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Series Rotation in
Igor Stravinsky's Requiem Canticles

Stravinsky adopted serial techniques in the 1950s. Though his early serial works like the 1953 Septet were sometimes uncharacteristic, he experimented until he evolved an approach to fit his style and ear. The result was a handful of late masterpieces which were pure Stravinsky yet refreshingly new -- a remarkable journey for a man already in his seventies.

Stravinsky's serial works feature strong tonal centers. He derived his serial tables in a special way to emphasize certain tones. Rather than transposing the series by successive half-steps to generate his tables, he rotated the series then transposed it back to the original starting pitch. This produced the usual 12 permutations, but emphasized the starting pitch.

Here's an example of this rotation, using letters instead of notes for clarity:

1 2 3 4
Choose a word.
Place the word in a grid with as many rows as the word has letters.
Rotate row #2 once, row #3 twice, etc.
Transform each row to begin with the row #1's first letter. The O in the row #2 is 4 less than S, for instance, so add 4 to each letter in that row.
See how this accentuates the letter S? The final table in Step 4 features new letters Q I W K Y U G C A which weren't in the original, but the letter S dominates the table. If you were to attempt to pronounce the 4-letter words listed in Step 4, you'd start each with an "ess" sound. That sound is the "tonal center" in Stravinsky's technique. This is a gross simplification, of course, but illuminating nonetheless.

In our example below, notice how the cellos in the Prelude from the 1966 Requiem Canticles start and end the movement on F -- a sure sign that that note is more-than-usually important. It's a tonal center.

Here's the series:

That starting F is important as a pitch, but the rest of the notes are more important for the intervals they form with their neighbors. In Stravinsky's serial works, intervals and tonal centers constitute the music's basic materials.

As an example, let's look now towards the end of the series at the pitches G#-F#-E:

Those three pitches are less important than the two descending major seconds they form. Intervals survive transposition intact, where pitches by definition do not. In traditional tonal music, the pitches are important, the intervals less so. Serial music reverses this.

Now let's take the series and generate one of the serial tables. A serial table is a series translated repeatedly to form a grid. The tones specified within the grid are the basic "building blocks" of the work, which often moves freely between the variations.

Notice how those two intervals initially spelled out by G#-F#-E are transposed and rotated leftwards in each line.

 
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