A Crash-Course In Writing Fugues

There have been a number of requests here lately for information on counterpoint, and I received a request yesterday for more detailed instructions/hints/pointers on fugue construction.

I thought it might be interesting to see whether I could provide a simplified, illustrated guide to the art of fugue writing as I understand it. There may be pedagogues here who know more about this subject than I do, and I welcome their input. I am simply hoping this will be helpful as a starting-off point for those interested in trying to understand the anatomy of a fugue and how it is constructed, along with a few examples of just some of the many advanced techniques one can employ in writing a fugue.

In looking for a subject that would be easy to hear in almost any texture, I chose an old French folk tune, Ah, vous dirais-je, maman. Mozart used it as a theme for a famous set of piano varations. Almost everyone here will recognise it, either from that source, or as the English nursery tune Twinkle, Twinkle Little Star , or as the classroom primer The Alphabet Song.

Once the subject was chosen, I spent Sunday evening throwing together a fugue on it, annotating the score as I progressed. The fugue isn't deathless great, but it does what I wanted it to do - demonstrate the basics of fugue writing.

A PDF score of the Fugue Lesson is attached, which once you see it should be self-explanatory. Also attached is a MIDI of the Fugue Lesson. I chose easily distinguishable instruments to serve as the "voices" of the fugue: Soprano - oboe; Alto - clarinet; Tenor - bassoon; Bass - 'cello. Listen along with the MIDI while examining the PDF score; you may want to print out the PDF and make notes. Also attached is a PDF with errata - problems I ran into and mistakes I made, which you might find helpful in avoiding similar pitfalls yourself.

If you have any questions, please post them here, and I (or another willing pedagogue) will answer. I sincerely hope this is helpful.

Great Lesson, Lee. Thank you.

I do have a few questions:

1) Must the answer(s) follow the exact relative tones in another key? I've been looking at Bach's #2 Cm Fuge (From Book1) and I notice that one of the tones is changed in the first answer. This fits the harmony of the counter subject, but I'm wondering if there are some basic guidelines to follow. The answer is exact in every other way, in the Dominant, except for that one tone.

2) Following on from question #1 - I would assume that a variant of the answer is allowed near the beginning of the exposition (as long as it obviously derives from the subject, follows the same notes, adds/subtracts passing tones etc...)

2½) I notice the only two choices in "answers" are "tonal" and "real" whereas a tonal would use the relative pitches but keep them in the same key. For example. Subject C,B,C,E,G Answer G,F(instead of F#),G,B,D. Is there any more licence than this? For instance, the answer to the above subject pitch tones (following the same rhythm) being - D,C,D,F#,A (key of G, but not stating the tonic chord of this key in the answer)

3) I've been working on #8 (G) fuge subject for some time now. Originally, the pattern of subject/answer entries was thus:

Subject(Tonic), Answer(Dominant), Subject (Dominant of Dominant), Answer (Dominant)

I assume that the Tonic-Dominant-Tonic-Dominant is a basic guideline only for statements and answers of the subject?

4) You state at the end of the exposition "from here it is not neccessary to Answer as was done strictly in the exposition".

Are there many more licences after the end of the exposition? If you notice I depended on alot of false statements after the exposition and especially at the end of my (edit: Gm) fuge. I assume the form is more relaxed after this?

JLG, if this isn't the coolest thing I’ve seen on this site! - First of all, it's an incredible display of technique - but more importantly, you have the gift of being able to communicate your compositional thoughts in an exceptionally clear manner. This is an absolutely stunning pedagogical work, combining depth of insight with an easy sense of accessibility - And I'm going to have to ask you right here and now if I can use it with my students, with all due credit given to you.

I have one technical question - is that a parallel octave I spy between the alto and the bass at measure 53 - or do you consider the E in the alto as a passing note. My ears say something's wrong. Please tell me I'm right and keep it in as a no-no. (or tell me I'm wrong and keep it because.. ummm... it's not wrong )- I wonder that a few documented mistakes might be a fun way to show what to avoid - but then the performance suffers - unless you include the fix.

Thank you for taking on this project. I should hope that you are beginning to feel a bit excited about this ability of yours. I am very impressed.

I have one technical question - is that a parallel octave I spy between the alto and the bass at measure 53 - or do you consider the E in the alto as a passing note. My ears say something's wrong. Please tell me I'm right and keep it in as a no-no. (or tell me I'm wrong and keep it because.. ummm... it's not wrong )- I wonder that a few documented mistakes might be a fun way to show what to avoid - but then the performance suffers - unless you include the fix.

