The Collected Essays of Milton Babbitt

permission.

PREFACE

Of American composers of the postwar era few have had a more profound influence on the course of the music of that time than Milton Babbitt. Surely none of equivalent musical stature has so consistently committed his thought to print, and the remarkable series of texts produced by Babbitt over that half-century rank among the most influential, widely discussed, and often misunderstood of the period.

As recognition of Babbitt’s prominence among the intellectuals of his generation has grown over the years, so has the interest of these essays extended far beyond the boundaries of the community of composers and theorists who were their earliest readers. The present volume is thus intended to meet what has become a long-standing need, by making available to cultural historians, musicologists, music theorists, composers, and others the complete writings of this seminal American thinker. To that end we have excluded little, save such unavoidable but comparatively insignificant by-products of the composerly life as the humble program note, as well as those essays which have appeared in substantially identical form under different titles; neither have we included Babbitt’s unpublished 1946 dissertation The Function of Set Structure in the Twelve-Tone System (Ph.D. dissertation: Princeton, 1992) or Words About Music: The Madison Lectures (Stephen Dembski and Joseph N. Straus, eds., [Madison: University of Wisconsin Press, 1987]). Apart from these we have included all that was available at the time we began the project, an average of almost one article for each of the fifty years of work represented. Not a few of the essays originally appeared in what some readers might think to be unlikely places, and most have long been out of print. Doubtless there will be something new here even for Babbitt scholars.

In the pages to follow the reader will encounter Babbitt in the dual role of maker of history and witness to history, and a considerable history it has been. Schoenberg, Steuermann, Stravinsky, Weisse, Krenek, and a host of other Europeans share the stage with Babbitt’s American colleagues too numerous to mention here; Babbitt knew them all, and woven through these often dauntingly theoretical texts is a unique eyewitness account of one of the most turbulent and exciting periods of American musical history, an account that emerges more poignantly as the essays are read ad seriatim. But there is more here than musical history, for many of the texts directly reflect Babbitt’s abiding interest (and not inconsiderable expertise) in analytical philosophy, linguistics, and literature; along the way the reader thus will have as companions Rudolph Carnap, Noam Chomsky, Carl Hempel, and others, introduced either by name or through Babbitt’s personal engagement with their work. What follows, in short, is a documentary account of the life of an American intellectual. And, although not usually remarked upon, it is an account couched in a strikingly original and erudite literary style.

Since these essays are, therefore, historical documents as well as literary works, we had two good reasons, among other obviously good ones, for presenting them here with a minimum of alteration from their original form. To be sure, obvious typographical errors have been corrected and we have done so without notice, except in the rare instance where the change has substantially altered the meaning of the text; in these cases we have indicated the change in a note. And we have also compared the published texts with Babbitt’s original typescripts where these were available to us and made a number of changes from the published version in favor of the original; again, all such changes of substance to the previously published versions have been duly noted. But apart from these modest improvements and the occasional change of punctuation readers may assume that what they read here accurately represents the texts as first published, and any notes not explicitly claimed by the editors as their own may be assumed to have been present in the original.

We have, on the other hand, deemed it necessary for a variety of reasons to provide a fair amount of annotation. Certain passages in Babbitt’s texts no doubt were difficult for readers even at the time of first publication; others have increasingly become so with the passage of the years. Difficulties of the first sort most often have merely to do with the nature (or at least the unfamiliarity) of the material; this is particularly so with Babbitt’s more technical discussions of twelve-tone matters. Difficulties of the second sort arise from the allusive quality of Babbitt’s prose, which reflects his aforementioned active interest in fields outside of music—a difficulty which has compounded over time, since what may have been an academic household name in 1960 may be hopelessly obscure today. But to fail to recognize such allusions is often to miss an important part of the meaning of the text; it is almost always to miss one or more levels of inter– and intratextual connectedness which makes these texts such a purely literary adventure to read, and, worst of all, it is often to miss a perfectly good joke. For these reasons and others we have endeavored in our notes to provide the reader with what we felt was necessary amplification or clarification in the face of difficulties of either sort.

A joke explained is often a joke spoiled, of course, and early on we were confronted by the problem of determining precisely which items most urgently needed annotation and precisely for whom such annotations were intended—a deeply vexing problem since the audience for these texts is, and always has been, as far removed from an appropriately idealized Chomskian homogeneous speech-community as one can imagine, and to focus on a single constituency would inevitably give the unintended impression of patronizing others, while still leaving some understandably scratching their heads. In the end we somewhat arbitrarily decided to put each proposed annotation to the test of whether we could safely assume that it provided a useful bit of information that we could not be certain a twenty-five-year-old graduate student of music theory, musicology, or composition would know without being told. We have tried, however, to be flexible in the pursuit of even this admittedly nebulous standard, so as not to leave twenty-four-year-old theorists, twenty-six-year-old musicologists, or composers of any age entirely out in the cold.

A scant few hundred years ago a war could be won consuming fewer resources than were needed for the production of this volume. In addition to the work of the four editors (which verged on full-time employment at numerous points) the project required the help of two editorial assistants; one music typesetter; the support of one Ivy League university music department, the computer center of another university; the expertise of a major university press; the aid of a major professional society; the efforts of a host of often anonymous librarians working through the interlibrary loan system; and, of course, Federal Express and the Internet. We are grateful to all. In particular, we express our thanks to the Princeton University Department of Music for its financial support (and especially to Scott Burnham, Paul Lansky, Claudio Spies, and Peter Westergaard for their moral support and advice); to the Society for Music Theory and the University of Alabama for generous subvention grants, which helped support the typesetting of the musical examples, the cost of permissions, and the preparation of the Index; to Bruce Samet, who began the work on this project and who did important preliminary editorial work on four of the essays; to our editorial assistants Joshua Martin and Timothy Murray; to Gary Smoke, who typeset the musical examples; to Scott Gleason for preparing the Index and for other editorial assistance; to Michael Berry for reading the proofs; and to Fred Appel of Princeton University Press for guiding this book and its editors through the production process.

