Pitch/Time Swaps

as applied to the Fugue subjects of

J.S. Bach's Das Wohltemperierte Klavier

Op. 39

scored for solo piano

[5-15 min.]

GENERATION
Encoded as an X/Y dot graph, rotated 90 degrees, then read in that position left-to-right,
musical scoring is seen with its essential parameters exchanged, pitch indications having
become instead relative attack times and vice versa. With the rotation anticlockwise (as
in these examples), pitchwise top/bottom translate to timewise first/last, etc.

I have applied this procedure to the Fugue subjects of J.S. Bach's Das Wohltemperierte
Klavier, trusting that juxtaposition of such originals (linear only) and their rotations (mainly
chordal) may enhance its promise as a compositional option.

As used here, the rotation addresses its source's sounding notes only (not also rests) and
without subsequent reportioning of the results (as with many integral‐serialist algorithms).
For a representative graph see Appendix A.

RE "X/Y‐>Y/X" SECTIONS:
NOTATION
– Notehead colors: green, the original's recurrent pitches; red, the rotation's corresponding
   simultaneities; grey, exceptions (applying in both senses).
– Accidentals (default '#' in their generating graph) are respelled in their score as appears
   harmonically and voice‐leading‐wise most plausible.
– Meter signatures and articulation markings are chosen post‐process as best to convey
   emergent patterns.

PERFORMANCE
– Accidentals apply once only, c/o LilyPond's style "forget".
– Tied anticipations, unless slashed, are to occur on‐beat.
– Legato connection is intended only within slurs, not also from their final note.
– Damper pedal use is expected for realizing slurs where necessary, or for enhancing
   immediate resonance, but not for connecting non‐slurred notes.
– I suggest programming as a selection of perhaps six of these pages with their order,
   tempi, dynamics and hand distributions at player's discretion.

MISCELLANY
– WTC I:19 – I have extended this quoted subject a full bar beyond its answer's entry.
– WTC II:10 is the only subject rotated in separate sections; its length otherwise forces
   unworkably overstacked chords.
– WTC I:24 – Source pitches recurring only in embellishment are not counted for rotation.
– Rotating fugue subjects alone presents only recurrence‐>simultaneity. For an example
   including also the reverse, see Appendix B.

Access: score.