A Crash-Course In Writing Fugues

[J. Lee Graham]

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.

Fugue_Lesson.pdf

Fugue_Lesson___MIDI.MID

PDF

• Fugue_Lesson

[PaulP]

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...)

2

[leightwing]

JLG, if this isn't the coolest thing I

[PaulP]

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.

[leightwing]

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.

[Majesty]

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.

[J. Lee Graham]

* 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!

[J. Lee Graham]

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.

[J. Lee Graham]

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.

2

[PaulP]

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.

[The Baroque Enthusiast]

Great work, JLG! A clear and concise introduction to the world of fugues!

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.

A few years ago, when I was just starting out with all of this fugue business, I tried a tonic/subdominant/tonic/subdominant pattern for the exposition. Even though the rest of the fugue was solid, the faulty exposition made it difficult for the ears to "zone in" on the tonic.

Do you have an example, or reference for me to seek out, where a subdominant tonal answer is acceptable? - BE

[J. Lee Graham]

I thought I just saw one in Alfred Mann's "The Study of Fugue," but now I can't find it. :(

[PaulP]

I need to give J.Lee the credit he's due. I ignored his advice and wrote a fuge on the Cm theme (well - partially, anyway-unfinished) - with an exposition that followed a Tonic-Mediant-Tonic-Dominant format. Needless to say - Tonic doesn't feel like home. Mediant does, for some reason.

Here it is for example sake.

My revolutionary days are over. :happy:

Thanks J Lee. :)

CmFuge_unfinished_.mid

[PaulP]

Thank you Chris, I like it too - but it still does lack that strong central tonality that J. Lee alluded to in his answer to me.

[J. Lee Graham]

This is why "the rules" are what they are...our forebears in composion crossed all these bridges before us, and we have the benefit of their experience if we pay heed.

Paul, I'm going to try to find the MIDI to the Agnus Dei of my Missa Brevis today or tonight and post it. I'll listen to what you've posted when I'm not at work, prolly tonight!

Chris, my pleasure.

[cmajchord]

I'm sure someone's asked this already, but I don't want to look everywhere for the answer...

J. Lee, why do you post your scores in that weird, quasi-neume notation?

[J. Lee Graham]

I'm not sure what you're seeing on your end, but it's standard modern notation. Was that a dig at Finale's font? Or maybe you're commenting on what Acrobat does to it?

[cmajchord]

I'm talking about the pdf files. I get little boxes everywhere instead on notes.....

Same thing with your other stuff, like from the chorale challenge.

I thought you were just eccentric or something.

By the way, have you listened to my treatments of your melody #1 in "harmonize a melody?"

[J. Lee Graham]

I have updated the original files to correct the hidden parallel octaves I committed in measure 53. The error is now included in the errata. Thanks to Leightwing for his sharp ears and eagle eyes.

Paul Poehler - per your request and pursuant to our discussion, I have (finally) attached the Agnus Dei of my Missa Brevis hereto as a MIDI. If you'd like a PDF, I can e-mail it to you.

The brief fugato I mentioned begins at measure 53, after the key and metre change at the dona nobis pacem. The subject of the fugue is a reprise of the main theme of the Gloria to the dona text.

Note the entrance of the bass at measure 63; it begins on B, the mediant of G on which the tenor begins the exposition, which is rather irregular; by sheer luck, I get away with it because in that tonality, the bass' statement of the subject ends squarely on G, which leads to a cadence in the tonic key of the movement. I also get away with it because this is not a stand-alone fugue, nor is it by any means a complete one: after the exposition, there is only one more statement of the subject in the soprano before I take off into an extended pedal point under partial harmonic statements of the subject in all four parts (measures 68-69) in stretto - the alto and tenor with simultaneous statements (peculiar in that the opening leap of a fourth is augmented in both), followed by simultaneous statements in the soprano and bass two beats later, the bass' statement in inversion - after which there is an elaborate modulation over the pedal point to a deceptive cadence and an Adagio coda.

[PaulP]

Thanks for replying Lee.

