been written in Cöthen; it was certainly completed before 1738. The well-known C-minor fantasia was probably composed in 1738; of the fugue which was to follow it, nothing but a fragment remains. In 1747 appeared the "Musikalische Opfer" and in 1749 "Die Kunst der Fugue," these two works forming the conclusion of the whole series of compositions. The former is a collection of various fugues and canons, together with a four-movement sonata for violin, flute and clavier. Ingenious and important as the single pieces are, they cannot be said to form a symmetrical whole, while with regard to "The Art of Fugue" the contrary is true. In the original engraved edition of this work, which Bach was able to revise only in part, much extraneous matter had crept in. After this was excluded, there remained fifteen fugues and four canons, all composed upon the same theme. The fugues belong together and seem to be arranged in four groups in order to facilitate the hearer's comprehension of them; strictly speaking, however, they form all together a single gigantic fugue in fifteen divisions. Because Bach wished to show in this work the utmost that could be accomplished with a single theme, it should not be assumed that in writing it, his sole purpose was to instruct. The same may also be said of the "Orgelbüchlein," the "Inventionen und Sinfonien" and the "Wohltemperirte Clavier," which had also been composed by him for the benefit of rising artists. Yet the practical purpose had the effect of giving wings to his imagination; he strove to produce not only the most artistic work of which he was capable, but also the most beautiful, and in this he was successful. In fact the "Art of Fugue" is one of the most sublime instrumental works of the composer. But its deep and solemn earnestness, only rising to passionate emotion in the central fugues, in order to sink back into itself again, as well as the difficulty of understanding so great a number of complicated pieces, all bearing a certain relation to each other, has thus far interfered with the proper appreciation of this last great monument erected to himself by the master. In a still later fugue, Bach wished to make use of his own name, having perceived that its four letters, regarded as notes, formed a characteristic melody. The intention was not carried out, but several fugues upon the family name are still extant, one of which at least is well known, has been frequently printed, and may very easily have proceeded from the hand of Sebastian Bach.