Volume 2 (2009)

An Analytic Method for Atonal Music that Combines Straus' Pattern-Completion and Associational Models with Selection Criteria Based on Cognitive Considerations

by YeaJin Kim

Introduction

[1] There have been numerous attempts to logically explain structural principles latent in atonal music. Theorists have used diverse analytic methods, most of which start from attempts to apply analytic logics from tonal music to the domain of atonal music. Of various analytic methods of tonal music, the theory of Heinrich Schenker (1868–1935)—which combines harmony with counterpoint—served as a primary influential method in the United States. Felix Salzer, as Schenker's pupil and advocate, developed Schenker's theory and expanded its applicable possibility to musical works written in the pre-tonal and post-tonal musical idioms. However, many theorists criticized the analytic method because Schenkerian theory is designed essentially for tonal music, in which a hierarchy of tones and chords is assumed and in which strict principles of voice leading govern how music flows.

[2] In 1987 Joseph Straus provided four reasons why analytic methods for tonal music could not be applied equally to atonal music as tonal music and has since searched for appropriate methods by which one could explore superficial and large-scale internal interactions between selected pitch-class sets in tonal space that lacks tonality.1 Before this (at the beginning of the 1980s), Straus proposed the concept of pattern-completion, which provided for an interdisciplinary link between cognitive psychology and musical analysis. Although Straus' pattern-completion was obviously a significant concept—not only because it involved human's cognitive capacity, but also because it showed practical possibilities of connecting musical events that are far apart from one another by depending upon solid theoretical assumptions—it still awaited further logical and theoretical explanation. Straus later presented the associational model—in which tones interspersed in a large-scale tonal space could be interrelated through a specific pitch-class set—and finally established theoretical justifications for what he did in his earlier writings. However, the theoretical justification for pattern-completion and the reliable evidence regarding its analytic validity are still necessary and increase the need of subsequent research.

[3] In this respect, I plan to examine a brief history of analytic methods for twentieth-century music written in atonal idioms and then compare the prolongational model with Straus' associational model, which are seemingly quite similar but differ considerably in conception. I will then critically examine Straus' concept of pattern-completion and search for possibilities of applying it to atonal music by synthesizing—in a dialectical way—two separate analytic tools proposed by a single theorist: pattern-completion and the association model.2

[4] The dialectic result of genuine combination, a new analytic method for atonal music, will be applied to musical works by Yun Isang, one of the representative contemporary composers in Korea, in order to prove its applicable possibility. As one of the influential composers who absorbed the western musical styles and techniques of the second Viennese School and integrated them into the Korean traditional musical idioms, he wrote musical works that are considered to contain both Korean traditional emotions and Western European musical expressions. Applying the new alanalytic method to his works will not only demonstrate its value, but also illuminate structural traits of the selected works to contribute to a stylistic generalization of Yun Isang's music. The works that I will discuss are Glissees (1970) for solo cello and Gasa (1963) for violin and piano.

[5] Although this research starts from a critical review of three analytic methods that Straus has introduced as a tool for the analysis of atonal music—the Schenkerian prolongational model, Straus' associational model and, finally, the Lewinian transformational network model3—I will not discuss them to equal extent. I will focus, rather, on highlighting conceptual differences of the first two models—the prolongational and associational models—derived essentially from tonal music analysis because my goal is to determine the validity and effectiveness of the associational model. For this reason, I radically curtail the historical review of past attempts at applying analytic methods for tonal music to the domain of atonal music by pointing out basic premises of each camp in brief: I focus on a comparison between Straus' associational model and Paul Wilson's prolongational model.4 I will take Allen Forte's pitch-class set theory as a labeling tool for diverse sonorities, but omit its further discussion as a method.

Toward an Appropriate Analytic Method

Primary Methods for Atonal-Music Analysis

[6] Joseph Straus categorized the primary analytic methods for atonal music into three: the Schenkerian prolongational model, Straus' associational model and, finally, the Lewinian transformational-network model.5 The first is the analytic method of Schenkerian theory—what Straus called the "prologational model"—while the second method, the associational model, was proposed by Straus himself as a result of poignant criticism on previous attempts to apply prolongation. The associational model combines one tone with other tones, even though they are far apart from one another, and then focuses on the relation formed among them. The last method is the transformational networks of David Lewin.

