Motivic Variation
Site ©1996 Timothy A. Smith

| Bach | Baroque | Beyond | Assignment | Notes |

Please begin this lesson by listening to the C-minor fugue.

In 1802 German musicologist and director of music at the University of Göttingen, Johann Nicolaus Forkel, wrote: "Bach united with his great and lofty style the most refined elegance and the greatest precision in the single parts that compose the great whole.... He thought the whole could not be perfect if anything were wanting to the perfect precision of the single parts." In this statement Forkel was perhaps the first to articulate a characteristic we have come to recognize as one of the most important in western art music--that of motivic variation, development and saturation. Berkeley professor and editor of Nineteenth-Century Music, Joseph Kerman, describes such music as "organic" meaning that the whole cannot be understood without reference to its parts and the parts cannot be appreciated without understanding of the whole.

In this unit we consider the concept of organicism as it exists at the most elemental level in musical structure: variation of the motive. In the next we shall explore the manner in which motives (and their variations) are developed into full-fledged musical works, and how such works are characterized, in the western tradition, by motivic saturation.

Although it was practiced prior to the baroque, the custom of structuring music organically accelerated in the eighteenth century. Driving this explosion was the philosophical concept of Affekt. Having its origin in the rediscovery of classical Greek drama, what we now call the "doctrine of affections" was a belief that music was the physical embodiment of feelings, moods and emotions. Bukofzer describes the doctrine of affections as an:

...highly characteristic attitude toward concrete and abstract concepts in baroque thought, which tried to render abstract ideas concretely and concrete things abstractly. A strictly musical idea was therefore at once concrete and abstract, it presented an abstract affection in concrete form, and for this reason the figure had a structural significance for the entire composition.

If, as musicians of the baroque believed, music was the physical embodiment of feelings, moods and emotions, then one musical idea ought to be linked to one emotion, and the Affekt could only be confused by filling a composition with too many musical ideas. Paramount it was, therefore, that a composition employ but one or two motives, and that it should explore many facets of the motive by expressing it in various forms. Again quoting Bukofzer: "The unity, achieved by consistent elaboration of the chosen figure, vouched at the same time for the unity of affection that governed the piece." Bach's contemporary, Mattheson put it positively when he stipulated that the aria must employ "a short theme or subjectum wherein the whole content and affection must be contained as much as possible," while Dresden composer and writer, Christoph Bernhard (1627-1692), put it negatively when he warned that "What cannot be justified by figures should be banished from music as a monstrosity."

Proscriptions, like that of Bernhard, made it necessary for composers of the eighteenth century to find means of articulating a motive repeatedly in ways that would not tire the ear but would reinforce the Affekt throughout the duration of a composition. Their solution--variation of the motive--came to permeate not only music of the baroque...but also beyond.

Fugue in C Minor from the Well-Tempered Clavier Book I

Please continue this section by listening to the C-minor fugue again, this time following the motivic timeline.
Consider a simple idea--a skip followed by a step in the opposite direction. How could such a motive be elaborated? Well, the first thing that comes to mind is that the skip could be ascending or descending. This alone would yield two possible "spins" on the skip/step idea. Another possibility is that the skip could be small or large--four more "spins." Then the composer could reverse the order of events, placing the step first, followed by a skip in the opposite direction. Using only the parameters of direction, size of leap and skip/step order, it is possible to transform the original idea into eight more. Add to this the possibility of various scale degrees, mode or key, and the potential for elaboration becomes mind-boggling. Normally composers find it necessary to limit variation to a few choice transformations in order to maintain continuity (although, in the upcoming analysis of the A Major Intermezzo, we shall see that Brahms does not).

Bach's c-minor fugue from the Well-Tempered Clavier Book I is a good place to begin our study of motivic variation. The subject of this fugue develops the skip/step idea of the preceding paragraph. Of the eight possible ways that a skip/step could be developed, Bach uses three. First he employs a falling skip of a fourth, followed by a rising second. He then reverses the order so that the motive begins with a rising step followed by a falling fifth (bigger skip). The next elaboration follows the rising step with a falling sixth (bigger yet). Notice that in each variation, the skips are descending. The unidirectional transformations of this particular motive lend continuity to the subject while at the same time promoting variety. Can you find each of these motivic transformations in the subject? How does the composer depart from the skip/step idea at analogous points in the answer?

subject and answer from the c-minor fugue of the WTC book I

Before abandoning Bach, we should consider a problem of terminology. "Motive" is often used in reference to a musical idea made of more elemental stuff such as the skip/step formation we have been studying. Leon Stein suggests that the term "figure" might better describe these, and that "motive" should be reserved for Bach's two- and three-part inventions. Thus, in Stein's usage, the "motive" of the Two-Part Invention in C major would be comprised of a scalar, followed by a skipping, "figure." While I believe that Stein has a point, I do recognize that "motive" is used both ways and have titled this unit "motivic" variation in the sense that Stein might have used "figural."