THE COLLECTED ESSAYS OF

MILTON BABBITT

The String Quartets of Bartók

1949

This article was originally published in The Musical Quarterly 35 (1949): 377–85. The dates of composition of the six String Quartets of Bartók are as follows: No. 1, Op.7, 1908–9; No. 2, Op. 17, 1914–17; No. 3, 1927; No. 4, 1928; No. 5, 1934; and No. 6, 1939.

The recent performance of the String Quartets of Béla Bartók by the Juilliard String Quartet served, by virtue of the stylistic unity of the presentation and the fortuity of nonchronological programming, to emphasize above all the homogeneity and consistent single-mindedness of Bartók’s achievement in his works for this medium.1 The superficially striking idiomatic differences between the first two quartets and the later four appeared entirely secondary to the basic unity of purpose that invested all six with the character of a single, self-contained creative act. For all that these works span an entire creative career, there is, throughout, a single conceptual attitude, and, from the Second Quartet on, a personal sound is present, through which this conception is disclosed. Most important, the unity of purpose emerges in all its significance as the identification of the personal exigency with the fundamental musical exigency of the epoch, emphasizing the impossibility of divorcing the qualitative aspect of the musical achievement from its strategic aspect. For it is in this respect that Bartók’s music is so completely of its time, and achieves a contemporaneity far transcending mere considerations of style or idiom. It is nonprovincial music that reveals a thorough awareness of the crucial problems confronting contemporary musical composition, and attempts to achieve a total and personally unique solution of these problems.

Bartók, from the outset of his career, and throughout all the observable stages of formulation and eventual fulfillment (and this certainly appears to be the relationship between the Third and Fourth Quartets) remained a traditionalist, in that he was unwilling to abandon completely the employment of generalized functional tonal relationships, existing prior to a specific composition; yet he was aware of the hazards inherent in the use of a language overladen with connotations, in which the scarcely suggested is perceived as the explicitly stated. At the same time, the exclusive employment of unique, internally defined relationships, which can avoid this danger, leads to a considerable sacrifice of tonal motivation. Bartók’s problem was that of achieving an assimilated balance between these two methods, without oversimplifying the problem by assigning discrete regions of control to each, for such a solution is indeed no solution, substituting as it does segmentation for integration. Yet, since the connotative is most dangerously explicit in the small, and the self-defined least structurally explicit in the large, there is, in a general sense, an inverse relationship between harmonic definition and temporal span in Bartók’s Quartets, but the relationship is revealed through virtually nonperceptible phases of change in the relative autonomy of the two organizational principles. There is, however, no avoiding, on the one hand, a highly attenuated functionality, or, on the other, a constant mutation, rather than more easily perceived reiterations, of the thematic elements. In this resides the difficulty and apparent complexity of Bartók’s music.

Bartók’s concern for the total composition, and the resultant evolution of the maximum structure from a minimum assumption, makes it irrelevant whether one initiates a consideration of his music with the detail or the entirety. In Bartók’s case, to consider thematic structure is quite a different thing from thematic analysis; rather, it is a means of entering the total composition.

Bartók’s thematic material, for the reasons indicated above, is in no sense unequivocal in tonal orientation; it consists, characteristically, of a small number of chromatically related tones stated in their minimal linear span. Such a theme can, by alterations of relative durations, metrical placement, and dynamic emphases, serve as the elaboration of almost any one of its component elements, without sacrificing its initial character. Then, rather than functioning as a fixed unit that is acted upon, such a theme can itself act as a generator, avoiding redundancy through continual variation, but creating, at the same time, continuous phases of association. An important element in the first and last movements of the Fourth Quartet has the following form on its first appearance:

EXAMPLE 1.

Only the external factors of dynamics and pause cause the last note to predominate. But, when true finality is to be achieved with this motif, at the end of the first and last movements, it is altered to the following form: great emphasis being placed on the upper third of the final note.

EXAMPLE 2.

The final note may function merely as a neighboring tone in an expansion of the motif which emphasizes the second note:

EXAMPLE 3.

or the span of the motif may be extended to a fourth:

EXAMPLE 4.

or, finally, the motif may assume an extended form in which only the general rhythmic characteristics of the original are present:2

EXAMPLE 5.

From his thematic assumption arises Bartók’s polyphony, every line of which is a thematic variation and expansion, progressing tonally in terms of the successive elaborations of the tonal area controlled by single thematic elements. At the same time, the polyphonic lines are coordinated and given unified harmonic direction through the relationships existing among the simultaneously elaborated central tones. This procedure often appears to be an organic employment of what has been mistermed polytonality, a self-contradictory expression which, if it is to possess any meaning at all, can only be used as a label to designate a certain degree of expansion of the individual elements of a well-defined harmonic or voice-leading unit.

In general, it is impossible to determine the harmonic orientation of a Bartók quartet from the implications of a single harmonic event. Rather, the harmonic region is revealed through polyphonic unfolding, while the specifically harmonic events serve often merely to state secondary relationships which make it possible for certain dissonant polyphonic events to acquire a relative stability arising not from their inherent structure, but from their relationships to these harmonic statements. Thus is the polyphony functionally framed, but deriving its internal character from the nature of the thematic assumption. The effect of true harmonic progression is often achieved analogically rather than absolutely, through the transposition of a harmonically indefinite unit, where the harmonic relationship associated with the interval of transposition affects the total harmonic relationship. This type of progression by translation is one of tonal association rather than of tonal function. It also serves to articulate sections through the return and restatement of such characteristic, fundamental combinations. In the first movement of the Fourth Quartet, the first strong harmonic emphasis is placed upon the following harmonically ambiguous whole-tone chord:

EXAMPLE 6.

At what may be considered the end of the exposition, or the beginning of the development, the following passage appears:

EXAMPLE 7.

which has the effect of moving the original harmony, in its root position, up a major third through whole-tone steps, that is, in terms of its own components.3 So, in spite of the lack of a decisive absolute tonal level, the first harmonic section contains the second, and is expanded by it, as surely as the tonic contains the dominant. It is also interesting to note that, following the initial statement of this whole-tone chord, an elaboration of its elements follows, ending with the following chord:

EXAMPLE 8.