Analytic Tool for Applying Schenkerian Theory

[7] Among the theorists who attempted to search for an analytic tool for atonal music by relying upon Schenker's theory, Adele Katz not only expanded the pool of acceptable structural harmonies—such as augmented and diminished-7th chords in Debussy's music—but also explained poly-tonality as a combination of a secondary key against the central tonality.6

[8] After Katz, Felix Salzer, who concretized the analytic possibility of atonal-music analysis through tonal-music methodology, defined tonality broadly as a prolongational motion in a single key by radically extending the traditional concept of prolongation, which assumes tonality.7 He defined the concept of consonance and dissonance as a relative difference in dissonant extents. However, by taking a more or less conventional standpoint regarding the chord itself, he saw a tertian sonority as a structural entity. For him, dissonant chords are just embellishment for colorful flavors: they are against both the rules of voice leading and functional motion.

[9] Roy Travis, who saw musical intuition as an essential factor for analysis, defined tonality in a broader sense than his predecessors as a phenomenon such that a specific tone, interval or chord is unfolded over tonal space in time.8 He placed structural significance on chords located at the beginning and at cadential junctures and also regarded the bass line as a decisive motion for voice-leading. Travis realized the problem that, although a listener can recognize a structural chord in tonal music because of musical intuition, such a listener usually fails to reconize such a central chord in atonal music because it is not easily grasped in the foreground.

[10] By pointing out Travis's lack of logic and his tendency to depend too much on an analyst's musical intuition, James Baker tried to systematize Travis's method by incorporating Allen Forte's pitch-class set theory. In spite of his attempts to juxtapose Forte's method for atonal-music analysis and the Schenkerian concept of prolongation, Baker's approach to atonal music still depended to a considerable degree upon music intuition with the analytic methodology of tonal music.9

[11] In the 1980s Joseph Straus suggested his associational model as a solution to the limits and problems that the prolongational model poses; he enumerates the reasons that an analytic tool for tonal music can not be applied equally to atonal music analysis. However, his approach is also criticized for the same reason: the analyst's intuitive subjectivity is inevitably involved in the analytic process of choosing a specific pitch-class set.10

[12] In spite of Straus' strong objection to such attempts, Paul Wilson favored the analytic values that the Schenkerian prolongational model poses and proposed the idea of the projected set.11 Wilson, who stands in opposition to Straus, asserts that the quintessential concept, prolongation, must be cautiously, but in a broader sense, redefined. According to Wilson, the projected set is a process, in which the analyst selects structurally important notes occurring at strategic junctures and combines them to make a germ pitch-class set. He discusses the interaction between the same pitch-class sets in multiple levels: the germ pitch-class set, which forms a primary motive appearing at the opening of the piece, is embedded in the large-scale musical span. The analyst is allowed to relate members of the germ pitch-class set interspersed in a large-scale musical space with one another by virtue of the extended concept of prolongation.

[13] Wilson's analyses of Bartok's music quite successfully demonstrate how the projected sets served as a structural apparatus to accomplish musical coherence. A combination of a series of notes chosen by Wilson's criteria leads to what he calls a "privileged pattern," which enables the analyst to illuminate the pitch class structure of a piece in an efficient way. The adoption of Schenkerian notation by means of the presumed concept of prolongation makes possible such a hierarchical differentiation in graphs that the analyst may distinguish more structural events from embellishing ones.

[14] Fred Lerdahl attained more objectivity in analysis by proposing what he calls "salient conditions," by which one could differentiate structurally important tones from others in terms of a hierarchy from which prolongation stems.12 Salient conditions are objective and systematic criteria to guide the analyst's choice, which take the place of prompt judgments based on musical intuition. According to Lerdahl, notes located on relatively strong beats, at structurally important points and at extreme registers are hierarchically superior to other notes. A long-held note, a series of notes that participate in a significant grouping as a primary motive, and notes placed at the beginning and ending point of a specific formal unit aquire a more structural importance than others.13

[15] Recently, Olli Väisälä, after Wilson and Lerdahl, also criticized Straus because he rejected the applicable possibility of incorporating the Schenkerian model into atonal music analysis too rigidly.14 In the analysis of Schoenberg's piano piece Op. 19/2, he employed the prolongational model. However, Väisälä's position is quite different from previous standpoints, not only because he adopted the registrally-ordered interval instead of Straus' unordered pitch-class set as a basic premise, but also because he relied to a considerable degree upon theoretical assumptions of auditory psychology. By means of the registrally-ordered interval and the virtual pitch originating from Paul Hindemith's harmonic theorem, Väisälä suggests solutions to Straus' four conditions: solutions to differentiating between consonance and dissonance and for determining scale-degree and hierarchy in atonal music are discussed in detail. According to Väisälä, who absorbed Hindemith's harmonic theory based on the unique interpretation of the overtone series, the major third and perfect fifth are more stable than their inversions, the minor sixth and perfect fourth. Väisälä's analytic system is remarkable in that he presented tentative conditions by which one could measure relatively stable degrees between intervals.

