The Rhythmic Structure of Music (Chicago and London: University of Chicago Press, 1960); Erwin Stein, Form and Performance (New York: Alfred A. Knopf, 1962); Susanne Langer, Feeling and Form (New York: Charles Scribner's Sons, 1953); Jan LaRue, Guidelines for Style Analysis (New York: W.W. Norton & Co., Inc., 1970); James Lockhart Mursell, The Psychology of Music (New York: W.W. Norton & Co., Inc., 1937); Frederick Dorian, The History of Music in Performance (New York: W.W. Norton & Co., Inc., 1942); Karl Eschmann, Changing Forms in Modern Music, 2nd ed. (Boston: E.C. Schirmer Music Co., 1968); Curt Sachs, Rhythm and Tempo (New York: W.W. Norton & Co., Inc., 1953); Konrad Wolff, The Teaching of Artur Schnabel (New York and Washington: Praeger Publishers, 1973); H.D. Aiken, "The Aesthetic Relevance of Belief," Journal of Aesthetics IX (1950): 301-315; Walter Piston, Harmony (New York: W.W. Norton & Co., Inc., 1948); Donald Francis Tovey, The Forms of Music (London: Oxford University Press, 1944), pp. 175-91; Howard E. Smither, "The Rhythmic Analysis of 20th Century Music," Journal of Music Theory VIII (1964): 82.
2Jan LaRue, Guidelines for Style Analysis, p. 115.
3Many writers make fine distinctions in the usage of the terms "pulse," "beat," "basic duration," and "basic pulse." Cooper and Meyer define "pulses" as regularly recurring stimuli that are undifferentiated. They then define "beats" as regularly recurring stimuli that are differentiated by accent and the lack of accent. I will adhere to these definitions. "Basic pulse" as used here will mean the regularly recurring stimuli by which tempo is experienced. This means that pulses can be experienced on higher and lower levels, but unless they are the tempo controlling pulses they will not be considered as "basic pulses." Past composers have presented such startling experiments in rhythm that fluctuations on the level of the basic pulse occur. However, on a lower (shorter durations) level, a common denominator of pulses assumes significance as the unifying factor in passages where such fluctuations occur. This common denominator of pulses will be referred to here as "basic duration."
4The terms "Takt" and "tactus" have historical implications and are associated primarily with the sixteenth century. For this article, the term "basic pulse" will be used since it has no historical connotations.
5Cone, Musical Form and Musical Performance, p. 73 (emphasis mine).
6Smither, "The Rhythmic Analysis of 20th Century Music," p. 82 (emphasis mine).
7LaRue, Guidelines for Style Analysis, p. 106.
8Stein, Form and Performance, p. 126.
9Cone, Musical Form and Musical Performance, p. 45.
10James W. Krehbiel, Rhythm, Meter, and Syncopation (Bloomington: School of Music, Indiana University, 1958) p. 19.
11Bach's contemporary, Rameau, posed the theory of the invertibility of chords. The idea's significance was twofold: a change from a horizontal orientation to a vertical one, and the new potential to identify chords as units—one chord with three positions rather than three different chords. Bach's rejection of Rameau's theory strongly indicates that his orientation was definitely linear and not chordal. In his Introduction to C.P.E. Bach's Essay on the True Art of Playing Keyboard Instruments, editor and translator William J. Mitchell (New York: W.W. Norton & Co., Inc., 1949) mentions both J.S. Bach's and C.P.E. Bach's rejection of Rameau's theory. Mitchell cites C.P.E. Bach's letter to Kirnberger, specified in his Kunst des reinen Satzes (pt. II, Sec. 3, p. 188). See C.P.E. Bach's Essay, Mitchell translation, pp. 17-19.
12Stein, Form and Performance, p. 46.
13Stein, Form and Performance, p. 57.