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General Music Theory and Tutorials => Basic Harmony and Counterpoint => Topic started by: Michel.R.E on October 23, 2012, 12:09:55 PM

Title: fugal form and development 101
Post by: Michel.R.E on October 23, 2012, 12:09:55 PM
Since the topic has come up, and I KNOW how difficult it can be when one has less experience in counterpoint, I thought I'd give a few simple, vague, and general pointers on how you can advance material that is fugal in nature, even when you don't exactly have a solid background in the study of fugue itself.

quick "dictionary" of fugal terminology:
Quote from: Michel's dictionary of fugal terminology
  • subject: the "theme" of the fugue, as stated in its "home key"
  • answer: the 2nd entrance of the fugue theme, nominally in the dominant
  • countersubject: a different thematic element which accompanies the "answer" (or "theme" in a non-tonal fugue) which (when used) will ALWAYS be present during expositions.
  • exposition: the statement of the subject/answer in all "accounted voices" (ie: a 4-part fugue would have four statements of the material one after another)
  • episode: what happens BETWEEN each exposition of the subject/answer
  • stretto: superimposition of the subject upon itself at a shorter interval than the complete length of the subject (ie: entrances coming 2 beats apart, rather than a full measure)
  • pedal: held note in the bass, over which contrapuntal elements will play, generally reserved for near the end of a fugue, shortly before its final cadence (the effect of a pedal is to create anticipation for the final cadence. in "classic" fugue, the pedal can be on the dominant (generally) or on a secondary dominant (rarer)
  • parallel octave: two voices playing the same notes in a row. This does not refer to an octave doubling as might occur during the process of orchestrating a passage. In this particular case, it refers to generally only two notes in a row (if you are doing three notes in a row as parallel octaves then you got some work to do!!). If your soprano plays E - F - G, and your bass plays G - F - G, then the F and G are parallel octaves.

it seems that almost everyone knows how to do a fugal exposition. it seems almost instinctual, even! but still, a quick cover of the basic principle.

1) your subject should be "unique". Try to avoid fugue subjects that change tempo, change rhythmic values dramatically (ie: very slow beginning, very fast ending). This isn't a "rule". It's a suggestion to help along the way to learning how to do it, and gaining more ease.
The interest in a fugue is rarely the exposition itself. Where the true "creativity" appears, is in what's AFTER the exposition. Thus the suggestion to keep the fugue theme itself simple and easily identifiable. Your goal is not to obfuscate the fugal subject. Your goal is to create a sense of expectation for when it returns.

2) Countersubjects should not make reference to the subject itself. It is, as its name suggests, "counter" or contrary to the subject. The countersubject should have a uniqueness of its own.
This said, the use of a countersubject is NOT obligatory. There are many perfectly satisfying fugues that do not contain countersubjects. In my opinion, the use of a countersubject might be preferable in shorter fugues, while a freer approach to counterpoint might be more desirable in longer-form fugues.

3) entrances in the fugal exposition should be in different keys. In a classical fugue, those entrances are normally: tonic -> dominant -> tonic -> dominant. But using expanded tonality, or non-tonal harmonic systems, you can obviously break from this.
Still, try to keep a certain consistency to the process. I've done quartal fugues, where each subsequent/answer entrance was a 5th/4th away. And I've seen some do fugues where subjects/answers come in at the 3rd. Schuman's 3rd symphony starts with what he calls a "Passacaglia", but which is in essence a large-scale fugal exposition, with each theme coming in at the interval of a 2nd.

There's that word now... what the hell is an episode?
It is a modulatory passage that links two expositions in a fugue. In other words, your first exposition starts "in one key" (or tonal area). You then have a modulatory passage, an "episode", which leads into a new exposition, which itself is now in a different key from the first exposition.

Episodes should generally avoid any reference to the subject of the theme. however, you may use the countersubject as a source for thematic material to construct episodes.
In a classic tonal fugue, episodes are often quite simply harmonic marches. However, nothing stops you from taking a freer approach to episodes. You might make some episodes harmonic marches, while others are free counterpoint, all within the same fugue.

A suggestion: keep any material drawn from the subject for as close to the end of your fugue as possible. For example, your very last episode, which precedes a pedal, COULD be based upon the very head of your subject (the first beat, or few beats) IF the head of your subject has a very characteristic nature.  In this way, you are augmenting the anticipation for the actual return of your subject.

I'll try to add to this post as we go along.
Please feel free to pose questions

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Title: re: fugal form and development 101
Post by: Michel.R.E on October 23, 2012, 12:20:05 PM
More info:

Generally speaking, an episode will have one fewer voice than an exposition.
So if you have a 4-part fugue, your episodes will generally have 3 (or fewer even) voices.

