Compositional Uses of The Crossing Phenomenon In Recent Music

Compositional Uses of The Crossing Phenomenon In Recent Music

Gerald Ruffertshoefer Gabel

The evolution of musical stylistic traits from one era to another has, in part, been achieved gradually through a particular treatment of musical elements or phenomena which had been either avoided or unrecognized in previous epochs. For instance, dynamics were not indicated in music until the early Baroque. Once it was recognized that composers could more accurately depict a musical idea through their use, dynamics became an integral force in the shaping of musical materials. The manner of their implementation contributed to the characterization of musical style in succeeding centuries.¹ Similar evolutionary tendencies have occurred in relation to other musical elements.

While engaged in a study of musical texture, it was found that the phenomenon of "crossing" was being utilized to a greater extent in this century than in times past. While it is difficult to say that crossing is characteristic of 20th century musical style, one can argue that its use is important in the music of composers such as Webern, Xenakis, Ligeti, Lutoslawski, Nancarrow, Debussy and others. For instance, part crossing occurs with such regularity in the rhythmically free sections of Lutoslawski's orchestral works that it may be considered a feature of his compositional language. Crossing implies the intersection of musical phenomena to such a degree that their relative placement is reversed. Perhaps the most common form is part crossing.² In this case, the relative pitch ranges of two or more parts are reversed; the lower part becomes the higher part and the higher becomes the lower. While it is true that the crossing phenomenon is seldom employed as a focal structural .element in the compositional process, the numerous examples of its use in this century suggest that it is an exploitable phenomenon which is worthy of observation and discussion.

Since the crossing of two melodic lines is somewhat common in music from previous centuries and since the aforementioned article addresses common practice usage; this paper will focus upon examples from the present century which provide new insights into the use of the crossing phenomenon. Specifically, part crossing will be discussed in the context of unorthodox contrapuntal settings. This will include examples which exhibit atypical melodic construction, unusual contrapuntal interaction between component lines in a texture, and the production of part crossing in textures which feature the accumulation of many component lines (mass-like textures).

There are also several musical phenomena besides pitch which have been subjected to treatment, similar to part crossing. One is a technical device utilized in piano literature in which the hands physically cross one another. A second technique is the use of different tempos in concurrent lines. At a designated point in the unfolding of the composition, each tempo may articulate beat 1 of a measure simultaneously. Then, due to the differing temporal rates, they will digress from one another again. One may think of this as a temporal crossing in the formal sense. There is another crossing phenomenon that is closely related to temporal crossing. One may create the illusion of increasing tempo without a tempo change. This is achieved by decreasing the duration of notes within a line. The pulse remains constant, yet the increasing linear density of articulations, for example, causes the sequence to accelerate. A third technique, which is found only in twelve-tone and serial musics, features the crossing of various farms of a row. Finally, the phenomenon of crossing has been extensively applied to the movement of sound in musical and physical space.

Part Crossing as a Product of Unconventional Contrapuntal Procedures.

After the Baroque era, counterpoint became of secondary importance to harmony as the focal point of structural organization in music. By the turn of the twentieth century, tonal practice had been stretched to the point that composers had begun to search for alternative modes of construction which would instill their creative endeavors with new vitality. One of the primary developments was the gradual re-implementation of contrapuntal devices. As the harmonic vocabulary became more inflected and the limits of tonality tested to the extreme, greater emphasis was placed on linear relationships in order that composers might maintain adequate control over compositional materials. This "reactivation of the polyphonic evolution" took place primarily in the music of Arnold Schoenberg and his disciples Anton Webern and Alban Berg.

Anton Webern's music portrayed an extended view of the traditional contrapuntal implications found in Schoenberg's music. The lines that make up Schoenberg's textures were constructed according to traditional rhythmic percepts, were distinguishable as independent lines, and were combined according to traditional considerations of complementary rhythm. Schoenberg's treatment of the row was thematically oriented. On the other hand, Webern utilized it as a more abstract phenomenon and did not view it as a source for melodic construction. In fact, he tended more towards condensation and fragmentation (or athematic construction) particularly in terms of rhythm.

