Prologue: Bach presents a Musical Offering
The date is
May 7, 1747.
The place is the grounds of the ornate palace of Frederick the Great, King of Prussia.
Johann Sebastian Bach, the greatest musician of his time, now 62-years-old, has just arrived at the lodgings of his son, Carl Philip Emanuel Bach, the court’s musical director.
Inside the palace, an officer, approaching a large room where the King is to be found, hears the high-pitched strains of a melodious flute, and the sounds of sonorous stringed instruments tuning up. He carries the list of newcomers to the court. It is Frederick, himself, who is warming up his flute, for the private concert to be held that night, as every other night.
Flute in hand,
looks down the list, and turns to the assembled musicians, exclaiming, with a kind of agitation in his voice, “Gentlemen, old Bach is come.” He lays his flute back in its case, and gives the order that there will be no regular concert tonight. Frederick
Even before Bach has time to change his dusty traveling clothes, he is summoned to appear before the King. Frederick, after listening to Bach’s apology for his appearance, says, “Alte Bach (Old Bach), I have looked forward to meeting you for a long time. Come, let me show you my collection of new Silbermann fortepianos, which you can try out.”
The King guides Bach to the first fortepiano, with all the musicians following. Bach, known throughout the land for his great improvisational abilities, sits down, and begins to play. The musicians have never before heard someone play unpremeditated compositions like this. They all proceed, from room to room, and at each fortepiano, Bach invents yet another beautiful polyphonic (many-voiced) piece, even more inspired than usual by the new possibilities to create dynamical shading.
After awhile, Bach asks the King, “Would you be so kind as to give me a subject upon which I can play a fugue?” The King, with a twinkle in his eye, goes to the keyboard, and plays:
Listen to the King's Royal Theme
The King’s theme begins with a C minor triad, (“c - e flat – g”), is raised to the next half-note above that, “a flat,” and then takes a dramatic downward leap of a seventh from the "a flat" down to “B,” not included in C minor, but found in C major. This creates musical tension between two pairs of half-step intervals: from the ”B” back to the beginning “C,” and the “g - a flat” interval.
Picking up on these half-steps from the first part, the second part of the Royal theme is a revolutionary ambiguous step-wise descent from the top of the triad, “g” one octave down to "G," comprised of a chromatic descent from "g" to "B", and then, down by major scale steps to “G.” The concluding section hops up through "c" to "f," and ends with a stepwise journey down the C-minor scale from f, through "e flat," to end where it began on "c." 
Bach accepts the challenge. He brings in the "Royal theme" three times, in succession, and through counterpoint, the art of composing music with several voices (literally: point against point –writing another musical voice, or a series of notes or “points,” to a given voice, or series of “points”), which creates musical development by intertwining the voices in a beautifully provocative way, he explores the developmental possibilities of the King’s theme:
3-voiced Ricercar exposition (until the end of the entrance of the third voice):
Here is an MP3 file with a flute playing the 1st voice, and a piano playing the 2nd voice. Add the 3rd voice (singing voice or instrument) to hear the complete exposition:
Supply MP3 file of exposition with flute, piano
Link to pdf version of the notes for Bach's 3-voiced Ricercar
Listen here the the entire 3-voiced Ricercar, performed on the piano by Carlo Levi-Minzi from a recording by the Humanist Academy.
Find the Royal theme as it presented in three voices at the beginning of the piece.
Are they all the same?
If not, how do they differ?
Find the Royal theme’s appearance in the rest of the piece.
After you have thought about this, see: footnote [i].
The King, admiring the learned manner in which Bach develops his theme with three voices, asks to hear a fugue with six independent voices. Bach, fearing that he cannot, without preparation, invent such a complex fugue on the King’s subject, instead, chooses a subject of his own, and, to the astonishment of all, proceeds to execute it in the same magnificent and learned manner as before.
