This paper is an examination of several musical processes that function in lieu of tonal syntactical relationships in the second movement of Bartók's Music for Strings, Percussion, and Celesta. Three related processes based on the idea of "expansion-contraction" are examined: general intervallic expansion-contraction; motivic variation through expansion-contraction; and structural expansion-contraction. A fourth and slightly different procedure, octatonic completion, is also examined, but functions more often as the goal of some process than as independent operation. Several of these processes are brought to light through the use of Richard Cohn's concept of "transpositional combination." 

Bartók's use of these processes has a tremendous impact on the function of the parts within the movement's sonata schema. The most striking is the combination of a highly developmental "exposition" with a central "development" section that contains no real working-out of material. The traditional functions of these sections are transformed, but the conception of sonata as both schema and dynamic process is conserved. Although this transformation of function may seem counter to the ideals of sonata form, there are grounds, as Elliott Antokoletz has demonstrated, for regarding the movement as a part of an on-going development within the two central movements. One can thus see the second movement as part of a large-scale symphonic process in which its function is to develop ideas set forth in the opening fugue. 

Among the numerous efforts at contribution toward the "new branch of theory" wihch Arthur Berger prophesied for Stravinsky's music, perhaps the most conspicuous is that inaugurated by Berger himself and further developed by Pieter van den Toorn, in which Stravinsky's tone structures are classified according to octatonic, diatonic, and interaction octatonic-diatonic pitch organization. The Berger-van den Toorn method has yielded discoveries of such a magnitude that a stage appears to have been reached at which, as Richard Taruskin has put it, "no further objection to those findings can, I think, be entertained." It is for this reason that a next logical step twoard the "new branch of theory" which Berger predicted could comprise the development of principles centering not upon the isolation and classification of relevant pitch collections--this procedure would now be considered a requisite preliminary step--but rather upon a science of dynamic relations existing among the collections themselves. With this purpose in mind I introduce principles of well-defined collection, communication, and interaction, and present examples of these principles at work in Stravinsky's early composition for orchestra, Scherzo fantastique (1907-08). 

The problem of mode in the sixteenth century has been a frequent subject of controversy in the last decades. To what extent does the polyphonic modal system depart from its ancestor, medieval chant modality? Does mode affect the compositional and formal structure of polyphonic music in any way? Is polyphonic modality only an "early stage" of later functional tonality, or is it a mature, independent system? 

The present paper is an analytical exposition of modal structure in the organ tientos of Antonio de Cabezón. The point of departure for the analytical methodology is Tomás de Santa María's modal presentation in his treatise, Arte de tañer fantasía (1565). The study shows the existence of a consistent set of critera and modal elements which define each mode, and suggests that Santa María and Cabezón thought of mode as a precompositional entity which provided a mold for their compositions. 

The eight modes are thus considered in the present paper as distinct formal and structural paradigms. Modal structure is defined not only as a set of pitch relationships which rules the melodic aspects of composition by means of the characteristic ambitus and spieces, but also as a set of imitation patterns and cadential schemes which shape the form of a composition. The modes are further established by such elements as subject structure and use of the seculorums and Magnificats as literal quotations or as sources for thematic material. Variety within the paradigms is provided by alteration of the imitative or cadential schemes, by use of accidentals that do not affect the structure of the mode, and most of all, by a skillful handling of modal commixture. Polyphonic modality in the sixteenth century can thus be viewed as a mature and fully-articulated system, whose structural order differs substantially--in spite of their points of similarity--from that of later functional tonality.  

Interval structures in the atonal music of Arnold Schoenberg and interval structures in tonal music emanate from a common process, which Schoenberg calls developing variation. Although several recent authors invoke this process in their studies of tonal music, analyses of Schoenberg's atonal music rarely make use of it. My paper shows how developing variation generates an atonal piece, highlighting ways in which atonal and tonal variation are similar.