Whichever term one uses, it is important to recognize that, when musicians say "motive," they usually refer NOT to the most elemental or generative material, but to something larger. It is often useful, therefore, to have terms which will allow the atomization of such "motives" by the identification of "motivettes" or figures from which they themselves are made. A case in point: while not normally called a "motive," the subject of a fugue is often described as the most elemental formation, when in fact it is invariably comprised of smaller units. In the case of the c-minor fugue we have been studying, the subject consists of two such units: a lower neighbor tone followed by variations of skip-and-a-step.

Brahms: Intermezzo in A Major, Opus 118, No. 2

Please continue this lesson by ejecting the WTC disk, inserting the "Brahms: The Late Piano Music" (Philips 442 589-2) and listening to the Intermezzo in A Major.
Here we consider how Brahms uses a skip-and-a-step as the primary motive of his Intermezzo in A Major for piano. Recall, from our earlier discussion, how this idea can express itself in the following ways.

The overall form of the Intermezzo is ternary (ABA). The "A" section is binary (parts 1 & 2) In Part 1 Brahms states the motive as a FALLING step followed by a SMALL RISING skip (p. 1, m. 1). Immediately he transforms this into a LARGE RISING skip (p. 1, m. 2). In Part 2 he reiterates these two ideas but in reverse direction--first stating the motive as a RISING step followed by a SMALL FALLING skip (p. 3, m. 35). This he transforms immediately into a LARGE FALLING skip (p. 3, m. 36). This completes section "A."

In section "B" Brahms reverses the step/skip of the preceding section, developing a skip/step idea instead. In m. 49 (p. 4) he states a RISING SMALL skip followed by a step in the opposite direction. In playing this last example you will have noticed that the motive is treated in free canon with the leader in the high voice and the follower in the middle. As you study mm. 49 and following (p. 4), you will also notice that this is a sophisticated augmentation canon in which the durations of the follower are increasingly lengthened in relation to the leader. In bar 65 (p. 5), after having mutated the motive to major mode, Brahms repeats this rising-skip/falling-step motive, in canon, but this time with the middle voice leading and the high voice following (double counterpoint at the octave). Section "B" climaxes when the SMALL RISING leap with which it began is transformed into a LARGE RISING leap (p. 5, m. 69).

Upon the return of section "A," Brahms transforms the motive yet one more time to give a sense of climax and closure. Most notably, the falling-second/rising-leap idea employs an octave leap (p. 6, m. 82) which had not appeared the first time around. The one skip/step variation we have not yet discussed--a FALLING skip followed by a RISING step (p. 3, m. 42)--does not appear often, but, when it does, it also has a closure function.

In conclusion, let us consider the form-defining aspects of motivic variation in the Intermezzo. Brahms does not merely develop the skip/step idea in every conceivable way, he utilizes specific permutations to reinforce the overall ABA form. Whereas in section "A" (beginning p. 1) he concentrates on STEP/SKIP, in section "B" (beginning p. 4, m. 49) he concentrates on the reverse--SKIP/STEP. The formal outline of the Intermezzo could be represented as follows:


Listen to the Intermezzo while following the score. After you have become thoroughly familiar with the piece, listen again while following the motivic analysis of each page.
  1. As represented in the motivic analysis, count the number of times each of the following occur.
    • falling-step/rising-skip
    • rising-step/falling-skip
    • falling-skip/rising-step
    • rising-skip/falling-step

  2. You will have noticed that many of the above structures are nested: for example, the ending skip of one step/skip formation might become the beginning skip of a skip/step formation. While you can make your ear hear it both ways, musical considerations, such as where the formation occurs in the measure, will determine which idea comes to the foreground. Having gotten a visual count of each type of skip/step, listen to the Intermezzo again, without score, and count the number of times that each species of skip/step is at the foreground of the hearing process. Of course this will be a subjective hearing, but give some numbers nonetheless. I am especially interested in learning if you hear certain formations more often toward the beginning, others toward the middle, and still others toward the end. Theorize about some of the factors that might bring one formation to the foreground and cause others to recede into the background.
Make sure that your answers are numbered as above. Briefly restate the question before you answer it using complete sentences, correct grammatical construction and spelling.


  1. Joseph Kerman, "How We Got Into Analysis, and How We Can Get Out" Critical Inquiry (Vol. 7, 1981), p. 315.

  2. Manfred Bukofzer, Music in the Baroque Era (W. W. Norton, 1947), pp. 389-390.

  3. Leon Stein, Structure & Style (Summy-Birchard, 1979), pp. 3-4.
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