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=== Expositions that modulate to other keys === The key of the second subject may be something other than the dominant (for a major-mode sonata movement) or relative major (for a minor-key movement). A second option for minor-mode sonata form movements was to modulate to the minor dominant; this option, however, robs the sonata structure of the space of relief and comfort that a major-mode second theme would bring, and was therefore used primarily for a bleak, grim effect, as Beethoven did with some frequency. [[Felix Mendelssohn|Mendelssohn]] also did this in the first movement of his [[Symphony No. 3 (Mendelssohn)|Symphony No. 3]] and the last movement of his [[Symphony No. 4 (Mendelssohn)|Symphony No. 4]]. About halfway through his career, Beethoven also began to experiment with other tonal relationships between the tonic and the second subject group. The most common practice, for Beethoven and many other composers from the Romantic era, was to use the [[mediant]] or [[submediant]], rather than the dominant, for the second group. For instance, the first movement of the [[Piano Sonata No. 21 (Beethoven)|"Waldstein" sonata]], in [[C major]], modulates to the mediant [[E major]], while the opening movement of the [[Piano Sonata No. 29 (Beethoven)|"Hammerklavier" sonata]], in [[B-flat major|B{{music|b}} major]], modulates to the submediant [[G major]], and [[String Quartet No. 13 (Beethoven)|String Quartet No. 13]] in the same key modulating to the flattened [[submediant]] key of [[G-flat major|G{{music|b}} major]]. [[Pyotr Ilyich Tchaikovsky|Tchaikovsky]] also implemented this practice in the last movement of his [[Symphony No. 2 (Tchaikovsky)|Symphony No. 2]]; the movement is in [[C major]] and modulates to the flattened submediant [[A-flat major|A{{music|b}} major]]. The young Chopin even experimented with expositions that do not modulate at all, in the opening movements of his [[Piano Sonata No. 1 (Chopin)|Piano Sonata No. 1]] (remaining in C minor throughout) and his [[Piano Concerto No. 1 (Chopin)|Piano Concerto No. 1]] (moving from E minor to E major). Beethoven began also to use the submediant major with more frequency in minor-key sonata-form movements, as in the first movements of [[Symphony No. 9 (Beethoven)|Symphony No. 9]], [[Piano Sonata No. 32 (Beethoven)|Piano Sonata No. 32]], and String Quartets [[String Quartet No. 11 (Beethoven)|No. 11]] and [[String Quartet No. 15 (Beethoven)|No. 15]]. The latter case transposes the second repeat of its exposition by a fifth, starting on the minor dominant (instead of the tonic) and finishing on the major mediant (instead of the submediant). The first movement of [[Richard Strauss]]'s [[Symphony No. 2 (Strauss)|Symphony No. 2]], in [[F minor]], modulates to the submediant [[D-flat major|D{{music|b}} major]], as do the F minor first movements of Brahms' [[Clarinet Sonatas (Brahms)|first clarinet sonata]] and [[Piano Quintet (Brahms)|piano quintet]]; all three works balance this downward third by moving up to the major mediant ([[A-flat major|A{{music|b}} major]]) for the key of the second movement. Rarely, a major-mode sonata form movement will modulate to a minor key for the second subject area, such as the mediant minor (Beethoven Sonata Op. 31/1, i), the relative minor (first movements of Beethoven Triple Concerto and Brahms Piano Trio No. 1) or even the minor dominant (Brahms Piano Concerto No. 2, i). In such cases, the second theme will often return initially in the tonic minor in the recapitulation, with the major mode restored later on. During the late Romantic period, it was also possible to modulate to remote tonal areas to represent divisions of the octave. In the first movement of Tchaikovsky's [[Symphony No. 4 (Tchaikovsky)|Symphony No. 4]], the first subject group is in the tonic [[F minor]] but modulates to [[G-sharp minor|G{{music|#}} minor]] and then to [[B major]] for the second subject group. The recapitulation begins in [[D minor]] and modulates to [[F major]], and goes back to the parallel [[F minor]] for the coda. Also in the late Romantic period, it was possible for a minor-key sonata form movement to modulate to the major dominant, as in the first movements of Tchaikovsky's [[Symphony No. 1 (Tchaikovsky)|Symphony No. 1]] and Brahms' [[Symphony No. 4 (Brahms)|Symphony No. 4]].
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