Daniel James Wolf

Traditionally and universally, musical form was identified with the metrics of the accompanied song lyrics or dance and the materials of music were deployed in time to reinforce this identity. The basic processes of tonal music – tonicity, repetition, assonance, contrast – perceptably marked and identified the divisions in the form of a musical work and functioned in parallel to meter, rhyme, and stanza and repeated dance steps or positions and their combinations.

Each of the world’s classical music styles developed its own formal schemes but all of them bear deep similarities. Whether in a Karnatic (South Indian) recital, a Javanese Klenengan, or a European concert, individual pieces on a classical program are identified as belonging to particular forms: Kriti, Varnam; Ladrang, Gendhing; Sonata, Rondo. This suggests that all the pieces sharing such an identification reflect the same ideal form and, in fact, there are long traditions in all of these cultures for describing such forms – musical, poetic, or choreographic – in terms that evoke mathematical precision: ABA, AABB, ABA¹CA²DA³ ...

The West, perhaps uniquely, developed musical forms which became largely independent in their performance context and in their content from the song and dance repertoires. This development was intimately related with the evolution of a polyphonic harmonic texture. However, these so-called "absolute" forms, most notably the Fugue and the Sonata, not only retained and upon the basic connection between tonal contrast and formal division but expanded further on the concept, remaining ever more dependent upon a connection between tonal function and formal demarcation.

However, in the last century or so, the West has witnessed a substantial tension between form and material. This tension has arisen as the material has developed in complexity and divorced itself from the traditional functions. This has happened in parallel in music, poetry, and dance and these parallels are instructive. In poetry, rhyme and meter virtually disappeared as essential features, and with them the whole formal tradition. In their place came a kind of "form by assertion" (much as Stravinsky would write of creating a "tonic by assertion"), developed uniquely for the individual poem. Released from rhyme and metric foot, the poem was atomized to the point where any number of the basic building blocks, the syllables, might be struck together to create the poetic line. The resulting line was more prosaic in that the flexible length reflected more closely the patterns of natural breath and speech. In dance, the long move from social dancing to staged choreography, accompanied by both the introduction of narrative and its eventual abandonment for abstraction, was marked by the decline of common repertoires of fixed steps and combinations. The individual, choreographed, dance became more specialized and less generic, its form ever more unique and less reflective of an external ideal. For even the greatest neo-classical choreographer, Balanchine, the restoration of a fixed repertoire of positions was unaccompanied by a fixed syntax for their performance.

In music, the expansion of the possible musical materials in all parameters has been extraordinary. Dynamics and timbral resources have increases in both quantity and notable subtlety, acquiring ever more importance. Rhythm has achieved astonishing new levels of complexity, distanced ever further from any origins in dance or lyric. The possibilities for pitch usage have expanded horizontally and vertically. A melody might now have such a wide range and chords may be so dense that questions of cohesion and segregations are vital to both performer and listener. The harmonic resources of the standard temperament were basically exhausted in the 19^th century with such chords as those found in the Vorspiel to Tristan und Isolde or the following:

(Musical Example)

This chord is inversionally symmetrical, ambiguously placed between the major and harmonic, on one hand, and the minor and subharmonic on the other. In Just intonation, the ambiguity would be removed by making the distinction explicit in the tuning, while the 12 tone temperament consolidates both interpretation into a single sonority. Such a harmony represents precisely the outermost limits of Major-minor tonality in 12 tone equal temperament. In response to such limits in the tonal system, some composers have advocated innovations in the tuning system, including both expanded systems of Just intonation, and irrationally-based systems of microtonal tuning, as well as composition with tonal resources which are in large part, composed of noises, unparseable as pitches with clear fundamentals and harmonic overtones.

For Arnold Schoenberg, the music theorist, the identification of form with tonal structure still remained complete. The title of his English language textbook The Structural Functions of Harmony was translated, at his apparent approval, in German, to The Form-building Tendencies of Harmony. A single musical event was uninterpretable outside of a particular function-defining context.

