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In the Fifth Quartet Bartók pursued metric symbolism even further. Again there are five movements, but the corresponding outer movements are in contrasting meters, the first mainly in
, the fifth in
. The second and fourth movements can be heard as a theme in
and a variation in
. At the center is a scherzo marked “Alla bulgarese,” and it, too, is in an arch form, with the outer section in bars of nine eighth notes divided as 4 + 2 + 3, while the central section, the very heart of the entire quartet, is in
divided as 3 + 2 + 2 + 3. To make things even more systematic, Bartók associates his duple rhythms with the interval of the fourth, his triplet rhythms with thirds; the nine-beat scherzo is a cascade of thirds.

Bartók became fascinated with Bulgarian rhythms in the 1930s; he may have felt that they were evidence, in nature, of the larger symbolic order. These dance rhythms are based on “slow” and “quick” beats, beats of different lengths. Although ethnomusicologists disagree about the relation of the beat lengths, especially when at rapid tempos, Bartók heard the beat patterns in terms of a 3:2 ratio, represented by fast beats of quarter notes (two eighths) and slower beats of dotted quarters (three eighths). Bartók pursued possible combinations of beats in a variety of compositions. Two studies in Bulgarian rhythm appear in the fourth volume of
Mikrokosmos
, and the sixth volume concludes with Six Dances in Bulgarian Rhythm. They present rhythms of 3 + 2, 2 + 2 + 3, 4 + 2 + 3, 2 + 3, 3 + 2 + 3, 2 + 2 + 2 + 3, and our old friend 3 + 3 + 2. Similar rhythms also appear in
Music for Strings, Percussion and Celesta
(fourth movement 3 + 3 + 2), the Sonata for Two Pianos and Percussion (first movement 3 + 2 + 2 + 2),
Contrasts
(third movement 3 + 2 + 3 + 2 + 3), and the Concerto for Orchestra (fourth movement 2 + 2 + 2 + 3).

Apart from their possible symbolic function and evident musical charm, these Bulgarian rhythms have a few notable properties. First, in Bartók's usage they are real meters, regularly occurring accentual patterns articulated through harmonic change, not the variably accented figures found elsewhere in Bartók's music (such as the “Syncopation” study no. 133 in
Mikrokosmos
, volume 5) or in Copland or Stravinsky. Unlike clave-based music, where hand and feet have different,
complementary rhythms, in Bulgarian music they coincide. A Cuban
son
pattern puts three unequal beats of the clave against two equal foot beats. In Bulgarian rhythm the 3 + 3 + 2 pattern is heard as three steps; in “I Got Rhythm” it has two (or four).

Although Bartók was one of the few European composers to appear untouched by jazz in the 1920s, he nevertheless realized that Bulgarian meters bore an uncanny relation to jazz, and he took advantage of the connection in 1938 when he composed
Contrasts
for Joseph Szigeti and Benny Goodman. The King of Swing was also a serious classical clarinetist; his jazz style, moreover had Eastern European klezmer overtones (most obviously in Ziggy Elman's “And the Angels Sing” based on the klezmer tune “Der Shtiler Bulgar”). Goodman comfortably crossed over to Bartók's world; a year later Bartók moved into Goodman's territory with the fourth and sixth of the Bulgarian dances, both written, as Bartók himself pointed out, in the blues-inflected style of Gershwin. The Hungarian composer must have known
Rhapsody in Blue
and the
Preludes
, which are full of 3 + 3 + 2 patterns.
46

Jazz fans know Bulgarian rhythms through Dave Brubeck's “Take Five” (written by Paul Desmond), “Unsquare Dance,” and particularly “Blue Rondo à la Turk,” with a theme written as three bars of 2 + 2 + 2 + 3 plus one in 3 + 3 + 3. Though some jazz critics viewed Brubeck's hugely popular experiments as heavy-handed gimmicks,
47
they could more sympathetically be heard (as many of Bartók's works can be heard) as anticipations of world music parallel to the global outreach of Ellington's
Far East Suite.

Many jazz players (and rock musicians as well) have continued Brubeck's experiments (and “Take Five” became a jazz standard), but these rhythms can become ponderous, especially when players slam the downbeats. Bartók's treatment of the rhythms in his “Alla bulgarese” shows more finesse, and perhaps more of a jazz feel. He begins his melody off the beat and phrases it in call-and-response two-bar units. Instead of repeating the opening phrase Bartók turns the rhythmic shape around by making the “call” in the cello sound like an upbeat to the “response” in the violin and viola. In the recapitulation Bartók intensifies the rhythmic development, stretching and contracting the phrases over the bar lines and creating new cross-rhythmic counterpoints. From a classical point of view we might say that Bartók is developing his rhythms very much in the way Beethoven would; from a jazz point of view we might say that he is pushing them in the direction of supermelodic liberation,
with a shoutlike ecstasy in the final crescendo (bar 74), followed by an ending as quietly concise as the last phrase of “Cotton Tail.”

STRAVINSKY: CONCERTO IN E
, “DUMBARTON OAKS”

In the concert and ballet worlds Stravinsky's name is synonymous with rhythm; not surprisingly, he borrowed from jazz, as he admitted, throughout his life. Jazz musicians, especially in the bebop period, liked to show their respect to the Russian master by inserting a phrase of
Petrouchka
or
Le sacre
into a solo, especially when their composer was present. The young Billy Strayhorn introduced
Le sacre
(along with
La Mer
and
Alborada del gracioso
) to Lena Horne; it was difficult, but she liked it “when I'm a little juiced.”
48
As the “separate but equal” remark at the top of the section shows, Stravinsky didn't exactly return the compliment, at least not when sober. Or when composing:
Ebony Concerto
, written for Woody Herman and full of details lovingly lifted from some of the Herd's greatest hits, remains the highest, hippest compliment that classical musical modernism paid to the jazz world.

Stravinsky's waspish statement about jazz from the first
Conversation
book uses the dismissive tone he often employed to deal with serious rivals, but his distinction between “rhythm” and “beat” sheds light on his idiosyncratic methods for creating cubist rhythms. Where Bartók often worked from music he heard in the field, Stravinsky always worked from written sources, whether they were transcriptions of folk music or scores by other composers, from Gesualdo to Webern. Where the Hungarian composer thought of basic rhythmic shapes almost like atoms, as part of the essential material of music, Stravinsky conceived musical ideas, or
“matières sonores,”
as static but malleable objects, to be twisted, extended, chopped; rhythm was not inherent in those materials but was a way of shaping them. To compose he would find a sound, a chord, an instrumental effect, or an entire existing piece of music, then animate it with a varied collection of techniques that I'll call Igor's tool kit.

For Stravinsky, the temporal was also spatial. Composition was a matter of shuffling, repositioning, cutting, pasting, juxtaposing and superimposing—disruptive processes that, nevertheless, like the magician's spell in
Petrouchka
, endowed static material with dynamic life; often at the end of the piece Stravinsky (again as magician) would restore them to their pretemporal condition.

Many of Stravinsky's rhythmic techniques had their roots in earlier Russian music. Unusual and changing meters, protocubist rhythms, were common in the music of the Russian nationalist school. Richard Taruskin shows how Glinka, in
Ruslan and Lyudmila
, set pentasyllabic folk poetry “isochronously” in a quintuple meter.
49
Rimsky-Korsakov, Stravinsky's teacher, similarly wrote the final chorus of his opera
Snegurochka
in
. The “scientific” anthology of Russian folk songs by Istomin and Lyapunov transcribed folk melodies with constantly changing meters, a way of hearing already transfigured into art music in the Promenade sections of Mussorgsky's
Pictures at an Exhibition.

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