As befits this deep thinking musical polymath, the programme for Stephen Hough's Barbican concert was carefully constructed to reveal every side of his personality – artistic, creative and philosophical. The concert showcased Hough's new Piano Sonata III, written to celebrate the 175th anniversary of The Tablet, which Hough intelligently linked to his choice of other composers. The spiritual preoccupations of Schubert, Franck and Liszt match Hough's own, but there were motivic connections between the works in the programme too: for example, the final movement of Hough's Piano Sonata mirrored the grandeur and hymn-like qualities of Franck's Fugue. Liszt's Valses oubliées looked forward to Schoenberg and his cohort in their unexpected harmonies and fragmentary melodies, while Hough's own work looked back to the 12-tone compositional technique, originally conceived by Schoenberg. There was also virtuosity aplenty too – in his own work and in two of Liszt's Transcendental Études, which closed the concert.

The concert opened with Schubert's Piano Sonata in A minor D784, written in February 1823, one of the darkest times in the composer's life and possibly a reaction to the knowledge that he had syphilis. The opening of the first movement is bleak, bare and harsh, and Hough's almost Beethovenian fortes amply highlighted the desperation inherent in this movement, and the whole work. There was much sensitivity in the softer dynamic range of the second subject, and also in the Andante, revealing the intimacy of Schubert's writing.

César Franck's Prélude, Choral et Fugue is one of his most serious works and one which does not seek to charm. Rather, it draws the listener in with its dark intensity, its falling figures and recurring motifs which emphatically drive its message home. This is music with which Hough is obviously very familiar, for he brought not only a clear sense of the grandeur and overall architecture of the work, but also its quasi-improvisatory nature, most apparent in the Prelude which had a distinctly ethereal quality.

After the interval came the première of Hough's Piano Sonata III, “Trinitas”, commissioned by The Tablet, the second-oldest surviving weekly journal in Britain after The Spectator. The Tablet is a journal which combines loyalty to the Catholic Church with an irrepressible inquisitiveness, and thus its special connection with Stephen Hough seems especially appropriate.

In his new Sonata, Hough explores the 12-note row, the compositional technique of "serialism". It is a form of musical dogma, and Hough cleverly links this back to The Tablet and Catholicism by scoring the work in three movements and subtitling it “Trinitas”, Latin for "Trinity", another dogma, the theological ordering of numbers. To guide the listener, each movement is helpfully described ("bold, stark", "punchy, jazzy" and "majestic, proud"). The starkness of the opening movement reflected the bare, plaintive first subject of the Schubert sonata. The middle movement, rhythmically vibrant with its lively syncopations, rapid tinkling notes high in the treble and colourful note clusters, was redolent of Messiaen, another devout Catholic, while its virtuosity referenced Liszt. The final movement, which reflected the Fugue of the Franck in its rich textures and majesty, quotes a familiar hymn tune (Nicea, a setting of the Trinitarian text “Holy, Holy, Holy”) which is disrupted by discordant sounds and a hint of Schoenberg's Sechs Kleine Klavierstücke (to me, at least) towards its conclusion. Yet despite the dogma and metaphysics, this work was accessible and at times witty, quirky and playful, and it is exciting to know that such variety and imagination is readily available for other pianists to tackle and enjoy.

The works by Liszt showed Hough as the virtuoso-at-ease, making light of the technical challenges in two Transcendental Études, and wittily highlighting Liszt's forward vision in the Valses oubliées.

Three charming and increasingly playful encores concluded this satisfying and thoughtful concert: Liszt's Consolation no. 3 was followed by a fleeting extract from Don Quixote by Minkus, transcribed by Hough, and to finish By The Sleepy Lagoon by Eric Coates (better known as the theme tune from BBC Radio 4's Desert Island Discs).