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By far the dominant form of instrumental music in the early 18th century was the set of dances that we now call a suite. In northern Europe, musicians and their listeners were familiar with national or local forms of (to give their French names, because most of them were French in origin) the allemande, menuet, gavotte, sarabande, courante, bourrée, passepied, forlane, rigaudon, and gigue. They danced these dances in social gatherings and saw them danced on stage, and were as familiar with them as with social customs and manners.

A dance would likely evolve with time and location. It might slow down as the generation that danced it aged, or become more vigorous in one country than it was in another, or speed up as a result of changes in shoe styles or how voluminous women’s skirts were. To us, surveying them over about a century in which composers wrote them, their titles suggest a general range of tempo and rhythmic accents, but it may be that to a person in a specific time and place (Leipzig in 1730, for example), “gavotte” at the top of the page was so specific that it told a musician everything a modern musician would get from performance directions and a metronome marking.

Composers wrote lots of these dances, even if they never wrote a note actually intended for the dance floor. They composed semi-standardized sequences of dance movements titled suite or partita (or partie or parthia). The movements were normally all in the same key, so contrast was achieved through the varying speeds and rhythms of the dances. The dances were part of the musical vocabulary of composer and listener, and they even show up in vocal or liturgical music.

An important subset of the suite was what both French and Germans called the ouverture. It developed in 17th-century France with the practice of publishing suites of instrumental and ballet numbers from operas, and performing them outside the opera house. Each suite would begin with the opera’s overture, which in France by the 1670s, and later everywhere else, had already taken the form it would keep through the high Baroque: a stately or pompous slow introduction, followed by a faster more-or-less fugal section.

Other suites — most suites for solo lute or harpsichord among them — normally began with an allemande, or a non-dance prelude or fantasy. The ones that began with a French overture — which included most of those for orchestra — became known as ouvertures, which is the title Bach used. They became extremely popular in Germany, where composers expanded the fast section with extended sections for solo instruments, as in a concerto. Some composers of Bach’s generation turned out ouvertures in impressive numbers: 85 by Christoph Graupner and almost 100 by Johann Friedrich Fasch. There 135 surviving ouvertures by Telemann, but he is known to have written many more.

Bach, by contrast, has left us only four orchestral ouvertures, and we know remarkably little about them. Bach often seems to have conducted his affairs so as to confound historians. Sometimes we have reliable information about his works. We know, for example, that the “Brandenburg” Concertos were assembled in a manuscript sent to the Margrave of Brandenburg as a sort of musical resume in 1721, and were versions of works Bach had composed for the orchestra at the court of Duke Leopold of Anhalt-Cöthen in the preceding years.

There is no such certainty with regard to the ouvertures. There are no known versions of them in Bach’s handwriting, and no way to tell for certain when they were originally written or why. They are not thought to have been written or compiled as a coherent set. While the Third and Fourth Ouvertures, with their brilliant trumpet parts, could be of a piece, they are drastically different from the delicate B-minor Ouverture for flute and strings or the C-major Ouverture. Variety is no proof of heterogeneous origin, of course: there could hardly be six more varied works than the “Brandenburg” Concertos, but Bach thought they made a good set.

The ouvertures were long thought to have been written during Bach’s years as Kapellmeister at the court of Duke Leopold of Anhalt-Cöthen (1717-1723), the only time in his 50-year career as a professional musician that his job did not involve supplying music for Lutheran church services. The young Duke was a Calvinist, so elaborate church music was out of the question, but he was an avid music-lover and capable musician who assembled a first-rate instrumental ensemble in which he played violin himself. In 1723 Bach left Cöthen to became the Cantor of the St. Thomasschule in Leipzig, a job that combined directing music in three churches, being principal of the choir school, and teaching music and Latin. It did not, on its face, involve writing purely instrumental music.

