Fugal Science, Volume 2: Introduction, Part 2

In Part 1 of this introduction, I presented the first fugue in the collection, a two-voice fugue at the octave for solo guitar. Now we fast forward to the final piece, which is a five-part Ricercare for Orchestra. The three and four part fugues have yet to be composed, though I think the three-voice one should be relatively straight forward. Not sure about the four-voice fugue yet, as I can see how there could be some problems working it through.

Here is the audio file for the Ricercare for Orchestra.

Again, this is a CD-quality AIFF file, so you'll need to have QuickTime activated in your browser, and I suggest opening another tab for the audio so you can follow the score while you listen.

Since the soundfonts are just a convenience for composing and orchestrating within Encore for me, I do put up with some obvious limitations: The woodwinds and brass I chose are all solo instrument sounds, so there are no tutti sections, and the muted strings were not available either, so they are un-muted throughout. This is a tad annoying, as I can't wait to hear the combination of soli winds with muted strings that I start out with here. I hear it in my head as being very etherial and subtly menacing, due to the chromatic nature of the subject.

The score is a MIDI score of my own devising, so it is in concert pitch, and the wind and brass choirs are just reflections of the strings. That means there are 15 channels used, with the sixteenth still available for percussion (I have some definite ideas there, but I'm not ready to include them in the score or sound file yet). Another sound font issue is that there is no piccolo trumpet available to me, so I used a very high and pinched-sounding jazz trumpet timbre. It's not awful, but a properly played piccolo trumpet will sound more... "at home" up there in the stratosphere.

This page, then, is just the initial statement of the subject, which is five measures long, has the range of a minor ninth, and contains eleven of the twelve pitch classes. The only one missing is the Phrygian second degree of ra, which I save for the penultimate note at the very end of the piece.

Due to the highly chromatic nature of the subject, the answer must be real, and not tonal. So, here we have that real answer at the usual interval of a fifth above. This gives the exposition the feeling of rocking back and forth between tonic and dominant more than with a tonal answer, and I use this effect for every modulation in the piece, which only alternates between the tonic and dominant regions throughout. Let me point out again that the counter-answer starting in measure eight is the head of the answer in augmentation, which foreshadows all of the Musical Escher Morphs to come. I'll also note that Encore makes it very convenient to compress the MIDI dynamic range by specifying exactly and numerically what those should be (And I haven't put most of the dynamics in yet), but a few of the ">" accented notes stand out a bit more than I'd like, especially when the brass come in.

Back to the tonic for the third thematic entrance, and now you can see how ascetic my style is these days: Lots of slow movement in the accompaniment - nothing shorter than a quarter note - and I don't worry about achieving an even cumulative rhythm, because I find that gets boring. Far superior to devise the rhythms of the parts subtly, so the cumulative effect is interesting, but not busy.

Here we get a version of the episode - and I mean, the episode, as this is the only one, along with different contrapuntal inversions and voice numbers, in the entire piece - within the exposition. This is unusual, but there is no way to execute a dominant region answer at sixteen: The episode is necessary to set up the next entrance of the real answer at twenty. I devised this subject back in 2003, and had the concluding five-voice perpetual canon done by 2006, and then it sat around like that for seven years until I finally came up with this episode to get the exposition done. That was a good day! And then, the middle entries came together within a couple of months in 2013. These delayed gratification payoffs - a genuine jackpot, in this case - make composing the most interesting and rewarding of all human endeavors, in my estimation.

The high note of the entire piece comes in the second real answer here, which is the c-natural in measure twenty-one. At the beginning of the five-part perpetual canon that is the recapitulation of the piece, this statement is back on the tonic, so this piece is basically a 5, 4, 3, 2, 1, in Schenkerian terms (Not that I put much stock in his theories). This is not normative, obviously, as the most natural position for a pitch climax in a piece would be 2/3 of the way through. 2/3 of the exposition is, however, 19.33 measures, so that's another picture frame through which to view it. The bottom line is, the pitch climax can be the first note, or the last note, or any note in between (Or, there can be no explicit pitch climax at all). You just need to have compelling musical logic to support wherever you put it... or don't (The two-voice fugue for guitar has no unique pitch climax, for example).

Here at twenty-five, we get the final subject statement back on the tonic level, and the five-part texture is complete. Note how spare and reserved my accompaniment style is here. This texture owes much more to Palestrina than Bach, and the harmony is very deep with modal effects, just spicily seasoned by the chromatic subject. Just magnificent, if I do say so myself. So, the exposition is a mighty twenty-nine measures long.