In the paper, I systematically extend remarks that Schoenberg made in a radio lecture on the Vier Lieder für Gesang und Orchester, Op. 22. The structure-building processes I cover include: (1) varying a motive (a series of pitch intervals) by inverting one or more intervals, reordering the pitch representatives of the interval series, or expanding one or more intervals by semitone; (2) overlapping unvaried and varied motive-forms to generate phrases; (3) applying the three motivic transformations to phrases to create varied phrase-forms.

In the analysis of the first stanza of "Seraphita" (Op. 22/1) I show that two considerations motivate the chains of phrase-forms that gradually increase and decrease in remoteness from the motivic source: Schoenberg's obligations to delimit sections within the form and to characterize those sections in accordance with the text.

I claim that the primary organizing principle in much music from Beethoven to Shostakovich is thematic interaction and transformation patterned by analogy to literary plot structures. My system for analyzing musical plot is similar to that which Vladimir Propp applied to Russian fairy tales in his Morphology of the Folktale of 1928. Like characters in Propp's tales, musical themes and motives fulfill a limited number of dramatic roles, and enter into relationships and interactions which form the essential units of plot. These units, which I call functions, are of two types, relational functions and indexical functions. Relational functions define (1) dramatically significant relationships among thematic elements including contrast, conflict, control, enclosure, subversion, and causation, or (2) systematic changes in these relationships including divergence, synthesis, and shifting control. Indexical procedures provide an overall sense of direction by analogy to a series of states or conditions that form a dramatically or psychologically meaningful sequence.

Works discussed include the first movements of Beethoven's Eroica Symphony and Sonata Op. 57, as well as a number of cyclic works including Shostakovich's Symphony No. 10. In each case the essential deep structure is conceived as a series of functions governing the interaction of themes playing antagonist and protagonist roles. 

The paper proceeds from the premise that music is a meaningful mode of discourse and is therefore properly within the scope of semiotics. It attempts to develop a methodology whereby an aspect of Peircean semiotics can be applied profitably to music.

Charles Peirce defines an icon as a sign which denotes its object by virtue of qualitative similarity. One type of icon is the diagram, which represents the relations of the parts of its object by analogous relations among its own parts. This type of icon need not have any simple qualities in common with its object. Peirce's diagram can be applicable to music if one understands the relations to be temporal (rather than spatial as his term implies). If temporal musical relations can be considered analogous to the relations of an extramusical object, then music can be considered an icon of that object even if it bears no simple qualitative likeness to it.

It is argued that music generally is an icon for the way in which we conceptualize time as 'passing,' and that this "myth of passage" is a necessary aspect of music. It is suggested that the distinction between meter and rhythm in common-practice music can be understood to be an icon for the distinction between absolute and relational theories of time, respectively. This issue is considered historically with regard to a debate between Leibniz and Newton in the early eighteenth century. 

The essay falls into three sections. The first introduces and explains some tenns and concepts used in the analysis of verbal narrative (such as intertextuality, episodic and configurational reading, narrative functions, coding and normalization) and how they specifically relate to musical analysis. Section two looks at portions of the Seven Last Words, a work whose episodic presentation of the Passion story lends itself especially well to narrative analysis. I provide criteria for segmentation of the work into narrative sub-units; describe word-music interaction in terms of meaning (intra-piece relations) and significance (extra-piece relations); and derive certain narrative codes operative in the work (drawing upon modal theory, biblical exegesis, rhetorical modes of Schutz's day and his own writings about music) .. Diagrams and musical examples accompany the analysis. The essay closes with a discussion of three main conclusions following from the analysis: (1) The notion of coding provides a normative basis for analyzing word-music interaction in terms of extra-textual significance. (2) Deep parallels exist between narrative and music: both can be organized into series of actions and functions, and, as temporal arts, both elicit analogous listener /reader responses. (3) Literary criticism, and narratology in particular, furnishes analytic concepts and models that with modification can enrich the analysis of both music-with-narrative (such as the Seven Last Words) and music-as-narrative. 