-E, which had been diatonically filled by the whole-tone chord.4 This harmony (Ex. 8) recurs at the same tonal level at the end of the next phrase thus fulfilling an articulative role, and demonstrating the possibility of stating a harmonic structure at a fixed tonal level in different contexts in such a way that the harmonic structure itself possesses different implications.

The developmental nature of the motival structure in the work leads to the identification of linear and vertical statements. The following quotation from the opening of the second movement of the Fourth Quartet is a striking example of this:5

EXAMPLE 9.

The linear elements stated by the cello and viola are accompanied by the same elements stated in successive pairs by the violins. This serialization appears as early as the opening of the Second Quartet:

EXAMPLE 10.

and becomes increasingly characteristic and important;6 it has also led to a comparison of Bartók’s music with that of the school of composers whose music is based entirely upon, or stems from, serial methods. But serialization in Bartók is but one of many integrative methods in the small, and its specific character is determined by the context in which it occurs. Never does it create the context. Likewise, Bartók’s considerable use of inversion, retrogression, and free permutation is essentially a traditional one, concerned with varying linear characteristics while preserving their relative contours. Never does he use inversion, for instance, in its abstract structural role of maintaining the harmonic invariance of successive dyads, as is done in twelve-tone music. Even in those rare cases where inversion is employed over a large structural unit, its function is variational and thematically explicit. The following example, from the first movement of the Fifth Quartet, where the entire recapitulation is stated in free inversion, indicates how Bartók inverts not only the individual lines, but the entire score:

EXAMPLE 11.

The first of these quotations is from the exposition, the second, from the corresponding point in the recapitulation.7

The evolution of the theme in Bartók is not confined to the region of a single movement. In all of Bartók’s Quartets, thematic relationships among movements occur. This, of course, is not a new notion; indeed, it is one that has been employed in the most ingenuous manner as a means of securing a unity of a merely mechanical, quotational sort. In Bartók, this procedure is employed in two basic ways. The first has as its goal the creation of a type of structural climax by the gradual emergence of the theme through various stages of increasing functional importance from movement to movement. This method, which is already used in the First Quartet, is brought to its fulfillment in the last, an essentially monothematic work. The theme of this work, which is stated at the head of the movement, in successive one-, two-, three-, and four-part settings, generates each of the movements, with the entire fourth movement functioning as its most direct and complete expansion. The second technique, rather than associating all of the movements, has as its purpose the revelation of the symmetrical structural conception of the entire work, through the identification of symmetrically disposed movements, as in the Fourth and Fifth Quartets. Naturally, these thematic identifications are seldom exact; the theme is altered to permit quite different exploitations in its development, while the identification functions associatively rather than literally.

The preoccupation with structural completeness through the use of such methods as these has led to Bartók’s music being accused of formalism and constructivism. Such a criticism presumably implies that the structure of the work was predetermined without reference to the specific materials. On the contrary, Bartók’s formal conception emerges as the ultimate statement of relationships embodied in successive phases of musical growth. The arch-form structure of the total Fifth Quartet is explicitly foreshadowed in the structure of the first movement. The analogous structure of the Fourth Quartet is revealed through a carefully planned symmetry of tonal centers that arise as the goals of harmonic directions established previously. However, it is probably true that these thematic methods, which Bartók is obliged to use to achieve a sense of completeness, are symptomatic of a difficulty inherent in an idiom where independent formalism is inhibited by the presence of functional harmony, but where the tonal functionality itself is too rarified and complex to effect unambiguous formal finality.

In so fluid a harmonic idiom, true cadential articulation can easily lead to textural inconsistency. Bartók employs the instrumental resources of the quartet to achieve phrase and sectional articulation. Extreme shifts in purely sonic effect are used to define large formal relationships, while more subtle shifts in tonal balance, often effected through doublings, define smaller sections. Striking color characteristics associated with a harmonically ambiguous combination of tones may serve to endow it with an individuality that makes it possible for it to function in the role of a tonic sonority, at least to the extent of achieving a sense of return.

Perhaps more problematical than any aspect of Bartók’s music itself is the future of the attitude it embodies. Bartók’s solution was a specific one, it cannot be duplicated, but the question of whether it can be extended depends largely upon whether or not Bartók has reduced the use of generalized functionality to the minimum point at which it can exert structural influence. There is some evidence in Bartók’s own work that such an exhaustion may have taken place. The Sixth Quartet is in many respects a retreat from the position of the Fourth and the Fifth. But such a question cannot be answered in the abstract; the answer can be found only in the music that will or will not be written.

Notes

1. The Juilliard Quartet (Robert Mann, first violin; Robert Koff, second violin; Raphael Hillyer, viola; and Arthur Winograd, cello) performed the six String Quartets of Bartók in two concerts in 1949 in Times Hall in New York. At the first concert, on 28 February they played Nos. 3, 2, and 5. At the second concert, on 28 March they played Nos. 4, 1, and 6. (eds.)

2. Examples 1–5 come from the following locations in the Fourth Quartet: Example 1, first movement, m. 7; Example 2, first movement, mm. 160–61, and fifth movement, mm. 391–92; Example 3, fifth movement, mm. 183–84; Example 4, fifth movement, mm. 141–42; Example 5, fifth movement, mm. 160–63. (eds.)

, C, D, E}. The chords in Example 7 are {C, D, E, F#} and {D, E, F#, G#}. (eds.)

, B, C, C#, E} returns in m. 26, as Babbitt notes in the following sentence. (eds.)

5. Example 9 is from the second movement of the Fourth Quartet: mm. 1–7. (eds.)

-D, shared among cello, viola, and second violin, returns transposed in the first violin, as A-D-C#. (eds.)

7. Examples 11a and 11b are from the first movement of the Fifth Quartet: mm. 26–27 and 148–49. (eds.)

Review of Schoenberg et son école and Qu’est ce que la musique de douze sons? by René Leibowitz.

1950

This review appeared in the Journal of the American Musicological Society 3, no. 1 (1950): 57–60. René Leibowitz (1913–1972), noted conductor, composer and teacher, had been a student of Arnold Schoenberg. During his career he was involved in a number of performances and recordings of the music of Schoenberg, Webern, and Berg, and he counted Pierre Boulez among his students. His writings about twelve-tone music, two of which are reviewed here, were some of the first book-length studies of the music of the Second Viennese School. This review contains Babbitt’s first published remarks about twelve-tone theory, and in retrospect it is clear that he had already developed many of the ideas that were to inform his major articles on the subject.