It is important to consider the extent to which linear elements can be called lines in Webern's music. Example 1, extracted from the first movement of the String Quartet, Op. 28, illustrates the angular and fragmented nature of his "melodic" construction. Not only are the two note groupings indistinguishable as lines, but they are separated by internal silences of equivalent duration, further inhibiting their perception as lines. Instead of a texture of lines, one finds a texture which is frequently called " pointillistic." The paradox is that even though we are dealing with music that is strictly canonic, it cannot be called contrapuntal in the traditional sense. Although Example 1 is set in canon, one hears only a series of independent two note groupings. Having been integrated as an important structural element, the silences disrupt not only the sense of linearity but also the sense of contrapuntal flow.

There was also a marked tendency towards angularity (disjunctness) in Webern's use of intervals linearly. This resulted in part crossing. Webern's use of angularity contributed to a lack of separateness and, thus, to the equivalence of parts. Through the initial viola entrance in Example 1, the domains of the parts remain relatively distinct with minimal incursion from each other and no instances of crossing.

Example 1: Webern's String Quartet, Op.. 28 First Movement, mm. 22-24

Copyright 1939 by Hawkes & Son (London) Ltd., Copyright assigned 1955 toUniversal Edition A.G., Wien. Copyright renewed. All rights reserved.Used by permission of European American Music Distributors Corporation, sole U.S. agent for Universal Edition.

In the third measure, the situation alters noticeably. On the second beat, the viola (F5)⁴ crosses the second violin part (D5). This is immediately followed by the violoncello (G4) crossing with the second violin (E flat 4), significantly affecting their relative placement. The combination of angular intervallic successions and pointillistic texture creates a considerable number of crossings. Without a doubt, Webern utilizes the technique to such an extent that crossing may be considered characteristic of his style.

Part crossing may also create a lack of separateness even in textures which feature a more traditional melodic design. Beginning in m. 52 of my Saraph for Three Bassoons (Example 2), lines one and three engage in a two measure passage which features a predominance of wide skips. Unlike Webern, this example does not feature skips beyond the octave, nor are rests functional in the melodic construction. Nevertheless, one confronts a similar unrelenting invasion of the parts into one another's pitch domains. In fact, the domains of the two parts are virtually the same. Until the third beat of m. 53, they do not engage in crossing to any appreciable degree. On the first beat of m. 53 the first part does supersede the third. Since they had only engaged in a unison up to this point in the example, it is premature to call this a crossing since the first line returns to the unison before any pitch change in the other one. Beginning with the fourth beat of m. 53, they begin a series of crossings which culminate with the return of the original Unison. Due primarily to the number of unisons on the pitch E flat 4, they never achieve melodic independence. This is evident even prior to the point at which they engage in crossing. The singular nature of the shared domain coupled with the persistent articulation of a unison and subsequent crossing, lock them into a singular identity; a complex, angular texture with Eb4 as the focus of pitch activity.

Another example of crossing in an extended contrapuntal setting is found at rehearsal 24 of "Repos dans le Malheur" from Trois Poernes d'Henri Michaux by Witold Lutoslawski (Example 3). The texture is characterized by a plethora of crossings which are achieved through the massing technique. It involves the accumulation of, at times, an extreme number of independent, imitatively conceived parts (in this case 20). In effect, the individual attributes of each line are subsumed into a global identity: the texture of the passage. The domains of the vocal sections within the choir overlap considerably. However, each choral section contains five lines which evolve independently of each other. Lutoslawski called this "collective ad libitum." By this process, each performer proceeds at his own pace. In the performance instructions Lutoslawki writes:

The duration of the notes is in general free, except for those having pauses, which should be longer than the others. The greatest naturalness in sound-production and interpretation is recommended. Thus, the more difficult intervals may be attacked slowly and the easier ones more quickly. The performance of the whole section, however, should be free of haste, for which reason the duration of the individual notes should not be less than 0.5 seconds^.5

One can expect significant part crossing within each choral section as well as between them. Following individual lines is impossible under such circumstances, which, in this instance, is the desired result.

Example 3: Lutoslawski's "Repos dans le Malheur" from Example 3 of Lutoslawski's "Repos dans le Malheur" from Trois Poemes d'Henri Michaux, Rehearsal numbers 24-25

Reproduced by kind permission of the copyright owner, & W Chester/Edition Wilhelm Hansen London Ltd.