[16] As observed so far, although there were numerous attempts at searching for an appropriate analytic method influenced either directly or indirectly by Schenkerian theory, theorists have not reached a consensus yet that they all agree with satisfactorily. Some theorists do analyze atonal pieces by depending to a considerable degree upon their musical intuition, whereas others do so even without theoretical assumptions. In other words, the analytic method using the Schenkerian prolongational tool still needs a systematization and modification. In the next section, I will concentrate on the associational model, Straus' antithesis to the prolongational model and illuminate how the former distinguishes from the latter and finally what merits of the analysis could be obtained when the former is applied to atonal music.

Analytic Tool Applying the Associational Model

[17] Prolongation—as one of the core concepts in the Schenkerian theory, a tentative assumption that either a note or a chord could still have an influence on the remainder of the passage although it is not literally present in a specific moment—admits a hierarchical differentiation between diverse musical events. Prolongation, which presumes a conceptual separation between structural and embellishing events, leads to a structural hearing of a piece and thus to an efficient illumination of organic unity latent in multiple levels of music.15

[18] Straus' associational model begins with a full rejection of the existence of prolongation in atonal music although it is quite similar in terms of its outlook. The associational model takes unordered-pitch-class-set theory as its point of departure and connects notes interspersed in large-scale tonal space without the concept of prolongation. The analyst in the associational model tends to select a series of notes because they are members of a specific pitch-class set that the analyst wishes to bear in mind; the chosen members of the specific pitch-class set are contextually significant. By eliminating the core—but problematic—concept prolongation in the previous analytic system, Straus is endowed with the license of associating notes far apart conceptually. However, he failed to propose concrete conditions of how one might elevate a specific note out of a group of notes or chords as structural. In the end, this method can not avoid blame that it is a result of the analyst's excessive subjectivity. Straus' insufficient explanation for criteria by which one could select a note as structural or embellishment opened the possibility of further debates on the topic and eventually led me to my proposal of an analytic model.

Pattern-Completion as an Analytic Method

[19] Pattern-completion is an analytic method for atonal-music analysis proposed by Straus in his article "A Principle of Voice Leading in the Music of Stravinsky" (1982): it presumes a combination of cognitive psychology and the Schekerian assumption, by which the analyst associates notes interspersed far apart from one another. In this section, I will examine the theoretical assumptions and subsequent problems of pattern-completion and then propose ways of attenuating its drawbacks.

Theoretical assumptions

[20] Straus' concept of pattern-completion has three basic assumptions. First, it takes a four-note cell as a complete pattern in tonal space as an unordered pitch-class set. According to Straus, the reason for choosing the specific number 4 is based on an assumption borrowed from cognitive psychology that the human tends to memorize 3- or 4-digit numbers easily. However, he failed to provide satisfactory information and theoretical foundation to support the assumption in terms of music.

[21] Straus' second basic assumption focused upon a listener's expectation that, if a listener hears a specific pitch-class set as a strongly memorable germ motive, he will tend to recognize it without difficulty even though a member of the pitch-class set is missing because the listener will conceptually fill in the missing note to complete the entire germ motive. In other words, by virtue of strong expectations, the listener is eager to complete the germ motive perceptually and will have heard it in conception although a member of the motive is incompletely presented.

[22] The last assumption concerns the Schenkerian perspective, although he does not state as such clearly. By means of an extension to the concept of prolongation, one could have license to associate notes interspersed in the large-scale tonal space, if the process feels meaningful. Straus allowed the analyst to illuminate musical events not only in the foreground, but also in the middleground and background.16

Problems and Suggestions

[23] Straus' pattern-completion has some problems in terms of its logics. First, it lacks a full explanation of why Straus has chosen the number 4, the human memory-capacity for digits. The most important question is whether human-capacity regarding numeral information could be equally transferred into other media, here as aural information. Straus' theoretical justifications for his choice are too weak to accept without question.

