Brahms himself was no slouch as a pianist. He had the technique and knowledge of the keyboard to write a brilliant virtuoso work. His Opus 35 set of variations prove it. He wrote them for the virtuoso Carl Tausig who was a student of Liszt and a pianist Brahms admired. He wrote the variations on a theme of Paganini taken from the 24th Caprice For Solo Violin In A Minor, a work that Liszt had already written a transcription for piano for, and a work that was to inspire many other composers in the future.
Brahms had something different in mind, even in the title of the work. He called the work Studies For Pianoforte, Variations On A Theme Of Paganini, with the implication being that each of the variations are an etude that explores a particular aspect of piano playing. The work is divided into two books of 14 variations, each one being an independent work in itself. Many times both books are played in recitals. Brahms version of the theme is played to lead off both books, and most of the variations are in the original key of A Minor.
Book One
Theme - Brahms begins with the theme, but not in its original form. He adds grace notes to the melody in the right hand in the first section, adds grace notes to the left hand in the second section and, unlike the original, repeats the second section thus making the theme 24 bars long instead of the original 16:
Brahms keeps the general outline of the theme throughout the first thirteen variations, with all the variations being in the key of A minor except the 11th and 12th, which are in A major. But that is not to say that the variations are simple variants. The variations throw every kind of technical challenge at the pianist; intervals of all kinds, huge jumps, hand crossings, etc. The 13th variation is noteworthy for its use of octave glissandos in the right hand, quite difficult on the piano of Brahms day as well as the modern piano. The 14th variation is an extended section that goes beyond the 24-bar length of the theme and previous thirteen variations. Brahms introduces music that sounds like yet another variation before he adds a coda that rounds out and ends the first book.
Book Two
The theme is played again, all of the variations are in A minor, except for Variation 4 which is in A major and Variation 12 which is in F major. Again, Brahms writes variations of great difficulty but still stays within the same general outline of the theme. As with Book One, the 14th variation is an extended section that adds yet another two un-numbered variations that lead material that fully closes out Book Two.
Clara Schumann, widow of Robert Schumann called the piece Hexenvariationen (Witch's Variations) because they were so fiendishly difficult, and though she was one of the great pianists of the 19th century she could not play them. The piece remains one of the few examples of outwardly virtuosic piano music Brahms ever wrote. Along with the Goldberg Variations of J.S. Bach and the Diabelli Variations of Beethoven, Brahm's set is one of the greatest variations written.