Then, here at thirty, we get the second appearance of the episode, now fully fleshed out in four voices. I should mention that I avoid unisons in these sound font MIDI scores because of phase and attack problems, or the flutes and first violins would end in unison with the oboes and second violins. The uneasy closeness between the bass and contrabass also plays a big part in the unfolding drama of the piece, reaching a low-pitch climax between them just before the final episode and interlude.

Now we get the first of two appearances of the interlude, and the disquieting rumbles between bass and contrabass continue. By thirty-nine, the middle entries are set up. Note that the strings have been muted and the winds have been soli this entire time. The mutes will come off for when the strings return next time.

The winds, however, remain soli for the beginning of the middle entries, which begin with a duet between the oboe and clarinet. This is the same stretto as was first in the two-part guitar version, so it makes a perfect dovetail between the subject and countersubject statements.

At the end of the stretto, I present the two-voice version of the episode, and we are now set up for the three-part entries.

I modulate to the dominant level for the tree-voice stretti, and transition by having the first two entries play out over a dominant pedal point (On this, the dominant level, so b-natural).

The bassoon then takes over for the clarinet, and we begin the first Musical Escher Morph, where the augmented form of the subject begins in measure fifty-seven. This is where the strings reenter, now un-muted, as they will be taking over during the doubly-augmented section (I'd hate to asphyxiate the wind players). Note that, in the original note values, the stretto is at two measures of distance/three measures of overlap, but the augmented form of the subject equates to a single measure of delay/four measures of overlap back in the original values: Mensural canons like this are very interesting that way.

By sixty-one, the three voices of un-muted strings are complete for this section, and the soli winds have been moved to the background. Notice that in measure sixty-five, there is a beautiful cross-rhythm exposed by the slow, augmented pace, between the quarter note triplet in the top voice, and the straight quarter in the bass. This goes by quite fast in the original note values, so bringing this out is one of my favorite features of the augmented statements.

As the backgrounded winds finish their augmented statements, they drop out for a much needed break as the doubly-augmented transition begins. The strings are the only choir that can sustain this without committing suicide, so it was both a natural and unavoidable orchestration choice to make. Note again that, in this new doubly-augmented environment, the delay between the statements would be a half-measure. This works only for the head of the subject. I had to modify the tail to make it work.

What I did to make the tail work - well, the body of the subject, leaving out the measure with the triplets - was to keep the doubly-augmented rhythms, but make the line diatonic instead of chromatic. The results are astonishing. So much so, that when I analyzed the results, I was not completely certain that it would sound as I imagined. It just breaks some, "rules" for harmonic interaction. For example, the harmony in measure seventy-three is the C(M7) that lives on the bVI degree of our current tonic key of e-minor. But, the root is in the lead, with the major-seventh underneath, creating the interval of a minor ninth. Then, this is supported by the fifth in the bass, and the major third is missing. The result is a dissonance both empty - in terms of interval density - and searingly hot, and yet it is sublimely beautiful. The dorks of the so-called Second Viennese School - Schoenberg, Webern, et al - used structures like this, and they sounded terrible. What's the difference? Context. They rejected true musical logic, and went off on a tangent in which everything was arbitrary, and therefore ugly. And not just ugly, but meaningless. Here, canon - the supreme musical logic of all musical logic - perfectly justifies everything and the results are stunningly beautiful.

This is no fluke, as you can see in measure seventy-five, where even the fifth is gone, and all that is left is a major seventh on top of a minor ninth! This was an earth shattering discovery for me: The real liberation of the dissonance, done naturally via canon, not artificially and arbitrarily by rejecting musical logic. The three-part harmony then reappears in seventy-seven and seventy-eight, but now as a very sweet sounding major seventh, due to the compelling logic of the context. Anyone who says everything that can be done with tonality/modality has been done is a hack utterly lacking imagination. Flee from them as you would a cloud of poison gas, because that's what such utterances are.

What separates my idea of Musical Escher Morphs from simpler mensural canons is the fact that they re-transition back to an earlier version of the theme, thereby creating perpetual canons of three or more voices. Here, that manifests itself as the reappearance of the augmented form of the subject starting at eighty-three. The winds now rejoin the orchestration, and if this was a real orchestra, they would be in tutti to be more of a force versus the un-muted strings (And there could be more than two of each, depending on the orchestral resources available).

