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Contents

Music in the Early Twentieth Century

SYMMETRICAL FUGUE, SYMMETRICAL SONATA

Chapter:
CHAPTER 7 Social Validation
Source:
MUSIC IN THE EARLY TWENTIETH CENTURY
Author(s):
Richard Taruskin

To show how thoroughly (and literally) the relationships mapped out in these charts and diagrams could function as an alternative tonal system (easily grasped by the ear without the help of charts or diagrams), we can look ahead to two of Bartók’s best-known works, composed considerably later in his career. Once their basic outlines were established in the music he composed around 1908, his methods served him faithfully to the end, making his style a remarkably consistent one over the whole course of his creative life.

We will start with the later of the two, Music for Strings, Percussion, and Celesta, composed in 1936 on commission from Paul Sacher (1906–99), a Swiss conductor who had married into a wealthy industrial family and paid many famous composers to write music suitable for the organization he led, the Basel Chamber Orchestra. We will start with it because its first movement, remarkably, projects the selfsame tonal trajectory as Bagatelle no. 2 of 1908, but over a far longer span of time and with far from whimsical effect.

Music for Strings, Percussion, and Celesta is a four-movement composition comparable in that respect to a traditional symphony. Its movements, however, possibly in keeping with the fact that it was commissioned by a chamber orchestra whose main business at first was performing an eighteenth-century repertoire, are in a slow-fast-slow-fast sequence more reminiscent of an old Italian concerto grosso. The fast movements are distinctly “neonationalist” in style, being cast in a modernistic idiom obviously based on folklore. The third movement is typical of a genre Bartók called “night music”—not, however, in the sense of the eighteenth-century convivial notturno or serenade, which was aristocratic party music; nor in that of the Chopinesque nocturne, which was a dreamy mood piece; but in the sense of a night spent camping outdoors, in proximity to enigmatic, indefinable sounds of nature.

The night music in Music for Strings, Percussion, and Celesta is particularly noted for its pioneering use of the timpani glissando, a technique made possible only a few years earlier when improved models of pedal timpani became available. (Bartók’s first use of this uncanny effect, possibly the first by anyone, was in his Cantata profana of 1930, a setting of a folk legend in verse, where it accompanies a magical transformation.) In Ex. 7-16a, which reproduces the first page of the score, the timpani glissandos are cast in dialogue with another typical Bartók night sound, a nattering diminution-augmentation or accelerando-ritardando effect on a single note, here played by the xylophone. (The first partial use of this effect in Bartók’s music, indeed his first “night piece,” is found—not surprisingly—in that same remarkable set of Bagatelles, op. 6, the crucible of Bartók’s maximalistic style; see Ex. 7-16b.)

Symmetrical Fugue, Symmetrical Sonata

ex. 7-16a Béla Bartók, Music for Strings, Percussion and Celesta, III, mm. 1–10

Symmetrical Fugue, Symmetrical Sonata

ex. 7-16b Béla Bartók, Bagatelle, Op. 6, no. 12, mm. 1–8

Symmetrical Fugue, Symmetrical Sonata

ex. 7-16c Béla Bartók, Music for Strings, Percussion and Celesta, III, 1 after letter B

Against this background, the violas enter with a melody that in its chromaticism is obviously no folk tune, but which nevertheless bears traces of “Hungarianness” in its rhythm, its tiny accented note-values on the beat aping the short tonic stress patterns of Magyar speech as if placing a human “figure” against a landscape. Accompanying the viola melody is a sustained tremolo in the lower strings that sounds the tritone C/F♯ as a pedal that will last until m. 16. Although we must again tantalizingly postpone pursuit of its ramifications, it is worth noting one more fact: the pedal tritone, plus the xylophone pitch (F) and the pitches of the timpani glissandos (B/F♯)—in other words, all the pitches that accompany the “Hungarian” melody—together form what has already been cryptically identified as a “Z-tetrachord.” Now compare Ex. 7-16c, drawn from a later passage in the third movement, where the rustling night sounds (represented by a murmured cacophony of simultaneous arpeggios or glissandos from celesta, harp, and piano) reach their peak. The pedal, now in the double basses and timpani, has moved to a doubled E≭, while the glissandos pit black-key pentatonic scales, of which E≭ is a member, against various scales from which it stands out: white-key pentatonic, whole-tone, white-key glissandos. Without implying that Debussy would have necessarily recognized or sanctioned it, the texture here could be aptly characterized as maximalized “impressionism.”

Putting the pedals together—C/F♯ + E≭—and noting that they make up a diminished triad, we might be tempted to relate the harmony here to the /0 3 6 9/ circle of minor thirds that is so familiar by now from its use by Liszt, Ravel, and Stravinsky, all composers with whose works Bartók was enthusiastically familiar, and that we have already observed in Bagatelle no. 2. But where Liszt, Ravel, and Stravinsky would most likely have integrated the circle of thirds with its octatonic scalar extension (a technique to which Bartók was certainly no stranger), we now have another, uniquely Bartókian context with which to ally it—namely, the “sum 6” symmetrical array already displayed in Ex. 7-14, where E≭ is one of the axes along with A, and where the C/F♯G≭ pair is situated right between the axes on both sides.

