Monday, January 09, 2012

Fugal Science, Volume 1, Numbers 1-3

Back in 1994 when I was a Doctoral candidate at UNT, I came up with a magnificent and stately fugue subject that I composed as a four-part canon. With that subject, I composed a string quartet fugue that you can see and hear here.

That subject came out so spectacularly well, that I knew I would return to it at some point and write a series of fugal works with it. Well, back in 2010 I finally reduced it to its smallest form possible, that of a two-voice fugue at the octave (Bach called these two-part inventions, feeling they weren't worthy of the title of fugue, but they are just fugues with the answer at the octave), and that got me onto a very scientific track toward building it back up to a four voice fugue again.

As an aside, I have been preparing this post for a long, long time, and I was hoping to be able to use the Sibelius Classical Guitar sound file... but it was not to be. So, I'm still stuck with my soundfont collection. I'm so disgusted that Sibelius failed so spectacularly, that I'm planning to return to external sound modules again. Hard to believe that in 2012 there is still NO SINGLE PROGRAM THAT CAN TAKE A COMPOSITION FROM CONCEPTION TO FINISHED SCORE AND TRACK WITHIN THE COMPUTER. But, I'm sure the market for such things is small.

Anyway, here is the M4A file of Fugue Number 1 in A Minor for solo guitar.

One of the reasons that it took me so long to get back to this subject is that I had to completely invent a noble/stately fugal stile for the guitar. Bach's keyboard fugues usually built up to a constant eighth or sixteenth surface rhythm, but that's not an option for the guitar. Well, I have been reading about modal style vocal fugues, and I noticed that the rhythm is more based on quarter notes, and the rhythms breathe instead of building up to a motoric effect. By mixing the vocal and instrumental rhythmic styles - and basing things on quarter notes - I finally came up with the solution.

So, we get the five measure subject on the top system, and then the subject an octave higher combined with a countersubject on the second system. Measures eleven through sixteen are the first sequential episode, and there is no modulation.

Starting at seventeen, we get the subject again in the lower octave, but this time with the countersubject above. In 21, however, the countersubject is interrupted by a stretto entrance of the subject with a single measure of overlap. This would be a trivial stretto, except for the fact that I made a perfect dovetail joint out of it: The countersubject is unmodified at the point of interruption, and it continues in the bass with no modifications there either. I've never found anything like this in other fugues, so it may be a unique idea.

The unusual feature from measure 22 on is that the music is exactly the same as back in the exposition, which is basically unheard of in traditional fugues. What I'm doing is using repetition in different situations and varied repetition to affect the listener. Things get really strange by the time the second sequential episode comes up, because, "The Song Remains the Same." At the last possible point, the written-out trill figure interrupts to make a modulation to the dominant level. The bass line continues as it did the first time, and so there is an ever-so-brief augmented sixth on the final sixteenth note (Yes, that cross-rhythm is difficult to get just right). These kinds of things delight me, but I fear they are lost on most listeners.

Note that the exposition was ten measures, and the dovetail section was only nine. Also that the first sequential episode was six measures, but this one is only five. So, the first section of the fugue was sixteen measures, and the second is fourteen: The pace is quickening.

For the third section the piece modulates in a rather dramatic fashion to the dominant for a new, closer stretto with two measures of overlap. The rising bass line is really spooky, containing, as it does, an augmented triad rising into a diminished seventh arpeggio. At that point it has synched up with being the countersubject, but then the subject again interrupts in 34.

Note how the cumulative rhythm pauses there. I would never have done that in years past, but it does fall into the category of a, "dramatic pause." Once I discovered this, I decided to use it more. lol.

In 36 I got the opportunity to use an ascending chromatic tetrachord in the accompaniment line, and that leads into a slightly varied figure in 37. So, all of the joints are totally smooth, but it is not a strict dovetail.

In my fugal terminology, there are episodes and there are interludes. The first two that were variations are obviously episodes, and they have the trademark episodic sequencing. This third one comes in the place where I would put an interlude, because I discovered a wonderful contrapuntal combination as I was working with this material: The subject works over the bass line of the episode. Now, when I say, "works," I mean that in the strictest technical sense according to my laws of pure counterpoint. You'll have to look those up, as there is not space here.

Part of my two-voice style is the idea that, if it's OK in three or more voices, it's OK in only two. So, at the longest possible dramatic pause in 42, we get a diminished twelfth approached by parallel motion from a perfect twelfth above (I love this effect). Then, the music makes a turn and effects a modulation to the relative. So, this section is only one measure shorter - the extra measure of stretto overlap - because the middle entry was shorter, but the, "interlude" was as long as the previous episode.

In the relative major we get another measure of overlap, and it sounds very sunny and optimistic, which is a nice respite from too much... seriousness. ;^)

The final episode is like the first two, but starting out from the relative. It is also truncated an additional measure, so this section is only eleven measures. Finally, it melds nicely into a miniature pedal point, which is quite effective.

At 55 we're back to the tonic minor, so this is the recap, and I used the closest two-part canon for it. I believe the word is splendifferous.

At the end of the canon, I grafted the final measure of the countersubject onto the subject to get a six measures canon. That false ending is, well, false. That's why it's not emphatic.

The grand finale is a two-voice hyper-stretto - both parts start simultaneously - between the subject above, and the augmented subject in the bass. This was originally a four-voice texture, so that makes this two voice extraction very, um, dramatic. The pitch climax of the fugue is the F at the beginning of 64. The interval over the bass is a minor ninth plus an octave. This is super-pungent, but it works because the listener knows the harmony is a V(m7m9) sonority.

At 66, the interval is a diminished eleventh, plus an octave. This obviously implies an augmented triad, so this came out amazingly well. After the subject finishes, it launches into a rising sequential line that becomes chromatic in the second half of 69. This leads to a rousing final cadence confirmation on the bottom system. Discovering that written-out trill variation at the end was a nice moment.

So, eighteen years after I wrote the string quartet fugue, I figured out how to reduce it to have the least possible number of elements as a two-part invention, and to get it to work for the guitar.


Now, I could turn this into a two-voice fugue with the answer at the twelfth just by using the tonal answer a fifth higher in measure six (And then composing a counter-answer, of course). That would work, but it would introduce an imperfection because you would only hear the answer in the original exposition: A new section will be necessary, which you'll see in the next post.


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