[24] According to music psychologists, such as L. L. Cuddy, A. J. Cohen and J. Miller, perception and memory of a musical tone are related closely to a tonality of a melody and a harmonic background, in which the melody unfolds, because listeners are accustomed to tonal music, although they differ according to the musical experience of each listener.17

[25] Cuddy, Cohen, and Miller see diatonicism and cadence as a central factor to recognizing melodic structure; in turn, diatonicism and cadence could serve an internal criterion for judgment when a listener encounters a tune that deviates from the expected flow. The analytic data obtained through multiple experiments report that a listener's recognition of a melody is closely related to the aural circumstances and thus that recognition capacity could be deteriorated when a listening process is made in non-diatonic structures. Therefore, the cognition of a certain pattern is decided by a listener's pre-learning and thus serialization of aural information differs in listeners, works, etc., because of differences among the basic units for information.

[26] Straus' first theoretical assumption remains questionable in that he has neglected a listener's pre-learning and an individual work's originality. Moreover, it is also dubious that his "4-digit number" condition could be transferred to the 4-note cell in atonal music that lacks diatonicism and the sense of tonality.

[27] Another problem that Straus' approach poses lies at his instant application of a Schekerian perspective to the analysis without a full explanation of its theoretical assumptions. It is as late as 1988 that he proposed his associational model, which is contrasted to the previous prolongational model. Furthermore, he still failed to present unequivocal criteria that determines how an analyst chooses a note as a more structural one than others.18 To sum up, he did not explain what theoretical bases enable the analyst to relate notes interspersed in large-scale tonal space and what criteria guide the process of choosing a note as important.

[28] I will ultimately suggest a new analytic model by depending upon a critical examination not only of Straus' theoretical assumptions and his actual analyses, but also of other later theorists' supplements and modification to his method. For this, I will take Straus' concept of pattern-completion and thus concentrate on a specific germ set that carries an important role in each piece. However, I will not limit the choice of the specific germ set to the "4-digit number" restraint. Rather, I will allow for freedom to choose 3-, 4- or 5-note cells as a significant unit if the chosen cell carries a decisive function in relating itself to the entire piece organically. The specific pitch-class set must serve minimally as a motive and repeat itself either literally or in a disguised form (in transposition or inversion) to give to a listener a strongly memorable impression.

[29] When I select the specific members of a germ cell, I will depend upon what I call prerequisite conditions, which are originated from Fred Lerdahl's salient conditions. I have adjusted and supplemented Lerdahl's conditions for the effective analysis of Yun Isang's works. Prerequisite conditions reflect the following circumstances: 1) notes that are located in the same register; 2) notes that have the same dynamics; 3) notes that have the same musical articulations or techniques; 4) notes that appear in the same metrical position (it does not matter that those be located either on strong beat or weak beats); 5) notes that have relatively long durations; and 6) finally notes that appear in important positions such as at the beginning or ending of a phrase.

[30] A comparison between my prerequisite conditions and Lerdahl's salient conditions illuminates a few subtle differences: First, while Lerdahl stresses the metrically strong beat, I include weak beats as well as strong beats because the metrical conditions in atonal music are deliberately deviated from the norm. Second, while he presents the use of extreme registers as a factor, I propose the condition of the same register: in other words, two notes to be selected are not necessarily located at extreme registers, but are eligible if they are located in the same register. Lerdahl's condition of same dynamics could be understood and adjusted in a vein. The reason that I try to apply Lerdahl's salient conditions in a more or less loose way is to reflect the diverse and expressionistic compositional techniques that have emerged since 1950—such as in Yun Isang's works—into the analysis. I also add another condition concerning articulation and extended techniques because notes highlighted by such a musical device could be audible and discernible and thus recognized as a significant event by a listener. To put it in another way, my prerequisite conditions are more suitable to atonal music containing diverse techniques than Lerdahl's salient conditions.19

Analytic Exemplars by Straus

[31] Straus' pattern-completion is deployed on the following assumptions: 1) a germ cell is recognized by a listener through literal or disguised repetitions; and 2) once the germ cell is strongly recognized, the listener tends to hear the cell even when all members are not present by completing the missing note conceptually. He adds that such a cognitive process of pattern-completion involves large-scale tonal space as well as the foreground, in which a web of adjacent notes form a specific unit. Straus' analysis of Sravinsky's Symphony for Woodwinds shows various uses and interactions of the tetrachord [0 1 3 5] in multiple levels. Straus asserts that, once the tetrachord [0 1 3 5] is strongly memorized through repetition, the missing pitch class 5 is conceptually heard when the listener hears the remainders of the pitch-class set: 0, 1 and 3. The bass progression, F-E-D, which forms a [0 1 3] in its prime form, leads a listener to complete the missing member C, which corresponds to the pitch class 5 in this case. Stravinsky places the missing member at the end of a specific formal unit and thus completes the germ cell.

