Travis-Directed Motion in Schoenberg and Webern (1966)

Directed Motion in Schoenberg and WebernAuthor(s): Roy TravisSource: Perspectives of New Music, Vol. 4, No. 2 (Spring - Summer, 1966), pp. 85-89Published by: Perspectives of New MusicStable URL: http://www.jstor.org/stable/832217 .Accessed: 29/06/2013 12:31

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DIRECTED MOTION IN SCHOENBERG AND WEBERN

ROY TRAVIS

FELIX SAL Z ER 'S Structural Hearing has already provided eloquent evidence that valuable insights into the music of Bart6k, Hindemith, and Stravinsky can be gained by a broader application of the concepts of Heinrich Schenker. But there have been few attempts to explain the music of Schoenberg, Berg, and Webern in these terms; the music of atonality and serialism does not readily yield to analysis from the standpoint of directed motion. Such an approach implies not only the possibility of recognizing clearly established origins and goals of motion, but the concomitant possibility of understanding the details of such motions as elaborations on various levels (foreground, middle- ground, or background) of a primordial progression or structure which can be assumed to underlie the entire composition and to unfold through time some sort of tonic sonority, triadic or otherwise.'

The difficulty of attacking atonal and serial music with this set of assumptions seems obvious. Nevertheless, in reconsidering two brief piano pieces by Schoenberg and Webern, respectively, I have been tempted to set down in the discussion that follows a number of observations made from this point of view. As it happens, both of the compositions in question have been analyzed from quite different vantage points in separate articles that appeared in the second issue of PERSPECTIVES (Vol. 1, No. 2).2

I. SCHOENBERG, OP. 19, NO. 2

It is possible to explain the chordal materials of the second of the Sechs Kleine Klavierstiicke without invoking either imaginary triads of resolution3 or the cumbersome if stylish irrelevancies of mathe-

1 In an earlier article I have discussed several examples from Stravinsky and Bart6k involving dissonant tonic sonorities. (See "Toward a New Concept of Tonality?" Journal of Music Theory, Vol. III, No. 2.) 2 Allen Forte, "Context and Continuity in an Atonal Work: A Set-Theoretic Ap- proach," and Peter Westergaard, "Webern and 'Total Organization': An Analysis of the Second Movement of Piano Variations, Op. 27."

3 Hugo Leichtentritt, Musical Form, Harvard University Press, Cambridge, 1961, pp. 445-46.

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matical set-theory.4 This brief composition is concerned with the gradual approach to a complex tonic-sonority reached only at the end of m. 9. Contained within the sonority itself are a C-major-minor chord with a major seventh, plus an analogous chord-form built upon the dominant degree (Ex. 1).

The essential motion is accomplished by means of two diverging streams of thirds, each of which has its source in the reiterated "dominant" third, G/B. The tones of this interval are retained through- out, and eventually take on the meaning of inner-voices. This activity can be schematically summarized as in Ex. 2.

In rhythmic context, these events succeed each other as in Ex- ample 3.

It is necessary to subject the sketch in Ex. 3 to several manipula- tions, both registral and motivic, in order to relate it to the Schoenberg piano piece. (Compare Ex. 3 to Ex. 4.)

For instance, the lower tone of Gb/Bb (the second member of the descending stream of thirds) is deployed over no less than four distinct registers, in mm. 2, 5, and 6. Another detail is the chromatic ascent from the D of m. 2 (an upper voice of the V chord), via Eb (mm. 3 and 4) and E (m. 5), to the F in the bass register of m. 6. This F, presented together with Gb in m. 6, is in fact an anticipation of the lower voice of the subsequent third, F/A to which Gb/Bb progresses in m. 7. The succeeding bass descent is obvious. Note however the effect of acceleration as the lower stream of thirds ap- proaches the final tonic (mm. 51/--9). When one considers the structural outer voices (indicated in boldly stemmed half-notes), the significance of the reiterated motive G/B-C/Eb-G/B in mm. 4 and 5 becomes evident. It is a diminution on the foreground level of the structural events of the entire piece (from G/B of m.1 to C/Eb of m. 9). This diminution is also hinted at in the espressivo melody of mm. 2-3. An attempt has been made to unravel the complexities of this

