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Writings in Music Theory
By James Tenney, Larry Polansky, Lauren Pratt, Robert Wannamaker, Michael Winter
UNIVERSITY OF ILLINOIS PRESSCopyright © 2015 Board of Trustees of the University of Illinois
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On the Development of the Structural Potentialities of Rhythm, Dynamics, and Timbre in the Early Nontonal Music of Arnold Schoenberg (1959)
Beginning with the Three Piano Pieces, op. 11, and continuing through Pierrot Lunaire and the Four Songs with Orchestra, opp. 21 and 22, Arnold Schoenberg developed a style that he later characterized as one based on "the emancipation of the dissonance," which "treats dissonances like consonances and renounces a tonal center" — and his further descriptions of the developments of this period are almost exclusively in terms of harmonic innovations. Analytical writings by others have reflected this same concern with the harmonic (and, to a lesser extent, the melodic) aspects of the music. Although anyone who is familiar with the music of this period must be aware of the innovations in other areas, little attempt has been made to study these innovations in detail or to incorporate them into a consistent analytical or descriptive method. Schoenberg himself gave little theoretical consideration to what might be called the nonharmonic aspects of music — i.e., rhythm, dynamics, timbre, etc. — and most traditional methods of analysis have practically ignored them. This may have been justified, insofar as most of the music to which these methods were applied (music of the late baroque, classic, and romantic periods) was primarily conditioned by structural potentialities inherent in the system of tonality. That these methods do not thoroughly describe the music is undoubtedly true, but they do perhaps describe adequately the most important structural forces involved. Nevertheless, this single-mindedness is surprising. With the gradual dissolution of the tonal system in the music of this period, we are faced with a situation in which harmonic-melodic analysis is obviously inadequate to describe the actual formal processes in the music. It is no longer possible to ignore the rhythmic and other nonharmonic aspects, because it is frequently these very aspects that are the most potent shaping forces or that give a piece its particular form and character. Indeed, the results of the various attempts at harmonic analysis should have led to this conclusion, unless one assumes either that new harmonic "laws" may yet be discovered, more or less analogous to the old laws, which can account for the musical facts, or, alternatively, that the music of this earlier period only represents a transitional or incipient stage in a longer development — that is, in the development toward the 12-tone technique. The first assumption seems highly unlikely (though certainly not impossible), considering the fact that analysts have been looking for such laws almost exclusively these last fifty years, and consequently these should have been the first to be found, if they exist at all. But the second assumption, it seems to me, overlooks the real integrity and completeness — the relative perfection — of this music, which stands on its own, in terms of formal coherence and stylistic consistency, without any justification through reference to later developments. It is true that the 12-tone method represents a logical development of certain procedures employed earlier in a spontaneous or even perhaps unconscious way (and thus, unsystematically), but I should like to emphasize the qualification "certain procedures" in the above statement: only some of the many innovations in the earlier music actually became an explicit part of the 12-tone technique; others remained as implicit elements in the style; still others seem to have been abandoned; while certain aspects of the later method can hardly have been derived from the earlier music at all but seem rather to have been "grafted on" from the outside or to have been conceived simultaneously with the codification of the 12-tone method in the 1920s. That this method is a partial systematization of procedures that Schoenberg had already used (and that had been, as he said, "conceived as in a dream") is one of the points I hope to demonstrate in this paper. Eventually, there might be possible a broader generalization of the basic ideas underlying this same method, which could account for many more of the earlier procedures, and at the same time include the propositions of the 12-tone technique as a special case. I have not attempted to do this here, of course, but it is to be hoped that the observations made in this paper might later serve as the basis for such a generalization.
I said above that the nonharmonic elements of music are often the strongest shaping forces in Schoenberg's works of this period. That this should have happened simultaneously with or immediately following the breakdown of the system of tonality seems inevitable. Something was needed to replace the older structural functions of harmony, and it is obvious that Schoenberg did not wait for the 12-tone method to restore these functions (although this is what is implied in most accounts of his development). If we are to accept the pieces from op. 11 through op. 22 as self-sufficient and "perfect," we must try to find the forces that actually were called into play in the absence of the traditional harmonic functions, and in many cases these will be found in the development of the other attributes or parameters of sound — duration, intensity, timbre, etc. — as well as pitch. It will be seen that one of the most significant characteristics of the music of this period is that it greatly extended the structural potentialities of all the attributes of sound.
