"Bach is the father. We are the children!" No one with a smattering of musical knowledge will be surprised by this remark of Mozart's, made to the Viennese aristocrat and influential patron Gottfried van Swieten. It is well known that Mozart held the composer in the highest esteem and, some would even argue that it was his interest in the contrapuntal, learned style of "Old Sebastian", as he called him, which gave his music its edge.

But when Mozart referred to Bach as his musical father, it was in fact not Johann Sebastian he had in mind, but his second son, Carl Philipp Emanuel. Indeed, in the second half of the 18th century, the name "Bach" was almost exclusively associated with the initials "CPE".

Born in 1714 to Johann Sebastian and his first wife Maria Barbara, Emanuel followed the example of his godfather Georg Philipp Telemann by qualifying as a lawyer before pursuing a musical career. But his first main job couldn't have been along more traditional lines. He moved from Leipzig to Berlin in 1740 to be a harpsichordist in the court of Frederick the Great. Despite the fact that his appointment seems to have been made directly by Frederick – he was chosen to accompany the newly crowned monarch and musician for his first solo flute concert – Bach didn't appear to make much headway in the Prussian court, never becoming credited as an official composer. Even the visit of his father to Frederick's court in 1747 – the now legendary meeting that led to the composition of the Musical Offering – did nothing to advance the son's career, dogged by quarrels and criticism of his unorthodox and "affected" playing style.

It is perhaps unsurprising that in his autobiography – notably, CPE Bach was one of the first composers who considered himself suitable as a literary subject – the composer looked back on his 20 years in Berlin as a time of frustration and hardship. Nonetheless, a comparatively generous salary and a contract that required him to play only every other week meant that his years at the Prussian court were extremely productive. He wrote reams of keyboard music which, though he considered most of it unchallenging hack work ("sonatas for the ladies", as he put it), generated a significant second income. Surviving correspondence with his publisher revealed Bach to be not just a skilful negotiator but an innovative businessman, too. His system of establishing agents in the major musical capitals of Europe ensured a much wider circulation for his works than was usual. His vocal music, meanwhile, attracted the praise of FW Marpurg, an influential Berlin music critic and theorist who numbered Voltaire and D'Alembert among his acquaintance.

But Bach's greatest achievement from these years was a composition not of music but of prose. The Essay on the True Art of Playing Keyboard Instruments remains the most famous treatise of its kind. The book combines technical advice about ornamentation, improvisation and the importance of correct fingering ("more is lost by incorrect fingering than can be compensated for by all the art and good taste in the world"). The now-standard practice of using thumbs in keyboard playing can be attributed to it. But the text also prescribes a philosophy of performance which for the first time placed the expression of emotion on a par with technical competence. "Since a musician cannot move others unless he himself is moved," the essay argues, "he must of necessity feel all of the affects that he hopes to arouse in his listeners." Both Haydn and Beethoven swore by it; its use remained widespread long into the 19th century.

One of the illustrative examples composed for the essay subsequently became one of the Bach's best-known pieces of music. Written in 1753, just three years after the death of Johann Sebastian, the Fantasia in C Minor bears little resemblance either to his father's music or to the elegant and balanced "galant" style then in vogue across Europe, and of which one of the chief exponents, besides Emanuel himself, was his London-based half-brother, JC Bach. Free in tempo and full of intriguing harmonic shifts and palpitating rhythms, the fantasy is self-consciously operatic in style, intended to give expression to a quick succession of extreme and contrasting emotions.

The Fantasia is a prime example of the Empfindsamer or "sentimental" style of which Bach became the foremost representative, especially after leaving the staid Prussian court and, in 1768, moving to the much more cosmopolitan and culturally progressive city of Hamburg. Giving preference to intimacy over elegance and to passion over balance and poise, the aesthetics of Empfindsamkeit tried to forge a direct emotional connection between musician and listener. It was first and foremost a literary aesthetic, associated in the minds of many German-speaking intellectuals with the Irish-born English novelist Laurence Sterne, whose Sentimental Journey Through France and Italy had been translated as Empfindsame Reise.

According to the musicologist Annette Richards, whose work on CPE Bach has emphasised its Sterneian inflections, the composer's wider cultural influences are the key to understanding his music. "Outside music, the cultural references of JS Bach were more or less exclusively theological. But with CPE Bach, things are completely different. Engaged with poets, painters, philosophers, his music is a reflection of the burgeoning secular discourse of his time."

"Even among his contemporaries", says Richards, "you get a sense that CPE Bach is an acquired taste. His music – or the music he considered representative of his talents – is miles away from the elegance and balance we associate with this period. Timelines are crisscrossed, he is endlessly stopping and starting, wrong-footing the listener and causing his audience to reconsider its relation to the music. In that sense, it's very postmodern, a kind of meta-music."

Roger Norrington, who next month conducts an extremely rare all-CPE Bach programme with the Orchestra of the Age of Enlightenment, broadly agrees. "Though his music is hardly ever done now, there is little doubt that Emanuel is the best of the Bach sons. More tongue-in-cheek and heart-on-sleeve than his father, there's a wonderful feeling of openness to his music that you rarely find in baroque music. It's more reminiscent of Lully and Couperin."

But where Norrington emphasises Bach's status as a transitional composer, filling in the huge stylistic gap between the music of his father and that of Haydn and Mozart, Richards accords the composer a more significant historical role. "The lines of musical history have been very narrowly drawn, and figures like CPE Bach who don't fit well with Viennese mainstream get squeezed out. But Bach is part of an equally important northern German tradition which, via such writers and philosophers as Herder, Jean Paul and the Schlegels, resurfaces as a central part of the Romantic aesthetic of Schumann and Chopin."

Another aspect of CPE Bach that aligns him with much more modern figures is his overriding concern with posterity and his place with music history. His letters frequently make reference to how others will remember him, and his autobiography, written in 1773, marks a clear division between the music he wrote for purely commercial reasons and that which he wrote for himself. By his death, he had assembled a collection of over 400 portraits of artists, thinkers and musicians he admired. "A kind of personal pantheon", as Richards puts it, "in which he did not hesitate to accord himself a prominent position."

In retrospect, of course, CPE's reputation has dwindled, dwarfed by that of his father. But there is a strong argument that his influence on subsequent composers such as Haydn and Beethoven – both of whom were avid collectors of his music – was in many respects greater than his father's. Indeed, in tirelessly promoting an aesthetic that aims to liberate instrumental music from service as polite entertainment, he is many ways the most significant progenitor of the "absolute music" which came to dominate conceptions of the art in the 19th century, and still – to a very large extent – presides over the life of our concert halls today.

Roger Norrington conducts the OAE in an all-CPE Bach programme at the Southbank Centre, London on 3 March. The Other Amazing Mr Bach, a study day, is at the Purcell Room on 5 March.