Excellent evidence that this was Bartók’s own way of conceptualizing the harmonic symmetry that his pedals expressed can be found in the notation of the glissandi in Ex. 7-16c, especially the upward-sweeping white-key glissandos in the piano part. Ex. 7-14 was introduced in conjunction with the Bagatelle no. 2 and used the note-spellings found there, including F≭ in place of the more usual E, presumably so that the expansion from F≭/D to the axis octave E≭ could be represented as a pair of leading-tone resolutions, as in a traditional augmented sixth chord. The F≭–D spelling is retained in Ex. 7-16c.

But anyone encountering that passage in the context of a performance of Music for Strings, Percussion, and Celesta, or a sequential perusal of the score, would have had even better evidence that Bartók conceptualized its tonality in terms of the “sum 6” array in Ex. 7-14; for the implications of that array are worked out both systematically and startlingly over the course of the first movement. Perhaps in response to the concerto grosso idea (also reflected in the occasional concertante writing for keyboard instruments and string soloists in the fast movements), Bartók cast the movement as a fugue. Here is how he described it, in his own dry and halting English, in the preface to a revised edition of the score, published after he had already taken wartime refuge in America:

On certain principles fairly strictly executed form of a fugue, i.e. the 2nd entry appears one fifth higher, the 4th again one fifth higher than the 2nd, the 6th, 8th and so forth again a fifth higher than the preceding one. The 3rd, 5th, 7th, etc. on the other hand enter each a fifth lower. After the remotest key—E flat—has been reached (the climax of the movement) the following entries render the theme in contrary movement until the fundamental key—A—is reached again, after which a short Coda follows.13

For the sake (he evidently thought) of clarity, Bartók’s description emphasizes the procedural similarity between his fugue and the familiar textbook rules of fugue writing. A traditional fugue begins with “an entry one fifth higher,” and so does Bartók’s. But his fugue keeps on mounting higher—and plunging lower—by fifths, as may be seen in Ex. 7-17a, which shows the start of the process: violas starting on axis-pitch A, the third and fourth violins entering at the fifth above (E), the cellos at the fifth below (D), the second violins another fifth above (B). A “maximalized fugue,” then? Yes, but to leave it at that would do scant justice to the plan. To take it all in at once, and also see its relationship to the other music of Bartók that we have looked at, we need a diagram (Diagram 7-1 shown following Ex. 7-17a). Numbers in parentheses in Diagram 7-1 refer to the measures in which each entry of the subject takes place; numbers in brackets show the relationship of each vertical pair to the axis pitch as in Ex. 7-14.

Symmetrical Fugue, Symmetrical Sonata

ex. 7-17a Béla Bartók, Music for Strings, Percussion and Celesta, I, mm. 1–15

Symmetrical Fugue, Symmetrical Sonata

DIAGRAM 7-1

By pairing the entries at the upper fifth with those at the lower fifth, as in the diagram, we can see that Bartók’s “fugal” procedure is in reality another way of projecting the same “sum 6” symmetrical matrix from which Bagatelle no. 2 had been derived, but doing it in a grand way that covers an imposing span of time and invokes a long and distinguished fugue-writing heritage that it, in effect, caps. Each of the pairs in the diagram above has its counterpart in Ex. 7-14.

The crucial theoretical point that Bartók’s fugue thus demonstrates is the way in which the circle of fifths can be mapped onto the chromatic scale (the “circle of semitones”), the only other interval cycle to exhaust all the pitch classes, so as to traverse the same progression from an axis pitch to its reciprocal. The achievement of E≭ (Ex. 7-17b), which takes place in both the ascending and descending “voices” as conceptualized in the diagram, provides the same tangible sense of climax as the continually foreshadowed but evaded E≭s had done in the bagatelle. That sense of climax or completion conditions the same out-and-back tonal trajectory, utterly different yet wholly analogous to the out-and-back trajectories of tonal music. The much-truncated coda, which begins with the upbeat to the fourth measure of Ex. 7-17b in the cellos and basses with the subject in inversion, spells out the idea of axial symmetry in as many ways as Bartók could think of. At the very end (Ex. 7-17c), in a summary that manages to be both grave and witty, the two violin parts play the second phrase of the subject, covering exactly the range between the primary axis (A) and its reciprocal (E≭), in note-against-note counterpoint with its inversion. It is almost as if they were actually performing a slightly abbreviated version of Ex. 7-14 itself.

Notes:

(13) Bartók, Music for String Instruments, Percussion and Celesta (London: Boosey & Hawkes, 1939), p. iii.

Citation (MLA):
Richard Taruskin. "Chapter 7 Social Validation." The Oxford History of Western Music. Oxford University Press. New York, USA. n.d. Web. 18 Oct. 2021. <https://www.oxfordwesternmusic.com/view/Volume4/actrade-9780195384840-div1-007005.xml>.
Citation (APA):
Taruskin, R. (n.d.). Chapter 7 Social Validation. In Oxford University Press, Music in the Early Twentieth Century. New York, USA. Retrieved 18 Oct. 2021, from https://www.oxfordwesternmusic.com/view/Volume4/actrade-9780195384840-div1-007005.xml
Citation (Chicago):
Richard Taruskin. "Chapter 7 Social Validation." In Music in the Early Twentieth Century, Oxford University Press. (New York, USA, n.d.). Retrieved 18 Oct. 2021, from https://www.oxfordwesternmusic.com/view/Volume4/actrade-9780195384840-div1-007005.xml