Webern's Piano Variations, Op. 27 is an excellent example of the extended use of crossing. Two types are found in the work: row and hand crossing. The second movement (Example 5a) is a strict canon in contrary motion. The subject begins in the left hand and is imitated at the temporal interval of an eighth note in the right. The original form of the row is found in the right hand (01) at the beginning of the movement. A cursory look through the example reveals that the last note of the realization of one row is simultaneously the first note of the realization of the next row form in the same hand. The hand in which a particular sequence of row realizations appears changes in five places: measures 5, 6, 8, 17 and 18. Each of these crossings produces a change of function for the rows. In each case, the subject row becomes the countersubject row and vice versa. Additionally, as the first main section is repeated there is a crossing of the function of the entire sequence of rows found in each hand. In the initial pass, the sequence of rows indicated by a solid line begin in the right while those indicated by a dotted line are found in the left. At the end of this section this arrangement has been registrally reordered. Therefore, the repeat will begin with the "dotted line" in the right hand and the "solid line" in the left and end as the piece began. Ideally, the second main section should begin with the "solid line" sequence of rows in the right and "dotted line" in the left. However, for clarity in viewing the unfolding of the rows, it was decided to overlook the repeat at the end of the first main section. Therefore, the actual row sequences for the hands are reversed. It is possible that, since he was not prone to repeating entire sections of a composition, Webern purposefully employed the technique of crossing the row sequence in order to provide a structural distinction between the original statement and repetition of both sections of the movement.

Example 4: Debussy's Images I, Third Movement, mm. 1-17

Example 5b: Webern's Piano Variations, Op. 27 Hand Crossing in the Second Movement

In Anton Von Webern: A Chronicle of His Life and Work, Hans and Rosaleen Moldenhauer clarify Webern's reason for including hand crossing in the Variations:

Dwelling on some of the pianistic details of the work, Stadlen⁶ referred to the awkward crossing of hands demanded for the proper execution of of the Scherzo movement movement: 'Webern said that the inevitable difficulty in bringing it off would invest it with just the right kind of phrasing.⁷

In Example 5a, brackets indicate phrasing based upon Weliern s implementation of hand crossing. Each phrase includes a hand crossing followed b a reversal of direction to another crossing thereby re-establishing the placement of the hands encountered at the beginning of the phrase. Therefore, phrase #1 is wade up of five successive diads, the next phrase by the next seven diads, and the final phrase of the first half of the work by three dials. The 5 + 7 + 3 construction is reflected in the second half although with 'a subtle change. The final diad before the repeat in m. 11 serves simultaneously as the beginning of the repeat and as the beginning of the second half of the work. However, the second half, as notated, begin N after the repeat. For phrasing purposes, the fourth phrase begins in m. 11 but the hand crossing pattern begins at in. 12. With this in mind, the grouping of diads^. into phrases in the second half is 6 + 7 + 3. Webern, then, had at least two reasons for the sectionalization of this movement. First, the phrase structure (which is conditioned by the ordering of hand crossing) divides it into two groups of three phrases. The ordering of phrase lengths provides a sense of unity in the first_, half of the movement. Secondly, the row crossings provide the means by which both halves of the work are repeated. Therefore, crossing principles as related to row manipulation and phrase structure provide a tactic for formal sectionalization and unity in this movement. Unity is also achieved through the implementation of the limited number of diads.

Unlike Webern's exposure of musical elements to crossing at various structural levels, Conlon Nancarrow crosses four tempos in his Canon #36 ( 17 / 18 / 19 20 ) (Example 6a). Nancarrow's music is important in that not only does he establish tempo as the primary temporal element but the tempo relationships themselves are often the modus operandi of his compositional inspiration. In his article "Inexorable Continuities," Roger Reynolds wrote:

There is a tendency to think of a musical element 'rhythm' as though it included meter and tempo (in the sense that they are supportive conditions over which rhythmic invention takes place). Nancarrow, however, seems to identify tempo as the prime temporal consideration and to relegate other time-related elements to lesser status.⁸

