Wednesday, October 26, 2016

Fugal Science: Vol. 2, No. 3 - Four-Part Fugue for String Choir

EDIT: This is part 7 of 8. Here are the links to the entire series:

Index of Fugal Science, Volumes 1 and 2

Here is today's audio file:

Four-Part Fugue for String Choir

As usual, it's an AIFF file of the sound fonts I compose with, so you'll need to use QuickTime.

Aside from being down in the key of f-sharp minor now, the exposition is as it was in three voices.

After the third entry, however, we need to use the episode to set up the final one. That's because it's impossible to do a direct modulation to the dominant after the three-part subject statement. This volume was on ice as just the concluding perpetual canon for years - since 2006 - because I couldn't figure out what to do here. So, this is actually the origin point of the episode, though I completed the five-voice fugue first, back in 2013.

With four entries and real answers, the exposition leaves us on the dominant level. This means the episode is on the dominant, and has to modulate back to the tonic for the interlude (After two episodes, the interlude is required). So, instead of four measures, that makes this one five. All you have to do to get the modulation is to make the dominant resolution to a major chord, and then introduce the minor seventh to make it the dominant seventh of the tonic. I was able to make the dominant a major add-9 chord, and then I used the thematic triplet to make that a minor ninth, and down through the tonic to the minor seventh. This took a while to figure out as well. I had more elaborate ideas, but the most compelling solution turned out to be the simplest.

Now we get the four part version of the interlude, and we're ready for the middle entries. The two- and three-part versions maintained their voice numbers throughout, but here I reduce the texture to two voices to demonstrate the possibility of a two-part stretto at three measures of delay/two measures of overlap that is a perfect dovetail. As I alluded to in the last post, the single measure overlap stretto is possible, but trivial, so I didn't include it in the plan.

After the stretto, it's time for the episode again, now back in its normative form.

With the three-voice Escher morph/perpetual canon comes the first modulation of this volume outside of the expositions. It is the same direct modulation as in the expositions, it just continues on instead of returning to the tonic immediately after the answer statement. So, the real answer becomes the tonic and has it's time in the sun.

The plan of this stunning canon is the same as it was in the three-part fugue, only before it was on the tonic: The subject morphs into the subject in augmentation, and then the modified subject in double-augmentation, and then back to the augmented form, all conforming to the laws of pure counterpoint.

Though I didn't break any laws, the dissonances I employ are not something any of the Bach-era composers would have used. Basically, the deceptive resolution to the bVI(M7) is to an inversion with the root above the seventh, yielding a minor ninth. This creates a kind of creepy sounding dissonance flow, with the chord of resolution more dissonant than the dominant that targets it. This excruciatingly beautiful passage is proof that any musical effect can be employed to achieve something wonderful, if it is presented in a logical musical context. There is no musical context more logical than canon.

The canon then re-transitions back to the augmented form of the subject.

Once the perpetual nature of the canon is proven, the piece modulates directly back to the tonic with the cellos entering with the subject in the bass. The order of entry for this canon is reversed, however, which leads to some glorious conflicts.

The canon is broken by the first violins at measure 196, when they repeat the subject. This turns the rest of the section into a roiling cauldron that uses nothing but the subject.

This topsy-turvy action comes to a head in measure 109, when the cellos and violas land on the unison d-natural. The violas then dip below the bases to play the c-sharp, d-sharp, e-sharp triplet against that sustained d-natural. This is the climax of the section, after which, the augmented head figure reappears, the tension ebbs, and the episode appears again.

That makes two episodes, so it's time for the interlude again, and now it's seven measures so that it can come to a full stop before the concluding perpetual canon begins, which is introduced by the diminished triad triplet figure in the first violins.

The concluding perpetual canon is much fuller and more complete in four parts than has hitherto been the case with the three voiced versions.

For example, in measure 132 we now get a complete bVI(M7) in first inversion. Reading from the bottom, major-third, perfect-fifth, major-seventh, and the root on top. I came up with the concept of beautiful dissonance when I was at Berklee College of Music back in the early 80's, but I was writing in jazz and jazz-fusion idioms then, so I was thinking of colorful jazz-fusion harmonies. I intentionally pursued that concept with counterpoint, and this is the flowering of those efforts. Next path will be to recover more complex harmonies in counterpoint (Which reminds me that I need to analyze the Beethoven Op. 131 string quartet fugue).

So, the canon in original note values reenters, and once the perpetual nature of the canon is proven, the piece winds down over the ostinato of the tail figure in the bass. With more than three parts, we can now get the pluperfect ending in which all of the voices come to rest on the tonic. Note the momentary major chord at the beginning of measure 149: This a feint to get the final triplet figure in, which has the missing Phrygian degree, which is the only one absent from the subject on the tonic level. Ta da!

I have to do a digital fair copy of the five-part ricercare, so I'll be back in a few days.


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