What makes a good fugue subject?

Question

Realization

I think I might have found my weakness in fugue writing, and it is one that isn't easily helped by all the counterpoint studies that I have been doing. That is the part of the fugue that is super essential, namely, the subject. If the fugue is like the human body, the subject is like the heart, essential to the piece. Without a subject, you don't have a fugue. Even if you go contrapuntal, all you would have without a subject is free counterpoint, with the only organization being via cadences or maybe a canon.

If free counterpoint is like a liquid, always changing, than a subject entry is like a crystal, neat and predictable. A fugue then is like the perfect balance between the liquidity of free counterpoint and the predictability of subject entries. My counterpoint skills are good. I can take a melody and write another melody that is contrapuntally compatible. But, when I try to write a fugue, again and again, I fail. Closest I have gotten is an almost finished exposition in 4 voices(3 voices complete, 4th voice unfinished). With my first fugue attempt, I went ahead and wrote an episode. By the time I got to the next subject entry, I realized my mistake, I failed to make a good fugue.

Studies into Fugues

A few years of counterpoint studies pass and I am able to write free counterpoint and canons with no problems. But the beast of the fugue keeps getting me. And don't get me started on double fugues, those are much trickier to pull off and I only know of about 10 or so double fugues(Some by Bach, the Kyrie from Mozart's Requiem, Grosse Fuge by Beethoven, and the fugal variation of the Ode to Joy theme in Beethoven's Ninth). Most of the ones I know of have overlapping expositions(for example the Kyrie from Mozart's Requiem has a 1 measure delay between its first subject, the slow "Kyrie Eleison" subject, and it's second subject, the sixteenth note "Christe Eleison" subject, both of which are in a single exposition(or you could think of it as 2 overlapping expositions)). The few that I know that have 2 completely separate expositions are all by Bach.

But, back to my main point, I think my weakness in writing fugues has to do with the subject. It obviously has to either be melodic in nature(like most fugue subjects) and/or to have an obvious rhythm and interval component(like the subject of Fugue in D major WTC Book II, with it's rhythmic component that reminds me a lot of Beethoven's Fifth. Speaking of which, I have made some progress with the fugal variation of it. I now have a countersubject to go with the Beethoven's Fifth subject. I decided to go with the whole first 8 bars of the first theme as my subject. Here is that countersubject combined with the Beethoven subject:

Anyway, I think there is something more to a good fugue subject than melody or rhythm. There has to be, otherwise you could have the C major scale as a viable fugue subject. Clearly, that isn't the case that a bare scale is a viable fugue subject, there has to be some wave in the melodic contour, even if it goes up or down or stays the same overall. But then again, all of my fugue subjects have had this wave in the melodic contour and I have always failed to complete the fugue.

Countersubject works, Subject fails

I have this whole systematic approach to my countersubject that involves building up from a harmonic backbone and fixing any errors that result. But with my subject, I have no such approach, I just improvise a melody that I think will work and then write the fugue exposition in the hope that the subject works. With my Beethoven fugue, that is a clear "Yes, this totally works as a subject." But with my improvised melodies it isn't clear until I start writing the exposition whether the supposed subject is going to work or not.

Going this improvisation route for my fugue subjects has always lead to me failing to complete the fugue and with one exception, I have failed to complete the exposition. Here is the one and only improvised subject for which I have been able to complete the exposition(all the others have lead to contrapuntal errors like crazy):

That is my first ever fugue subject, which happens to share a few things in common with the Beethoven subject I showed earlier. Here they are:

1. They both start on the dominant note of the scale
2. They are both in C minor
3. They both have a clear harmony they are outlining. In the case of the Beethoven subject, it is an alternation between I and V7. This is the harmony that my first ever fugue subject outlines(at least if you take the Bb's and raise them to B naturals):

Again, mostly an alternation between tonic and dominant with the one exception of the diminished seventh. Major difference has to do with melodic grace(or the lack thereof).

So, now what? If the subject is my weakness in writing fugues because of melodic improvisation, should I take a chord progression and then write a melody that emphasizes those chords and use it as my fugue subject? Should I try writing a fugue using one of my preexisting countersubjects as the subject and see if that improves anything? Because when I search "Tips on writing a fugue subject", all I get are either research papers and books on Bach's fugues or guidance on writing an entire fugue. Nothing shows up that goes into what makes a good or bad fugue subject.

Answer 1

I'm going to assume that the question is attempting to write a fugue in the baroque/early classical style. (Fugal works in renaissance style are a different matter, which allow somewhat more leeway in the intervallic construction of a subject, but restrict other elements much more severely.)

