In the Spring of 1747, Bach traveled to Berlin with his son Friedemann to visit Philipp Emanuel who was engaged as chamber harpsichordist at the court of Frederick ll. The “Berlinische Nachrichten“ of May 11,1747 carried a report of his visit. “From Potsdam we learn that on the Sunday just past (May 7) the famous Capellmeister from Leipzig. Mr. Bach, arrived in the city for the purpose of enjoying the pleasure of hearing the excellent Royal Music here. ln the evening, shortly before the time that the chamber music customarily commences in the King's apartements, it was reported to His Majesty that Capellmeister Bach had arrived in Potsdam and that he has waiting in the ante-chamber in the hope of receiving His Majesty’s permission to attend the performance of the music.
His Majesty immediately ordered his admission and, upon his entry,went to the so-called "Forte and Piano" (the newly invented Hammerklavier) and without any preparation personally condescended to play Capellmeister Bach a theme that the latter should improvise into a fugue. This was accomplished by the aforesaid Capellmeister Bach so successfully that not only was His Majesty inclined to indicate his pleasure, but all other persons present were given to great astonishment. Mr. Bach found the theme so exceedingly lovely that he wanted to write it down on paper as a properfugue and have it engraved on copper. There is also another account of this memorable visit, namely, the dedication with which Bach prefaced the "Musical Offering": "Most respectfully I do hereby dedicate a ’Musical Offering’ to Your Majesty, from whose hand the noblest part personally stems. lt is with reverential pleasure that l still recall the very exceptional Royal kindness when, upon my presence in Potsdam some time ago, Your Majesty personally condescended to play me a theme for a fugue on the piano and at the same time most graciously enjoined upon me that it be improvised immediately in the presence of Your High Person. To obey Your Majesty's command was my most respectful duty. I soon noticed, however, that due to the lack of the necessary preparation the improvisation did not want to succeed as befitted such an excellent theme. Thereupon I resolved, and undertook forthwith to work out this very Royal theme more perfectly and then to make it known to the world. Within my powers, this resolution has now been realized..."
Completely sold to the modern musical style of Graun and Hasse, the young king of Prussia wanted to hear the legendary grandmaster of improvisation and counterpoint. At the same time he wanted to lake a look into the musical past by having the most famous master of the old - by that time already 'antiquated' - style display his prowesses. It was totally clear to Bach that he was hardly any longer respected there as a fully valid musician since even his sons also composed exclusively in the modern style.
Bach politely praised the theme altough it was entirely unsuited for use as a fugue theme. lt is probable that the musically versed king deliberately posed such a difficult theme to see how Bach would get around it.
The composer’s answer was indeed just as ingenious and clever: He had received an almost unsolvable task and responded with an almost insurmountable task for the flute-playing king. The Trio Sonata for Flute, Violin and Continuo was almost impossible to play on the flute of that time. Frederick cannot possibly have played the sonata, but perhaps his flute-teacher Quantz did. On July 7, 1747, in the name of his father, Bach’s son Carl Philipp Emanuel (then court harpsichordist of Frederick the Great) presented the king an engraved copy of the "Musical Offering." Bach had dedicated the work to His Royal Majesty "most respectfully" after his visit at Potsdam had inspired him to Write it . The thema regium, the improvisation of which had at the time not wanted to “succeed”, he had "worked out more perfectly" and wanted then to "make it known to the world" by having it printed.
Although to a great extent Bach's scoring can be determined from his markings and musical demands, distorting revisions and attempts at instrumentation especially of the two ricercare, have often been made.
The work is opened by a three-part ricereare (an old term designating a movement in fugue style) for harpsichord. This fugue of great dimensions is followed by a series of canons that are miniature gems of counterpoint. There are very few indications of the scoring for this part, Still, since some instruments are definite the transverse flute in the Trio in the Canon perpetuus, the two violins in Canon a 2, and the Cello as bass instrument in the Trio and the Canon perpetuus, the division of parts becomes almost self-evident. A viola and a tenor viola need to be added to but a few of the canons. Some of the voices, by way of their range, show that they are flute parts.
Flute and bass play the first canon in double octaves while the violin plays the thema regium as cantus firmus. - The next five canons are as different in construction and tonal structure as can be imagined: In the first canon (for two voices) the same part is simultaneously played in its normal forward movement and cancrizans, in crab fashion. The second canon is for two violins playing at the unison - the answering voice enters one measure after the first - above a harpsichord accompaniment of the theme. In the third canon the top voice plays the subject while the second and third play per motum contrarium, hence in contrary motion, answering a half-measure later. Above the fourth canon per augmentationem, contrario motu (by augmentation and contrary movement) Bach wrote in Latin “Like the note values, may the king’s happiness also increase.” This complicated canon is executed by the first and third voices; the lower voice part must be repeated so that the inversion in the upper voice can answer by playing the entire piece in notes of doubled length. The last canon of this group is taken per tonos (through various keys); it, too, has a symbolical meaning: “Like the ascending modulation, may the king's glory also rise.” The subject in the upper voice is varied almost to the point that it cannot be recognized. The canon at the fifth, with subject and answer separated by one measure in their commencement, is repeated six times, each time a whole tone highter.
The Canonic Fugue is a canon of strict and large dimensions for the two upper voices at the fifth over an independent bass. - Next comes the real heart of the work, the six-part Ricercare. With this piece Bach wanted to comply with the king's wish for a six-part fugue for harpsichord. The six voices never leave the range of the harpsichordist's two hands. ln the dedicatory printing the notes appear in six different lines (the cause of many misunderstandings); there is also an autograph scored in two lines.
Next follows a puzzle canon inscribed “He who seeks will find,” in which one voice is given (a variation of the theme) and the second voice must be found from it. The solution is the inversion that enters two and a half measures later and a seventh lower. - ln the following four-part canon at unison, with one voice in the base range, each  voice begins with the theme.
ln the great Trio Sonata the theme is cited only in fragmentary hints and harmonies until it finally returns as main theme in the last movement.This trio is written in the somewhat modern gallant style, perhaps in deference to the king’s tastes, The concluding canon is a very special gem. Flute and violin play in inversion over a free figured-bass.