It helps, of course, if it happens to be the right arm. A paradox? After all, the majority of pianists are doubtless right-handed like the rest of the population and piano texture is traditionally conceived as being led by the melodic right hand with the left supplying the accompaniment. But if such a texture is attempted by the right hand alone, it means that the melodic top line has largely to be sustained by the relatively weak little finger. On the other hand (literally), the fingers of the left ripple away far more naturally under a strong leading thumb.
Moreover, the pedagogic founding fathers of modern pianism - Clementi, Czerny, Cramer - were concerned from the start to counter the assumption of 19th-century keyboard amateurs that the tune was all that mattered, with a stream of exercises for developing the strength, flexibility and independence of the left hand (what mixed emotions generations of students must have felt on first opening Czerny's 24 Easy Studies, Op 718). And every so often, such mono-manual acrobatics have burgeoned into something more creative, as in Brahms's marvellously sonorous left-hand transcription of the great chaconne from Bach's solo violin Partita in D minor (1877), or Saint-Saens's elegant and touching Six Studies for Piano (left hand), Op 135 (1912). But no composer we now remember seems to have tried a work for piano, left hand, plus ensemble or orchestra until the up-and-coming Viennese pianist Paul Wittgenstein lost his right arm during the First World War.
Younger brother of the philosopher and heir to the colossal wealth of an entire Jewish industrial dynasty, young Wittgenstein also seems to have inherited his family's impregnable conservatism where music was concerned. As a result, his heroic inter-war enterprise not only to remake his career but to invoke an entire new repertoire was regularly punctuated by bust-ups with the composers he commissioned - even eventually with Franz Schmidt, the figure most obviously identified with his own Viennese classical background. In fact, the earliest of Schmidt's pieces for Wittgenstein, the Concertante Variations on a Theme of Beethoven (1923), stuck relatively close to the Beethoven style itself. Far more substantial was his three-movement left-hand Piano Concerto (1934), not only in its subtle extended melodism but its peculiarly personal fusion of diatonic and chromatic harmony.
But Schmidt's essential contribution is to be found in the three luminous and leisurely piano quintets - two of them also featuring clarinet - which he completed for Wittgenstein respectively in 1926, 1932 and 1938. By treating the piano part essentially as a single florid line with only sparing harmony, Schmidt found he could entirely transcend the congested textures that afflict so much Romantic chamber music for piano and strings, and it seems a shame that the only printed editions currently available have the piano parts editorially thickened and redistributed for two hands. As heard in their original versions, the Schmidt quintets sustain that rarest quality in 20th-century music: an almost Schubertian lucidity, ease and flow.
Wittgenstein's other earliest commission, a left-hand Piano Concerto (1923) from the Viennese wunderkind Erich Wolfgang Korngold, has not tended to resurface more recently, but three of his later ones have established themselves in the repertory, while another pair at least constitute curiosities in the output of one of this century's greatest composers. In 1925 and 1927, Richard Strauss responded to Wittgenstein's advances with successive concertante scores of weltering difficulty. The first, entitled Parergon, is a kind of tone poem submitting the baby's theme from the far earlier Sinfonia Domestica to a programme depicting the dangerous fever and happy recovery of Strauss's own son, Franz. The second, uniquely in his output, is a more or less strict large-scale passacaglia of some 50 variations on a repeating ground bass; a processional evocation of ancient Greek festivities under the title Panathenaenzug. But the 1920s was a flattish patch in Strauss's compositional evolution and neither work proved consistently memorable.
Nor did he seem to care unduly about the changes and even additions his dedicatee made to the scores, whereas when Wittgenstein adopted the same proprietorial attitude to his 1930 commission from Ravel, the sparks flew. A year later, on receiving Prokofiev's Fourth Piano Concerto, specially written for the left hand, Wittgenstein declared his incomprehension and flatly refused to play it at all - indeed, the work was to languish until after Prokofiev's death, being premiered only in 1956 by Siegfried Rapp, another pianist who had lost his right arm in the Great War. Britten was slightly luckier in his response of 1940, for after initial objections, Wittgenstein came quite to like the Diversions for piano (left hand) and orchestra, Op 21.
Yet neither Ravel, Prokofiev nor Britten undertook Wittgenstein's commissions lightly; each in his own way evidently relished the technical challenge of writing for this specially limited medium. Britten's solution was to set up a particularly schematic theme - essentially a chain of fifths - and to construct upon it a sequence of 11 variations, each exploiting a different left-hand technique; the work's charm residing in the economy, grace and sardonic incisiveness with which these ultimately balance up. Prokofiev's intensely characteristic four-movement concerto, with its chattering toccata textures and long, side-slipping melodies, tends rather to keep all the possibilities in play in a more volatile continuity.
Ravel's compound single-movement Concerto pour le main gauche, however, remains the work that drew the grandest rhetoric and, possibly, the profoundest expression from the medium of single hand versus orchestra. As if to safeguard its stark formal concept, Ravel found himself simultaneously working off all his more playful and exotic proclivities on a second, two-hand concerto composed at the same time. The left-hand work accordingly opens with the most imposing of his dark risings from the depths; proceeds in its sarabande-like main subject with one of his most elevated apostrophes; issues, in the long, central march section, in one of his most unsettlingly mechanistic visions; and divulges, in the rippling cadenza towards the end, perhaps the most nearly confessional passage in his entire, guarded output. If for nothing else, Wittgenstein's difficult reputation should endure for fathering this most unexpected of Ravel's late works.
Yet the oddest of all left-hand pieces owed nothing to Wittgenstein. Even by Janacek's own standards, the engaging Capriccio for left hand and wind instruments composed in 1926 is a pungent and quirky production. He wrote it for Otakar Hollmann, yet another pianistic victim of 1914-18. But Hollmann had only suffered right-hand impairment, not lost an arm. And this hints at a lasting function for the left-hand repertoire. Since the last war, the ever-intensifying pianistic rat-race has thrown up some ominous cases of repetitive strain syndrome. Losing right-hand flexibility in mid-careers, the eminent American pianists Gary Graffman and Leon Fleisher were virtually forced to concentrate on left-hand repertoire - though Fleisher, a profoundly gifted Schnabel pupil, has taken to playing Schmidt exquisitely, and even to commissioning new solo pieces. Two-hand pianists will doubtless go on periodically tackling the left-hand concertos, if only as an enjoyable set of post-Czerny super-exercises. Whether composers will continue to write more of them remains to be seen. But there is something to be said for the stringent challenge of a medium that stimulated composers even as ingenious as Ravel, Prokofiev and Britten into lines and textures so fresh, agile and so clear.
Ravel concerto at the Proms: Monday 7.30pm Royal Albert Hall, London SW7 (071-589 8212) and live on Radio 3