The third of the Three Piano Pieces, op. 11, is an example of a kind of musical development in which harmonic-melodic elements are so constantly varied that there is virtually no thematic relationship between different parts of the piece — at least not in any commonly accepted sense of the word "thematic," implying more or less invariant interval-relations among the constituent tones of a melodic line. There are no motives subject to variation and development — again in the harmonic-melodic sense. I must emphasize this qualification, "harmonic-melodic," because if the terms "motive" and (more especially) "theme" are defined more broadly to include other attributes of sound, we may find them here and in similar pieces. Conversely, if we are to demonstrate thematic correspondence in such pieces, it will be necessary to include all parameters in our definitions. The motivic or thematic organization of this piece is primarily in terms of rhythmic patterns. There are two (or perhaps three) basic rhythmic ideas heard simultaneously at the beginning of the piece, and while the pitch patterns undergo a constant, kaleidoscopic process of alteration, these rhythmic patterns remain relatively invariant — or rather, certain relations within the patterns remain invariant, while the ideas themselves are subjected to more or less straightforward techniques of variation. In example 1, the various forms of one of these rhythmic ideas are superposed in such a way that one may see the correspondences between the different versions, as well as the variation-processes to which they have been subjected.
In addition to this thematic or motivic use of rhythm, another aspect of the duration-parameter, namely tempo, or temporal density (to distinguish between the tempo as notated and the actual "speed" of the music, which involves both the tempo and the note-values), is one of the most important means of marking structural divisions within the piece. There are three main sections in the piece, and the divisions between these sections (at measures 10 and 24) are both marked by a significant slowing of the tempo, followed by a faster tempo. The same is true of most of the smaller sections and subordinate groups. In fact, changes in temporal density (along with other factors that will be described in a moment) actually serve to create these divisions, not merely to emphasize them. The other factors that participate here in the creation of structural divisions — sometimes paralleling the effect of tempo, sometimes independently of this — are dynamic level, and a factor that is related to this, conditioning the dynamic level to a great extent, which might be called vertical- or pitch-density, i.e., the number of simultaneously sounding tones at any given moment. In measure 9, the dynamic level is pianissimo the pitch-density decreases from five to three tones (or less, since the F and G[flat] will have partially died away by the time the A is played), and the second section follows with a sudden forte-crescendo and a pitch-density of six or seven. Similarly, the third section is separated from the second by a change in level from ppp to f, although there is little significant change in pitch-density at this point. Such general (or even "statistical") aspects of sound do not fully account for the formal structure of the piece, which will also depend upon the more specific thematic relations, but it is clear that they do have a powerful effect in the articulation of the form and that they can, to some extent, replace the earlier harmonic functions.
The relatively independent development of rhythmic ideas in this piece is somewhat rare in Schoenberg's work: usually the rhythmic patterns are treated as subordinate features of an idea that is primarily characterized by melodic or harmonic relations. This approach was implied by Schoenberg when he said: "In every composition preceding the method of composing with twelve tones, all the thematic and harmonic material is primarily derived from three sources: the tonality, the basic motive which in turn is a derivative of the tonality, and the rhythm, which is included in the basic motive." Here, the basic motive — from which the "thematic material" is derived — is primarily a melodic unit that includes, as one of its features, the rhythm. (I am assuming that his statement also refers to his own pre-12-note music, in spite of the reference to tonality.) In most cases this description would be appropriate, but in op. 11, no. 3, the rhythm is the "basic motive," while the pitch-elements might almost be considered as derivatives of the rhythm. With this interpretation, the roles of the rhythmic and melodic ideas are seen to be reversed, and his description is not applicable. Another statement by Schoenberg, however, is relevant to the problem here, in which he says, regarding the Rondo of the Wind Quintet, op. 26: "While rhythm and phrasing significantly preserve the character of the theme so that it can easily be recognized, the tones and intervals are changed through a different use of BS (the 'Basic Set') and mirror forms." In this case, as in the piano piece, the rhythm is relatively independent of pitch-relations as a thematic determinant (by which I mean that attribute — or those attributes, since there may be several operating at once — that is the most effective shaping factor in a sound-idea and is thus the one by which later variations of an idea may be recognized). Rufer calls this use of rhythm the "isorhythmic principle," and it has certainly had an important place in musical composition prior to Schoenberg, although there would seem to be a significant difference between the use of invariant rhythmic relations as a thematic feature and the original isorhythmic devices employed by early Renaissance composers. In the latter case, the rhythmic pattern functions in a way similar to that of the cantus firmus in the harmonic-melodic field, providing a kind of unifying "base" to the flow of the music. That it did not have a thematic function is indicated by the fact that the actual phrase-structure often did not coincide with the isorhythmic patterns but overlapped these in various ways. Furthermore, the very idea of thematic development — implying thematic recognition — was relatively unimportant in Renaissance music, and we should not expect that the rhythmic patterns have any such thematic functions. Nonthematic isorhythmic procedures, however, do constitute an important structural force to be acknowledged along with the other potentialities of the rhythmic factor, but I have not yet found an example in Schoenberg's music of this period of the use of rhythm in this particular way. Nevertheless, in their use of specific rhythmic patterns as thematic determinants, and in their use of changes in temporal density to mark structural divisions within a piece, Schoenberg's works of this period show that the duration-parameter is capable of manifold structural functions at both the smaller and larger formal levels.