Each of the four lines in Canon #36 possesses a tempo distinct from that of the other parts. One line progresses at the rate of a whole note equaling MM=85, another at MM=90, the third at MM=95, and the last at MM=100. The ratio of these tempi is the ratio in the title of the work (17/18/19/20). In the time it takes for the MM=85 line to progress through 17 measures, the MM=90 line will have stated 18 measures, the MM=95 line 19 measures, and the MM=100 line 20 measures. At this point, all four parts articulate beat 1 of their next measure simultaneously. There will not be another simultaneous articulation of beat 1 in any measure until the cycle has been re-stated. Once all four lines have entered, there are 33 statements of the cycle after which they one at a time drop out in the reverse order in which they entered. The incessant implementation of the temporal cycle, at times, acts as a formal delimiter in the work. In fact, Nancarrow many times effects an abrupt textural change at points of temporal simultaneity. As a result, one's sense of expectancy can be, in a sense, shaped by the anticipated return of temporal simultaneity.

For the purposes of this discussion, the formal implications are not as critical as the actual temporal relationships within each cycle. Between any two temporal simultaneities in the work, the same succession of skewed pulse relationships between lines exists (Example 6b). As one approaches a point halfway between two simultaneities, the duration between articulations of the downbeats of measures (in fact of any beat within any measure) between parts becomes greater. After the half-way point, the duration between articulations of downbeats gradually decreases (perceptually) resulting in the next temporal simultaneity. This effect is similar to incursion and excursion in the crossing of parts (melodic lines). As they incur towards a unison, their pitch separation decreases. As they, excur from one another, their separation increases. It is in this process of incursion and excursion (increase and decrease of distance or duration) that a similarity exists between the crossing of pitched lines and the crossing of lines with concurrently differing tempos. However, a difference does exist between these types of crossing (besides the differences between pitch and time). There is not a real crossing in the tempo domain per se (at least not in the sense of lines displacing one another as is the case in the pitch domain). Part crossing is contingent upon a condition in which the domains of parts have distinction: they move from separateness to a point of intersection and back to separateness. However, in Canon #36 the opposite is the case. The formal inclination of the tempo cycle establishes an expectancy of intersection. Therefore, the tempo model moves from intersection to separation and back towards another intersection. Even though the conditions are very much the same, the results achieved through pitch and tempo crossing are markedly different.

and more highly control led rate of change. Furthermore, the temporal changes themselves tend to fluctuate gradually whereas those in Canon #36 were stable within each part. The work is subtitled "Canon X." The designation "X" is a graphic suggestion of the temporal crossing by the two lines in the work. In his article

"Conlon Nancarrow's Studies for Player Piano," James Tenney described the temporal effect achieved in Canon X:

The first part (in the bass) begins at a relatively slow tempo (3.5 notes/second- the numerical values here and following are my [Tenney's] own estimates). The second (treble) voice begins, in the next system, at a very fast tempo (37 notes/second). From the beginning to the end of the piece the tempo of the first voice gradually increases, while that of the second voice decreases. A little before the half-way point in the piece the tempos of the two voices "cross", reversing the fast/slow relationship between them. By the end of the piece, the originally fast voice has slowed down from its initial 37 notes/second to a tempo of 2.33 notes/second, while the other voice has accelerated to an incredible 111 notes per second! The tempo\-changes in the course of the piece are linear functions of elapsed time only when plotted with respect to note-duration (not tempo as such), which means- among other things that the rate of change of tempo is itself a function of tempo. That is, the faster the tempo, the faster the rate of change of tempo.⁹

The entirety of this work is an ingeniously conceived illustration of the process of incursion and excursion in the crossing of parts. Unlike Canon #36, the temporal crossing in this example is very similar to the model for crossing in the pitch domain. There is no consistently repeating cycle of temporal relationships between parts. Therefore, one's sense of expectation is shaped differently. In Canon, X, the temporal relationship begins with a relatively high degree of separateness, proceeds towards a point of intersection, and then excurs to an even greater degree of separateness. The effect is made even more pronounced by the fact that the pitch relationships between the two parts coincide_, precisely with the temporal relationships. The bass part moves from low to high while the treble moves from high to low. The pitch crossing occurs at the same time as the tempo crossing. Therefore, Canon X is a rare example of a "double cross" in which two primary musical elements are structured such that their deployment produces a synchronized crossing.

