Motivic Development & Saturation
| Bach | Baroque | Beyond | Assignment | Links | Notes |
Site ©1996 Timothy A. Smith
| Bach | Baroque | Beyond | Assignment | Links | Notes |
Recognizing the motive as the basis for all composition, baroque theorists devised a system, known as loci topici, in which the various affetti (sadness, joy, passion, etc.) were associated with specific musical motives. Bukofzer describes this systemization as beginning with the writings of: "Nucius, Crüger, Schönsleder, and Herbst," continuing with "the more explicit treatise of Bernhard, and finally crystallized in definitive form with Vogt, Mattheson, and Scheibe." The term that these writers used to describe the motive was inventio. Implied by the inventiois the idea that such motives had the potential to be transformed into new ideas (development) and therefore permeate the entire composition (saturation). This process of variation was known by the baroque theorists as elaboratio. Motivic elaboration became so important, especially to the Germans, that later generations invented a word for it: Fortspinnung, meaning the "spinning out" of a motive, or ideas generated from it, throughout the duration of a musical work. Partly because the baroque term inventio in association with our word "motive" is suggestive of Bach's own inventionen & sinfonien, I have chosen to begin this study of motivic development and saturation with a peek at one of his Two-Part Inventions.
The techniques represented in the foregoing paragraph represent the limit of motivic variation techniques employed in the C Major Invention. But in this lesson we are after something else...how does the composer DEVELOP the motive, and its variations, in a tonal context? We wish to consider, further, some of the formal operations Bach employs to SATURATE the composition with not only motivic, but also tonal and contrapuntal variants? Bach uses four techniques:
In the two hundred years separating Bach and Schoenberg, the techniques for writing organically structured music had evolved to the point that Schoenberg would be able to articulate relationships unimaginable in the eighteenth century. Whereas Bach's music was organic at the motivic level, it relied upon tonal centricity for development. The first part of this lesson listed some of these techniques as found in the C-Major Invention: repetition of the motive on other scale degrees and in other keys or modes. Thus, from Bach to Schoenberg, tonality was the sine qua non of development; it was assumed that no musical idea could be developed without it.
By the turn of the 20th century, however, tonality as the primary means of motivic development had broken down. Richard Wagner's brinkmanship with the tonal system had left composers with nowhere to go and they were looking for new models. The impressionists, the "Russian Five," Charles Ives and others had experimented with non-western and nationalistic idioms, but it was Arnold Schoenberg who grasped the fundamental significance of the motive itself, apart from its tonal centeredness, as cornerstone of the great organic tradition. Picking up where Brahms and Wagner had diverged (Brahms too having understood the importance of the motive) Schoenberg showed that it was possible to develop the motive without recourse to a tonal center.
Schoenberg's twelve-tone system of composition was nothing less than a systematic attempt to insure that a composition was fully saturated with variations of the motive. To be sure, his tone rows were calculated to avoid the hint of tonality (dominants, triadic formulations, leading tones etc.) it is unfortunate, in contemporary descriptions of this "new system" as Schoenberg himself called it, that the emphasis is often placed upon the absence of tonality rather than the presence of motive. Schoenberg is often called, for example, the "grandfather of the atonal system" as if his main contribution to western art was to have rid music of tonal centricity. In truth this riddance had happened long before Schoenberg's invention of the twelve-tone row. Schoenberg himself might have preferred to have been called the "grandson" of the motivic tradition (Bach having been the father, and Brahms the son). It is this sophisticated concept of the motive that Schoenberg called Grundgestalt elaborated in the first paragraph of this section.
If motivic development and saturation were to exist "beyond Bach and Brahms" it was necessary to find ways of expressing the motive as a static--as opposed to temporal--entity. In the baroque, the tonal center provided an element of stasis against which it was possible to hear the motive--essentially a melodic/rhythmic construct--as having relationship to it. This relationship we have expressed in terms like: "the motive is now reiterated on the fifth scale degree," or "the motive is now stated in the relative minor key." Statements like these are possible only in the presence of something bigger than motive, something the motive is subservient to, something that operates independently of motive. That something, in the music of Bach and Brahms, had been tonality. But Schoenberg's "new system" admitted no such something, for, without tonal centeredness, there are no scale degrees, no keys and no modes. In terms of development, this left him only the techniques of transposition (not to a new key, but to a new tessitura) and textural development. However, the baroque resources of variation inherent in the motive itself--contrary motion and augmentation--remained intact.
Schoenberg's solution was to make the motive itself sine qua non, subservient to nothing, and compared to which all else was subsidiary. To the excision of tonal stasis, Schoenberg responded by extending the baroque techniques of motivic variation to the chord. If it was possible, he reasoned, to express a melody in contrary motion, then it should be possible to express a chord (a static and atemporal element) in the same manner. Now this may seem, on the face of it, to be a contradiction in terms...for there to be motion there must also be time. But Schoenberg's insight was his perception of the fundamental motivic relationship as consisting, at its most primal level, not only in the ORDER and DIRECTION in which intervals are expressed, but also in the QUALITY of the INTERVAL itself. This quality, Schoenberg reasoned, could provide the element of stasis vacated by the tonal system.
To understand the possibilities afforded by interval stasis as surrogate for tonal centricity, it shall be helpful to begin with a concept familiar to all musicians--that of chord quality. A major triad, for example is comprised of three pitch classes in the following relationship. The triad's third is a Major third, while the fifth is a Perfect fifth, above the root. In the 18th century, Bach's contemporary, Rameau, was the first to recognize that regardless of how such a chord was voiced, its "fundamental bass" was always the root of the chord. This eventuated in what we now call the "invertibility" of the triad, meaning that whether the triad sounded with its root, third, or fifth in the bass, and regardless of which triad factors the upper voices took, the chord had a qualitative "sameness" about it. This sameness expressed itself in the perception that a major triad sounds "different" from a minor triad, which sounds different from diminished, etc.
