I haven’t posted to this blog in ages, in part because I’ve been doing more music than maps (though not a lot of either). Finally decided despite the intended focus of this blog I might as well use it for publishing whatever it is I’ve been fooling around with. So, …let’s shift to music:
I finally finished ruining Bach’s double fugue Contrapunctus IX, from the Art of Fugue. Soundfile here:
Some notes about the ruining and the piece itself:
To ruin Bach’s fugue Contrapuctus IX, I first butchered the rhythm by forcing the meter to change nearly every bar, mostly between about 5/8 and 15/8 time. Second, well, Bach didn’t indicate what instrument(s) were to play the four voices, but muscicologists agree unanimously that he intended synthesizers with lots of hard syncing, so I went with that. Oh and a drum machine, as was standard for all music during the 1740s.
Contrapunctus IX is a double fugue, meaning two melodies serve as fugue “subjects” or themes. The first theme features an offbeat octave jump up followed by a fast cascade downward to a trill, then a little more fast cascading down. The four voices enter one by one, playing this theme, then continuing in counterpoint harmony with the other voices. In standard fugue form the first entrance is in the tonic key of D (mostly minor), the second in the dominant key of A (mixed minor and major). The third entry is again on the tonic and the fourth on the dominant.
Then the double fugue proper begins. The second fugue theme is the Art of Fugue’s main theme—four long notes outlining a minor chord followed by a little cadence figure (notation here). After the introduction the two themes are always sounded at the same time, on two of the four voices. The simultaneous themes enter a number of times, moving from voice to voice in a patterned way. The key of the themes change with each entry (er, “key” isn’t the right word—they are transposed in pitch to various degrees, so not “key of D” so much as “starting and centered on D”). Sometimes both themes are in the same “key”, sometimes they are a 12th apart (an octave and a fifth).
After the initial four statements of the first theme there are seven double fugue theme statements. These seven statements occur in pairs, plus a final ending statement. Each paired statement is first in “D (minor)”, the tonic, then another key. The progression runs like this: 1st pair: D minor (tonic), voices enter on D; then F (relative major), voices enter on F and C. 2nd pair: D minor (tonic), voices enter on D; then A minor (“dominant”, but minor), voices enter on A and E (E major chords acting as the dominant of the dominant). 3rd pair: D minor (tonic), voices enter on D and A; then G minor (subdominant), voices enter on G and D. Finally, the double theme is stated in D minor, both voices starting on D, ending the piece.
Make sense? There will be a listening test tomorrow.