Dr Bradley Lehman,
spring 1992; reformatted 2003 & 2004; ©2004
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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" |
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Simple
fugues |
1 |
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Recta -
simple, almost "textbook" fugue on KdF subject to be developed much
further later; embarking on a journey |
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3 |
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Inversa,
with chromatic countersubject |
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2 |
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Recta,
with rhythmic alteration (sharpening); ends on dominant |
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stretto,
various intervals |
5 |
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octave |
R &
I combined |
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9 |
12th |
double
fugue, with new subject |
R |
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10 |
10th |
double
fugue, with new subject |
R &
I |
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stretto,
with mensuration |
6 |
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diminution;
R & I (4 forms of subject); "French style" |
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7 |
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dimin
& aug; R & I (6 forms of subject) |
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combination
fugues |
15 |
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canon at
lower octave; perpetual; d Inv - a Inv - a Rec - d Rec – (repeat) - d Inv in
coda; first occurrence of triple meter (compound) |
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8 |
3 vox |
Inversus;
two new chromatic subjects |
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11 |
4 vox |
three
subjects of 11 inverted; new CS to principal subject of 8 (yet more
chromaticism) |
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14 |
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early
version of augmentation canon, in invertible counterpoint and with inversion;
perpetual; KdF subject is Recta |
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mirror
fugues |
12a |
4 vox |
Rectus -
simple mirroring; first occurrence of simple triple meter |
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12b |
4 vox |
Inversus |
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13b |
3 vox |
first
occ of compound duple meter; R & I versions of subject combined |
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13a |
3 vox |
Rectus |
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reworking |
14 |
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extensive
reworking of augmentation canon; extended from first version using same
incipit; longer; differs in a few details from the later print version |
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appendices |
14 |
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printer's
copy of augmentation canon, in 3rd (latest) version; no longer perpetual;
note values doubled from earlier versions |
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18b/a |
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two-harpsichord
arrangements of 13b/a |
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19 |
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triple
or "unfinished" quadruple fugue, continued 7 bars further than in
later print; in keyboard score |
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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. |
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Simple
fugues |
1 |
Recta - essentially stile antico except for the use of
simultaneous rests at the cadential 6/4: implying homophony or possibly a
cadenza?; addition of a new coda |
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2 |
Recta -
rhythmic alteration of end of subject; subject syncopated in last tenor
statement; frequent non-thematic entrances, breaking the strictness of fugal
technique; ending revised to conclude on tonic d |
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3 |
Inversa
- chromatic countersubject; subject twice syncopated, a continuation of that
metamorphosis hinted at near end of #2 |
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4 |
Inversa
- new piece; new cuckoo motif, demonstration of how a fugue in a "newer
style" can be enriched by long episodes of nonthematic music; subject
again syncopated; first appearance of stretto, leading to the next set of
fugues |
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stretto,
and passing notes in subject |
5 |
R &
I combined - 2 versions of subject |
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6 |
R &
I, and diminution - 4 versions of subject |
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7 |
R &
I, dimin, aug - 6 versions of subject |
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new
subjects in combination (increasing difficulty) |
8 |
3v,
triple fugue, counterpoint at octave only |
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9 |
4v,
double fugue, counterpoint at 12th |
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10 |
4v,
double fugue, counterpoint at 10th |
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11 |
4v,
triple fugue using inverted subjects of #8, and a new chromatic CS |
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mirror
fugues |
12b |
Inversus
(note the reversals from autograph order) |
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12a |
Rectus -
simple mirroring; now the first occurrence of any sort of triple metric
division |
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13a |
Rectus -
inside-out mirroring; first occurrence of compound meter (triple) |
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13b |
Inversus |
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quadruple
fugue, with invertible subjects |
19 |
triple
(quadruple?) counterpoint, combinatorial, very long; all three subjects can
work in inversion, as well as in combination with the KdF subject |
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canons,
increasing complexity |
15 |
canon at
octave - Inversa but with all permutations, as in manuscript version;
beginning display of variety of meters, here 3x3; perpetual |
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16 |
canon at
10th - Inversa; new piece; syncopated subject; meter 4x3; inverts at 10th |
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17 |
canon at
12th - Recta; new piece; mixture of duple and triple rhythmic figures; meter
2x6, 2x4; inverts at 12th; contains extra modulatory bar to preserve
perpetuality |
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14 |
augmentation
canon in inversion - Recta; revision of earlier piece; entirely invertible as
voices are exchanged midway; meter 4x2 (full circle back to the duple meter
with which KdF began) |
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practical
arrangements |
18a/ 18b |
Inversa,
Recta; demonstrating how these solo keyboard or theoretical pieces can be
adapted to practical performance as ensemble music: free adaptation of 13a/b
shows that addition of a free accompanimental voice or voices does not
destroy the integrity of "fugue"; original lines are not preserved
intact, as parts are shuffled among the four hands; fugal lines altered in
bars 14, 21, 49 to fit the free parts; various changes of accidentals to
avoid cross-relations; neither is complete mirror inversion sacrosanct, since
new material is independent of its counterpart |
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extraneous |
19 |
moved to follow canons because "incomplete"; 10a
inserted after 13b to fill up some of the pages left blank because a complete
#19 was not available (final page(s) lost?); canon 14 moved to fill remaining
space after 10a, thereby becoming coincidentally the first canon rather than
the last; compensatory chorale to rationalize the lack of a complete #19,
suggesting that the composer died before finishing it, and composed this
instead as his last testament |