However, for the composer Schoenberg, the connection between the continuity of a musical work and the tonal materials was continually called into question. The search to establish new forms of connection was the subject of highly varied compositional solutions. The 12 tone series and its variants did not lend itself to identifying particular sections of a musical work with segments of the available pitch collection, as all forms of the series were structurally equivalent under a small set of transformations. The simple adoption of traditional tonal forms to a 12 tone pitch vocabulary was never a completely satisfactory solution (evidence the Serenade and the curious "fugue" in the Prelude to the "Genesis Suite"). Very likely, Schoenberg was not sufficiently distant from the traditional forms to consider a radical divorce of his tonal materials from any fixed formal functions.

For John Cage, Schoenberg’s American student with a confessed "lack of feeling for harmony," his identification of form with tonal structure was absent. Structure was simply the division of the whole into parts, which Cage defined as units of time, while form was the morphology of a continuity (Cage, Composition as Process).

Cage’s identification of structure with temporal division was a fundamental departure from the entire tonal tradition. The essential device for the audible articulation of the form in time was an opposition not between tonal functions – that is, tonic and dominant – but rather between sounds and silences. The category of sounds was simultaneously expanded to include not just the pitches of the tonal system as played by instruments and voices with timbres of largely harmonic content. It was also to include all possible noises, whether of traditionally musical or other origin. Cage often recognized the music of Edgard Varese as pioneering in this regard, but his own works for percussion ensembles, the prepared piano, and electronic media were equally pioneering efforts. Moreover, the explicitness of their rhythmic structures makes it more clear what Cage meant by his distinction between structure and form.

A classical tonal composer might compose, for example, a Sonata in the tonality of A Major, with a more-or-less fixed form marked by the tonal functions of the given tonality. In contrast, Cage composed his Sonatas and Interludes for prepared piano with a specific division of the whole duration into lengths of time. That is to say, a temporality as opposed to a tonality. These rhythmic structures are typically found on the title pages of many of Cage’s scores, precisely like the tonality indications printed on classical sheet music.

The morphology of a continuity. Cage’s terms evoke a modern mathematical sensibility but perhaps they are really a return to something much older, indeed pre-Socratic. Classical tonal forms shared a morphology of ideal forms, very much in the Platonic spirit. All ballades share some aspect of an ideal form, as do all minuets, all sonatas. Cage, however, decisively shifts the focus of the morphology from an external, ideal form onto the specific continuity of the work at hand. The morphology is less a matter of discrete segments or building blocks, all the As, Bs, and Cs of the conventional theory of musical forms, but rather one of continuities, shapes, curves, Gestalts in a space without discrete steps. The Cage Sonatas do share aspects of discrete structure with the whole tradition of the sonata, e.g., the use of two repeated sections in succession. However, the surface of the music, that which the listener hangs onto, follows very much a continuity of its own, with its complex timbres a world apart from the chords of a functional tonality. With the Cagean approach to form, it is not even a question of stepping into the same river twice. There is no "same river."

In his Meta+Hodos: A Phenomenology of 20^th Century Musical Materials and an Approach to the Study of Form (written in 1961 as a Masters Thesis, and widely circulated afterwards in typescript, published by Frog Peak Music in 1986), the composer James Tenney proposed an approach to the perception of a repertoire of musical materials that had gone beyond the explanatory powers of traditional music theory. This music had largely abandoned the tradition of western music theory where the acoustical simplicity or complexity of pitched sounds and their relation to a given tonal center largely delineated the sense of musical form. As an alternative, Tenney began not with the assumption that the individual sounds in a work of music might be analyzed in real time and related to an external, prior set of tonal relations. Rather he proposed that the listener immediately identified individual sounds as themselves, without prior characterization or further analysis, and then placed in a hierarchical context defined first by time, and then by other parameters.

The repertoire of central interest to Tenney was that of the heroic experimenters of the first half of the century. This included the Americans Ives, Ruggles, Varese, the Viennese Schoenberg, and Webern, especially in their free-atonal years, and Stravinsky and Bartok thrown in for good measure. It should be noted that Tenney was active as pianist, conductor, and co-leader of the Tone Roads ensemble in New York City. In these roles he was a significant performer of this repertoire, with the important addition of composers of an intermediate generation, Cage and Feldman. His approach was thus not only theoretically sound in the abstract but directly related to the experience of making sound from the scores.