In my work Dragon for Orchestra (Example 7a), the effect found in Nancarrow's Canon X is augmented by increasing the number of musical phenomena affected by crossing. One part begins very low in the contrabasses and tuba and gradually increases in both the rate of articulation and upward ascent. The other, glissandi in the upper strings, begins very high and gradually descends to the contrabasses (at a lower pitch level than that found at the beginning of the ascending lines). However, there is not a decrease in the rate of articulation or, in this case, the distance covered as was found in Nancarrow's example. The glissando maintains a strict one octave per beat rate. Additionally there is a rather consistent one octave cut-off of the high pitch range every measure (this changes to a perfect fourth in measure 200 in order to end the passage on E1 rather than on A). Even though the crossings occur at the half-way point in the passage (between mm. 199 and 200), they are not structured as precisely as Nancarrow's. This is partially due to the rather short length of the excerpt (approximately 16 seconds as opposed to several minutes for Canon X). Under such compressed conditions it was not considered necessary to achieve a near exponential increase or decrease in note duration (or tempo). Instead, primary consideration was placed upon the effect of a rather sudden and quickly achieved pitch and tempo crossing as well as a crossing of the paths the sonic materials would traverse through the physical arrangement of the orchestra on stage. Example 7b shows the intended arrangement of the orchestra. The broken lines plot the path of the ascending line as it travels from instrument to instrument in the orchestra while the solid line plots the path of the descending glissandi. The basic idea is that the descending line moves from the left side of the orchestra to the right side while the ascending one moves from right to left. Not only does crossing occur in the frequency and tempo domains but also in the spatial and the dynamic domains (the ascending line changes from "p" to "f" and the descending line from "f" to " p" ). Altogether, this excerpt from Dragon for Orchestra features four concurrently synchronized crossings of diverse musical elements and/or phenomena.

Example 7a: Gabel: Dragon for Orchestra, mm. 197-206

Example 7b: Orchestral Seating Plan in Dragon for Orchestra

Many of the examples cited in this paper are from works traditionally performed in a proscenium arrangement, with the performers arranged in close proximity to one another facing the audience. The listener is faced with the task of attempting to isolate and "hear out" lines which are engaged in part crossing and which emanate from a single spatial locale. If, on the other hand, the instrumental forces are separated in physical space, the listener may attend to sounds emanating from more than one location which may enable him/her to avoid confusion of the functions of crossing parts. This makes it possible for sounds to be separated in space. This manipulation has emerged as an important phenomenon in recent compositional practice.

In several of his works, • Roger Reynolds utilizes the manipulation of physical and musical space as a primary structural element. His conception of space as an organizational element involves the physical dispersement of performers (or groups of performers) within the performance space. Space is also utilized as an expanse through which sounds can be passed from one performance group to another (or from one loudspeaker to another). In Quick Are the Mouths of Earth, he experiments with three types of spatial interplay between three groups of performers: 1) clusters of marked entrances which emanate from all locations within the ensemble; 2) the passing of similar materials from group to group; and 3) the continuous flow of one sound from left to right (or right to left, etc.) across the ensemble. The results, though sometimes extremely delicate_, and subtle, are very effective if there is sufficient separation between the groups of performers.

At measure 62 of his Threshold for orchestra (Example 8a), Reynolds passes a chordal structure intact from the strings to the winds. However, the designated seating arrangement of the orchestra (Example 8b) shows that the chord does not move toward the back of the stage (which would have been the case with a conventional arrangement) but backwards to the horns, back to the right to the woodwinds, forward to the right to a brass group, and forward to the left to another brass group. As a result, the chord radiates in all directions from the center to the outer periphery of the orchestra. In the interchange from strings to winds, pitch components of the chord can be thought to move and cross in space.

Example 8b: Reynolds' Threshold pp, 6-7

Example 8b: Orchestral Seating Plan in Threshold

The spatial deployment of performers is still undergoing experimentation. The electronic media of synthesized and computed sounds emanating from loud speakers at various locations within or surrounding a performing space are providing the composer with greater control in working with musical and physical space than is possible by conventional means. The manipulation of space is becoming increasingly integrated into the practice of musical composition. This is partially true because more sophisticated instruments (computers, tape, loud speakers) are available.

