A Crash-Course In Writing Fugues

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.

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.

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.

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

Thanks!

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.

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.

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...

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.

If you do decide to re-write the fugato, I would be interested in hearing it. No one else has commented on it in this thread, but I think it may serve as part of the instruction in fuges. I'm still not seeing how the Dominant(key) establishes the tonality, besides it being (like the Subdominant) of the same nature (major or minor) as the tonic.

I started a short little fuge recently - nothing earth shattering, on a Tonic-SubMediant-Tonic-Submediant exposition plan. It's different - and if it's not a fuge simply because it doesn't follow what's commonly done on that one point, I'd like to know exactly what it is.

I may post it later when I finish it if your interested.

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 love choral music - only wish more of it was in English. I don't remember all the Latin. I've recently ordered the scores for Bach's B minor Mass and Mozart's Mass in Cminor - K 427 for study.

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.

I know you can recommend a good biography in book form. Classical music changed my life, and Mozart's in particular - although I've never bothered to look in depth into the history. I watch the movie at least twice a year though - I know it's probably inaccurate - but I enjoy it every time.

If you do decide to re-write the fugato, I would be interested in hearing it. No one else has commented on it in this thread, but I think it may serve as part of the instruction in fuges. I'm still not seeing how the Dominant(key) establishes the tonality, besides it being (like the Subdominant) of the same nature (major or minor) as the tonic.

I should clarify that entrances at the sub-dominant (fourth) and octave are also acceptable, but the arrangement of tonic-dominant-tonic-dominant is by far the most common. I can find very few examples of tonal fugues of less than 5 voices where this is not the case.

In his "The Study of Fugue," Alfred Mann quotes Giambattista Martini (Mozart's counterpont teacher) from his Esemplare o sia saggio fondamentale prattico di contrappunto fugato as follows, commenting on a very fine six-part fugue by Claudio Montiverdi: "The composer introduces in this Agnus Dei a subject in the second tenor...which is answered in the bass...Since the tenor uses the skip of a descending fifth from d to g and the bass uses a skip of a descending fourth from g to d, a tonal fugue arises...the [1st] tenor takes up the opening statement at the unison, and...the second soprano takes up the answer at the upper octave...the alto and the first soprano answer at the third of the fifth degree [sub-mediant] and at the third of the first degree [mediant], respectively, rather than at the first or fifth degrees proper, as the other parts did. The license of letting these two parts answer differently from the other four parts has been justly adopted by the great masters, for whenever four parts, which in themselves can constitute a full harmony, have served this purpose, the parts which exceed the number of four may answer at any interval which is convenient and which will produce a good sound. Nevertheless, later in the fugue, the first soprano takes up the subject at the fifth degree...and the alto takes up the subject at the octave...Thus even these parts eventually follow the strict rule of the answer at the fifth or octave."

Now I admit that I am still very much a student myself, and I have not read every word of Mann's book cover-to-cover, but I'm basing what I know of this practise on what I have read, the many examples Mann provides, the other examples I've studied, and quotations like this from a relatively modern pedagogue, as well as garden-variety definitions of fugue that I have read elsewhere. Perhaps at some point I shall have to acquire another source of fugue and/or counterpoint instruction to get a different point of view. Mann seems to favour the strict and traditional.

At some point, we need to differentiate between a fugue for the sake of study and a fugue for the sake of art. We are modern composers, after all, and while I choose to remain faithful to the stricter interpretations of an earlier time in my artistic applications in the interest of authenticity (now that I understand them), I don't see any reason why you may not do as you please in your own artistic applications. Nowadays I doubt anyone is going to object to your handling something that is obviously a fugue in your art music on the grounds that it doesn't adhere strictly to 18th Century practice and aesthetics. That said, I believe that for the sake of study, it might be best to observe and adopt tradition. The best learning happens in a controlled environment. I'm willing to allow that experimentation that runs contrary to tradition, as you are doing, might be a useful part of this process, especially since you appear fully to understand the tradition and are questioning its validity. I would still try treating the same subject twice, once in a conventional manner, and again in an unconventional manner - like a controlled experiment - and judge the results.

I started a short little fuge recently - nothing earth shattering, on a Tonic-SubMediant-Tonic-Submediant exposition plan. It's different - and if it's not a fuge simply because it doesn't follow what's commonly done on that one point, I'd like to know exactly what it is.

I may post it later when I finish it if your interested. [/b]

By all means! You may post it here if you like, but it might be better to post it in its own thread so that you can get comments from people who are not interested in the didactic nature of this thread. Be sure to draw my attention to it when you do post, because I do a great deal of skimming nowadays.

I know you can recommend a good biography in book form. Classical music changed my life, and Mozart's in particular - although I've never bothered to look in depth into the history. I watch the movie at least twice a year though - I know it's probably inaccurate - but I enjoy it every time.

Actually, I don't own a Mozart biography in the strictly narrative sense. I do have a book called "Mozart - His Character, His Work" by Alfred Einstein, which examines Mozart from the standpoint of who he was as a human being and how it affected his work; in the process, a great deal of biographical information is conveyed. The book is arranged in major sections titled The Man, The Musician, The Instrumental Works, The Vocal Works, and Opera, with subsections within each going into greater detail. I've found it fascinating and I recommend it.

The film "Amadeus" is famously inaccurate on historical details - Mozart had two surviving children, not one; he didn't die the night of the Die Zauberflote premiere, etc...to say nothing of the whole Salieri murder premise - but it is quite accurate in its depiction of Mozart as a person, right down to that ridiculous laugh. I understand that much study was done in this area in preparation for the filming. In my opinion it doesn't dwell enough on how heartfelt and warm a person Mozart could be at times, and it gives only glimpses of how cruel and unkind he could be ("when one hears such sounds, what can one say but 'Salieri'!"). Mozart was a complex man, and there was more to him than can be adequately portrayed in 2-1/2 hours; but it's a very vivid sketch.

I'm told that Einstein recounts Mozart having told his father that he cheated on a canonic exercise in order to meet a school requirement. Evidently, the fugue wasn't one of Mozart's strong suits, even though we have examples like his Kyrie that would suggest otherwise.