It is noteworthy that Tenney began from not only the noised-based musics of Varese and Cage, but also a body of late tonal and atonal music whose pitch structures "opaque" to the ear. Tenney writes:

This is an approach to this repertoire that was very different from the then-contemporary academic style. There, the goal of music analysis was understood largely as being able to account for each single note in a score in terms of an external abstract structure.

In parallel with Cage’s theoretic writings, it is the music of Varese, in particular, to which Tenney’s theory appears most directly to speak. It is the music of Varese that has – despite the small size of Varese’s catalog – more than any other major composer of this century, defied meaningful analysis. Varese’s music is all clearly of a distinctive, individual style, but defining how that style was composed and how it works for the listener has been a constant exercise in analytical defeat. I think this is largely because would-be analysts begin by looking for some kind of precompositional system to define the musical syntax. Such an equivalent for tonality is simply not to be found, at least in the parameter of pitch. One looks in vain for harmonic cadences and tonal centers to define form in the music of Varese and finds the music marked instead by contrast and climaxes in dynamics and orchestration, density and texture.

In his theoretical approach, Tenney has always been close to ideas and approaches found in the natural sciences. In itself, this is not an unusual posture for a composer in the second half of this century (Babbitt was a professional mathematician, Stockhausen studied the acoustics of speech, Xenakis has interests across a broad spectrum of the science), but Tenney’s sources are uniquely focused on the issue of music perception. Meta+Hodos was informed by notions used in the (then-current) field of Gestalt psychology and the (still-fashionable) study of phenomenology. A later appendage to Meta+Hodos, essentially an abstract of his theoretical approach titled META Meta+Hodos, borrows from information theory to add some ideas on variation, using entropy as a measure of variation in states, shapes, or structures. From a pure music-theoretic tradition, his acknowledged sources are the writings of Schoenberg and musique concrète pioneer Pierre Schaeffer’s ideas of the objet sonore and the cellule.

The music analysis proposed in Meta+Hodos is a layered approach. The smallest distinctive sound events or gestalt, are called "clangs" (to be distinguished from, but not unrelated to, the Klangs of Heinrich Schenker, that other notable layered analysis theorist), are segments of larger "temporal gestalt-units" (TG’s) which may be gathered as applicable into ever larger TG’s, corresponding to individual layers in a polyphonic texture or linear subphrases, phrases, sections, movements, entire works, or entire compositional catalogues or repertoires. Clangs themselves may be composed of any number of smaller, internal "elements", but elements are in and of themselves without perceptual significance. The neologism "clang" introduces into English the dual meaning in German of Klang, which is both sound, in general, and musical tones, specifically. Tenney’s clangs differ from Schaeffer’s objets sonores, in that the objets sonores, existing prior to their perception, are uninterpreted segments of recorded sound. An objet sonores has the potential to become a clang when so distinguished by a listener.

Meta+Hodos and the appended META Meta+Hodos go on to present an overview, adopted from Gestalt theory, of the ways in which clangs and higher TGs cohere or segregate. These are, primarily, proximity and similarity, and secondarily, intensity, repetition, objective set and subjective set. (The latter terms identify the expectations which are generated, respectively, from within audition of the work itself and from one’s experience prior to hearing the work.) Interestingly, the theory developed in Meta+Hodos can be said to be general enough to subtend the traditional theoretical approaches. It does not preclude music in a clear tonality. Indeed, it would be instructive to hear what his method might construe of musical works from outside of the 20^th century, western repertoire to which his study is devoted. What would an analysis of Tristan und Isolde or Jeux in terms of a succession of Tenney’s clangs tell us about their forms?