Schoenberg's departure from tonality hinged upon a recognition that, while major and minor triads do sound different, they, too, have a fundamental "sameness" based upon the intervals of which they are made. Whereas a major triad is made of a M3 and P5 ABOVE the bass, a minor triad is made of a M3 and P5 BELOW the fifth. Thus, the interval resources of the major and minor triad are identical. What is different, Schoenberg reasoned, is that they are mirror images of each other. While theorists also call this mirroring "inversion," it is a species of inversion exceedingly different from that of Rameau and the common practice. Eighteenth-century inversion involved re voicing of the same sonority by the placement of a different pitch in the bass (e.g. C major triad with E in the bass rather than C). In other words, 18th-century inversion resulted when the same PITCHES were put into a different order. By contrast, Schoenbergian inversion resulted when the same INTERVALS were put into a different order (mirror image) to produce a new set of pitch classes (e.g. C major becomes f minor). In Schoenberg's mind, this fundamental equivalence of INTERVAL content was one of motivic sameness or Grundgestalt, and could function as the static element unifying a composition as the tonal system had functioned before it.
Returning now to the skip/step idea of our lesson on motivic variation, here is how Schoenberg expresses, and develops, the same idea in his Klavierstücke Opus 11, Number 1. Let the step be a minor second, and let the skip be a Major third. Now let us express this skip/step motive as a chord of three pitches. Let us represent the first pitch--it could be any pitch--by the number zero . The minor second is ONE half step away and therefore could be represented by the number 1--the two pitches of the set now being represented by [0,1]. The Major third is FOUR half steps away and therefore represented by the number 4--the set now being [0,1,4]. Notice that, when the m2 is subtracted from the M3 [4-1], the motive also allows the possibility of a m3 (interval class 3). The [0,1,4] set is what we call the "P-form" of the motive (P for Prime) because it expresses the set with the smallest interval toward the left. Inversion involves reconfiguration of the P-form in mirror image, so that the smallest interval appears at the other end: [0,3,4]. The inversion is called the "I-form" of the set. P- and I-forms of a motive may sound as different as major and minor, but, because they are unified by interval content, the ear hears them, in the context of non-tertian sonorities, as motivic variations of each other.
The following represents the first five measures of No. 1 from Schoenberg's Klavierstücke Op. 11. Follow the animation as it illustrates imbrications of the [0,1,4] motive (yellow) and its inversion [0,3,4] (green). Notice that every pitch, whether it be in the melody or a chord, is generated from the motive. Although the animation is not synchronized with the CD, you can play the movement by clicking on the score. At the beginning of this "beyond" module you were asked to listen to this work. Did you recognize, at that time, its motivic tightness? While Bach's Invention was motivically dense, it was, by comparison, only partially saturated. It is in the music of "beyond" that composers found the words to complete a chapter they had begun to write three hundred years earlier--in the baroque.
That Opus 11 predates Schoenberg's system of composition by twelve-tones, shows that his conception of motivic preeminence was fully formed before he conceived of his "new system" for composition. For Schoenberg, the composing out of the "fundamental Gestalt" required more than the concatenation of pitches developed from the motive. Measures 1-10 illustrate how the [0,1,4] motive manifests itself at a higher level. These measures contain four phrases in which Schoenberg articulates four chords. These chords employ the bass notes Gb-Bb-Bb-G, the P-form [0,1,4] of the motive. Similarly, the highest melodic pitches of each phrase are B, G, G, G#, not only the P-form of the motive, but also the first three pitches of the piece! Thus, the "fundamental shape" replicates itself not only in contiguous melodic and harmonic entities, but also in non-contiguous units analogous to each other by means of texture, function, or register.
Listen to the Two-Voice Invention in C-Major while following the score. After you have become thoroughly familiar with the invention, listen again while following the motivic analysis. You will have noticed that my explanation of textural development did not specify WHERE, in the Bach invention, each of these two-measure chunks were located. This omission was deliberate inasmuch as your assignment, now, is to locate them yourself. You will find this assignment difficult to do without a thorough understanding of the textural variations and repositioning of voices illustrated by the animated analysis. Begin by reviewing the discussion of textural development, training your ear to distinguish material in the high voice from material in the low. Write down what you hear. Next listen for the motive variant that sounds in each voice--is it the original, or does the motive appear in contrary motion? Now do the same for the analogous section, then compare notes.
Questions pertaining to the Schoenberg Klavierstücke Op. 11, No. 1:
[5, 6, 9 ] set bConvert the negative to a positive value by adding 12 to it, and the T-factor is 10. Set (b) is generated from set (a) by a T-factor of 10...which is another way of saying that set (b) is a transposition of set (a) up 10 half steps. This relation could be expressed as follows: set (b) is generated from set (a) at T10.
[7, 8, 11] set a
The fact that the sum is the same value all the way across indicates that set (y) is generated from set (x) by a process of inversion with a T-factor of 4...another way of saying that set (y) is a mirror image (counterclockwise reading on the clock diagram) of the intervals of set (x), transposed up 4 half steps (T4I). For every set there will exist one inversion that is untransposed, in which case we would say that the T-factor is zero: i.e. the relation of each set to the other is T0I.
Which sets in the Schoenberg example represent TRANSPOSED INVERSIONS of set (a)? Which sets represent TRANSPOSITION of (a) without inversion?