How can a listener evaluate and appreciate serial music? The pitch material of tonal music is so familiar that most listeners can achieve some level of understanding and pleasure with very little effort. If serial music is approached through the techniques of its pitch material, a monumental task is required of the listener. That task is made manageable, however, by approaching a serial piece through musical devices which are familiar to the listener.

I focus on the use of familiar musical devices in my examination of the first half of Milton Babbitt's All Set, composed in 1957. In conformance to the classification of All Set as third stream jazz, these familiar musical devices are attributed to both the Classical and jazz idioms. In general, global organizational features reflect influence from Classical music, especially from previous serial composers, while more local organizational features are founded in jazz.

Babbitt employs pitch constructs made familiar through their use by Schoenberg and Webem. A process from the electronic music medium governs the organization of the piece: the technique of phasing. The sections into which the piece is divided are articulated by traditional motivic and textural procedures. One of the textures can be attributed to the characteristic sound of a popular jazz ensemble of the 1950s. Influence from the jazz idiom is apparent in the roles of the instruments in the rhythm section and in the use of scale types common to jazz improvisation and composition. 

In a recent interview, Toru Takemitsu discussed his use of octatonic pitch materials and described, for the first time, a three-hour "lesson" he had with Olivier Messiaen. Takemitsu states that during -this meeting he was so moved by Messiaen's Quartet for the End of Time that he asked Messiaen for permission to use the same instrumentation in a work of his own. This paper examines the work which grew out of this encounter, Takemitsu's Quatrain II, and excerpts from other pieces by Takemitsu and Messiaen, showing that in the music of both composers, local and global pitch relations are generated through interpenetrating references to octatonic, whole tone and other symmetrical pitch class collections.

The study also establishes that the music of Takemitsu, like that of Messiaen, is essentially metaphorical, and that while these musical metaphors derive from very different cultural and spiritual traditions, they give rise to temporal and· pitch structures which function similarly. In Takemitsu' s music, a characteristically Japanese image of time is created in the juxtaposed metaphors of time and timelessness, as relatively autonomous sound events dissolve into a silence imbued with meaning. This paper documents Takemitsu's affinity for the music of Messiaen, showing how both composers take a transcendental approach in shaping musical time to evoke spiritual qualities in their music. 

The Sonatina for flute and piano occupies a unique position within Boulez' s oeuvre. Completed in May 1946, it is Boulez's first attempt at composition with a 12-tone row, and it reveals the influences which characterized his early pre-serial period: the Sonatina contains passages based upon Messiaen's technique of rhythmic trans-formation, and reflects the 11thematic" and formal design of Schoenberg's Kammersymphonie Op. 9, particularly in its adoption of a one-movement sonata (cycle) form.

This study examines Boulez' s approach to sonata form by examining the roles played by articulation types, pitch space (p-space), and especially contour pitches and chordal spacings. Boulez's 'shapes', contour-pitch sets or chord-spacing sets combined with rhythmic cells, act as the primary means of clarifying the formal role of thematic statements built on identical or similar rows in the Sonatina. In conjunction with other parameters, these shapes define each section of the Sonatina and provide means for development in a form which Boulez would soon view as 'archaic' and 'harmful' to modem composition. 

Counterpoint based on semitonal displacement-half-step voice leading-is examined in two late Liszt works. In Aux Cypres de la Villa d'Este I semitonal displacement controls both surface and deep level harmonic connections: the surface voice-leading is limited to semitonal motion and the general harmonic plan is a non-functional series of semitone-related triads-B" aug, Glt maj, F# min, G dim, G maj. The "Kyrie" from Liszt's Missa pro Organo is a palindrome based on semitonal displacement. In this brief movement the second half of each contrapuntal voice restates the pitches of the first half in reverse order. 