The reason I asked this question is because I simply don't understand why a Tonic-Dominant-Tonic-Dominant establishes the root key of the tonic. I understand that (within a key) this establishes it quite well (that is, with Dom7), but here we're talking about 2 different keys. Keys that are only 1 sharp or flat away, no different in this respect than other nearly related keys to the tonic.

Earlier when I asked about a different key format for the exposition you gave as an example this fugato - which I'm looking at now. The entry of the mediant in the Bass voice is nice - but you're right, it does get a little awkward from there.

I'm wondering if you have ever tried to modify it so the bass enters on the Dominant per the exposition rules, then keep the same (rhythmic) changes in key you've done from there.

I'm going to look at this further, but one thing I notice right away is that when T,S,A voices state the theme, the key is pretty uniform throughout each statement. Tonic key, Dominant key, Tonic Key. However, when the Bass enters, before reaching the end of Bass's statement of the theme, you move through quite a few keys.

I'm no expert in this, but it would seem to me that tonal center for the Bass part sounds a little awkward solely for this reason. For each of the other entries you stay in the key it enters on for the most part. For the Bass entry, you move through quite a few. This isn't exactly "harmonic rhythm" - but it is sort of - key rhythm, if you will.

53-55 Key of C - 3 bars

56-58 Key of G - 3 bars

59-62 key of C - 3 bars

63 Key of Em - 1.1 bar only

64.2 Modulate to C through G7

65.1-65.3 Establish G key

65.4-66.1 Establish C key

66.2 Re-establish G key

66.3 Re-establish C key

What do you think?

I'm going to look at this more in depth later. Thanks again for sharing it. I hope you don't mind me analysing it like I've done here. I'm just trying to understand the reasons for the exposition key layout.

On the whole, I enjoyed this music, btw.

[J. Lee Graham]

I'm wondering if you have ever tried to modify it so the bass enters on the Dominant per the exposition rules, then keep the same (rhythmic) changes in key you've done from there.

No, I never have. I tend not to revise pieces once I deem them finished, rather allowing them to serve as a evidence of who I was as a composer at that particular point in time - warts and all. I'm going to look more closely at your comment when I get home, and perhaps just for the sake of edification, I may try to re-write the bass entrance; it's the only thing marring an otherwise satisfying movement. I would still want to end up at the same place for the pedal point because I rather like the tension built up and resolved there, but with a quick modulation, that's likely quite possible.

On the whole, I enjoyed this music, btw.

I'm glad! I decided not to post the whole Mass here because YC people don't really pay much attention to choral music, for whatever reason, and also because this is a rather personal religious expression.

I don't know if you're familiar with Mozart's early Masses written in Salzburg, but this Missa Brevis is built on that model. The Archbishop was a rather secular clergyman and didn't like to spend much time saying Mass, so he gave directions to Mozart that his settings for the Canon of the Mass should in their entirety take up no more than "a quarter of an hour." They're also scored for relatively modest forces, though festively arrayed: mixed chorus with soloists, 2 trumpets, timpani, 2 violins and continuo - also the scoring of my piece. Mine differs from Mozart's primarily in that I have not set the Credo , on account of it not being liturgically feasible nowadays; I was trying for a setting at once artistic and viable liturgically.

Incidentally, this Agnus Dei was written while I was recovering from an appendectomy. Go figure.

[EmmDoubleEw]

Thank you so much for this! I will read the whole thing.

Thanks!

[cmajchord]

I have been inspired by this thread and the fugue challenge thread. I've written several little stand-alone fugues, of which I'm happy with 2. I am now going to try to incorporate a fugue into the development of a symphonic movement I'm writing. I do however need some words of advice.

The expo. if myy symphony has so far been an unashamed attempt to clone Mozart. I am also using a small orchestra, 2 flutes, 2 horns +strings. Here are my questions:

1. Should I do an actual fugue or is a fugue-like (fugato) section more appropriate?

2. If I write a fugue, should it necessarily be 4 or more voices as opposed to 3 voice?

3. Should I use the entire orchestra by doubling voices?

4. If the voices are doubled, should they go violin I+flute 1, Viloin II+Fl. 2, etc or Violins I+II, Fl 1+2?

5. Would it be appropriate to attempt a double fugue in which the first subject uses either strings or winds and the other subject uses the other group?