phrase in Ex. 5. The sonority in the final measure of the Schoenberg piece can be

regarded as a diminution in another sense as well. The retention of the upper voices belonging to the V chord (F4, Bb, D) summarizes in essence the motion of the entire composition, which in the last analysis is concerned with the movement from the chord-form built on V to the same chord-form built on I. By stating both chords simul- taneously at the end, Schoenberg reminds the listener of the genesis of the entire piece. (Bart6k, of course, does very much the same thing in m. 13 of his Fourth Quartet, where the eighth-note sff chord

4 Allen Forte, op.cit.

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on the second beat of the measure summarizes the activity of mm. 4-13, which is concerned with the progression from the four-tone chromatic cluster at the end of m. 5 to the whole-tone cluster at the end of m. 7 [Ex. 6]. )5

II. WEBERN, PIANO VARIATIONS, OP. 27, SECOND MOVEMENT

In an analysis virtually as rigorous as the composition it describes, Peter Westergaard not only codifies the interrelationships among:

i. the seven dyads formed by the inversion symmetry around A... ; ii. ... the four pairs of row forms; iii. .... registers; iv. .... dynamic levels; and v. ... rhythmic variables

but he interprets the effects of these interrelationships "in such tradi- tional terms as: use of the medium, rhythm and meter, intervallic detail, . . . harmonic motion, and . . . form."6 Although one hesitates to add anything to such a formidable and thoroughgoing discourse, Mr. Westergaard's emphasis on the importance of registration and his discussion of the harmonic motion (not to mention the music itself) has stimulated a line of inquiry which I find difficult to resist.

First of all, to what extent has "the inversion symmetry around A" been expressed in terms of a fixed system of registration?7 In mm. 1-25 of the Webern Symphony, Op. 21, another context in which "inver- sionally related row-forms are canonically disposed," the "axis of symmetry"8 is not only A (in this case the A below middle-C), but every single tone within the first 25 measures is confined to the system of registration illustrated in Ex. 7.

The question arises whether a similar system of registration is employed in the second movement of the Op. 27 Piano Variations. In Ex. 8 I have eliminated the hand-crossings in order to reveal more clearly the actual sequence of auditory events so that a possible system of registration might become more evident.

What emerges is not a single system for the entire piece, but four slightly different systems corresponding to each of the four pairs of row-forms. All four systems have in common not only the axis of symmetry A, but the three other dyads circled (Fj/C, C#/F, and

5 See Milton Babbitt, "The String Quartets of Bart6k," Musical Quarterly, Vol. xxxv, No. 3, Ex. 8, pp. 381-82, and George Perle, "Symmetrical Formations in the String Quartets of B61a Bart6k," Music Review, Vol. 16, No. 4, Ex. 2a, p. 311. 6 See Peter Westergaard, op.cit., p. 109.

7 I am indebted to Andrew Imbrie for alerting me to the presence of fixed systems of registration in the music of Webern.

8s To borrow George Perle's term (see op.cit.).

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G#/Bb). Two other dyads (Eb/D# and D/E) are shared by three of the four systems.

It is evident that a tension arises between the clear canonic state- ment of a row-form and its inversion, and the voice-crossings necessi- tated by such "pre-ordained" systems of registration. It might be argued that the prevailing eighth-note lag between canonic "voices" (pointed out by Mr. Westergaard) is sufficient to distinguish them. However, the marked dynamic contrast between successive articulation patterns tends to emphasize a given dyad rather than its com- ponent canonic "voices."9 Furthermore, these are only partially clari- fied by the elaborate pantomime of crossing hands, because the hands exchange row-forms several times in mid-row (e.g., in mm. 5, 8, 17, and 19). Therefore if discrete row forms in canonic relationship emerge at all in performance, they do so imperfectly, and in terms primarily of a visual rather than an auditory experience.