The interaction of recursive semitonal displacements with an underlying sonority produces either a centripetal, centrifugal, or static region, depe~ding on whether the sonority is reclaimed, abandoned, or prolonged. By factoring out registral shifts and voice exchanges a generalized model of pitch-class displacement results, relevant to a variety of network types. Semitonal displacement at deep levels of structure reflects the 19th-century evolution away from single tonic schemes in diatonic space towards personalized combinations of the four triad types and their trans-positions in chromatic space. 

In nineteenth-century harmonic practice symmetrical divisions of the octave occasionally result from successions based on equal-third relationships (e.g., triads on C-E~-G~/F#-A-C or C-E-G#/ A~-C). Recent studies have identified only isolated occurrences of such patterns, often in the context of some evolutionary trend pointing to the more significant role played by symmetrical constructions in the early twentieth century. Passing notes inserted between chord members in these successions, for example, may produce octatonic or whole-tone collections.

No evidence has yet been offered to suggest that any composer in the first half of the nineteenth century employed equal-third divisions as symmetrical structure per se. Rather, such passages seem to serve simply as prolongations of their initial/terminal harmonies. Liszt's Un sospiro (from the Trois Etudes de Concert of 1848) is an exceptional piece in which numerous equal-interval cycles are systemati-cally developed and interwoven with tonal elements.

All the symmetrical surface-level successions in Un sospiro are concentrated in the retransition and coda. The cycles in the retransition, however, retain certain functional tendencies, whereas the corresponding cycles in the coda are free of any tonal implications. A similar connection exists between the overall tonal scheme, in which key areas are established by conventional progressions, and the concluding measures of the coda, where those same harmonies reappear in a static symmetrical succession. The relationships between the various octave-partitions in this piece suggest that, at this stage in his career, Liszt was already pursuing symmetry as a structural element. 

The constitution of a musical text is a process in which listeners and composers cooperate, the score being a field on which a variety of possible performances can be played out. Constituting a musical text, then, is the activity of listeners playing on the field of possibilities described by a composer's score. Brahms plays upon conventional ways of listening, at one stroke subverting and satisfying those conventions with a kind of play that I term deviation. Deviating from a convention steers a middle course between satisfying and failing to satisfy that convention, a middle course that I as a listener steer between my own compositional activity and that presented in the work I hear. The paper explores how Brahms, in several of the later piano works, involves me in this playful activity, for the value I find in this music derives in large measure from the manner in which Brahms plays within and against stylistic conventions and contextual strategies, that is, the manner in which he suspends me between what is and what might have been, in a region never, so to speak, "there, in the music" but "always present" as I listen. 

The extant manuscript materials for Mahler's unfinished Tenth Symphony suggest a tonal design which pits the principal tonality of F# against several third-related subsidiary tonalities: A# (Ill, usually spelled as B~ ), D (~VI), and D# (VI). Richard Kaplan (1982) was the first to identify the "interaction" of the diatonic collections of F# and B~ as a crucial aspect of pitch structure in the Adagio movement. My analysis further develops Kaplan's idea, .exploring additional facets of this tonal pairing. The other third relations (F# and D; F# and 0#) are less prominent in the Adagio, yet there are striking examples of both. As is typical of Mahler's symphonies, the significance of the motivic third relations is not fully apparent until the Adagio is considered in the context of the entire symphony. To that end, excerpts from the drafts of the third (Purgatorio) and fifth movements will also be discussed. 

In many passages, details of harmony and voice leading seem unconventional or even inexplicable when viewed from traditional tonal analytical p~rspectives (including Schenkerian analysis). For example, foreground harmonies on F#, B~, D, and D# occur in quite unfamiliar contexts, often with no clear voice-leading or harmonic functions. Clearly these are local references to the motivic third relations which permeate the Adagio movement and the symphony as a whole. The present analysis illustrates the extent to which local harmonic details and large-scale tonal design are influenced by this contextually defined network of third relations.