Example 1. Graph of Stravinsky's Symphony for Woodwinds (after Straus).20

Example 1

[32] Straus implies that there are two possible pitch classes that a listener can expect when he hears three members of a tetrachord. For example, if a listener hears an incomplete tetrachod whose members are C, D and E (one member of the tetrachod is missing), he will expect either F or B. Whatever pitch class is added to the incomplete tetrachord will become a complete tetrachord [0 1 3 5]. The sense of expectation caused by the possibility of each selection arouses tension and relaxation, which serve as an important factor of the perception of a piece. Thus, analysis through pattern-completion becomes the process of illuminating a composer's intention.

Analyses of Selected Works by Yun Isang

Towards an Analytic Method

[33] I have reviewed in the previous sections Joseph Straus' core concepts—pattern-completion and the associational model—as seen in two of his articles. I have also pointed out the validity and values of the two concepts as an analytic method as well as problems and drawbacks of the two. In the course of presenting possible methods of modification to remedy such problems and drawbacks, I suggest a new method that results from a genuine synthesis of Straus' pattern-completion, associational model and my prerequisite conditions for an efficient analysis of Yun Isang's works. I will demonstrate analytic values and efficiencies of the new method by analyzing two of his works, Gasa (1963) for violin and piano and Glissees (1970) for solo cello.

Stylistic Traits of Yun Isang

[34] Yun Isang, born in 1917 in the KyungSang province of South Korea, is regarded as one of the representative modern composers in Korea, who absorbed both the oriental philosophy and diverse techniques of Korean traditional music and radically modern musical idioms of Western Europe—in particular, Schoenbergian and Webernian musical language—and integrated them into his unique musical style. He entered into the musical world in his forties and became one of the last members followed by the second Viennese School. His chamber works are famous for his extreme experiments with individual instruments. His contributions led to a high appraisal in germany, such as his rank as "one of the 56 influential composers" active in the world and as "one of the 5 greatest composers alive in the Europe."21

[35] One of Yun Isang's most important compositional techniques is Haupttontechnik or Hauptklangtechnik, in which embelishments are added to individual notes. The relationships between the structural notes and their embellishments produce heterophony that basically marks a single voice but contains embellishing motions to bring about a secondary voice. The primary purpose of such embellishments is not simply a technical decoration to the structural notes, but rather a device to express Korean emotions.

Analyses

Glissees (1970) for Solo Cello

[36] Yun Isang accomplishes motivic coherence in Glissees despite its rhythmic variety originating from the absence of bar lines and aperiodicity by focusing on a specific pitch-class set, SC 3-3. This obsession with motivic reworking implies stylistic influence from the Schoenbergian School.22 He calls for a variety of techniques on the cello that recall expressionistic gestures of Korean traditional music through various grace-notes. The cellist is even asked to produce a single note in a very special way: he should play it as if he performed the Korean traditional string instrument Gayaguem.23 The frequent uses of such special techniques could be a result of his ceaseless efforts to convey unique expressions and emotions of his own country Korea.

[37] The cello solo begins by presenting a very irregular rhythmic pattern in a calm mood. The very first note, F-sharp3, and its following two pitch classes, D2 and F2 in an octave lower, together form an important cell of the entire piece: SC 3-3, [0 1 4]. The SC 3-3 gains its crucial status as a germ motive by appearing repeatedly in diverse, transposed forms. A grace-note D4 and the following two notes—F-sharp3 and E-flat3—also form the SC 3-3, while the C4 and C-sharp4 reinforced by gradually increasing dynamics serve as a form of the SC 3-3 by joining the bottom note, E2 presented by the double stop. Interestingly enough, the top note G2 also forms the same set class with the remainders, G-sharp3 and B3 (See Example 2).

Example 2. The germ cell [0 1 4] and its association in the foreground.

Example 2

[38] The insistent occurrences of the same set class makes the SC 3-3 function as a germ cell for the piece. Yun Isang repeats a specific pitch class, B-flat3, by means of various grace-note embellishments and of extremely contrasting dynamics in order to make the listener recognize the pitch class as significant. This technique recalls one of the primary techniques in Korean traditional music, Haupttontechnik. Recognition of the specific germ cell [0 1 4] arouses an expectation that the specific cell will appear repeatedly. The listener's expectation evolves; he tends to hear the same set class as a complete unit even though a member of the set is missing.

[39] In the opening of Glissees, the primary notes that are stressed by the extreme dynamics, forte, are B-flat3 and F-sharp4. These two notes are able to serve as the SC 3-3 by joining the missing member either A or G conceptually. Yun Isang achieved the sense of tension by delaying deliberately a listener's expectation that the listener is eager to hear the missing member (See Example 3).

