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No contrapuntal form fascinated Beethoven more during the 1820s than double fugue. The monumental Et vitam venturi from the Missa solemnis takes this form, as does the concluding fugue of the Diabelli Variations, the fugato in the development of op. 111, both fugatos in the Ninth Symphony finale, the overture to Die Weihe des Hauses, and the final statement of the Heiliger Dankgesang. Crowning this formidable series comes the Grosse Fuge, the most ambitious of all Beethoven’s contrapuntal essays. In double fugue Beethoven found a nexus for his peculiar contrapuntal concerns. All the principles he had explored in the “prelude” and “fugue” themes of opp. 109 and 111 come together in his double-fugal subjects— linear construction, monolithic figuration, inversion, rhythmic diminution. The second fugato from the Ninth Symphony finale (Allegro energico) illustrates , point by point, the allure of this type of counterpoint. The two subjects exactly replicate the linear-harmonic skeleton of op. 109, the lower subject (“Seid umschlungen, Millionen”) outlining an octave descent by sequential thirds, the upper (“Freude, schöner Götterfunken”) tracing an alternating pattern of ⁵ ₃ and ⁶ ₃ chords. This scaffolding again supports a single figure, a trochaic motive as incessant as the Lombardic rhythm in the piano sonata. As the answer immediately demonstrates, the two subjects are invertible . The rhythmic texture, meanwhile, divides even more rigidly than in op. 111 into three strata—dotted half notes, alternating halves and quarters , and running eighths. In every way, this pristine fugato could serve as a primer of Beethoven’s later contrapuntal practice. The Allegro energico reveals a further resource of double fugue—the ability to combine opposing musical ideas. The fugue most obviously fuses the “Freude” theme from the D-major exposition with the new melody from the G-major Andante maestoso. At the same time, as David Levy has 133 6 Contrapunctus II: Double Fugue 134 / Contrapunctus II pointed out, the fugue recalls the B♭ Alla Marcia, not only in the compound meter (augmented to ⁶ ₄ to accommodate the new hymn), but also in the exact metronome marking (tactus = 84).1 Thus, the Allegro energico not only pulls together all three preceding sections of the finale, but its stratified texture also yokes two rhythmic extremes, the “white-note” hymn and the military march. The sturdy grip of double counterpoint can unite even the sacred and the profane, the cathedral and the parade ground. This counterpoint between cantus firmus and march resurfaces, still more obviously, in the Grosse Fuge. The upper subject of the opening B♭ fugue spins out a gapped rhythmic figure that Beethoven used interchangeably with dotted rhythms for marches.2 The lower subject is a version of the Baroque “pathotype” figure, which the Overtura has introduced as a whitenote cantus firmus. The explicit symbols of the Ninth Symphony thus pass unchanged into the rarefied world of the string quartet. The cantus firmus in the Grosse Fuge is, of course, a version of the notorious “common motive” running through the Quartets in A Minor, B-flat Major, and C-sharp Minor. The pathotype motive, introduced in the opening movement of op. 132, transformed in the finale of op. 130, and reprised in the outer movements of op. 131, has aroused much speculation. Critics from Paul Bekker to Deryck Cooke have seized upon this supposed Grundgestalt as evidence of a higher unity among the three quartets. Characteristic is Ivan Mahaim’s claim that “the climate of the Great Fugue ties these three quartets to one another, placing them as though under the same firmament.” Even Joseph Kerman, who resisted any suggestion of a cyclical connection among the quartets, did not deny the presence of the common motive.3 A simple fact has gone unnoticed in all these analyses: the common motive never appears outside a contrapuntal context. The Grosse Fuge and the first movement of op. 131 are fugues; the principal theme of the first movement of op.132 is a double counterpoint;and the principal theme of the finale of op. 131 turns into a double fugue subject. This list should also include the fugal theme of op. 111, the first example of the pathotype in the late works. Without exception, the analysts have been hunting after motives and ignoring the counterpoint.There is no lack of thematic “unity” between the three quartets, but it must be sought beyond the single dimension of pitch configurations ; this should be obvious even from the sketches for the late quartets, which Beethoven for the first time notated in score...

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