6. Any other suggestions?

I'm more than willing to experiment, but my fugue writing attempts so far have been VERY time consuming, and I'd rather not waste my time trying a "stupid" approach.

I welcome any comments. Thank you.

[J. Lee Graham]

I'm really glad that the counterpoint threads here have inspired you. I believe - as does Brandon Homayouni, the author of the Fugue Challenge thread - that nothing will speed and hone your development as a composer quicker and more surely than this kind of exercise. I find that it opens up new areas of my artistic mind every time I attempt it.

To answer your questions, here's my input - others are more than welcome to add their own:

1. Should I do an actual fugue or is a fugue-like (fugato) section more appropriate?

In the context of a symphonic development, a fugato is more appropriate in my opinion. It might typically consist of an exposition, an episode, and perhaps another full or partial exposition. Much more than that will be difficult to balance in the movement.

2. If I write a fugue, should it necessarily be 4 or more voices as opposed to 3 voice?

I don't think it matters how many voices you employ. There is something about four or five voices that is rather satisfying in a symphonic texture - the five voice fugato near the beginning of the finale of Mozart's 41st Symphony comes to mind - but a three voice fugato, while modest, will fit the bill nicely.

3. Should I use the entire orchestra by doubling voices?

Doubling can be very effective and colourful. In the Classical period (which you are emulating) it was probably more common for the strings to perform the exposition alone and be joined by winds afterward (again, the Jupiter Symphony comes to mind), either doubling contrapuntal voices or reinforcing harmony, but use your best judgment; in Mozart's "Die Zauberfloete" overture, he brings in the bassoons to double the cellos when they enter in the exposition, and it's wonderful.

4. If the voices are doubled, should they go violin I+flute 1, Viloin II+Fl. 2, etc or Violins I+II, Fl 1+2?

I would say that 1 woodwind to 1 string part would be the best doubling. I'd probably do it flute I + violin I, flute II + violin II in your case, maybe even with the flutes an octave higher if the string entrances are in a moderate register. For stylistic reasons, I wouldn't personally have the horns double anything...that kind of thing came later when horns were more flexible, but not in the classical period. If you had a bassoon, having it double the viola strengthens their line and adds colour, or having it double the cellos (and basses if they're on the same line) reinforces the bass. If you have a strong, penetrating woodwind (oboe, for example), it might take its own contrapuntal line.

5. Would it be appropriate to attempt a double fugue in which the first subject uses either strings or winds and the other subject uses the other group?

That would be wonderful if you could make it work. Double fugues are exponentially more difficult. I haven't personally mastered double fugues yet - I have yet to make one work convincingly to my satisfaction. It's a great idea, though, and I wish you the best of luck if you decide to attempt it. Maybe you should practise first before trying to do it within a symphonic movement...you don't want to lose your virginity in a an S&M orgy, if you know what I mean. :)

6. Any other suggestions?

Keep the overall structure of the symphonic movement in the back of your mind as you write the fugato in the development; it might be tempting to overdo it. I wouldn't overbalance the movement with too much in the development, unless what you have up until then and what you think you'll be doing afterward will balance it, either in length or by the weight of its character and subject matter. Classicism is all about order and balance. Indulgence in this area was the province of a later generation.

If you decide on a 3 voice fugato, it's going to have a Galant or Rococo feel about it...that texture was rather common in the 1740s and 50s. The authentic treatment would be to have the viola doubling the cellos and basses an octave higher for the exposition, then perhaps split off onto its own non-contrapuntal supporting line.

Above all, enjoy the process, and good luck to you! I look forward to hearing the result.

[cmajchord]

Well thank you so much for the suggestions. They are very clear. I will keep them in mind during my attempts. I welcome anyone else to add their 2 cents...