Thursday, July 14, 2005

Composing Fugue Subjects as Canons

I have not gotten the Cube back together yet, but after working with my 15" PowerBook for a few days, I find I can do more with it than I originally thought via some minor work-arounds, so that I can get back to posting.

The phrase for the sonata-process movement that I was working on earlier I have now finished composing by using a four voice canon that dissolves back to a second singularity, and that will be the subject of the next post, but I have decided I want to compose a fugatto for that piece next, so to get my fugue subject compositional juices flowing, I have decided to review for you how I composed the fugue subject for a string quartet I wrote about ten years back.

This fugue was intended to be an homage to J.S. Bach, and in a very close approximation to his late fugal style as exemplified by The Musical Offering and The Art of Fugue. As such, I wanted a subject that was similar to the head-and-tail subjects that those two collections are built around. However, I didn't want anything either so chromatically complex as the Royal Theme nor so spare as the Motto Theme. Rather, I wanted to get elements of both into a subject that would work as a four voice canonic stretto.

I should note that historians seem to have discovered that the Royal Theme was composed by Frederick the Great with the help of Bach's son Carl Phillip Emmanuel in an effort to embarrass the old man, and it was intended to be impossible to work with, or nearly so. There is a new book out about that meeting between Frederick and J.S. Bach entitled Evening in the Palace of Reason, which I have not yet read, but all who have that I have spoken to about it recommend it highly. Briefly, J.S. Bach was an Age of Reason product while C.P.E. and Frederick were Age of Enlightenment proponents: The meeting was supposed to show the superiority of the second philosophy by discrediting Bach the elder, but it ended up turning on the plotters magnificently, as Bach astonished everybody present.

And, concerning the Motto Theme, it was designed to work with the BACH musical anagram, and does not lend itself readily to very many contrapuntal combinations: Bach had an ulterior motive with that theme, and that he could do so much with it and the previously mentioned Royal Theme offers testament to his overwhelming greatness as a contrapuntist.

For my more modest aims, I wanted a subject that would work in stretto at the octave at consecutive measures of overlap: First one, then two, three, and finally at four, where the following voice would be at one measure's distance from the leader. So, the subject would have to be five measures long (Odd numbers of measures of length for fugue subjects is a highly desirable feature, as this more easily creates a freely flowing phraseology without the tyranny of four effect that so much music suffers from, and which is particularly damaging to a fugue), and it would have to be composed using basic canon technique.

In the example above, you can see that I chose the classic do-sol figure for the beginning of the head of the subject, and set it up to be composed as a four voice canonic stretto. One of the nice things about this figure is that it can be harmonized as a full measure of tonic harmony, or as a half measure each of tonic and dominant harmony. For the first measure of overlap, Bach chose me-do due to the BACH anagram he was composing it over, but this would not work well for this application. Instead, I chose the deceptive motion to the submediant degree for the first half of the second measure, which gave me the oportunity to use the le-ti melodic leap of a diminished seventh that is such a dominant feature of the Royal Theme: So I managed to work references to both it and the Motto Theme into the head of my subject, creating a better version of both of those in terms of stretto possibilities as I did so.

As you can see by our second example, the first thing that occured to me for the third measure was the obvious do-re movement in half notes. This worked so readily and obviously, that I stuck with it, and went on to compose the fourth measure, which you can see below. I should point out here that many of the best fugue subjects have a point of restance in them, such as the tied figure I have employed here, which is again directly from the Motto Theme of J.S.Bach.

Bach ended his Motto Theme at the point where the trajectory returns to the tonic for the third time, but I wanted to continue with that eighth note motion and in the process get the five measure subject I wanted, and also to complete the continuity of the surface rhythm of constant eighth notes: Fugue subjects of this type composed in canon and fugue subject/countersubject combinations should always rhythmically compliment one another so that they achieve this kind of an effect of surface continuity.

After finishing this intital version of the subject, I was unhappy with the third measure, as it did not progressively develop any kind of rhythmic acceleration, and it seemed overly abrupt when the eighth notes came in. So, I added the quarter note figure that you can see in the example on the bottom. This is a perfectly acceptable fugue subject in this form, but there are only four different rhythmic values in five measures, while there are eight different notes. This is a little weak on the rhythmic variety side for a subject this long with the range of a minor ninth.

On top above you can see where I have added the dotted-quarter/eighth rhythmic elaboration to the third measure. This gave five different note values for the subject, which is an improvement, but the straight eighth notes now sound a little flat by comparison. So, I took the same rhythmic figure in diminution and applied it to the tail, as you can see in the final example. The complex interaction of the dotted-quarter/eighth rhythm against the dotted-eighth/sixteenth rhythm adds just the right amount of "grease" to the combination, and the end result is quite wonderful, if I do say so myself.

For the fugatto I wish to write, I do not need so many contrapunhtal combinations as this theme offers (Only some of which are evident in this canon), so I won't necessarily compose it as a canon, but will probably go for a more rhythmically vigorous subject instead. Since a fugatto is basically just an exposition and a counterexposition most of the time, I can afford to be more lax in my development of it in this one speciffic way.

If perchance you would like to see the score of the completed fugue and listen to a MIDI file of it, it is posted on my fileshare page here along with a bunch of my early guitar miniatures. The score is posted as a PDF file, and if you have QuickTime, you will get the MIDI file with the string quartet sounds already attached to it.


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