René Leibowitz. Schoenberg et son école. Paris: J. B. Janin, 1947. 302 pp.

René Leibowitz. Qu’est ce que la musique de douze sons? Liege: Editions Dynamo, 1948. 61 pp.

The two volumes under discussion represent serious effort in the neglected field of analytical criticism. It is doubly unfortunate, therefore, that their criticism must be adjudged meaningless, their analysis inadequate. The failure is not so much that of the author; rather, it is the inevitable result of musical criticism’s refusal to learn and to use the strictness of method and the verbal consistency which alone make criticism possible. M. Leibowitz, as composer, critic, and conductor, is intimately aware of the problems of the music which he examines here. The weaknesses of his present volumes, therefore, are never the familiar ones. He knows his subject at first hand; he eschews hearsay and anecdote in order to devote himself to a discussion of the music itself. Yet, in these volumes, his analysis is merely description, the transformation of musical notation into verbal notation. The terms used in this verbal notation, moreover, are ambiguous and not clearly defined; they make it difficult to appraise either his critical assumptions or the conclusions derived therefrom.

Schoenberg et son école begins with a short historical survey. The approach is hypothetical, and the result is an extremely oversimplified statement of a chronological historical interpretation. Certain details of this interpretation are open to question; more important, however, is the basic impossibility of demonstrating specific conclusions from empirical data where both data and the method of deduction are unsystematic. Leibowitz, indeed, is much more concerned with establishing such generalities as the historical continuity of Schoenberg’s music, with Schoenberg’s role as reactivator of the polyphonic principle, than with determining the technical climate of his music. For, when Leibowitz turns to the music itself, it appears as something of an isolated phenomenon, unrelated in specific terms to other work and, in a sense, unmotivated from composition to composition.

The analytical method employed here consists primarily of the detailed description of details and the categorical description of the total work; this implies that the two aspects derive from entirely different realms of compositional criteria. The relationship of detail to larger section or to extended composition, the kind of relationship that is so often of generative force, is scarcely intimated. There is an almost exclusive concern with the motival aspect of composition, but it is motivic analysis subject to neither a priori nor effectual criteria. In addition to substituting a label for an explanation, the author apparently assumes that the label itself is endowed with the properties of an aesthetic determinant. Such limited analysis is not enough: identification is trivial. What of the significance of the event at precisely its own moment of occurrence, at its own tonal level, and in its relation to other such events and to the work as a whole?1 And, in its own terms, how far can motival identification be applied? Leibowitz, in discussing Berg’s Opus 5, identifies a two-note motive (ascending a whole step) as a new form of a previously stated three-note motive (which descends in half-steps). The first motive is said to derive from the second by inversion—or retrogression, which in this case leads to an identical result—and by the omission of the middle note. Such analysis leads ultimately to a point of nondifferentiation, thereby defeating the essential purpose of analysis.

At the other extreme, Leibowitz discusses the total composition in terms of the form labels of triadic music. Granted, the term sonata form in tonal music is an inorganic, nondiscriminatory description of a generalized organizational concept. Even so, it at least serves to identify the formalistic fulfillment of one interpretation of the forces inherent in tonal music. Once removed from its tonal motivations and from the assumptions which underlie them, however, such a term becomes the description of a mere formalism of thematic arrangement, entirely arbitrary and divorced from the specifically musical phenomena. If such a term is indeed the only one through which a nontriadic work can be given meaning, then that work itself would seem questionable. And, if one is seeking merely formalistic form, there are surely much more complex and ingenious arrangements than sonata form, though they lack this verbal identification with tradition.

When, after his preparatory discussion, Leibowitz comes to his actual consideration of twelve-tone music, he begins with a statement of the familiar properties of a twelve-tone set (used here in the sense of row or series) and the operations upon it. In dealing with the most influential hypothetico-deductive system in the history of music, its basic operations must be considered in terms of this special character of the system. To consider them, as does Leibowitz, as vehicles of historical continuity is to obscure their true nature and thus to perpetuate misconceptions regarding the system itself. It does not matter that these operations were chosen as the result of psychological and historical processes; once the operations were so determined, their meaning was no longer that associated with their utilization in earlier music. They are no longer linear, imitational, variational procedures within a system of composition whose character is determined by principles independent of these procedures. Rather, they have become precompositional operations, determining the system itself. It is impossible to assume that the enormous creative potentialities of the system can be divorced from its extraordinary properties. These properties can be understood only if the twelve-tone set is considered as a total linear ordering, its elements subject to complementation with respect to each of their two independent properties (pitch and order position). Essentially there is but one operator or integrated unit, under which all sets obtained in the above manner (including the transpositions) stand in closed and symmetric relationship.

But such systematic completeness does not automatically provide compositional completeness. To achieve this requires an awareness not merely of the explicit principles of the system, but of the implications of these principles. Leibowitz, in analyzing twelve-tone music, concerns himself primarily with the identification of these operations. He appears to accept as valid any deviation from, or extension of, these principles merely because such special cases exist in actual composition. This kind of uncritical empiricism leads to many questionable assertions, emphases, and omissions. To cite but one example: Leibowitz, in considering the first movement of Webern’s Variations, Opus 27, never debates the use of transposition in the oversimplified form there present. In that particular example, the interval of transposition is determined entirely on a basis of overlap and intersection, offering no means of aural differentiation between those tones which have a dual function and those which do not. The resulting uncertainty about the unit of progression constitutes a serious problem, at best.