Tenney’s own subsequent theoretical and compositional work outlines on the one hand an expanding investigation into the particulars of proximity and similarity, especially in the domain of pitched sounds. On the hand, however, they also outline a steady retreat from his own radical early position. While Meta+Hodos suggests – or even cries out for – a plethora of formal models, Tenney has really investigated only three in his compositional work. His dominant formal model is what he calls the "swell" form, encapsulated best in this postcard-sized score, HAVING NEVER WRITTEN A NOTE FOR PERCUSSION.

The trouble with the swell form, is, of course, its predictability. Cage was fond of saying, in reference to his own early, precisely symmetrical, Sonata for Clarinet, that "symmetry indicates the absence of an idea". Clearly, a composer can nuance the predictability of form with inventive content, playfully testing the edges of the form for rigidity (one inevitably thinks of Mozart in this regard, and Cage’s own Sonatas and Interludes should also not be forgotten), but the potentials and limits of a form with an inevitable and singular climax are manifold.

Another, more interesting, form to which Tenney has given some attention, which he identifies as ergodic form, is defined by the absence of formal markers. Any given sample or slice of the piece will contain statistically identical material in every parameter. This statistical fact is true as well for a piece of total serialism by Milton Babbitt as for Cage’s Music of Changes, but Tenney’s approach is unique in that his point of departure is the statistical state of the overall form while both Babbitt and Cage composed note-for-note. Thus, Babbitt and Cage achieved an ergodic state at the conclusion of a compositional process executed with great precision from the bottom up. Tenney, on the other hand, started with the ergodic state and then filled it in, from the top down, with content which satisfied the local conditions of that state.

In more recent years, Tenney’s has become increasing engaged with the harmonic series as a compositional resource. He projects the possible tonal resources onto a multi-dimensional lattice derived from the interval relationships found among the partials of a harmonic series. A piece of music may then be analyzed as a walk across the surface of this lattice. In this way, an interpretation of even the most complex of sounds in terms of an extended just intonation is introduced into his theoretical work. Previously, Tenney had expressed skepticism in the possibility of real-time analysis of the complex sounds found in much 20^th century music. But the theory outlined in his 1983 essay John Cage and the Theory of Harmony and the related essay describing the composition of his Changes for Six Harps place all possible sounds within a spectrum of relationships from the simplicity of the unison to the most complex imaginable. Thus, Tenney curiously returns musical analysis to terms that would be fundamentally familiar to any musician trained in the functional school of Hugo Riemann. What is new is that, inspired by the Cagean rejection of functional harmonic progressions and his own ergodic forms, Tenney’s theory of harmony is a theory of materials without an accompanying prescriptive theory of tonal progression.

Perhaps Tenney’s most interesting formal innovation comes in a long series of works – Clang for orchestra, Spectral Canon for Conlon Nancarrow for player piano, the various Harmoniae, Critical Band, the FORM series – where the harmonic series is used as material in not only the parameter of pitch, but also as a source of rhythmic structure. These works seek to make audible the cohesive force of the extended harmonic series itself, and to my ears they are successful in this regard. The over use of the harmonic series does, however, risk that the listener is left with a strong sense e of inevitability. One then wonders if Tenney’s path through 20^th century music history has not then made a return to a substitute form of function tonality.

What did Cage mean by this equation between "the principle of organization" and "man’s ability to think"? While emphasizing a link with past practice, he is clearly shifting form from the domain of the prescriptive and formulaic into that of the perceptual. This shift places form – including, one must add, such historical forms as the fugue or the sonata – outside of their identity in received theoretical discourse and within a biological property of human beings. That is to say that the form of a given piece of music is no longer what some authority tells us it may be. Rather, form is how the individual listener organizes his or her listening experience.

This recognition of a universal competency with regard to the perception of form constitutes an anarchization of the whole idea of form. The problem, then, becomes one of describing what we share when we listen to music together. Once we have recognized that each human is able to listen to music, and to construe the form of that music uniquely, are we then left only with the received vocabulary of discourse about musical form? Or is it possible that Tenney’s clangs, or something akin to them, might prove to be an alternate mode of describing the how we organize or think about music?

Frankfurt, July 1999