We are fortunate that many of Bach’s original manuscripts have survived. Most are readily available for viewing or pdf download at imslp.org, the International Music Score Library Project. The six Brandenburg concertos, notated in 1721 in Bach’s own hand as a gift for Christian Ludwig, the Margrave of Brandenburg, are works of graphic art, conveying their musical messages in calligraphy that is elegant, vigorous, shapely, and easy to read. Bach drew each notehead and its stem with a single quick motion of his quill pen, one after the next. When those notes are eighths or sixteenths grouped together, the thick strokes of his connecting beams curve and dance across the page as they follow the shape of the musical line.

Besides his own compositions, Bach went through a great deal of ink copying out the music of other composers, absorbing lessons from the study of their scores that enriched and broadened his own thinking about music’s building blocks. At the same time, as if in good-natured competition with his musical elders and contemporaries, he took what he found and explored its implications more comprehensively and profoundly than anyone else. In the case of his concertos, Bach drew especially on the models of Antonio Vivaldi, who, along with his teacher and fellow Italian Arcangelo Corelli, made the first great contributions to the genre. A Vivaldi concerto is a virtuoso showpiece for an instrumental soloist, usually violin, accompanied by a small orchestra of other string instruments. It typically has three movements, fast-slow-fast. As in all Baroque ensemble music, it includes a basso continuo part—the prominent bass melody given to cello and double bass. The harpsichordist also participates in the basso continuo, playing the melody with the left hand while improvising appropriate chords and ornamentations above it with the right.

There is an important type of Baroque concerto, the “concerto grosso,” which includes more than one solo instrument. Corelli and Vivaldi wrote many of them. The genre provides great opportunities for dialogue and competition between the soloists, as well as the dynamic contrasts made possible in the alternation of the solo group with the full ensemble. Bach’s double concerto for violin and oboe is a good example of the type. Unfortunately, its original score, probably written around 1720, has long been lost. But the complete piece survived in the form of a double-harpsichord concerto, one of the transcriptions Bach made of his own music for the Collegium Musicum concerts he directed in Leipzig during the 1730s. Several musicologists over the past century have created reconstructions of the original. One of those now appears in the Bach-Werke-Verzeichnis (Bach’s collected works), identified with an R appended to the harpsichord concerto’s catalog number: BWV1060R.

In works such as this double concerto and the Brandenburg concertos, Bach acknowledges the models of his predecessors, but also pushes the concerto grosso in new directions. Where, for example, are the violins in Brandenburg Concerto No. 6? There was likely never an ensemble like this one, before or since. Bach calls for two violas “da braccio” (“of the arm”: in other words, the viola as we know it today) and two violas “da gamba” (“of the leg,” the six-string fretted instrument held like a cello). The rest of the ensemble is simply a solo cello and the basso continuo. The piece begins with a high-speed imitative chase between the solo violas, one racing off on a zigzag path of arpeggios and scales while the other follows immediately behind, just a quick beat later, exactly matching its steps. It happens so fast that the sounds merge and you lose track of which note comes first and which is its echo. The other instruments cheer them on with driving repeated chords, a rhythm section behind the soloists in these opening bars. Periodically, the gambas and basso continuo drop out while the violas and solo cello take a turn on their own, calling attention to the contrast of texture and volume between the sound of the full ensemble and that of the smaller group. At other times, the violas are accompanied only by the two gambas. ln the slow second movement, the gambas rest while the soloists spin out a tender fugue over a simple walking bass from cello and continuo. The last movement is a high-speed romp in triple rhythm.

Bach multiplies his contrapuntal resources with a highly unusual ensemble for Brandenburg Concerto No. 3, writing for nine soloists in addition to the basso continuo—three each of violins, violas, and cellos. You can sense at every moment his audacious glee as he nimbly juggles nine balls at once instead of just three. Granted, the cellos are almost always playing exactly the same thing, so perhaps it’s more accurate to say seven balls. Still, Bach makes the most of the many possible ways these instruments can be combined together—imitation, call-and-response, collective unison, etc. One unusual feature of the piece is that Bach essentially dispenses with the second movement. It is replaced with a standard Baroque transitional device: simply two chords that create a sense of anticipation for the fast movement to follow.

The fourth Brandenburg concerto features a violin and two recorders as soloists. However, the extremely difficult and flashy passagework for the violin in the first and third movements makes this feel more like a solo violin concerto. The focus turns to the recorders in the Andante second movement, with solo violin in a more supportive role, even functioning at times as a treble-clef basso continuo. This movement is one of the rare instances where Bach specifies dynamics, alternately writing forte and piano in the score to indicate echo effects. This may explain why, in the title at the head of the score, he designated the recorders “fiauti d’echo,” or echo flutes. Or perhaps he had in mind a special kind of flute, not a recorder at all? (Starting in about 1960, that question has been debated extensively—and inconclusively—in music journals.)

Brandenburg Concerto No. 5, written around 1720, has pride of place as the first keyboard concerto in Western music. At first glance, it looks to be a typical concerto grosso, with flute and violin soloists and a small string orchestra. We may assume that the harpsichordist, as part of the basso continuo group, will be doing the usual thing—playing the bass melody while improvising right hand material according to standard Baroque conventions. Not so here. Bach has written out nearly every note for both hands, save for occasional brief passages of basso continuo accompaniment. That is unprecedented in Baroque orchestral music. The part is technically and musically demanding. For long stretches, the harpsichordist plays alone, most dramatically in a giant cadenza near the end of the first movement. The second movement, marked “Affetuoso” (“with affection and tenderness”), is an intimate conversation between the three soloists. No one else plays. The beginning of the last movement is also limited to the trio, one by one introducing a fugal theme before the rest of the ensemble joins them.