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Symmetry in Bartok’s Music (A look at Mvt. III of B.B.’s Fourth String Quartet)

March 28, 2012

This is a reposting of something on my old blog. Bartok’s Fourth String Quartet is one of my favorite pieces. There is always something new to hear in it, and the construction of it is amazing. In looking over the third movement I learned (as others probably have — I haven’t checked) that Bartok used symmetry as the structural basis for every note. But I also noticed that there is a real harmonic motion involved that is not too far removed from traditional tonality. I thought it worth writing about, so here it is, albeit somewhat edited for the new context:

One of the list-serves I belong to had an interesting discussion on the use of symmetry in the music of Bela Bartok a while back. The person who initiated it had been confused by the—ahem—esoteric writing in a book on the subject, and wanted some clarification. His questions had to do with how Bartok uses symmetry: Are there tonal centers (single pitches or intervals)? Is there a pull to some notes as in tonal music? I decided to take a look at one of my favorite Bartok works, the Fourth String Quartet, to see.

First of all, it helps to know that composers started using harmonic symmetry toward the end of the 19th century in tonal contexts (you’ll find it in Wagner’s Prelude to Tristan und Isolde, as well as in works by N. Rimsky-Korsakov, among others), and 20th-century composers became fascinated by it. (In different ways Schoenberg, Berg, Webern, and Stravinsky, as well as Bartok, all used it.) We tend to (rightly) think of Bartok as primarily a tonal composer, certainly compared to the second Viennese school composers, but he used symmetry in many of his works, and sometimes in different ways within the same work.

One “literal” case of symmetry in a Bartok work is the opening fugue of his Music for Strings, Percussion, and Celesta. The opening phrase (in the violas) begins on an A-natural. I’m leaving out details here, but essentially each subsequent entrance of the fugue theme is presented either a fifth higher or a fifth lower (a process I and other composers call “unfolding” an interval):

A, E (5th up), D (5th down from A), B (5th up from E), and so on.

Eventually the entrances unfold the interval of a perfect fifth until the orchestra reaches E-flat from both directions; that becomes the climax of the movement. The music then reverses on itself and quickly moves back through the same cycle to A-natural.

The example I gave in my response to the questioner is actually more interesting to me. The third movement of Bartok’s Fourth String Quartet begins with a six-note chord presented one note at a time in the violins and viola. When rearranged the component notes of the chord turn out to be a portion of the cycle of perfect fifths:

A, E, B, F#, C#, G#

The chord as presented is only mildly dissonant, and could even be heard as an extended tonal chord (A major 9/add 6?). When the cello enters in measure 6, it plays a D# followed immediately by a D-natural. This expands the cycle further:

D, A, E, B, F#, C#, G#, D#

Both the D and D# sound more dissonant in this context, an attribute Bartok plays with until measure 9. He begins expanding the cycle even further melodically, adding the ninth note G-natural (m. 9, a coincidence?), C-natural and F-natural (m.10), and A# (m.12). By measure 12 (another coincidence?) he has given us all twelve notes of the chromatic scale by fifths:

F, C, G, D, A, E, B, F#, C#, G#, D#, A#

(One thing I did not mention in my original response is how Bartok saves the A# for last, apparently because he had two additional notes to introduce by fifths going down.) I won’t go into details here about the rest of the movement, but suffice to say that it is this unfolding of a cycle of fifths, with the initial segment being A through G#, that forms the harmonic language of the movement.

One other thing: When I gave my original response, I didn’t make much of the next bit, but I now see (and hear it) as a motivating force. The last chord of the movement, which “fades out” as a mirror to the opening’s “fade in” of the first one, is also a six-note chord. Arranged as perfect fifths, it looks like this:

D, A, E, B, F#, C#

This is a perfect fifth down (or perfect fourth up) from the original chord, not entirely unlike (but obviously very different in sound from) a motion from the dominant (IV) to the tonic (I) in traditional tonal music. The aural result is one of resolution.

Ultimately, what symmetry can do is create an aural sense of “home base” — not like the tonic (key note) in tonal music, but still a place from which to start, move away from, and (if the composer wishes) which to return. Whatever that center point be, whether it’s a single note, an interval, or even a segment of a regular interval cycle, becomes the normative unit for the music. What is most important here is that this is audible; we can hear this.

©2012 Steven L. Rosenhaus

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