Example 3. The large-scale SC 3-3 as heard through pattern-completion in the opening of Yun's Glissees.

Example 3

(6, [7 or 9], 10): which one is missing? A or G?

[40] After a grand pause, the angular melodic segments, which recall Schoenberg's musical influence, are also instances of SC 3-3. In this second formal unit, Yun Isang achieved a sense of variety by means of harmonics, grace-notes, abrupt changes of dynamics and tremolos, while he maintains the structural coherence in terms of pitch class content.

[41] For instance, the double-stop figure (G-sharp, B, C), characterized by tremolo, is another instance of SC 3-3; and the rapid, angular melody containing successive large leaps has three instances of the SC 3-3—(F-sharp, G, B-flat), (D-flat, D, F) and incomplete (E-flat, E) are transposed versions of SC 3-3.

[42] To look at the large-scale pitch class structure provides a similar result: the SC 3-3 serves a crucial role not only in the foreground, but also in the various middleground spans. The B2 and B-flat2 are strongly recognized through relatively long note-values and the use of vibrato. The interval class 2 makes a listener expect a missing pitch class, either D or G, by functioniong as two members of SC 3-3 (See Example 4).

Example 4. The large-scale SC 3-3 as heard through pattern-completion in the second formal unit of Yun Isang's Glissees.

Example 4

(11, 10, [7 or 2]) which one is missing? G or D ?

[43] The germ cell [0 1 4] is embedded in the larger space of the music. As mentioned before, the F-sharp and B-flat, which are highlighted by repetition and strong dynamics; the B and B-flat having long durations and vibrato articulation; and finally E and E-flat, which appears at the end of the angular melody, are similarly two members of an instance of SC 3-3.24 Then, if the analyst wonders about a missing note of each, the plausible answer will be as follows: the first pitch class cell consisting of the F-sharp and B-flat would need either G or A to form SC 3-3; the B and B-flat would require either G or D; and the E and E-flat could be competed with the help of either C or G. Finally, if the analyst recognizes the common pitch class out of all the possible notes, then he will get to the pitch class G (See Example 5).

Example 5. A series of SC 3-3 through pattern-completions as seen in Glissees.

Example 5

[44] An interesting result has been induced. The final phrase cadences on the mysterious pitch class G, which has been the common missing member of the three incomplete set classes. The cadence on G psychologically suggests a dramatic resolution of the accumulative tension originating from the listener's expectation.

Gasa (1963) for Violin and Piano

[45] Yun Isang's Gasa features a broad range, radically large leaps, dramatic alternations of dynamics and frequent changes of meter. However, its pitch class structure is organized in a coherent way. The piece begins by the violin's lead. The very first note, C-sharp4, leaps to C5 an octave higher, up to G-sharp5 once again and finally down to A4. This angular motion articulates SC 4-7, which carries an important function as a germ cell of this piece. SC 4-7 also appears vertically in the piano part (See Example 6).

Example 6. The large-scale and foreground germ cell SC 4-7 as seen in Gasa, mm. 1–4.

Example 6

(0, 1, 7, 8) → SC 4-7 [0 1 4 5]

[46] SC 4-7, [0 1 4 5], appears not only in the foreground, but also in the large-scale tonal space. The use of the same register and same dynamics from the prerequisite conditions play a decisive role for selecting notes that are otherwise far apart. The F-sharp6 (m. 6) in the violin part is the first candidate that will be chosen as structural because it is presented at an extremely high register and at very soft dynamics. The same conditions have an effect upon the choice of the following notes: F6 at m. 11, A-sharp5 at m. 13, and A5 at m. 19 (See Example 7).

Example 7. A middleground graph of Gasa, mm. 5–20.

Example 7

[47] These notes, selected from multiple places, form SC 4-7. Thus, SC 4-7 gains its status as a germ cell by appearing both in the foreground and middleground of music and thus contributes to the motivic coherence by introducing connections on multiple levels. The notes selected for Example 8 are found metrically on strong beats and stressed by strong dynamics.

Example 8. SC 4-7 [0 1 4 5] active in Gasa, mm. 45–48.

Example 8

[48] Together with the strong-beat condition, long duration is another criterion that could arouse the listener's attention. The G-sharp6 in m. 55, which has a comparitively long duration, with the C-sharp5 in m. 56, A5 in m. 58, and C4 in m. 59, highlighted by grace-notes, carry structural functions by being contrasted with adjacent notes in terms of duration. The tetrachord (G-sharp, C-sharp, A, C) chosen by the long-duration condition is an inverted form of the germ cell, SC 4-7 (See Examples 9).

