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Experiment 0

To invert ゛Fuga a 3 Soggetti゛（unfinished fugue）

This experiment pioneers at the installation of the experiment room and
leads to the basis that the unfinished fugue could not be a mirror fugue if it
were completed.
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Because of its considerable length and difficulties to determine proper
halftone's treatment, we, therefore, only touch on the part of the
exposition and development of the second theme (bar114 - bar193), though
the best is to invert the whole piece upside down. (This troublesome
process itself reveals that the piece is unlikely to be a mirror fugue.) Since
the second theme takes a real response, the response after inversion
becomes in subdominant key, which is quite rare in the art of fugue,
mentioned in Cp.10 as well.



BGM, now you are listening is the outcome.
Quite an effort was necessary to make you bear listening.
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As mentioned in Cp.12, a mirror fugue requires various compositional
restrictions. Particularly, inversion with taking tonic in the highest voice
after dominant and having tonic duplicated bring about ambiguous key
because they are reflected to dominant.



The worst example is bar 193. Inversion with three tonics in subdominant
key causes empty chord, which is beyond any tonal solution. Unclear
tonality like above is found here and there.
I fixed them up as much as possible in BGM...
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I realized then the use of chromatic scale is not desirable for a mirror
fugue and worked out a compromise over many parts.



The music above is one of the examples. To be a precise mirror fugue, blue
notes in the bottom column have to be lowered halftone.
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As the example shows, the unfinished fugue cannot be a mirror fugue.
The statement from Bach's short biography saying゛final fugue with all
voices inverted later ゛should be interpreted from a different angles.

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