Wind Choir Invertible Canon (Or, "Clarinets Suck")

I wrote a piece for wind choir yesterday. Seriously: I wrote the whole thing in an afternoon and had no idea that was what I was going to do when I woke up. I had been tossing around this idea for a highly fractalized fugue subject for wind quartet, when I realized that it would dovetail into and out of the two fractal elements I used previously in the Five-Voice Perpetual Canon for string choir.

When I wrote the string choir piece I realized it could be inverted, but the conclusion just wasn't convincing with the two themes present in that canon, but this third dovetailing theme provided both a strong beginning and a powerful ending. Now, if I just move the first two fractal directional units down an octave (So the first theme does not move down an octave over its course) this too would be a five-voice perpetual canon, but I wanted that axial modulation so the Rectus of the canon would begin way up in the stratosphere, and the Inversus would begin at the bottom of the sea.

Here's why clarinets suck: I wanted this piece to be in F minor because that would fit into the overall scheme of Fuga da Camera, but nooooo; the clarinet in A only goes down to a C-sharp and not a C-natural. What's up with that, anyway? Even double basses go down to C-natural now with a fifth string or an extension, and the clarinet is stuck at C-sharp?! Arg! So, we're in F-sharp minor, which is like - I don't know - the weirdest possible key.


Check it out:

1) Three-Part Invention for String Trio in D Minor

2) Fugue on a Tone-Row for Wind Trio in D Minor

3) Fugue in F Minor for String Quartet

4) Crab Canon in A Minor for Wind Quartet

5) Five-Voice Perpetual Canon in A minor for String Choir

6) Five-Voice Invertible Canon in F-sharp Minor for Wind Choir

7) Fugato in D Minor for Chamber Orchestra

See what I mean? Jeez.


Anyway...

In order to maintain perfect intervallic reciprocity in an inversion from tonic minor to the fifth degree, the third degree of the key must be changed to the major gender in the inversion. For example, for sol, fa, me, re, do to maintain 1, 1, 1/2, 1 in the inversion, it must become do, re, mi, fa, sol (This is actually the rational melodic explaination for the minor mode by the way: You are just inverting the third within the fifth). Maintaining this perfect reciprocity is important if you make use of unequal parallels (Perfect fifths and fourths moving into and out of diminished or augmented versions of those intervals): If you don't maintain this perfection, parallel perfect intervals are bound to crop up.

This is one feature that gives the inverted form a "strange" sound: The minor key lower chromatic tetrachords combined with a major tonic triad. The other path to "embracing the strange" with these inverted forms is that harmony is only calculated in one direction: From the ground up. In other words, the overtone series does not invert: There are no "undertones" (Despite the claims of several musical quacks over the years: If they existed, they could be measured. They can't be measured... because they don't exist). So, what you get for harmonic structures in the inversion is often quite surprising: Weird, but wonderful. Since the contrapuntal logic is maintained, the progressions sound unorthodox, yet logically so.

Here is page one:



As can be seen, the first immitative structure is four measures in length, and it makes use of all three of the semitone directional units available in the minor mode. The seventh degree - fa - is saved for the tail figure. This first figure dovetails into an eight measure "subject" with a 2/2 base feel.



This eight measure theme is the second one from the previous perpetual canon, so this middle area is exactly like that canon in reverse (As far as the order of the themes: It is not a retrograde). At measure thirteen the third dovetailing "subject" comes in, which is the present one in diminution: In order to add the third theme to these two pre-existing ones, I had to basically compose it backwards.



Then, the original theme returns and dovetails out of the present one. The second slower theme begins again, but is interrupted by the final cadence of this section, which is upside-down from the way it "ought" to be because I want to save the more powerful conclusion for the end (The "real" end).



Here the Inversus begins. In measure thirty is that blasted C-sharp that limited the downward progression of the piece: Measure twenty-nine is so much more effective a semitone lower. It rattles the fillings out of your teeth there.



There really isn't that much to discuss now that the pattern is laid out.



And the conclusion...

An MP3 and a PDF of this piece are now at the top of my .Mac Downloads page for those interested.


What I'm doing with these fractal-theme based dovetailing canons is obvious: