LDV200

I thought up this sequence after examining the twomirror fugues and realising that Bach had obviously conceived counterpoint XIII/1 from the subject transformed inversus, and not from the rectus, which then appears mirrored in the following counterpoint XIII/2. Having thus observed the existence of a central axis of symmetry established around the first and last entries of the four contrapuntal pieces composing this group, I managed to reproduce the same system in the other sets, whilst following the criteria mentioned above. The diagram accompanying this text clearly shows the result obtained by means of this technique: astonishingly, we find that each group of fugues forms a perfect mirror. This approach collates the outer entries of each contrapuntal section with the overall structure of the group containing them, thus transposing the idea of symmetrical reflection to the larger scale of the work as a whole. Although it does not provide a definitive solution to the problemof sequence in Die Kunst der Fuge , this option nevertheless presents a new slant, within a context of speculation that will, in any case, go on for ever. André Isoir (March 1999) ANDRÉ ISOIR 29