# Ordering logic in both versions of Die Kunst der Fuge

Dr Bradley Lehman, spring 1992; reformatted 2003 & 2004; ©2004

 The following two charts show my guesses at Bach's purposes for the ordering of the movements: an attempt to describe the patterns within the structure. What might have been his goals, and his change of plans, during the creation of this monumental piece over almost eight years (c1742 to the end of his life)? Both versions have their own logical flow. In my opinion, the most interesting feature here is that the music works so well both ways, and in other possible sequences. These charts are a practical "road map" that I distribute to the audience in my concert performances, usually playing a sequence similar to the second one below. Numbering conventions: Cp 1-11 = numbered as in the print; 10a = extraneous version of 10, beginning at second exposition; 12a/b = 4-voiced mirror fugues; 13a/b = 3-voiced mirror fugues; 14 = augmentation canon; 15 = canon at octave; 16 = canon at 12th; 17 = canon at 10th; 18a/b = two-harpsichord arrangments of 13a/b; 19 = fugue on three subjects/"unfinished" quadruple fugue; Chorale = "Wenn wir in höchsten Nöten sein"

### Autograph - increasing complexity of counterpoint; rhythmic animation of subject

 Simple fugues 1 Recta - simple, almost "textbook" fugue on KdF subject to be developed much further later; embarking on a journey 3 Inversa, with chromatic countersubject 2 Recta, with rhythmic alteration (sharpening); ends on dominant stretto, various intervals 5 octave R & I combined 9 12th double fugue, with new subject R 10 10th double fugue, with new subject R & I stretto, with mensuration 6 diminution; R & I (4 forms of subject); "French style" 7 dimin & aug; R & I (6 forms of subject) combination fugues 15 canon at lower octave; perpetual; d Inv - a Inv - a Rec - d Rec – (repeat) - d Inv in coda; first occurrence of triple meter (compound) 8 3 vox Inversus; two new chromatic subjects 11 4 vox three subjects of 11 inverted; new CS to principal subject of 8 (yet more chromaticism) 14 early version of augmentation canon, in invertible counterpoint and with inversion; perpetual; KdF subject is Recta mirror fugues 12a 4 vox Rectus - simple mirroring; first occurrence of simple triple meter 12b 4 vox Inversus 13b 3 vox first occ of compound duple meter; R & I versions of subject combined 13a 3 vox Rectus reworking 14 extensive reworking of augmentation canon; extended from first version using same incipit; longer; differs in a few details from the later print version appendices 14 printer's copy of augmentation canon, in 3rd (latest) version; no longer perpetual; note values doubled from earlier versions 18b/a two-harpsichord arrangements of 13b/a 19 triple or "unfinished" quadruple fugue, continued 7 bars further than in later print; in keyboard score

### Print - increasing complexity; metamorphosis of subject; cumulative addition of new subjects

 The ordering given here is that proposed by Gregory Butler, from his examination of the print's pagination and erasures; presumably Bach's official and final intentions.