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Nearly three centuries after Bach sent six "Concertos with Several Instruments" to Christian Ludwig, Margraf of Brandenburg, the Concertos stand as a monument of instrumental music, and as a monumentally inept piece of self-promotion.

Bach's path first crossed the Margraf's in 1719, when Bach traveled to Berlin to buy a harpsichord for the Prince of Anhalt-Cöthen's court, where he was the music director. The Cöthen years were the only time in his 50-year professional career that Bach's job did not consist principally of producing music for Lutheran worship. Because the court religion was Calvinist, elaborate composed church music was not needed, or even permitted. Instead, Bach concentrated on writing music for the elite Cöthen orchestra.

In his mid-30s, he was already a legend among German musicians, and music-loving aristocrats were not likely to miss a chance to have him play his music for them. Nor would he have them miss the opportunity: in an era when there were no public concerts, a musician's fortune often depended on impressing the wealthy few who could employ musicians.

According to Bach's prefatory dedication of the Concertos, he had played for the Margraf, who "took some pleasure in the small talents which Heaven has given me for music and …deigned to honor me with the command to send your Highness some pieces of my own composition." Commoners always addressed nobility in that obsequious way. It would have been rude to do otherwise. But Bach waited two years before actually sending the Concertos, which were all works he had composed at Cöthen, reworked, revised, or recopied. The unexpected death of his wife in 1720 is one likely explanation for the delay. Satisfaction with his position at Cöthen is less likely, since Bach applied for another position in Hamburg in 1720. He might have doubted that his prospects could be advanced much by the Margraf, who was a man of great rank but little power. The Electorate of Brandenburg had for decades been part of the kingdom of Prussia, and the Margraf owed his title to being the Prussian king's younger brother.

What is clear is that the Margraf never acknowledged receiving the manuscript and never had the Concertos performed. The reason for this is equally clear: the Margraf's small musical establishment could not begin to cope with the Concertos' wide variety of instruments and extreme technical difficulty.

From a modern vantage point, it is not hard to see that the Concertos require top-flight players for the horn parts in the First Concerto, the violin in the Fourth, and the harpsichord in the Fifth. The trumpet part in the Second Concerto, written for the valveless Baroque trumpet, is still a major challenge for players on the valved piccolo trumpet (which makes for surer execution but creates balance problems since, unlike the Baroque trumpet, it is vastly louder than the other instruments in the ensemble).

What is less obvious to the modern concertgoer, accustomed to 100-piece orchestras supported by industrial wealth and cities with populations of millions, is that it would have been a major project for the Margraf's musicians just to cover all the parts, let alone play them well. Horns were new to the orchestra in 1721, and not available everywhere. Not every court had three oboes (for the First Concerto), or three cellos or violas (for the Third). The First Concerto calls for a piccolo violin tuned a minor third higher than a normal one. It was apparently not a common instrument, though its rarity would not have deterred Bach, an enthusiastic instrumental experimenter who elsewhere wrote for such unusual instruments as the viola pomposa (a five-string combination violin and viola), oboe da caccia, slide trumpet, violoncello piccolo, and tenor oboe.

Yet, paradoxically, the Brandenburgs present instrumentation problems that a modern symphony orchestra can cope with only by, as it were, faking it. Bach specified some instruments that modern symphonic players don't play, or which would be ineffective with modern instruments in a large concert hall. Piccolo violins are, if anything, harder to come by now than in 1721, and while period-instrument groups will use them, the mainstream symphonic violinist tends to play the First Concerto on a normal-sized instrument. The Sixth Concerto calls for two violas and two violas da gamba, a bowed six-string instrument tuned in fourths with frets on the neck (vestiges of it survive in many modern double basses). Symphony orchestras use cellos in place of the gambas, which in any case would have a tough time balancing modern violas, which are louder than their Baroque counterparts. The Second Concerto calls for a recorder, an instrument hopelessly overmatched by the modern trumpet, so the modern flute is often substituted.

Sometimes we can't be sure what instruments Bach intended. The bottom lines of most Baroque pieces are usually designated "bass" or "continuo" and are meant to be played by whatever instruments are available to play the bass and improvise chords. In the six Brandenburg Concertos, Bach indicated five different configurations on the bottom line, but it is not clear what distinctions he meant to make, and there have been numerous interpretations. Even more mysterious are the Flauti d'Echo ("echo flutes") that solo along with the violin in the Fourth Concerto. "Echo flute" appears nowhere else in German Baroque music. Did Bach mean some specific sort of instrument, or that the flutes were used in an echoing sort of way, or something else altogether?

"Concerto" was historically a loose term: for much of the 17th century, it was applied to sacred vocal music. In Bach's day, it could refer to works for any number of instruments, including one. For larger-scale concertos (say, more than five players), there were two prominent models: the multi-movement Corellian concerto grosso, which was essentially a trio sonata for two treble instruments and bass, with some fill-in parts, and the Vivaldian three-movement concerto, with more outgoing, soloistic writing. At the same time, there was a burgeoning German concerto style, with larger groups of instruments involved in a continual give and take.

Bach would have known the German concertos of Heinichen and Zelenka, and had so immersed himself in Vivaldi that he arranged ten Vivaldi concertos for keyboards, and showed himself quite capable of writing in Vivaldi's style. But the Brandenburgs don't really fit any mold. The First is the most full-throated and German in character, and also the only one that doesn't follow the three-movement Vivaldian fast-slow-fast model. Much of the Fifth feels like a Corellian concerto grosso, with the violin and flute taking the top voices of the trio and the harpsichord adding involved and virtuosic ornamentation.

In all the Concertos except the Fourth, the ensemble is reduced in the slow movement, a favorite Vivaldi device: the horns drop out in the First Concerto, the trumpet and ripieno strings in the Second, the ripieno strings in the Fifth, and the gamba parts in the Sixth. In the Third Concerto, the entire slow movement drops out: the movement consists of two chords constituting what Bach would have called a "Phrygian cadence" on B major, leading from the E-minor slow movement to the G-major fast movement (the Fourth Concerto uses the same cadence, but has a slow movement before it). The two-chord interlude has made many performers uneasy over the years, wondering if Bach intended the players to insert something more than the usual ornamentation expected at cadences. It has led to a variety of approaches that just accentuates the astonishing variety already present in Bach's misguided gift to an otherwise forgotten aristocrat.

- Lawyer and lutenist Howard Posner also annotates programs for the Salzburg Festival.