Again, at no time does Leibowitz suggest the extremely problematical nature of the twelve-tone system. A suggestion of this kind would not deny the immediate compositional significance of the system. Anything vital is problematical; the nonproblematical is static. Music of the latter kind would be reduced to formulation, to mechanistic demonstration. Twelve-tone music, however, has a highly problematical aspect all its own: the substitution of the operations themselves for the functional interaction between those various operations. The functionality of a twelve-tone composition is defined by the specific twelve-tone set. A functional norm is stated, and deviations from this norm appear; but there is no degree of deviation, no hierarchy of deviations such as is present in tonal music, to make possible progress and growth—stated in terms of the functional context—through various stages of compositional expansion. The manner in which this problem is to be solved, if only in terms of compensatory attributes, is not indicated by Leibowitz either in his discussion of individual works or in the final section of his book, which is devoted to categorical conclusions deduced from the music discussed. Here again, details, which are at best specific solutions of specific problems, are presented as generalized solutions. But these details of procedure imply their original immediate context, and cannot be enlarged into overall principles of composition.

In discussing the complex matter of harmonic structure in twelve-tone music, no mention is made of the existence and significance of the principle of combinatoriality. This principle, embodied in the structure of the type of set itself, provides for the simultaneous statement of various forms of the set in terms of an aggregate of tones which is in itself a partially ordered set. Also, by virtue of the symmetry of the system, this principle fosters linear progression in terms of secondary sets, thus making possible an interrelationship of the horizontal and vertical dimensions far beyond that of mere identity. The combinatorial principle determines the interval of transposition and establishes a referential norm which, by virtue of a complex internal structure, can be stated in a variety of ways without weakening its cognate function. The combinatorial unit (and there are numerous types and orders of combinatoriality) functions as a unit of harmonic progression in determining the limits of harmonic areas and coordinating the polyphonic components. The principle of combinatoriality is employed in all of Schoenberg’s twelve-tone music in the restricted sense of semicombinatoriality, of which total combinatoriality is an obvious and immediate generalization.

In discussing rhythm, Leibowitz again introduces examples of procedure which are in no sense primarily related to the twelve-tone conception. But it is precisely in the realm of rhythm that twelve-tone music may conceivably compensate for its loss of tonal functionality. In tonal music, the attendant presence of harmonic weight necessarily reduces rhythm to a resultant secondary role and provides no criteria for the development and structural use of the rhythmic element. With the dissolution of harmonic functionality, however, rhythm is free to emerge as a primary, independent element. Most importantly, twelve-tone principles are capable of giving meaning to this freedom, since the operation of complementation is as meaningful with relation to rhythmic characteristics (duration and order) as to the pitch sequence characteristics of the set. Thus there arises the reality of a rhythmic structuralization totally identical with the tonal structuralization, the two elements integrating with each other without harm to the individuality of either one.2 In addition, there is made possible the intimate interrelation of durational rhythm, accentual rhythm, textural rhythm, timbral rhythm, and the mutations of all of these.

Qu’est ce que la musique de douze sons? is the outgrowth of a lecture given by the author in connection with a performance of Webern’s Concerto, Opus 24; a condensed score of that piece is contained in the volume. After general considerations akin to those found in Schoenberg et son école, this volume is devoted to a note-by-note analysis of the work in question. The analysis is initiated with a comparison of the opening of the Concerto with that of Beethoven’s Sonata, Opus 2, Number 1. The purpose of this is presumably to establish by analogy the historical continuity of Webern’s music and the universal compositional principles which transcend technical assumptions. There is also present, however (at least by implication), the attempt to establish quality by transitivity. In any case, analogy is clearly false when it involves two systems between which there is no identification of assumptions and operations. In the immediate case, this is made apparent by the degree to which Leibowitz must overemphasize secondary factors in the Beethoven example; worse still, he is forced to secure his analogy almost entirely in verbal terms, using the terms themselves in ambiguous fashion. This reaches its extreme in the statement that the retrograde-inverted set functions as the twelve-tone equivalent of the dominant tonality in, at least, the specific case cited here.

Fortunately, this analysis by analogy is soon dispensed with, and there follows a detailed descriptive analysis of the Webern work. In its own terms, the analysis is quite complete and serves to present details that might otherwise be overlooked, but it is still an analysis of detail, with the large shape described in the jargon of tonal formalism. There is still no indication of the manner in which a specific shape is generated by its nucleus, the set. Moreover, the implications of the set structure of this composition demand further investigation than Leibowitz grants them. As he points out, the set of this composition is to be considered as the linearization of four three-note elements; one of these elements may be considered prime, with the other three derived from it by application of the basic twelve-tone operations. Such derived sets have been used extensively by Berg (in, for instance, his Lyric Suite and in the later version of Schliesse mir die Augen beide, in which six-note generators are used), by Schoenberg (in, for example, A Survivor From Warsaw), and in other works of Webern (as in the String Quartet, where a four-note generator is employed).

In the Webern Concerto, the derived set is employed as the fundamental one; and, particularly since a minimal generator is used, the desire is obviously to secure maximum homogeneity and interrelationship of sounds. It might even be questioned whether the result does not come perilously close to over-association and lack of differentiation, due to the extreme reduction of the available compositional material. To raise such a question is in no sense to minimize the general compositional importance of derivation as an operation with regard to the general set. All derived sets of the minimal type are combinatorial, possessing in fact generally two combinatorialities; consequently, derivation serves not only as a basic means of development and expansion, but as a method whereby the basic set can be coordinated with an expanded element of itself through the medium of a third unit, related to each yet equivalent to neither one. Similarly, elements of the set can be so coordinated with each other.

Derivation also furnishes a principle by which the total chromatic gamut can be spanned by the translation of elements of fixed internal structure, this structure itself being determined by the basic set; and harmonic change is achieved by means of a constant unit of tones. Again, derivation affords a means whereby the operational procedure may be extended from set part to set whole, with the resultant integration of structure; in this way, the unique formal implications of a given set are revealed in terms of the derivational interrelationships of its components. It is not too much to state that in the combined principles of combinatoriality, set derivation, and structural rhythm, twelve-tone music is approaching the compositional completeness which will make possible an enormous variety of significant creative achievements, far transcending considerations of idiom or style.

