6. _Einige kanonische Verdäderungen,_ “Canonic Variations on the Christmas Hymn ‘Vom Himmel hoch da komm ich her,’ for an Organ with two manuals and pedal. Published at Nürnberg by Balthasar Schmidt.” The work contains five canonic variations of the utmost ingenuity.(241) 7. _Musikalisches Opfer_, or “A Musical Offering,” dedicated to Frederick II., King of Prussia. The theme received by Bach from the King(242) is treated first as a three-part Fugue under the acrostic title “Ricercare” (Regis iussu cantio et reliqua canonica arte resoluta). There follows a six-part “Ricercare” and Thematis regii elaborationes canonicae of various kinds.(243) The work includes a Trio for Flute, Violin, and Clavier upon the same subject.(244) 8. _Die Kunst der Fuge_, or “The Art of Fugue.” This work, unique of its kind, did not appear till about 1752, after Bach’s death, though the greater part of it had been engraved by his sons during his lifetime.(245) Marpurg,(246) the leading German musical critic of that day, contributed a preface to this edition which contains many just observations on the value and utility of such treatises.(247) But, being too good for the general public, the work found only a small circulation among those who discerned its merit and eagerly bought copies. The plates were never used again and eventually were sold(248) by Bach’s heirs at the price of old copper. Written by a man of Bach’s transcendent genius, and commended as a masterpiece by a critic so highly regarded as Marpurg, a work of this kind, if published in any other country than Germany, would have passed through at least ten editions by now, if only at the bidding of patriotism. But in Germany not a sufficient number of copies was sold to pay for the plates used in engraving the work! The work consists of fugal Variations planned on the most elaborate scale.(249) The composer’s intention was to show in what a variety of ways the same theme can be treated fugally. The Variations (here called “Contrapunctus”)(250) are complete Fugues upon the same theme. The last Fugue of all has three subjects, in the third of which the composer signs his name, B A C H.(251) Bach was prevented from finishing it by the disorder of his eyes, and as an operation brought no relief the movement was never completed. It is said that Bach intended to introduce four themes into it and to bring it to an impressive conclusion by inverting them all. All the Fugues in the work are equally smooth and melodious.