Parallel octaves happen when two voices move in similiar motion to an octive, by an octive, not when one voice remains stationary, as happens with the base note at 53:3-4. There is however, a parallel octive between Alto and Bass at the first beat of 54.

Parallel octaves happen when two voices move in similiar motion to an octive, by an octive, not when one voice remains stationary, as happens with the base note at 53:3-4. There is however, a parallel octive between Alto and Bass at the first beat of 54.

Hmm.. I'm pretty sure we're talking about the same thing - perhaps I wasn't clear - The last beat of measure 53 going into the first beat of 54 (or as you say, "at the first beat of 54"), right? The Alto Plays an E at the last beat of 53 going to a D at the first beat of 54 - while the Bass has articulated an E at beat two of measure 53, which moves to a D at the first beat of measure 54.

The parallel between the alto and bass is a "technically" parallel octave, but since the voices
are crossing over into the next measure across the bar line you can "excuse" the parallel.

You do only have "tonal" and "real" as options for fugal answers in traditional fugues, anyway.

You do have a lot of licence with your options after the exposition of the fugue. But also,
if you take your time and think craftily you will find that you can take a few licence in the
exposition as well.

J. Lee Grahams's "crash-course" was a great idea and I think anyone interesting in writing
fugues would do well to look at his example for a good solid start with understanding fugues.

* Lee beats himself with a wet noodle *

Yep, you're right, Leightwing. That's an instance of hidden parallel octaves. As Majesty says, in some camps it's excusable; it's less egregious than the straightforward variety. Nevertheless, I invariably try to avoid them, especially in a fairly strict counterpoint exercise like this...except, apparently, when I'm focusing my attention on making an augmentation work. *sigh*

I'm really honoured that you're thinking of using this with your students. Since my goal was to set as good an example as I could, when I get home I'm going to fix it and add it to the errata; but if you'd like to leave it in the version you'd like to show your students as an example, that's fine by me. This is a perfect example of what can happen when you're labouring over one detail without paying attention to all the others.

If anyone finds any other errors, let me know! Thanks!

Paul, I want to double check a couple of sources before I answer one of your questions definitively.

Majesty is right when he says that you can take much more license after the Exposition (and first Episode) are out of the way, and the only options you have regarding the subject are "Real" (the same diatonic intervals as the original) and "Tonal" (with intervals altered to make the subject fit the prevailing tonality at the time of its entrance, but with the same overall contours as the original) - though you can turn it upside down (inverted), backwards (retrograde or al rovescio), or make some or all of the note values longer (augmentation) or shorter (diminution). After the Exposition, partial statements of the subject are acceptable.

I'll answer all your questions when I get home.

Paul, to answer your questions:

1) Must the answer(s) follow the exact relative tones in another key? I've been looking at Bach's #2 Cm Fuge (From Book1) and I notice that one of the tones is changed in the first answer. This fits the harmony of the counter subject, but I'm wondering if there are some basic guidelines to follow. The answer is exact in every other way, in the Dominant, except for that one tone.

See previous posts.

2) Following on from question #1 - I would assume that a variant of the answer is allowed near the beginning of the exposition (as long as it obviously derives from the subject, follows the same notes, adds/subtracts passing tones etc...)

I would avoid variants of any kind in the exposition. I checked my sources and I can find no example of this. While I can't find a written rule that says "thou shalt not...", the absence of any examples sets a precedent at least. Note that a tonal answer does not constitute a variant. Save your variants for later.

2½) I notice the only two choices in "answers" are "tonal" and "real" whereas a tonal would use the relative pitches but keep them in the same key. For example. Subject C,B,C,E,G Answer G,F(instead of F#),G,B,D. Is there any more licence than this? For instance, the answer to the above subject pitch tones (following the same rhythm) being - D,C,D,F#,A (key of G, but not stating the tonic chord of this key in the answer)

The example you give has the same diatonic intervals as the original, and is perfectly acceptable outside the exposition. In the exposition, since a tonal answer is acceptable there, it would seem that it's allowable. That said, I would not do what you're proposing inside the exposition. I'd save it for later to spice things up, but leave things solid at the begin.

