The variations on a theme of Paganini are, on the other hand, remarkably brilliant as a whole. They show the uttermost limits of the Brahms pianoforte technique and style, and are, of course, extremely difficult. The first two are studies in thirds and sixths, and in the second especially the upper registers of the piano are used with striking effect. In the fourth there are brilliant trills over wide figures in violin style. The eighth in the second set is in imitation of the passages in harmonies in the Paganini _Caprice_ from which the theme is taken. Particularly effective on the pianoforte are the eleventh and thirteenth in the first set, the former with its shadowy overtonesin the right hand, the latter with the sparkling _glissando_ octaves. The twelfth in this set is like others that have been mentioned, a study in complex rhythms, but is remarkably clear and bell-like in sound as well. The sixth, ninth, and tenth are less effective and less interesting. The second, fourth, and twelfth in the second set are conspicuous for a less scintillating but more expressive beauty. The sets as a whole are more in the style of Paganini than the études of Schumann and Liszt, which owe their being to the same source. There is more of wizardry in them, more variety and more that is wholly unusual. They give proof of enormous thought and ingenuity applied to the task of producing effects from the piano that have the quality of eeriness, which, in the playing of Paganini, suggested to the superstitious the coöperation of infernal powers. In the ‘Variations on a Theme of Handel,’ opus 24, the same powerful intellect may be seen at work in more orthodox efforts. The results are often of more scientific than musical interest. The set is extremely long in performance, and the cumbersome fugue at the end is hardly welcome. Some of the movements are heavily or thickly scored, like the mournful thirteenth and the twentieth. Others are intellectual or uninspired, like the sixth and the ninth. But others, like the second, the fifth, the eleventh, and the nineteenth, are truly beautiful, and many are brilliant or vivacious. There are three earlier sets of variations, opus 9, opus 21, Nos. 1 and 2, which are small beside the two later sets just discussed. As far as pianoforte music is concerned, the variations on a theme of Handel, and the subsequent variations on a theme of Paganini, represent the culmination of Brahms’ conscious technical development, the one in the direction of intellectual mastery, the other in the direction of keyboard effects. Behind them lie the sonatas, the scherzo, and the ballades, all in a measure inspired, yet all likewise tentative. After them come numerous sets of short pieces which constitute one of the most beautiful and one of the perfect contributions to pianoforte music.