As the doubly-augmented statements return to prove the perpetual canon - the morph doesn't work back to the original note values - the winds exit again in preparation for the brass entrances. Note that this entire three-voice section has been on the dominant level.

The four-voice section then begins back on the tonic level with the brass making a dramatic entrance with the tuba in the contrabass octave. This is not a Musical Escher Morph section, but rather a cauldron of canonic statements that begin at two measures of delay, stacking up from the bottom.

After the brass have stacked up with the entrance of the trumpet, the canon begins to repeat, now with the winds reentering. In traditional fugal style, voices rest before a new thematic entrance, but I defenestrated that idea, preferring the streamlined smoothness I've achieved here. So I rely on the orchestration to bring out the new thematic entrances instead.

The trumpets then break the canon by directly repeating the theme in measure 110, which makes the entrances one measure of delay/four measures of overlap. This sets up a clash between the bass and contrabass that will be the climax of the section.

As can be seen in measure 113, the bass and contrabass arrive on the unison of f-natural, and then the bass dips below the contrabass to e-natural, which creates a too-low minor second, followed by another too-low augmented unison between the f-natural and f-sharp, before the augmented second from f-natural to g-sharp at the end of the measure. These forbidden rumblings are below the usually recognized low interval limits for scoring, but they are brief and subtly dramatic. Once you notice them, they can't be un-heard. I like this effect a lot. Immediately thereafter, the augmented heads begin, but this is just a setup for the return of the episode and interlude to follow.

The last episode we heard was the two-voice version near the beginning of the middle entries, so this - a reproduction of the previous four-part version we heard after the exposition, but without the transition from five-voices - is the second episode since the last interlude, which means it's time for the interlude to reappear as well.

And so now we get the second and final interlude, here extended from the previous six measures to seven, in order to provide a more final resolution before the five-voice perpetual canon/Musical Escher Morph begins, the pickup for which is with the piccolo trumpet at the end of 127. If the form continued with more episodes and interludes, I would have needed to compose additional elements for that, as the repeat scheme for these two has been exhausted. As it is, all four of the episodes are different - three-voice, four-voice, two-voice, and four voice w/o the transition from five, in order - as are both of the interludes - the first six measures, and the second seven. Bach would have made every episode/interlude different, but this is a more thematically efficient scheme, and I think it is more in keeping with the times too.

This page is what I first composed back in 2003 when I came up with the concept for this fugue subject: A five-voice canon at the octave, which uses all five octaves of the orchestra - descending from the soprano octave - and that, resultantly, has all five measures of the subject appearing simultaneously in the fifth measure.

It wasn't until 2005 that I discovered that the original five-part canon would morph into the augmented version of the head figure like this. Probably needless to say, a very exciting revelation. As those augmented statements appear, the strings reappear, as we are now building to the final five-voice orchestral tutti. Note that in measure 136 the F(M7) harmony on the bVI degree is now complete, reading from bottom to top as A, A, C, E, and F, so we have that searing minor ninth on top, but the sonority is much fuller now with the increased interval densities present, versus the previous three-voice iteration.

The canon has the minor ninths progressively falling in the voicings - A, A, E, F, and E in 137; C, E, F, E, and E in 138 (An incomplete harmony); and E, F, E, C, and A in 139 - and then the root position chord in 140 as F, E, C, A, and A, so that the hot dissonances eventually disappear into a resolution at the major-major-seventh. Then the re-transition to the original begins in measure 141, and the tutti winds reenter as well, in the progressive buildup to the conclusion.

By measure 145 in the re-transition of this Musical Escher Morph, we have the full five-voice orchestral tutti for the first and only time. You can now fully conceptualize how the orchestration, and not voice rests, brings out the new subject entrances.

The Musical Escher Morph then proves that it is a five-part perpetual canon at the re-transition back to the augmented variant of the subject, and then we get to hear the delicious dissonances play out again, but this time subtly altered by the ostinato of the tail figure in the bass.

The wind-down is particularly nice over the ostinato, and as every line lands on the tonic, it becomes a drone until the conclusion. In the final measure - 154 (The half-measure is just a written-out fermata) - the piece appears to resolve to a major tonic, but this is just a setup for the final triplet figure, which has as the penultimate note b-flat, which is the only one of the twelve pitch classes that is missing from the subject in the tonic key. That makes the final resolution the most complete of all possible: Five octaves of pure tonic.

Next, I'll introduce Volume 1 of Fugal Science with its two-voice fugue for solo guitar. It is a much longer and more involved piece.