Since the nineteenth century, the analysis of music has undertaken to provide accounts of musical structure by explaining musical events and patterns that lend coherence to an individual work as well as contributing to its beauty and meaning. Drawing on a variety of musical building blocks – whether harmonic, contrapuntal, melodic, rhythmic or sectional – analysts of various theoretical persuasions have asked their readers to set aside their first impressions in order to pay attention to the way a piece of music works by examining the details of its ‘facture’. The ‘truth-value’ of such interpretations can of course never be divorced from the ideas an analyst holds about musical structure, since these notions or ‘theories’ largely determine which musical parameters count as structurally significant. Nonetheless within the realm of musical analysis – far different from, say, mathematics or physics – it has rarely been the elegance or grandiosity of a structural theory that has attracted adherents. Instead, successful analyses have always appealed to an inherently musical plausibility, fuzzy though such a concept must ultimately remain. For this reason, the seeming circularity of interpretation endemic to musical analysis will appear less troubling, especially when one realises that analysts – if they are to succeed – need to persuade a community of musicians that it is possible to hear a piece as proceeding ‘so and not otherwise’, to borrow a phrase of Theodor W. Adorno. And contrary to some popular perceptions, musicians are a famously hard-nosed lot when it comes to being told how to hear a piece with which they are intimate.

I shall attempt in this chapter to open up another mode of understanding Bach within his historical context. This involves comparing his attitude to music with the metaphysical theories of certain rationalist philosophers of the Baroque era. Much of what I propose here is certainly conjectural: there is no question of a direct line of influence, or even that Bach was necessarily conscious of these parallels. I intend rather to show that Bach's musical thinking and that of the metaphysicians might depend on a similar historical world-view and, more importantly, that Bach's musical mind is equal to the greatest intellects of the age, even though he had no academic pretensions himself.

Gottfried Leibniz (1646–1716) and particularly his pupil Christian Wolff (1679–1754) are certainly very close to Bach historically; indeed Leibniz's name has occurred intermittently in Bach criticism and research, particularly in the decades leading up to 1950. Bach was closely associated with a follower of Leibniz and Wolff, Lorenz Mizler, who published Leibniz's famous dictum concerning music in the second issue of his Musikalische Bibliothek: 'Music is the hidden arithmetical exercise of a mind unconscious that it is calculating.' But the metaphysics and personality of an older, consistently shunned figure, Benedict de (or Baruch) Spinoza (1632–77), may be even closer to Bach's creative personality, although – for religious reasons – this was something that Bach could not possibly have acknowledged consciously.

According to J. G. Walther's Musicalisches Lexicon (Leipzig, 1732), Bach ‘learned the first principia on the clavier from his eldest brother, Mr. Johann Christoph Bach, formerly organist and schoolmaster at Ohrdruf’. No mention is made here (or in Bach's Obituary, which gives a similar account) of composition, and Johann Christoph is not known to have been a composer. In answer to a query of J. N. Forkel's, Bach's son Carl Philipp Emanuel wrote in 1775: ‘The instruction received by [J. S. Bach] in Ohrdruf may well have been designed for an organist and nothing more.’ The clear implication is that composition was largely excluded.

Here we have a fact of great importance for the understanding of Bach's early development as a composer: unlike his great contemporary G. F. Handel, he seems to have received no formal tuition in the rudiments of composition. His early compositions, most of which are for keyboard, had dual roots: in his own rapidly growing skill as an organist and harpsichordist (‘In a short time he had fully mastered all the pieces his brother had voluntarily given him to learn’); and in his ‘observation of the works of the most famous and proficient composers of his day and … the fruits of his own reflection upon them’.

To judge by the character of Bach's early keyboard works, both the improvisatory and virtuoso aspects of his playing acted as spurs to his creativity. Improvisation was essential to the keyboard player's training in Bach's day, and numerous passages in the early keyboard works no doubt had an extempore basis, notably the free fantasy interludes in the sonata BWV 963 and in the toccatas BWV 910-15 or the ruminative elaborated chord sequences in the preludes BWV 921-3 and in the third section of the toccatas BWV 910 and 913.

The notion of consciously performing the works of Johann Sebastian Bach in a Baroque fashion, with Baroque forces, is a relatively recent development. Indeed, it is an idea that has taken firm hold only in the past fifty years. When we look back on the history of Bach's music – its birth in the Baroque, its eclipse in the Classical Period, its rediscovery in the Romantic era, and its canonisation in modern times – we find that musicians took many different approaches to playing it. The issues of what we now call ‘performance practice’ have constantly changed.

The Baroque era itself was a period of considerable stylistic self-consciousness, and this self-consciousness affected the way pieces were performed. As a German, Bach took an eclectic approach towards composition, calculatedly calling on aspects of at least five national styles: German, French, Italian, English and Polish. Each style implied particular forms, gestures, and – most importantly – modes of performance. For instance, the Overture in B Minor BWV 831, written in the French style ('nach Französischer Art’ as Bach put it), contains rhythms in the opening section that attempt to record the sharply dotted ‘French’ performing style. When Bach revised the early, C minor, version of this Overture, BWV 831a, for inclusion in Clavier-Übung II (where it is paired with an Italian Concerto ‘nach Italiaenischen Gusto’), he sharpened the rhythms to bring the execution more closely into line with the French manner of playing (Example 13.1). That is to say, he intentionally bowed to the conventions of French performance practice.