As an introduction to this topic, I'll defer to Robert Gauldin, who states in A Practical Approach to Eighteenth-Century Counterpoint (pp. 211-212):

According to Padre Martini, the subject (subjectum) falls into one of two categories: the soggetto coming out of the ricercar, which is a relatively short theme (usually two measures or less) employing longer note values; and the andamento, which is a longer, livelier melody in faster tempo, perhaps related to the older canzona. [...] The range of a typical subject lies approximately within an octave. Wider spans can create problems in composing an accompanying line in double counterpoint. It almost invariably opens with either scale degree 1̂ or 5̂ (rarely 3̂) and will normally cadence on either 1̂, 3̂, or a tonicized 5̂ (implying a modulation to the dominant). [...] Some subjects that cadence convincingly on 1̂ or 5̂ may be followed by a tiny melodic link connecting it to the ensuing counterpoint. [...] From the vast range of linear and rhythmic variety of fugue subjects, several striking melodic idioms recur.... The first of these is the use of a diminished seventh in the minor mode, usually between scale steps ♯7̂ and ♭6̂ either in rising or falling motion. This leap occurs in innumerable fugue themes... [and] even carries over into the Classical period.... The other melodic stereotype is actually a reduced framework which underlies many fugal subjects in the eighteenth century. It consists of scale degree 5̂ 6̂ 5̂ 4̂ 3̂ (2̂ 1̂) in either mode, the final descent to tonic being optional.

A few things to take away from this:

• Many fugue subjects follow the same simple patterns. Making your own new fugue subject was actually uncommon for beginning composers.
• Simple things like a major scale actually make fine fugue subjects with a little ornamentation. As noted in another answer, the whole tradition of Ut Re Mi Fa Sol La renaissance masses were built effectively on an ascending major scale subject, though baroque composers would likely use concepts of diminution (i.e., standard patterns of smaller duration note values that fill out a longer-scale musical gesture or pattern) to flesh out a scalar subject.
• Aside from the standard patterns, there are a wide variety of fugue subjects, but the clear emphasis on tonic and dominant is important.

So, my foremost piece of advice to you is to stop trying to compose your own subject and learn to write fugues first with standard baroque subjects. That's how historical composers often did it. Any textbook on fugal composition will usually provide several dozen, or you could find one from an existing composition and then write your own fugue.

If you're really intent on writing your own subject, the biggest problem I see in the examples you provide is the pacing and rhythm. Beethoven's Fifth is a pretty terrible subject for a fugue (which is why Beethoven himself probably avoids the fugato section he sort of sets up in the development of the first movement of the symphony). To make it workable, you'd need to chop it up and create a stronger sense of rhythm, rather than imitating the strange halting that occurs at the beginning of the movement.

As for your own subject, the problem to my mind is unclear harmonic implications and harmonic rhythm. You state, for example, that they both have a "clear harmony they are outlining." The harmony in your subject is not clearly implied. The first bar could easily be in either C minor or E-flat major. The agogic accent created by halting on the E♭ actually tends toward the second interpretation. This is not a failure in itself, as many baroque and classical fugue subjects often are somewhat tonally ambiguous at the outset.

However, the subsequent bars do not clearly outline the harmony you write, and the harmonic rhythm is very odd. I assume the B♭ on beat 3 of bar 2 is meant to be a B♮, so the whole second bar might imply V. However, the third bar's E♭ on beat one is odd. Ascending accented passing tones are rare in 18th-century style, unless there's a clear harmonic context. So, on beat 1 of bar 3, a listener might expect a return to tonic. Except that's undermined by what would then be an unusual neighbor tone figure to F on beat 2 (which sounds accented due to the syncoptation and agogic accent). The accented passing tone on the downbeat of bar 4 is also less idiomatic in 18th-century style, so again there's a bit of ambiguity about what chord we're supposed to hear and where.

The way to fix a melody like this is to recognize that implied chord changes in a subject should almost always only occur on relatively strong beats. They also need a clear pacing, for example, in a 4-bar subject, you might do:

• i | V | i | V
• i | i | V | V
• i | V | V | i

The chord changes should feel like they are occurring on downbeats. They should only occur on the third beat of a bar if the harmonic pace quickens later in the subject so that changes are occurring almost every half note. And they basically never should feel like they are occurring on a weak beat -- in fact, without harmonic context, they simply won't feel like they should occur there at all. (For example, there's no way I'd ever hear the tonic chord you write on beat 4 of bar 3 as the implied harmony; those notes would be heard as passing tones without harmonic context.)

If you begin with the assumption that you can only change chords on downbeats (or at least strong beats), then we need to move on to smaller details. Non-harmonic tone use is incredibly important in fugue subjects. In the early 18th century (Bach's time), the most common non-harmonic tones on strong beats were suspensions. Accented passing tones (especially descending) were somewhat common, but much less so than suspensions. Other non-harmonic tones on strong beats were quite rare (e.g., neighbor tones, appoggiaturas, etc.), especially in something meant to establish tonality like the beginning of a fugue subject.