It should be noted that, throughout both volumes under discussion here, the author makes reference to another work of his, Introduction a la musique de douze sons, which would seem to be a companion volume, prefatory to Schoenberg et son école. Unfortunately, that volume was not yet available at the time of this review; it seems possible that a reading of the Introduction would serve to eliminate certain objections raised in connection with the present volume. Also, it should be noted that Schoenberg et son école has recently appeared in an English translation.3

Notes

1. Babbitt uses tonal level here to refer to the pitch level or transposition at which an event occurs (eds).

2. Babbitt is using the term tonal in two senses in this review, both to refer to music of the common practice period (tonal music) and to refer, as here, to pitch structure in a more general sense. (eds.)

3. René Leibowitz, Schoenberg and His School, translated by D. Newlin, (New York: Philosophical Library, 1949). (eds.)

Review of Polyphonie—Revue musicale trimestrielle; Quatrième cahier: Le Système dodécaphonique

1950

First published in the Journal of the American Musicological Society 3, no. 3 (Fall 1950): 264–67, this was the last of four reviews in this issue of JAMS, each by a different author, of the first four published numbers of the then-new French periodical.

The article of primary interest in this issue of Polyphonie,1 devoted to the twelve-tone system, is Arnold Schoenberg’s La Composition à douze sons.2 This is Schoenberg’s only extended statement on the twelve-tone system, and though it was delivered as a lecture in 1939, it had not been generally available until this translation by René Leibowitz appeared;3 since then, it has appeared in its English version in a collection of Schoenberg’s essays issued under the title, Style and Idea.4 It is to be assumed that this article will serve henceforth as a source material in the history of twelve-tone music and of Schoenberg’s personal development. As such, it possesses interest and significance, but as a statement of the nature of the twelve-tone system it must be adjudged disappointing.

This article is concerned essentially with two aspects of the system: its origins, and its compositional characteristics as revealed in three of Schoenberg’s compositions: the piano suite, Opus 25; the Quintet, Opus 26; and the Variations for Orchestra, Opus 31.

With regard to origins, two sources are cited: the personal and the historical. The extremely mystical statement of the personal origins furnishes the basis neither for discussion nor for objective enlightenment. The historical discussion proceeds from the now familiar premise that musical pluralism, a perfectly valid concept, must be avoided at all costs. Thus, Schoenberg asserts the necessity of the system, an assertion that requires the identification of nonequivalent conditions: that which arises as the result of a historical development, and that which is offered as a possible solution of a historically initiated problem. The attempt to establish historical derivation leads to a sort of functional synecdoche, with unrelated functional constituents of a musical component equated in terms of the fixed character of a secondary aspect of the component. Schoenberg cites Beethoven’s Opus 135 as a work adumbrating, in motival form, the operations of the twelve-tone system, while admitting that the motival transformations in Beethoven are not literal, because of the tonal functions they must fulfill.

But this is the crux of the problem. For it is just this aspect of the tonal motive, which is subject to the predetermined boundary conditions of tonality, that completely differentiates it from the twelve-tone set and its transformations, which are themselves the fundamental boundary conditions. The tonal motive assumes functional meaning within a context and becomes, in turn, a vehicle of movement within this context; the twelve-tone set, however, is the instigator of movement, and defines the functional context. To equate a compositional element with a precompositional element is not only to confuse the nature of the systems, but to reduce the number of levels of musical meaning, and, as a result, to reduce the functional multiplicity of the individual note. It is unfortunate that in attempting to make of the twelve-tone system something more than it can be demonstrated to be, in historical terms, Schoenberg consequently reduces it to something less than it can be demonstrated to be, in autonomous terms.

In the discussion of his own twelve-tone compositions, Schoenberg’s analytic method tends toward paraphrastic description of musical events in terms of their embodying procedures of the system, but without indicating the particular inceptive and implicative character of such an embodiment with relation to other so characterized events or to the eventual totality. The result is an analysis of the complete work in terms of discrete parts, which are constantly referred back to a stage preceding the formulation of the specific work; this would appear to attribute a subordinate role to specific, internal properties. The emphasis is upon the possible rather than upon the demanded, upon the how rather than the why, with no indication of the particular, perhaps unique, implications for development and progression of the concrete musical statement. In compositional terms, this can lead only to a very real discontinuity in the progression from the region of the individual conformation to that of the totality.

It is regrettable that this analytic procedure is so much less satisfactory than that which Schoenberg has applied to tonal music, at least in his conception of tonal regions, which involves a unifying principle of tonal analysis. It is perhaps significant that this conception serves to indicate the basic systematic difference between tonal and twelve-tone composition, and the resultant impossibility of employing tonal principles analogically with regard to twelve-tone music. For the notion of regions involves a principle of containment, and these containment relations are constant for all tonal composition; only the normative factor is defined for the specific work, and this factor itself determines a region which occupies a fixed relative position of containment. But there are no such fixed relations in the twelve-tone system; the normative factor is determined without any reference to means of its being so recognized other than by internal structure, which is not true in tonal music, and by priority, which is not necessary in tonal music. And, although the totality of tonal operations is cyclic, the individual operations, unlike twelve-tone operations, are nonreflexive. Thus, the problem of true formal progression in twelve-tone music can be solved only within the system itself. Schoenberg does not indicate the nature of such a solution, and indeed, implies an attitude towards form as a separable vehicle of projection in the statement that form . . . aims primarily at comprehensibility.5

It is interesting to observe the emphasis, and the nature of the emphasis, that Schoenberg places upon the semicombinatorial set. (This is a set so constructed that one of its transformations, other than its retrograde, can be transposed so that its first six notes are equivalent, with regard only to content, to the last six notes of the original set. The first six notes of each of these two sets will then, together, contain all twelve notes. The same condition will hold for the second halves of the sets and, by symmetry, the same relations will hold between the remaining two basic forms of the set. The nature of the retrograde operation assures comparable linear properties. This principle can be generalized to the construction of the all-combinatorial set, which possesses such a relation to all of its transformations and one, or more, of its own transpositions.) Unfortunately, Schoenberg emphasizes the set’s negative property in avoiding octave-doubling rather than its positive properties in terms of harmonic and linear organization. Strangely too, in discussing his Quintet, Schoenberg remarks that in this work he had not yet begun utilizing a set in which combinatoriality is obtained by transposing the inversion down a perfect fifth. This emphasis upon the fifth can only be explained as a vestige of triadic thinking, since any odd transposition interval may be associated with the transposition necessary to effect combinatoriality. Indeed, the elements of the combinatorial segment may be subjected to any permutation without affecting the combinatorial property. But each such permutation that alters the first note changes the transposition interval. Therefore, there is no significance to be attached to a particular interval of transposition. The Quintet itself employs a set that effects combinatoriality by transposing the inversion down a minor second, and the principles of progression arising from this property differ in no basic manner from those of other works which require a different interval.

