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Authors: David Schiff

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For some listeners Debussy's groundbreaking piece may sound like orientalist mood music no matter how transgressive it might appear to the harmonic analyst, so let's look at a grittier piece, the “Pas d'action” from Stravinsky's 1947 ballet
Orpheus.
The score describes the action: “The Bacchantes attack Orpheus, seize him and tear him to pieces.” Stravinsky, following his trademark practice, defined the movement with a single chord that sounds like it was discovered at the keyboard: G#s in octaves in the bass, the pitches A and C, doubled in octaves, in the treble. Even though there are just three pitches the chord sounds harshly dissonant. By omitting the interval of the fifth, Stravinsky complicated interpretation of the chord. It could be heard either as implying an A
minor ninth, or as an inverted minor seventh chord, with the major seventh, G#, in the bass. Either way, it has something of the blues about it. Like jazz pianists, and like Ravel, Stravinsky required that every harmony in this movement include the interval of the seventh, or its inversions, the second and ninth.

The initial and inscrutable
“objet sonore,”
however, becomes the harmonic building block for the piece. Theorists would define it as a pitch class set [0,1,4] that contains the intervals of minor second, minor third, and major third. In this movement its structure reappears transposed, inverted, and revoiced in well over 90 percent of the chords. Through repetition it becomes the harmonic norm, a substitute triad, and departures from its sound stand out clearly. The remaining harmonies are similarly derived mainly from two compressed variants of the “tonic' chord: [0,1,3], containing a minor second, a major second, and a major third; and [0,1,2], containing only minor and major seconds. In analysis I'll call the main chord
X
and these two others
Y
and
Z
, respectively.

Throughout the movement the notes in the bass sound like dissonances while the tonal center appears in the treble. I call this “clothesline tonality”; we have already encountered it in “Et la lune descend,” and it is a characteristic that links Stravinsky's music to Debussy's. Looking at the score of
Orpheus
, it is hard to explain this inverted center of gravity acoustically except by noting that the upper line moves in stepwise fashion while the bass always jumps. The melodic notes (beginning with a motive that sounds, appropriately, like another Rodgers and Hart tune, “This Can't Be Love”) use the pitches of the a
minor scale, while the bass line outlines triads of A
major and c minor. Stravinsky deployed this harmonic clash as part of a carefully designed plan of harmonic motion based on the polarity of A and E
. In place of the extended ostinatos of his Russian works, Stravinsky composed this movement by alternating static harmonic plateaus with more unstable phrases of harmonic motion.

The movement closely resembles classical sonata form, albeit in a tightly coiled compression, and uses sonata-style strategies to achieve tonal contrast and tension. The poignant affect of the coda depends on our hearing its single harmony as a subdominant in relation to the tonic harmony (centered on A) announced at the beginning and affirmed climactically at the recapitulation. In its expressive use of harmonic relations the music could be by Beethoven, except for the fact that Stravinsky did not use any chords in the movement that Beethoven, or Brahms, or Schenker would have considered harmony. Monk, who wrote most of his tunes around the time that
Orpheus
appeared, would have felt right at home.

Let's venture still further out to the onset of Stravinsky's serial phase. The Bransle Double comes right in the middle of
Agon
and is the first movement based on a twelve-tone row. Previous movements used shorter rows, and in fact the Bransle Double combines two six-note rows that have already appeared:

Hexachord I: C D E
F E A

Hexachord II: G A
B
B D
G

As Peter van den Toorn points out, both of these hexachords contain recognizable chunks of the octatonic scale (alternating major and minor seconds), which underlies much of Stravinsky's music, especially of his Russian period.
7
But the Bransle Double doesn't sound Russian; it sounds like jazz. Hexachord I contains most of the notes you need for a blues in C. The first five pitches of Hexachord II make a nice jazz dominant with a flat fifth. This creates the possibility of a quasi-harmonic progression that Stravinsky gives us three chances to hear. The short movement consists of an eight-bar phrase (in
time) written in two-part counterpoint, followed by its repetition with a third voice added in the bass. There follows a contrasting middle section, thirteen bars of
, then a repeat of the opening eight bars followed by a fourteen-bar coda in
. (If you do the math you'll see that each of the phrases contains about the same number of beats.) It is essentially an extended AABA pop tune
form. This highly repetitive structure is not something you find in the music of the Viennese serialists, and neither is Stravinsky's manner of stuttering out the twelve-tone row, repeating two-note segments two or three times before moving on.

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