After returning home to
, Bach composes both a three-voiced and a six-voiced fugue on the King’s subject. He also writes ten canons, and a trio for flute, violin and keyboard instrument, on the same royal theme. Leipzig
Bach entitles the cycle Regis Jussu Cantio Et Reliqua Canonica Arte Resoluta, meaning "At the King's Command, the Song and the Remainder Resolved with Canonic Art." an acrostic spelling "ricercar," the old-fashioned precursor of the fugue, and also uses this title for the two fugues. (Albert Schweitzer, in his book on Bach, wrote, "The word [Ricercar] signifies a piece of music in which we have to "seek" something – namely a theme.")
Bach has the work engraved, and dedicates it to the royal inventor of the theme. The work has become known as the Musikalisches Opfer (The Musical Offering), after a phrase from Bach’s dedication to King Frederick. (See the following footnote for the text of Bach’s dedication. )
This masterpiece is rightly considered one of the milestones in the history of classical music.
To Part 2 -- The Concept of Transformation Principles in Music
 The following is this author’s dramatization of the account of Bach’s visit to King Frederick, related by Bach’s eldest son, William Friedemann, who accompanied his father, as told to Bach’s first biographer, Johann Nikolaus Forkel. The New Bach Reader, pp. 429-30.
 The Silbermann fortepianos were so-named because they were the first keyboard instruments constructed to play dynamical nuances from forte (loud) to piano (soft).
 The authorship of this ingenious theme has been debated. Was it really the King, or was it Bach, himself? It could actually be both – Look at the following theme by Bach from his Fantasy and Fugue in c from ??, and notice the similarities. Could the King have invented a variation of one of Bach's own themes with which to test the music master?
Music in the Baroque Era, by Manfred F. Bukofzer, W.W. Norton & Co.,
, 1947, pg 277. New York
 Thanks to Peter Billam’s homepage, which has several versions of elements of the Musical Offering: www.pjb.com.au
 In deepest humility I dedicate herewith to Your Majesty a musical offering, the noblest part of which derives from Your Majesty's own August Hand. With awesome pleasure I still remember the very special Royal Grace when, some time ago, during my visit in Potsdam, Your Majesty’s Self deigned to play to me a theme for a fugue upon the clavier, and at the same time charged me most graciously to carry it out in Your Majesty’s Most August Presence. To obey Your Majesty’s command was my most humble duty. I noticed very soon, however, that, for lack of necessary preparation, the execution of the task did not fare as well as such an excellent theme demanded. I resolved therefore and promptly pledged myself to work out this right Royal theme more fully and then make it known to the world. This resolve has now been carried out as well as possible, and it has none other that this irreproachable intent, to glorify, if only in a small point, the fame of a Monarch whose greatness and power, as in all the sciences of war and peace, so especially in music, everyone must admire and revere. I make bold to add this most humble request: may Your Majesty deign to dignify the present modest labor with a gracious acceptance, and continue to grant Your Majesty’s Most August Royal Grace to
Your Majesty’s most humble and obedient servant
Leipzig, July 7, 1747 The Author
Quoted from The New Bach Reader, p. 226-8
[i] The first voice begins on “c’.”
The second voice, the “answer,” appears in measure 10, and begins on “g.” This can be both considered as a fourth below “c’,” or an octave below the fifth above “c’” which is “g’.” In the most common type of fugues, the “answer” begins on the fifth above the first presentation of the theme (or, as in this case, the fifth above is transposed down by an octave).
Notice that the “answer” does not have exactly the same intervals as the first, for example, the interval between the second and third notes are decreased to one whole step, whereas, in the first voice, it was a major third (2 whole steps). Here, the interval between the 3rd and 4th is enlarged to become 1 ˝ steps. This slight shift enables the “answer” to be in the same key as the first voice, and is very common in fugues. Here you can get a sense of certain boundries in a "curved" musical space. In this example, if the theme were transposed up by exactly the same interval -- a fifth, the shape would, in fact, become distorted. What would the second voice be like, if it maintained the exact intervallic relationships as the first voice?
The third voice, beginning in measure 23, begins on “C,” two octaves below the first voice.