On the basis of Schoenberg’s preoccupation with questions of historical derivation, and his insistence on negative rather than positive aspects of the system, one is obliged to conclude that the system’s demonstrable consistency is an astounding fortuity, and that Schoenberg, like many other great innovators, was not, at least at this point, entirely aware of the implications of his own discovery. This is, in no sense, to minimize his achievement; on the contrary, it makes the achievement appear all the more remarkable.

Ernst Krenek’s article, Technique de douze sons et classicisme, though relatively short and general in nature, concerns itself with at least one question of great significance: that of the twelve-tone system’s supplying the basis for a common practice or a tradition.6 This involves the urgent and complex matter of the loss of a fixed body of conventions, a problem common to all the arts in our time, but particularly serious for the nonverbal arts, where the assumptions cannot be stated within the art work itself and must be sought, not only outside the work, but in a different medium. The art work becomes, at once, isolated and heteronomous. The absence of homogeneity of intent and belief has led to achievement by self-definition, an insistence on the qualitative character of means, and, in general, a complete circularity of thought with regard to the function of the individual work. Even the masterpieces of our time have existence as solitary achievements rather than as inheritable elements of a historical succession.

The need, then, for a genuine tradition cannot be overestimated, if only for the security of judgment it affords in making the inherently relative effectually absolute, for that period of time during which the elements of the tradition are assumed totally and exclusively.

Whether such a tradition will arise from twelve-tone principles is not dependent, by any means, on merely the immanent properties of the music or the system, or even, to state Krenek’s criterion, upon its clarity and ease of comprehension. (There is ample evidence on which to question this last criterion.) It would appear that a genuine tradition is not only dynamic but idiomatic. The composer of the latter half of the eighteenth century, for example, worked unquestioningly within a stylistic and technical domain. The nature of his achievement could be isolated within a closely defined and subtle frame of reference. But the twelve-tone system (and this is one of its virtues) does not imply a specific style or idiom. Indeed, there are already a multitude of styles within the system, and whereas change of idiom in the tonal system has been a gradual and linear process, in twelve-tone music there is no homogeneous core of style to serve as a point of origin. The reason for this may reside in what is, in a sense, another problem associated with the question of a twelve-tone tradition, the problem of license within a tradition. In the past, idiomatic change has usually been the surface manifestation of a systematic extension, demanded, or at least motivated, by the relations of the individual work. But much twelve-tone music has indulged in licenses which make it impossible to infer what stable properties the composer associates with the principles of the system. Often the licenses appear to be motivated by the desire to secure certain idiomatic events that do not imply a twelve-tone context at all. Thus, the work originates and eventuates outside the domain of the system, which seems to function merely as the source of sonic details, and as the basis for analytical rationalization after the fact.

Also, a tradition must be founded on the impossibility of an alternative. The conscious embracing of a tradition always implies the possibility of rejection. The mere presence of a technical body of beliefs serves, at best, only to define the location of the point of choice, even, perhaps, returning it closer to the creative origin. But a tradition is all or nothing; degrees of approximation are essentially irrelevant.

Bernard Saby’s Un Aspect des problèmes de la thématique sérielle is an interesting analysis of René Leibowitz’s Chamber Symphony, Opus 16, in terms of the creation of an autonomous twelve-tone form.7

Leibowitz’s Aspects récents de la technique de douze sons is an analytical discussion of three of Schoenberg’s most recent works: the Prelude, Opus 44; the String Trio, Opus 45; and A Survivor from Warsaw, Opus 46. This article also appears as the final chapter of Leibowitz’s Introduction à la musique de douze sons, and can be more profitably and fairly discussed in the context of that volume.8

Luigi Dallapiccola’s A propos d’un trait ‘expressionniste’ de Mozart is another example of attempted historical identification, this time in terms of stylistic characteristics.9 The author cites details, primarily from Don Giovanni, that he considers dramatically expressionistic or that foreshadow procedures employed in contemporary expressionist works.

The volume also contains: Frank Martin’s Schoenberg et nous,10 the Manifesto of the First International Congress for Twelve-Tone Music,11 a portrait of René Leibowitz, a Leibowitz chronology and bibliography, and an excerpt from his opera La Nuit close.12

Notes

1. Paris, Richard-Masse Editeurs; 1948–49; 82 pp. This issue, the Quatrième cahier, is undated, but likely from c. 1949. (eds.)

2. Pages 7–31, of which 7–9 contain René Leibowitz’ Translator’s preface; 30–31, Schoenberg’s addendum; and 9–30, the body of the paper. What Babbitt refers to as the English version (from 1950, on 102–143 of the first edition of Style and Idea; see note 4, below) includes neither preface nor addendum. The much-expanded volume also entitled Style and Idea, edited by Leonard Stein (New York: St. Martin’s Press, 1975) also contains this paper, with the addendum, on 214–245. While Babbitt, following Leibowitz’ preface, indicates that this paper was delivered as a lecture in 1939, both the 1950 and the 1975 editions of Style and Idea state that it was first delivered on 26 March 1941 at the University of California at Los Angeles, and then on 2 May 1946 at the University of Chicago. In Polyphonie, the addendum, signed by Schoenberg, is followed by the phrase Chicago, 1946. (eds.)

3. French music theorist, teacher, conductor, and composer of Polish-Latvian origin (1913–1973), closely associated with Schoenberg during the late 1940s. (eds.)

4. Style and Idea, ed. D. Newlin (New York: Philosophical Library, 1950). (eds.)

5. La forme dans les arts, et spécialement en musique, vise surtout à la compréhensibilité (La Composition à Douze Sons, 10). (eds.)