Perhaps the most ambitous experiments with the movement of sound in space were carried out recently by Roger Reynolds. While not specifically researching the crossing of sounds in space, his work does provide a basis for realizing greater control of this phenomenon. He summarizes his thoughts on the manipulation of sound in space in the article "Interview: Reynolds/Sollberger:"

"RR: The Poeme Electronique [by Edgard Varèse] and Gesang der Junglinge [by Karlheinz Stockhausen} were done with a concern for the spatial properties of sound. What seems to me absent there was an effort to discover what it is that constitutes a memorable, perceivable gesture within the field of movement. In other words, we know that we can notice the changing of position and the changing of relative size and speed...of sounds. But whether all these patterns of movement would be equally memorable or equally perceptible is not known. Nor do we know anything about the impact of changes in the nature of the illusory "host space" in which the sounds move.

HS: You're talking now about developing a language or a vocabulary

RR: Yes. Just quantifying, being able to build structures, to make the spatial properties of sounds and the change of spatial properties of sounds in some sense a structural dimension of music in the way that dynamics became, the way that timbre became, to a degree. I think there's no question that this is in the offing, and that, of course, computers are the key to that." ¹⁰

In his recent works, Reynolds very precisely plots, calculates, and computes the sound paths and space functions of sonic events in his compositions. The graphic representation of some of these paths and functions (Example 9) illustrates the highly complex nature of the sound paths.

In Archipelago, Reynolds explores a means by which the movement of sound in space can be precisely and effectively simulated. In discussing the desired effect he writes:

The liquid metaphor I adopted allows one to view sound as a fluid medium that can emanate from one point in space, spread out - perhaps surrounding the listener- and then contract again into a different final position:¹¹

The proposed effect is an illuminating metaphor for sounds emerging from afar and receding into the distance. Example 10a illustrates the eight channel speaker configuration which was used for the^. premiere of Archipelago at IRCAM in Paris. The use of eight channels, as opposed to the more conventional two or four channel model, maximizes" the variety of movement patterns - of paths or shifting expanses.¹²The configuration uses two quadraphonic systems. The upper system is rotated 90 degrees in relation to the lower system and is located slightly outside the quadrangle formed by the lower system. Reynolds graphs the sound flow paths of each sound event (Example10b). This graph illustrates that sounds move between close, normal, or distant references. An important cue for distance is given by the amount of reverberation present in the signal. The greater the relative amount of reverberation the greater the sense of distance. At times 1-2, the sound is distant and located in the front speaker (refer to Example 10a for speaker location). For times 3-4, the sound is located in the same speaker but has become more present with a specification of normal. At times 5-6, the sound spreads out to the front left and front right speakers with a continued normal distance cue. For times 7-8, the sound becomes very present in the same two speakers. Finally, at times 9-10, the sound moves to the back, back left, and back right speakers, ending in the distance. For times 1-8 the sound not only gets louder but it also seems to become more present spatially before quickly "passing" to its final destination at the rear of the hall.

Example 9: Reynolds' Voicespace IV, The Palace Location Sequence Stencil for Pulse Trains

From Roger Reynolds: Profile of a Composer.

The speaker configuration and its manner of usage in Archipelago suggests significant potential for the production of diverse crossing effects. The primary factor is the additional number of speakers from which sounds may both emanate from and move toward. Furthermore, the combination of two distinct spatial levels creates a multitude of new possibilities for the transmission of sound through space. It is possible that Reynolds' speaker configuration might be a step towards the construction of halls specifically designed for the performance of electronic and computer generated music. Such a performance space of the future might have as many as 200-300 speakers¹³ placed at pre-determined locations in the walls, ceiling, and floor. Thereby, the composer would be able to realize a formidable number of spatial paths. A facility of this type could become a vehicle by which new investigations into the nature of sounds crossing in space could be realized. Not only would one be able to conduct extensive research into basic relationships of the spatial crossing of sounds, but also one might be able to discover those relationships which produce ultimately effective crossings of sounds in space. These researches could contribute to the codification of a new musical/theoretical discipline - a "counterpoint" of sorts based upon the combination of sounds at various "points" in space. Crossing principles may not prove to be the only motivating force in the generation of a new contrapuntal art. However, they will undoubtedly be a topic of importance within the general scope of "spatial counterpoint."

Example 10a: Loud Speaker Configuration in Archipelago