The Principle of Compound Variation in Bartok's Second String Quartet

copyright © 2004 by Larry J Solomon

I would first like to make a distinction here between the principle of compound variation and that of developing variation, the latter practiced by Brahms and Schoenberg, first described by Schoenberg. "By developing variation", Schoenberg means the construction of a theme (usually of eight bars) by the continuous modification of the intervallic and/or rhythmic components of an initial (prime) idea. The intervals are 'developed' by such procedures as inversion and combination (e.g., two consecutive seconds make a fourth), the rhythms by such devices as augmentation and displacement." {1} The basic units used for modification are motives. "These motive forms do not 'develop' successively, of course, but simply constitute different individual alternatives of development." {2}

The principle of compound variation that I wish to discuss here differs from the Brahms/Schoenberg model in that new forms are generated successively; i.e., new variants are derived not from the original motive, but from the preceding variant. Therefore, each successive variant becomes more remote from the original form and may develop into entirely different forms.

The first movement of Bela Bartok's Second String Quartet (1917), is a remarkable example of the principle of compound variation. In the course of the first movement the initial theme is transformed from:

Ex 1

into:

Ex 2

Derivation of Ex 2 from Ex 1 seems to be very improbable. How does the statement at m156 come from the one at m2? This no less than a metamorphosis similar to that of the caterpillar into a butterfly. Ex 2 is not directly derived from Ex 1. Instead the intial statement is gradually changed through a series of remarkable transformations. To best illustrate this we will partition the theme as follows:

Ex 3

The types of voice leading motion are normally divided into categories: (1) no motion or repeating notes, (2) step motion, (3) small leaps (3rds and 4ths), (4) large leaps (larger than a perfect 4th).

For a key to abbreviations, see key to motivic analysis. In Ex 3, A1 and B1 represent the first transformations of A and B. The rhythmic profile and pitch contour of each part of A and B help to identify them as transformations; e.g., a1i is the inversion of the rising 4th of a1, a1.1 is a transformation of a1, and a2.1(interval expanded), a2.2, and a2.3 are transformations of a2, all using downward chromatic motion. a1> is an interval compressed version of a1. Notice that a2.1 expands the original step motion of a minor 2nd into a minor 3rd (small leap). Subsequently, a2.2 expands the minor 3rd to a major 3rd and fills it with step motion. The same is so for a2.3, but with a slightly altered rhythm. Thereby, we already have successive transformations developing in the intial statement.

Ex 4

The theme is developed rapidly throughout the exposition. In Ex 4 the intervals are expanded, with a2 becoming a perfect 5th, and a1i is compressed to a minor 2nd. a1> is inverted and expanded to a perfect 5th.

Ex 5

In Ex 5 the intervals of a1 are expanded beyond an octave. a2 stretches to an augmented 5th, and a1i is deleted or subsumed into the last two notes of Ex 4, which have stretched from a perfect 5th to a minor 7th. Thus, the Theme is truncated to 5 notes.

Now the intervals of the Theme are stretched even further while its length continues to truncate from the original seven-note figure to four, three, and two notes, and finally to just one note (Ex 6).

Ex 6

A rhythmic augmentation of the first three notes occurs in m11 and continues in the subsequent measures. The last note expands from an eighth to a quarter note. These radical transformations serve to compress the idea of the original theme into just a single note.

Next, the theme is presented in a new version, Ex 7.

Ex 7

After the first four notes identify the theme, there is a downward spinning motion over a seventh (B to C), which is derived from mm10-12. Here the falling seventh is filled in with triplet embellished turns, creating a new idea. Each turn brings the pitch down a third at a time, outlining the total motion of a seventh. The descending fifth of two of these turns (see also Ex 4) is then developed into:

Ex 8

The descending figure from Ex 7 (m24) (see marked notes) is then used to form the first measure of Ex 9 (m28). M29 comes from Ex 8.

Ex 9

Which is immediately expanded to:

Ex 10

a1> is then stated as:

Ex 11

Starting with the upward moving 3rd, Bartok adds a note in m33 and expands its interval in m35, which is also the inversion of the falling thirds in Ex 7, m24. Ex 12 is also generated from Ex 7.

Ex 12

The result is a diatonic sequence based upon the falling thirds. Bartok then extracts the step motion filling the third and inverts it to form:

Ex 13

This longer exerpt shows the remarkable process of compound variation at work, adding and subtracting notes, expanding and contracting intervals, etc. This continues:

Ex 14

Finally, these transformations settle into a Dorian diatonic theme:

The chords are mostly Bartok's, but some are substitutes. This is the same theme that is transposed at the end of the movement at bar 156.

Ex 15

Summary

The thematic process in the first movement of Bartok's Second Quartet is through compound variation, i.e., variations that are transformations of the immediately preceding variants, rather than those necessarily based upon the original theme. This process uses primarily interval modification, interpolations, and elisions. Thereby, new melodies are constantly being generated.

Notes

  1. Frisch, 9
  2. Ibid, 11

References

Frisch, Walter. Brahms and the Principle of Developing Variation, University of California Press, 1984.