Example 9. A middleground graph of mm. 55–61 Gasa, mm. 55–61.

Example 9

[49] As Example 10 reveals, the four-note cell (B, A-sharp, C-sharp, D) is also an inverted instance of the germ motive whose members are highlighted by grace-notes, trills—recalling a technique called "trembling" in Korean traditional music—and glissandos, similar to "sliding" technique. Notice the approach of the grace-notes through a contrary motion: they eventually also create the sonority of SC 4-7. The graces-notes did not carry important functions of forming an instance of the germ motive earlier in this piece, but now they become structural notes after m. 120. The special techniques assigned to the violin beginning at m. 120 makes the passage recognizable as a structural point.

Example 10. The SC 4-7 in the middleground span of Gasa, m. 120.

Example 10

[50] M. 120 has two discernible events which are separated from each other by register. Intriguingly, the F-sharp and B in the low register form SC 4-7 together with the embellishing G and A-sharp. On the contrary, the D located at the extremely high register takes part in the following set class. The very soft dynamics and instant assertions through the tenutos and fermatas elevate the D at m. 120, B, A-sharp, and E-flat at the next measure as a structural event, which also conforms to SC 4-7 (See Example 11).

Example 11. A middleground graph of Gasa, mm. 119–121.

Example 11

Conclusion and Suggestion

[51] I took Joseph Straus' two fundamental concepts toward a suggestion of an efficient analytic method for atonal music analysis, pattern-completion and the associational model. The two concepts prove to have conceptual problems in spite of their invaluable usefulness. Then, I criticized problems and drawbacks of the two concepts and suggested a new analytic model, which is a result of synthesizing a critical review of Straus' pattern-completion and associational model and a proposal of prerequisite conditions similar to Lerdahl's salient conditions.

[52] The analyses of Yun Isang's selected works, Glissees and Gasa through the new analytic method revealed the composer's strong obsession with a germ motive throughout each piece. SC 3-3, [0 1 4], and SC 4-7, [0 1 3 5], served as a germ motive respectively in Yun Isang's Glissees and Gasa to achieve motivic coherence. Moreover, the close examination through this method illuminates a skillful interaction of the germ motive among multiple levels. Such an analytic tool will be useful to illuminate structural secrets latent in post-tonal music.

Selected Bibliography

Baker, James. "Schenkerian Analysis and Post-Tonal Music." In Aspects of Schenkerian Theory, ed. David Beach. (New Haven: Yale University Press, 1983), 154–155.

Burkhart, Charles. "Schenker's 'Motivic Parallelism'." Journal of Music Theory vol. 2, no. 2 (1978): 145–175.

Katz, Adele. Challenge to Musical Tradition: A New Concept of Tonality. (New York and London, 1945).

Kim, YongWhan, ed. The Study of YunIsang. (Seoul: Sigongsa, 2001).

Lerdahl, Fred. "Atonal Prolongational Structure." Contemporary Music Review vol. 4 (1989): 65–87.

Radocy, Rudolf E. and J. David Boyle. Psychological Foundations of Musical Behavior. (Illinois: Charles C. Thomas Publisher Press, 1997).

Salzer, Felix. Structural Hearing: Tonal Coherence in Music. (New York: C. Boni, 1952). Reprinted by Dover Publication, 1962.

———. "Tonality in Early Medieval Polyphony: Towards a History of Tonality." Music Forum vol. 1 (1967): 35–98.

Straus, Joseph. "Voice Leading in Atonal Music." In Music Theory in Concept and Practice, ed., James Baker, David Beach, and Jonathan Bernard. (Rochester: University of Rochester Press, 1997), 237–243.

———. "Uniformity, Balance, Smoothness in Atonal Voice Leading." Music Theory Spectrum vol. 25 (2003): 305–352.

———. "The Problem of Prolongation in Post-Tonal Music." Journal of Music Theory vol. 31 no. 1 (1987): 1–21.

———. "A Principle of Voice Leading in the Music of Stravinsky." Music Theory Spectrum vol. 4 (1982): 106–124.

Travis, Roy. "Directed Motion in Schoenberg and Webern." Perspective of New Music vol. 4 (1966): 84–89.

———. "Tonal Coherence in the First Movement of Bartok's Fourth String Quartet." Music Forum 2 (1970): 198–371.

Väisälä, Olli. "Concepts of Harmony and Prolongation in Schoenberg's Op. 19/2." Music Theory Spectrum vol. 21 no. 2 (1999): 1–22.