It is interesting to speculate on the possible meanings that the Salzerian concept of melodic progression could have within the fixed systems of registration of this piece, in which the composer has legis- lated that all activity is to be confined to a particular group of dyads (or pairs of tones) of which each member and its counterpart are always to be equidistant from a common axis of symmetry. For example, there would seem to be three possible ways of interpreting progressions between tones in different registers.

1. Melodic progression may occur freely from any chromatic degree to any other, regardless of respective position within the fixed "galaxy" of tones. The chief impediment to hearing such progressions in this piece would be the one already mentioned, namely, that since a given melodic progression is always presented together with its inversion, in purely auditory terms there is no way for the listener to know when a voice-crossing is intended.

2. Melodic progression is to be understood only as motion from a given dyad to a directly adjacent dyad closer to or further away from the common axis of symmetry. This definition seems to offer the advantage of immediate auditory intelligibility. Unfortunately however, as far as I am able to determine, it is clearly applicable only to mm. 6-9 of this movement. (See bracketed context, Ex. 8.)

3. Melodic progression may occur from any degree to any other, regardless of octave registration, providing that it is not necessary to assume a voice-crossing or inversion of a dyad. For example, if the following octave transfers of register were admitted (Ex. 9), it

9 If, for example, the left hand were to have been played f and the right hand p, it might have been easier to hear a principal form crossing its inversion in the monochrome timbre of the piano.

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would be possible to explain the entire movement in terms of an alter- nation between the "Tonic Dyad" (G#/Bb) and the "Polar Dyad" (D/E). This repeated progression between major seconds a tritone apart would at the same time explain the over-all impression of harmonic stasis, and the apparently contradictory sense of harmonic thrust which impelled Mr. Westergaard to recognize "Haydnesque wit" in the built-in luftpause immediately preceding the inevitable return to the final "Tonic Dyad" of m. 22 (Ex. 10).

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Article Contentsp. 85p. 86p. 87p. 88p. 89

Issue Table of ContentsPerspectives of New Music, Vol. 4, No. 2 (Spring - Summer, 1966), pp. 1-184Front MatterErratum to Lewis and Epstein [pp. -]In Memoriam: Edgard Varse (1883-1965), Encounters with Edgard Varse[pp. 1-13]Edgard Varse: A Few Observations of His Music[pp. 14-22]Henry Cowell (1897-1965): A Memoir and an Appreciation [pp. 23-28]Conversation with Roger Sessions [pp. 29-46]Forum: NotationNotation in General-Articulation in Particular [pp. 47-58]

Forum: Computer ResearchToward Musical Information Retrieval [pp. 59-67]Music and Electronics: A Report [pp. 68-75]

Forum: Talking about MusicA Note on Discourse and Contemporary Musical Thought [pp. 76-80]Some Current Terms [pp. 81-84]

Directed Motion in Schoenberg and Webern [pp. 85-89]Toward a Twelve-Tone Polyphony [pp. 90-112]Richard Strauss. Part II [pp. 113-129]Colloquy and ReviewThe Israeli Composer and His Milieu [pp. 130-139]A Contemporary Role for American Music Libraries [pp. 140-143]Younger American ComposersMario Davidovsky: Contrastes No. 1 [pp. 144-149]

Reich Contra Berg [pp. 150-156]Willi Reich's "Alban Berg": Some Biographical and Critical Considerations [pp. 157-160]Review: untitled [pp. 161-171]Schoenberg by Pittsburgh and Steinberg [pp. 172-176]ReportsTanglewood, etc.: Sightreading as a Way of Life [pp. 177-181]Urbana. Report from the University of Illinois [pp. 181-183]

Back Matter [pp. 184-184]

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Travis-Directed Motion in Schoenberg and Webern (1966)