3) I've been working on #8 (G) fuge subject for some time now. Originally, the pattern of subject/answer entries was thus:

Subject(Tonic), Answer(Dominant), Subject (Dominant of Dominant), Answer (Dominant)

I assume that the Tonic-Dominant-Tonic-Dominant is a basic guideline only for statements and answers of the subject? [/b]

What you've done in your setting of #8 is not acceptable according to my sources. The tonic/dominant/tonic/dominant pattern is standard. Occasionally, depending upon the harmonic/modal implications of a subject, a tonal answer in the sub-dominant is acceptable, but it's rare.

I cannot stress enough how important it is to begin a fugue solidly. I wrote a fugato (incomplete fugue as part of a larger movement) at the end of the Agnus Dei to my Missa Brevis - before I'd studied counterpoint - and the last answer in the fourth voice entered on the mediant; while this was really interesting and dramatic, I always wondered why the whole structure of the fugato seemed to suffer from there on. I know now that it was because I had not anchored the tonality sufficiently by adhering to the exposition rules. Believe me, once you get past the exposition, things open up wonderfully. Be patient. My experience has been that if you can't get past the exposition without breaking rules, you're going to have a world of grief making the rest of the fugue work; while things open up and get freer from there, it's also much easier to make a mistake. Do yourself a favour and set your fugue up properly.

4) You state at the end of the exposition "from here it is not neccessary to Answer as was done strictly in the exposition".

Are there many more licences after the end of the exposition? If you notice I depended on alot of false statements after the exposition and especially at the end of my (edit: Gm) fuge. I assume the form is more relaxed after this?[/b]

That's right. Partial statements, incomplete expositions (though most composers do one more complete exposition after the 1st episode, it's not necessary, and they don't follow the strict subject/answer format of the first exposition), what I call "bells-and-whistles" techniques, episodes just about as long as you like. Just set the fugue up properly, i.e. according to the rules, and you're home free. As I just said, if you can't get past the exposition without breaking rules, you're building a house of cards.

Hope that helps. Let me know if I need to clarify.

See previous posts. [/b]

I'm not sure exactly what previous post you are refferring to, but I remember reading something along the lines that as long as the countour remains the same, small differences in restatement are acceptable.

The example you give has the same diatonic intervals as the original, and is perfectly acceptable outside the exposition. In the exposition, since a tonal answer is acceptable there, it would seem that it's allowable. That said, I would not do what you're proposing inside the exposition. I'd save it for later to spice things up, but leave things solid at the begin. [/b]

I'm not sure which your referring to. The melody example was C,B,C,E,G. A "tonal" answer would be G,F,G,B,D yes? D,C,D,F#,A would be something of a modal answer I'm guessing, the fifth mode in G.

In any case, I haven't come across a fuge that has a tonal answer yet. I'm not all that familiar, but perhaps you know of one offhand.

What you've done in your setting of #8 is not acceptable according to my sources. The tonic/dominant/tonic/dominant pattern is standard. Occasionally, depending upon the harmonic/modal implications of a subject, a tonal answer in the sub-dominant is acceptable, but it's rare.

I cannot stress enough how important it is to begin a fugue solidly. I wrote a fugato (incomplete fugue as part of a larger movement) at the end of the Agnus Dei to my Missa Brevis - before I'd studied counterpoint - and the last answer in the fourth voice entered on the mediant; while this was really interesting and dramatic, I always wondered why the whole structure of the fugato seemed to suffer from there on. I know now that it was because I had not anchored the tonality sufficiently by adhering to the exposition rules. Believe me, once you get past the exposition, things open up wonderfully. Be patient. My experience has been that if you can't get past the exposition without breaking rules, you're going to have a world of grief making the rest of the fugue work; while things open up and get freer from there, it's also much easier to make a mistake. Do yourself a favour and set your fugue up properly.

This makes alot of sense and I think that you're right. Thank you for responding as you did - however I must go through the process of self torture just to make sure that it can't be worked. I do appreciate the input though. If at the end of the writing I still feel unsatisfied, at the least I will have an idea as to why.

I'm curious if you would post (or send) your fugato at the end of your Agnus Dei, I'd like to hear it to know if I get the same feeling as you do - did you use the mediant key elsewhere in a restatement of the exposition or in episodes? I mean - does the mediant key feature as a regular part of the harmonic structure?

I don't want to impose. Up to you.

Anyway, thank you again for the lesson - it's very good - and for your thoughtful response.