But beginning in 1729, Bach directed the Leipzig Collegium Musicum, which gave concerts in Zimmerman’s Coffee House on Friday nights (there was no such thing as a public concert hall in 1729). There is evidence that some of his ouvertures would have been played in those concerts. The earliest known source of the Second Ouverture, for flute and strings in B minor, dates from 1739, but there is a good deal of opinion that the version we know now may not have been the original.

The earliest source we know of the C-major Ouverture was a set of parts copied in Leipzig around 1724, when he was newly appointed Cantor in Leipzig and was not involved with the Collegium. Does this mean he was composing orchestral music in Leipzig for other purposes, or that he was copying parts for a work he had composed in Cöthen? In either case, we don’t know why the work would have been performed in Leipzig at that time. We also cannot be sure of the instrumentation of the C-major Ouverture. It has no extant cello or contrabass part. This may or may not mean that Bach didn’t write such parts. The question is complicated because, like the other three ouvertures, the C-major Ouverture exists only in parts.

(Ensemble music can be written in a “score,” in which all the parts are set out vertically aligned on the page, or in “parts,” each of which has the music for only one instrument. A score shows at a glance what instruments are used and what they are all playing in a given measure, but since it can fit only part of most orchestral pieces on a page, it is useless for, say, the oboist, who needs both hands to play and cannot be constantly turning pages. The absence of a cello part in a score means no cello part was composed. The absence of a cello part in a collection of parts may mean no cello part was composed, but it could also mean the cellist took it home to practice and didn’t return it, or the part was returned and later destroyed by fire or mold or rats.)

There are theories that the Third and Fourth Ouvertures were originally composed without the three trumpets that so distinguish the versions we know. The overture of the Fourth Ouverture is known to have existed in three versions: a version without trumpets and tympani (now lost), a version with trumpets, tympani, and chorus that opens his 1725 Christmas Day cantata, “Unser Mund sei voll Lachens,” BWV 110, and the one commonly known now, with trumpets and tympani. The cantata chorus is an example of how dance gesture could find its way into the church: Bach took a French overture in which the fugal section was essentially a gigue, and superimposed a liturgical text.

The 24 pieces in Bach’s four ouvertures include the four French overtures and 20 other pieces bearing 12 different descriptive titles. The dance movements include types commonly found in suites, as well as less common ones like the whirling Forlane in the First Ouverture.

The only pieces that are not established dance forms are the Air in the Third Ouverture, the virtuosic Badinerie (the title can be translated as “playfulness,” or perhaps more usefully, “fooling around”) that ends the Second Ouverture, and the Réjouissance (literally “rejoicing”) that ends the Fourth Ouverture. The Air is the hit single of the set, having penetrated the ears of people who would not normally listen to Bach, and making so many appearances in popular music and movies that it should have hired an agent. It is still known in some circles as the “Air on the G String” because an arrangement by the violinist August Wilhelmj (1845-1908), with the melody transposed down more than an octave so that it could be played entirely on a violin’s lowest string, became fabulously popular in the days when it was rare that anyone would attempt to play Bach’s orchestral music in anything like its original form.

Indeed, in 1910 the publisher Schirmer came out with an edition of five movements taken from the Second and Third Ouvertures, edited by Gustav Mahler, no less, who fleshed out the continuo part with a written part for both piano and organ. (Bach followed universal practice in the 17th and 18th centuries in writing a bass line from which the continuo player could improvise chordal accompaniment, guided by number symbols indicating the basic harmony.) Mahler included an instruction in the flute part of the delicate Second Ouverture that the flute should be reinforced in loud passages by additional flutes and, if needed, a clarinet, which gives some idea of how large a body of strings Mahler was assuming.

For the ouvertures with trumpets, a substantial string section would have been essential in the days (through the 1960s, and much later in most of the world) before anyone played Bach on period valveless trumpets, and “Baroque trumpet” would have been understood to mean small valved trumpets that were much louder, and more shrill, than anything Bach could have imagined. The instruments Bach knew make balance with smaller forces far easier.

- Howard Posner