Dynamic level has already been referred to as an effective means of delineating different sections of a piece, but this parameter can operate in other ways, too. As accent, it can create a rhythmic shape in an otherwise undifferentiated succession of sounds. In the form of gradual changes of intensity — crescendo and diminuendo — it can give shape to a motive, phrase, section, or even sometimes an entire piece. A difference in dynamic level can serve to emphasize certain parts in a complex texture, or simply to separate or distinguish two individual lines in a polyphonic passage. An interesting use of the last effect can be found in Schoenberg's Six Short Piano Pieces, op. 19, in the third piece (see example 2) where the right-hand part is to be played forte, the left-hand part pianissimo, and the difference being clearly not intended for the purpose of bringing out the upper part. Here also, the dynamic distinction may be considered an important feature of the thematic idea, and this is similar in some respects to another effect of relative loudness, which is used in the last piece in this same set (example 3). The difference between the pppp of the highest part and the p of the D# in the next lower octave produces a unique "coloration" of the sound.
These various functions of the intensity-parameter might be summarized as follows: (1) the delineation of successive musical ideas and sections within a piece; (2) the separation of simultaneous lines in a polyphonic texture (simple emphasis of one part over another being a special case of this); (3) the creation of a rhythmic pattern through accent; (4) a kind of "color-effect" that gives a sound a unique quality or timbre; and (5) the shaping, in time, of a structural unit from the level of a single motive up through sections or entire pieces. There may be others, but these five are perhaps the most important, and of the five, only the last two indicate the possibility for independent development, or the kind of thematic significance that I have attempted to describe in the case of rhythm. There are two apparent reasons for this limitation, the most important one arising from a phenomenon that I call "parametric transference." In (2) above (separation of lines), the dynamic factor will tend to be absorbed into the pitch-factor by either focusing the attention on a particular melodic configuration or else conditioning the harmonic effect of the texture. In (3) (accent), there will be a similar transference to the rhythmic field whenever the accents superimpose larger duration-relations upon a series of undifferentiated note-values. Although superficially it might appear that (4) (the "color-effect") would also be a case of transference (to the field of timbre), it is rather more clearly a dynamic effect, as such, than (2) and (3); and of course the first of our five functions does not raise the question of "thematic significance" at all.
Excerpted from From Scratch by James Tenney, Larry Polansky, Lauren Pratt, Robert Wannamaker, Michael Winter. Copyright © 2015 Board of Trustees of the University of Illinois. Excerpted by permission of UNIVERSITY OF ILLINOIS PRESS.
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Table of Contents
Notes on the Edition ix
Introduction Larry Polansky xi
1 On the Development of the Structural Potentialities of Rhythm, Dynamics, and Timbre in the Early Nontonal Music of Arnold Schoenberg (1959) 1
2 Meta Hodos (1961) 13
3 Computer Music Experiences, 1961-1964 (1964) 97
4 On the Physical Correlates of Timbre (1965) 128
5 Excerpts from "An Experimental Investigation of Timbre-the Violin" (1966) 132
6 Form in Twentieth-Century Music (1969-70) 150
7 META Meta + Hodos (1975) 166
8 The Chronological Development of Carl Ruggles's Melodic Style (1977) 180
9 Hierarchical Temporal Gestalt Perception in Music: A Metric Space Model (with Larry Polansky) (1978-80) 201
10 Introduction to "Contributions toward a Quantitative Theory of Harmony" (1979) 234
11 The Structure of Harmonic Series Aggregates (1979) 240
12 John Cage and the Theory of Harmony (1983) 280
13 Reflections after Bridge (1984) 305
14 Review of Music as Heard by Thomas Clifton (1985) 309
15 About Changes: Sixty-Four Studies for Six Harps (1987) 327
16 Darmstadt Lecture (1990) 350
17 The Several Dimensions of Pitch (1993/2003) 368
18 On "Crystal Growth" in Harmonic Space (1993/2003) 383
19 About Diapason (1996) 394
Appendix 1 Pre-Meta + Hodos (1959) 397
Appendix 2 On Musical Parameters (ca. 1960-1961) 408
Appendix 3 Excerpt from A History of 'Consonance' and 'Dissonance' (1988) 424
Publication History 437