But I'd strongly suggest starting with a framework that assumes you have a chord tone on each strong beat. Then, if you know how to write a proper suspension in baroque/classical style, you might incorporate one or two somewhere. For example, in bar 4, the C-B♮ is rhythmically unidiomatic. But if you turned it into a suspension, prepared with a C on beat 4 of bar 3, hanging over and then resolving on beat 2 of bar 4 before moving to C at the close, that would be significantly better. (Though cadencing in the middle of the bar may not be the best set-up for pacing the arrival of your answer in the fugue exposition.) Only once you have more experience in writing subjects and have studied baroque diminution patterns (as historical composers would have) should you start including other types of non-harmonic tones on strong beats.

There's a lot more details to worry about -- and this is based on only looking at a few bars of your attempts. So far, I'd say clear harmonic rhythm and clear use of chord tones (as well as occasional suspensions) on strong beats is the first thing to fix. After that, from glancing at the counterpoint written with the Beethoven subject, I'd guess we'd need to talk about appropriate intervals, expected rhythms, proper use of dissonance (and leaps), etc., etc.

All of this is assuming you're trying to write a fugue in something vaguely resembling 18th-century style, as you cite Bach, Mozart, and Beethoven.

Answer 2

You may be overloading your expectations for the subject to be unique. You can treat the subject to some degree as generic. Minimally it needs to define the tonic/tonality. It's more important how the subject gets treated in the course of the fugue.

When looking at subjects in the Well Tempered Clavier, I notice many subjects will start with some elaboration of ^5 ^6 ^5, just a neighboring motion on the dominant. Many fugues from other composers use that same opening gesture. There are other common openings like a leap between tonic and dominant or some arpeggiation of the tonic chord. The point is these common patterns are used over and over again to provide the underlying structure of subjects.

Try using a common pattern for a subject.

Another thing worth mentioning is you haven't pointed out what you think is bad in your writing. You've only said the subject is weak an fails. What specifically makes you think so? If you can state that clearly, you should be able to fix it.

Answer 3

There is absolutely no reason why a fugue subject has to be "unique". The best known counterexample is probably the finale of Mozart's Jupiter symphony, where the principal fugue subject is a commonplace four notes shamelessly stolen from every textbook on elementary counterpoint from Fux onwards:

In fact Mozart may have stolen this idea from Haydn (Symphony 28, finale) rather than Fux, but no matter. Wherever it came from, it's not exactly "uniquely hand-crafted perfection".

Bach did almost the same thing with the first subject of the triple fugue in C# minor from WTC Book I:

And analysed by ear, the subject of the A major fugue from WTC I is just a single 8th note A, followed by a rest four times as long.

As for "fugues with a major scale as the subject", or at least "pieces which were entirely contrapuntal and where the main theme was a major scale" dozens of them were written in the 16th century. In fact the whole genre of pieces shared a common title, "Ut re mi fa sol la", which was of course the names of the first six notes of the scale. Some of the more adventurous ones had entries of the subject in all twelve keys in the course of the piece, plus sections based on the minor scale as well.

At the other extreme, here are the subjects of the colossal triple fugue (for 7 voices) forming the final movement of Sorabji's second organ sonata, which runs its course to an inexorable conclusion over about 2 1/2 hours (the total duration of the sonata is around 8 1/2 hours). Note the tempo marking (editorial, but based on live performances of the piece) - the length of first subject is well over a minute, and the first exposition is longer than many of Bach's complete fugues.

You can find examples of more or less everything in between these extremes, if only you look (and more important, listen).

Answer 4

I love the advice to try to write a fugue based on a classic subject. I love Mozart's double fugue in Kyrie Elision, he stole it from Handel's Messiah - "And By His Stripes We Are healed" but the second expo. of in Mozart's double fugue is original, a masterful accompaniment to an incredible subject invented by Handel.

I like to write fugues, All of mine are original. I have studied Bach carefully and seem to have noticed what makes, at least to my ear, and interesting subject - though, I think the mature composer recognizes (see Bach's master work - Art of Fugue) simplicity demonstrates mastery of form. If you can make a simple subject sing, than you are doing something right, moreover, it forces you to think of more creative ways to recycle the theme and transform it (diminution, inversion, etc).

Athanasius' advice is SUPERB! I couldn't agree more. To reiterate what he said, the problems with your subject are they dont outline a clear harmonic center, nor do the lines indicate melodic implications - this is what Bach was masterful at, every line or figure has melodic implications of direction, as well as harmonic implications. A good melody creates harmonic tension which is undergirded and enhanced rhythmically. Keep this in mind and you'll write melodies and subjects that have a clear melodic and harmonic direction. I also like to think of the subject like a good Passacaglia, if it wont, AT THE VERY LEAST, work in the bass (baritone), then its not good enough - the foundation of the melody is weak. The foundation of a double fugue is that the subjects were so melodicaly strong/clear in harmonic implication, that they could stand alone in any voice - even as a baseline.

Your subject would be a very poor bass/baritone part, let alone soprano part. A good melody implies a good bass/baritone part .