Whichever voice is silent during an episode is also the 1st one to restart the subsequent exposition.

a classical fugue might be constructed as follows:

exposition 1 (in the home key), 4 voices
episode 1, which modulates from home key into new key (NOT the dominant), in 3 voices
exposition 2 (in new key), 4 voices
episode 2 (modulates from "new key" into another key), 3 voices
exposition 3 (in new new key), 4 voices
episode 3 (modulates from new new key, toward the dominant), 2 or 3 voices
pedal on dominant, 3 or 4 voices
coda in tonic, often with stretto.

The point is to avoid presenting your subsequent expositions in a key that has already been stated in the very first exposition. (this is why I say "not the dominant" for valid destinations)

A fugue is, as its name suggests, a "running away from"... your home key, toward a distant key, to eventually return to your home key.

Other tricks that can be brought to your subject to lengthen a fugue:

You MAY create a modal variant of your subject/answer pair, and use that as an exposition later on in your fugue. For example, a subject that is "major" can be modulated to "minor" for an exposition or two.

Since we're talking about modern fugue as well, you may consider creating an abbreviated version of your subject/answer, which MUST still retain the characteristic elements that will make it recognizable to a listener. The use of a shorter version of the subject/answer pair can help in creating a sense of momentum.

Regardless of what type of harmonic language you are using, parallel octaves are always a thing to avoid.
Even in non contrapuntal music.

However, in a fugal setting, they are anathema.

So always check each note of each voice against the notes of each other voice, to see if there are unisons.
Unisons are permitted, but if you have ONE unison, you have to be doubly vigilant that you don't inadvertently add a 2nd one immediately afterward... that would make it parallel octaves.

Also, avoid landing on a unison or an octave from a leap. This really creates a sense of "voice disappearing".
Your goal is a fluid sense of independent voices, working separately, yet together.

Title: re: fugal form and development 101
Post by: Michel.R.E on October 23, 2012, 12:20:35 PM
Some examples of things to avoid while writing counterpoint of any sort are attached in a PDF I prepared.

It demonstrates parallel 8ves, direct octaves, and a few principles that are important to keep in mind at all times while writing anything contrapuntal.

Always remember that counterpoint involves the independence of voices. Not harmony. But voices.

In standard "scholastic" counterpoint (the type taught in school), you write as though for voices, so within a certain restricted range. This is an excellent learning tool. Because you are forced to write FOR each individual voice. An alto part cannot be a tenor part, and so forth.

In this type of strict counterpoint, voices should not cross. Unison is permitted (ONE note only, never two in a row, because that would be - all together now - parallel octaves).

Series of parallel 3rds are permitted, but within limits. Yes, writing a bunch of parallel 3rds will definitely avoid any potential parallel 8ve issues... but it won't be counterpoint. So try to create independent voices. Break rhythms, make counter-melodies, use lots and lots of contrary motion (a contrapuntalist's best friend).

If possible, make as much use of suspensions as possible. They are a fugue's greatest asset.

Now, while you ARE creating independent voices, the harmony that those voices implies MUST be clear, and logical.

Do not leap to non-chord tones unless you are resolving to a chord tone afterward.
Don't leave non-chord tones hanging. Regardless of what type of harmony you are using, you should be consistent within that framework.

Try to imply directionality with your voices. Don't pop in lots and lots of "colouristic" chromaticism that serves no harmonic purpose, if they don't actually LEAD to a new harmonic zone they are only confusing the linearity of the writing.
The above comment about linearity applies also to non-contrapuntal writing.

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Title: Re: fugal form and development 101
Post by: Michel.R.E on October 23, 2012, 12:20:52 PM

episodes can be very straightforward harmonic marches that bring you from one key into another.
or they can be relatively free moving counterpoint that also leads from one key into another.

Re-expositions may contain all entries of parts, or may be partial expositions.
for example, you have 4 voice fugue.
1) initial exposition in 4 parts.
2) 3-part episode
3) re-exposition only stated in one single voice,which immediately goes into (this is in 4-part counterpoint)
4) 3-part episode
5) re-exposition using only two statements of subject, but both in same key (this IS permitted in re-expositions, and again, is in 4-part counterpoint)
6) 3-part episode
7) full 4-part re-exposition

Title: re: fugal form and development 101
Post by: Michel.R.E on October 28, 2012, 12:02:22 PM
Updated to include a PDF skeletal layout of a short fugue.
(see the first post of the thread)