Issue No. 9: Collapsing Space in Carter's Cello Concerto
Composers have long utilized placement of sounds in specific registers to define larger formal shapes in their works. In other words, it matters not just what musical materials are heard but where in pitch space they occur. For example, consider the four-measure coda in the second movement of Beethoven’s Pathétique wherein a cadential reaffirmation is played three times in progressively lower octaves, closing out not only tonal but also registral spaces opened throughout the work.
Contemporary composers are no different. One of my favorite instances is in the conclusion of Elliott Carter’s brilliant Cello Concerto from 2001. The analytical example below is a reduction of eleven measures (mm. 428-439) from the coda of this piece. The orchestra boldly plays a fortissimo all-interval twelve-note chord at the end of a seven-measure climactic outburst while the cello remains silent (who would hear the low string soloist at any rate?). As the accompaniment quickly fades away, the cello resumes its energetic allegro fantastico material in measure 429. Supplementing the soloist's virtuosic passagework, the orchestra provides a sequence of staccato pianissimo tetrachords that sound like clockwork every four beats. In the wake of the roaring symphonic climax, these four-note chords initiate a long-range spatial collapse to effectively close out the registral space of the entire composition and bring the piece to a close. As one might expect in mature music by Carter, each of the four-note simultaneities is a realization of an all-interval tetrachord. (If you are curious as to what all-interval tetrachords and all-triad hexachords are, why they are significant, and the role they play in Carter’s music, read my essay on the subject here.)
This long-range wedge-shaped cadential spatial collapse surpasses even the impressive one heard in the coda of Carter’s Boston Concerto (analyzed in my dissertation), since it spans a lengthy eleven measures and folds down at a remarkably even pace in terms of temporality (every four beats) and spatial boundary (the majority of the occupied spaces shrink by five or four semitones from the previous iteration). Although I have not analyzed all of Carter's pieces from the final two decades of his career, I believe that this may be the composer's most impressive systematic long-range registral minimization that functions as a terminative formal device. As the collapse reaches its conclusion on an instantiation of an all-triad hexachord (a subtle shift in harmonic materials), so does the orchestra's musical narrative for the composition as a whole – a mere three pianississimo tones remain to be played by the accompaniment, isolated and at the edge of audibility. The piece is, ostensibly, over. However, the cellist resumes a fiery, rhapsodic, and ultimately playful cadenza, apparently unaware that the massive supporting orchestra has given up and walked away. A narrative conflict is presented, then, in the finale of Carter's Cello Concerto: the listener has received an obvious indication that the piece has concluded in the form of an epic spatial collapse, but the soloist willfully undermines this script, continues undeterred, and thumbs their nose at the ensemble with a final pizzicato flourish. Balance is one of the most difficult aspects of writing for cello and orchestra; Carter solved the climax problem by writing a dual narrative thread – one that wraps the musical discourse up tidily, and another that persists as if nothing had ever happened.
Listen a few times following the reduction below and, as always, let me know what you think in the comments, on social media posts, or via direct messages!
Elliott Carter, Cello Concerto, mm. 428-439. Measure numbers are shown in rectangles above the reduction; presence of all-interval twelve-note chords (AITN), all-interval tetrachords (prime forms 0137 and 0146), and all-triad hexachords (ATH) are shown under the reduction; total numbers of semitones occupied in pitch space are presented under the harmony labels.
Elliott Carter, Cello Concerto. (Analyzed excerpt begins at 20:24)