Notes

1 This research takes Joseph Straus' researches as a point of departure because his researches are primarily focused on attempts to examine structural principles of atonal music systematically and logically. See for his list of the "four reasons" Joseph Straus, "The Problem of Prolongation in Post-Tonal Music," Journal of Music Theory 31, no. 1 (1987): 1–21.

2 Theses are in a chronological order: Joseph Straus, "A Principle of Voice Leading in the Music of Stravinsky," Music Theory Spectrum 4 (1982): 106–12 and "The Problem of Prolongation in Post-Tonal Music," Journal of Music Theory 31, no. 1 (1987): 1–21.

3 I have omitted the introductory discussion of Lewinian transformational theory in this paper because its deviates from the primary scope that I concern.

4 A detailed discussion of the ceaseless debates among cons and pros is seen already in authorities' various sources, such as James Baker, Olli Väisälä, and others. See James Baker, "Schenkerian Analysis and Post-Tonal Music," in Aspects of Schenkerian Theory, ed. by David Beach, (New Haven: Yale University Press, 1983), 153–186 and Olli Väisälä, "Concepts of Harmony and Prolongation in Schoenberg's Op. 19/2," Music Theory Spectrum 21, no. 2 (1999): 1–22.

5 Joseph Straus, "Uniformity, Balance, Smoothness in Atonal Voice Leading," Music Theory Spectrum 25 (2003): 305–307.

6 Adele Katz, Challenge to Musical Tradition: A New Concept of Tonality (New York and London, 1945).

7 The conceptual difference between tonal and atonal music has been earlier debated in quite a detail by Joel Lester, Robert Morgan and others.

8 See Roy Travis, "Directed Motion in Schoenberg and Webern," Perspective of New Music 4 (1966): 84–89 and "Tonal Coherence in the First Movement of Bartok's Fourth String Quartet," Music Forum 2 (1970): 198–371.

9 James Baker, "Schenkerian Analysis and Post-Tonal Music," 156–158.

10 The discussion of this issue will be in detail made at the following chapter entitled the "associational model."

11 Paul Wilson, The Music of Bela Bartok (New Haven: Yale University Press, 1992).

12 Fred Lerdahl, "Atonal Prolongational Structure," Contemporary Music Review 4 (1989): 65–87.

13 Ibid., 230–259.

14 Olli Väisälä, "Concepts of Harmony and Prolongation in Schoenberg's Op. 19/2," Music Theory Spectrum 21, no. 2 (1999): 1–22.

15 See for a detailed discussion of multiple-level motivic interactions in tonal music Charles Burkhart, "Schenker's 'Motivic Parallelism'," Journal of Music Theory 22, no. 2 (1978): 145–175.

16 Joseph Straus, "A Principle of Voice Leading in the Music of Stravinsky," Music Theory Spectrum 4 (1982): 106–124.

17 Rudolf E. Radocy and David J. Boyle, Psychological Foundations of Musical Behavior, (Illinois: Charles C. Thomas Publisher Press, 1997).

18 These criteria are of course supplemented by later theorists like Fred Lerdahl who proposed the "salient conditions" in his 1988 article. I will discuss his salient conditions later in this paper. See Fred Lerdahl, "Atonal Prolongational Structure," Contemporary Music Review 4 (1989): 65–87.

19 I will apply these prerequisite conditions to selecting members of specific pitch-class sets in the later chapter concerning the analysis.

20 Joseph Straus, "The Problem of Prolongation in Post-Tonal Music," 111 (Example 6).

21 Yun Isang's awarding profile includes "Kiel Cultural Prize," "Greatest Medal endowed by the United Republic of germany," "Prize from the Hamburg Academy," "Prize awarded by Koussebitz foundation" and "Goethe Medal." He was a member of Hamburg and Berlin Academy and also served as an honorary member of ISCM until he passed away. See YongWhan Kim, ed., The Study of YunIsang (Seoul: Sigongsa, 2001), 18.

22 The Schoenbergian influence could be related to Yun Isang's earlier study in germany. Kim, 17.

23 The Korean traditional instruments produce diverse tones and tone colors through various peculiar techniques of individual instruments. In particular, grace-notes, which carry primarily on embellishing functions, are responsible for the heterophony. They are diverse from the glissandos between two long-distance notes to trembling or sliding techniques.

24 The criteria by which I choose notes as structural are by my prerequisite conditions that I proposed earlier in this paper. I also tell that I intentionally eliminated some grace-notes, slide notes, and others in choosing the structural events.