
One can't help wondering why it is that so much music has been written for the left hand alone and virtually none of any significance for the right hand. One answer is that almost all of the great music written for the left hand alone is the result of a determinedly heroic concert pianist having lost his right arm during World War I.
Paul Wittgenstein (1887-1961), an Austrian pianist and, interestingly, brother of the great philosopher Ludwig Wittgenstein, refused to allow his career as a concert pianist to be ended almost before it had begun in earnest by the loss of his right arm.
Fortunately for us all, his was by no means an insignificant family in the world of music. As a young man he had played duets with Richard Strauss, and Strauss, Brahms, Joseph Joachim, and Gustav Mahler were family friends. And of course, as a student of Theodor Leschetizky, he had an excellent pedigree as a pianist.
Wittgenstein was in a position to ask many of the most important composers of the day to compose music for for him to play. Among these were Richard Strauss, Sergei Prokofiev, Erich Wolfgang Korngold, Franz Schmidt, Paul Hindemith, Alexander Scriabin, Benjamin Britten, Josef Labor, Sergei Bortkiewicz and Maurice Ravel. The Ravel Piano Concerto for the Left Hand is a staple of the repertoire today. (Below is a brief video clip showing Wittgenstein in a performance of the Ravel concerto.)
For a complete performance of the concerto with Wittgenstein at the piano in a 1937 recording with Bruno Walter conducting the Concertgebouw Orchestra of Amsterdam , Part I and Part II can be found on YouTube.
The repertoire resulting from Wittgenstein's efforts has been a veritable lifeline for other pianists as well who, for one reason or another, lost the use of their right arms. Brilliant concert pianists such as Leon Fleisher, João Carlos Martins, and Cor de Groot would not have been able to continue their careers to any degree without it.
Prior to Wittgenstein's injury, a number of composers had composed or transcribed such piano music. Among these works is the transcription by Johannes Brahms of the Bach Chaconne in D minor from the 2nd Partita for solo violin BWV 1004. This is a work of sheer genius. It was transcribed for the left hand alone for Clara Schumann when she suffered an injury to her right hand. The Brahms transcription is more faithful to the original than the more famous and more popular Busoni two-hand transcription which it predates by 16 years. To hear and see it played by Anatol Ugorski, a fine Russian pianist, Part I and Part II can be found on YouTube.
The other answer is that among pianists, given the preponderance of right handed people, the left hand is generally the weaker and less proficient of the two. This has prompted a number of studies and exercises for the left hand alone.
Leopold Godowsky, who was considered by his peers, Arthur Rubinstein and Jozef Hofmann among them, to be the most amazingly gifted pianist of them all, transcribed a number of the Chopin Etudes for the left hand alone. The technical difficulty of these transcriptions is simply beyond belief. Listen to Canadian pianist Marc-André Hamelin play the Godowsky-Chopin Étude Opus 10 No 3. The beauty of this piece belies its difficulty.