6. Austrian composer and writer (1900–1991), also active in Germany and the United States. (eds.)

7. Probably the Bernard Saby (1925–1975) who became known as a painter. According to Andre Berne-Joffroy’s introduction to the catalog of a 1986 retrospective of Saby’s work, mounted at the Musée d’Art Moderne in Paris, Saby had been at first intent on a career in music composition, was a student of Leibowitz, and a friend of Pierre Boulez. (eds.)

8. Paris: L’Arche, 1949. Full title: Introduction à la musique de douze sons: les Variations pour orchestre op. 31, d’Arnold Schoenberg. The chapter in Introduction . . . differs in at least minor ways from the article in Polyphonie: for instance, the phrase que nous avons signalées in Polyphonie, reads que nous avons discutées; the musical examples are hand-copied in Polyphonie, while apparently engraved in Introduction . . .; and there are footnotes in the book that do not appear in Polyphonie. One might guess that the article in Polyphonie saw minor revisions on the way to its publication as a chapter of the book. (eds.)

9. Italian composer, pianist, and writer (1904–1975). (eds.)

10. Swiss composer (1890–1974). (eds.)

11. According to the Résolution du premier Congrès international pour la musique dodécaphonique, thirty composers representing (représentant) Germany, England, Austria, Belgium, Brazil, the United States of America, France, Italy, and Switzerland, met in Milan from 4–7 May 1949. In brief, on 7 May 1949, the Congress of Milan resolved to bring a greater understanding of la musique dodécaphonique to composers, performers, and the public. An article by Riccardo Malipiero, entitled La Dodecafonia come tecnica, invoking this meeting and apparently stimulated by his attendance at it, appeared in Rivista Musicale Italiana 55 (Anno LV, Fasciolo I, Gennaio–Marzo Milano, 1953): 277–300 (Fratelli Bocca—Editori, Roma-Milano). (eds.)

12. Opus 17, 1947–50: three scenes, text of G. Limbour. (eds.)

Review of Felix Salzer, Structural Hearing: Tonal Coherence in Music

1952

Felix Salzer (1904–1986) was an Austrian-born, American music theorist and student of Heinrich Schenker. Salzer’s influential Structural Hearing: Tonal Coherence in Music was one of the earliest English-language treatments of Schenker’s work, and the first to appear in textbook form. This review appeared in the Journal of the American Musicological Society 5, no. 3 (Fall 1952): 260–65.

Felix Salzer. Structural Hearing. New York: Charles Boni, 1952. Volume 1, 283 pp.; Volume 2 (musical examples), 349 pp.

Any discussion of Dr. Salzer’s book must begin with a consideration of two matters: the nature of Heinrich Schenker’s contributions to analytical theory, which furnish the admitted foundation for the present volume, and Dr. Salzer’s particular formulation and presentation of certain aspects of these contributions.

The work of Schenker has suffered, from its beginnings, the dual and not unrelated fates of being more discussed (usually uninformedly) than read, and of being the object of a kind of conspiracy of silence. Never translated, and not easily accessible even in the original German, the work has been judged indirectly through its presentations by commentators, explicators, and critics. For many, there is associated with Schenker’s name the concept of the Urlinie, and often nothing more. Since this concept is mistakenly assumed to be the most easily presented and the most obviously sensational aspect of his theory, it has been disassociated from the total body of his work, exposed and discussed as a thing in itself, and accepted or rejected in these terms. The result has been the widespread notion that the concept of the Urlinie came into being as an a priori, theoretical abstraction, fabricated from thin air, divorced from any aural motivation, and then employed as the rationale for deriving the remainder of the analytical method. Even a superficial investigation of Schenker’s writings demonstrates the total untruth of this notion. The gradual evolution of his thought—over a period of some thirty years—from the Harmonielehre through the analytical edition of the Chromatic Fantasie and Fugue, the first volume of the treatise on counterpoint, the volume on Beethoven’s Ninth Symphony, the analytical editions of four late Beethoven sonatas, the second volume of the treatise on counterpoint, the issues of Der Tonwille, the three volumes of Das Meisterwerk in der Musik, the Urlinie-Tafeln, and—finally—Der freie Satz reveals the constant growth, from the most tentative adumbrations, of the awareness of the basic continuity of the musical organism in terms of the correlation and interaction of the linear realization of a triadic span with the specific triadic harmonic articulations.

The evolution of this concept occurs neither deductively nor mechanistically but conceptually; at each stage it reflects Schenker’s ever-increasing aural awareness. At each point in this growth, the newest phase of temporal extension of this principle evolves from the preceding phases, and includes and reflects them. For example, the basic structural lines found in the analyses in Der Tonwille become middleground lines in Der freie Satz. The Urlinie, then, is chronologically and conceptually the final, and almost inevitable, stage in the evolution of this principle from level to level and is essentially meaningless and useless without relation to the other levels which it controls and orders and through which it evolves. Schenker’s analysis originated in aural experience, and the Urlinie is, at least indirectly, of empirical origins. On the other hand, it is (and this is merely an additional merit) completely acceptable as an axiomatic statement (not necessarily the axiomatic statement) of the dynamic nature of structural tonality. Stated in such terms, it becomes the assertion that the triadic principle must be realized linearly as well as vertically; that the points of structural origin and eventuation must be stabilized by a form of, or a representation of, the sole element of both structural and functional stability: the tonic triad. It asserts that melodic motion is, triadically, purely diatonic (of necessity, since any other intervallic motion is, at least relatively, triad-defining, and thus establishes multiple levels of linear motion, rather than a single, directed motion); that a work of music ends organically, not merely temporally, with a structurally and functionally stable statement, both linearly and harmonically, that is, with a representation of a tonic root-position triad, having moved according to the above requirements from an inceptually or contextually linearly less stable melodic statement.

This formulation, of course, includes not merely the Urlinie but the total Ursatz: the Urlinie with its correlated bass arpeggiation which is itself a spatialized statement of the definitive fifth of the tonic triad. The Ursatz is the projection in time of a single triad by means of synthesized linear and harmonic prolongations of this triad.

In the light of this, then, it should be obvious that the Urlinie was never intended as the basis for qualitative discrimination among works