The art of the fugue

[cptexas]

I'm attempting to write a fugue and I have a question about "proper" fugue form.

When each voice comes in it comes in a fifth higher (or fourth lower) than the previous voice did. By the time I get all the voices in, I've completed the entire circle of fifths!!

Should I put in mini developments that end up a couple spaces back on the circle of fifths? Or should the virtual musicicans just deal with playing all those sharps and flats? Eventually all those sharp additions or flat subtractions will get boring. It always goes the same interval. How do I add more interest? If I do put in mini developments, how do I morph into different keys?

Fugues are HARD!!

Thanks,
-Chris

[jesshmusic]

Not quite.

The first voice comes in on the tonic, the next on the dominant, the next on tonic, back and forth for as many voices as you have. So really, you only use two partials in the circle of fifths.

[newmewzikboy]

huh?

nononooooo

First voice Tonic ex A
Second Voice Dom ex E
Third voice Tonic ex A
4th voice Dom key ex E

and lots of trash in between

Get out your WTC

Can also be I - anything - I - anything etc,..

[jesshmusic]

Oh, and BTW, there is a good book by the same guy that did the translation of the Fux counterpoin book called "A Study of Fugue" or something similar. To add more interest, you get into counterfugues, double and triple fugues and imitation.

There is also a somewhat specific cadence formula to follow when learning. If I remember correctly you cadence on the third, fifth, then tonic to end. I may have the third and fifth reversed. There is no set length for the exposition. Bach was the ultimate master of fugue and his fugues should be thoroughly analyzed. I have always thought the fugue to be the great test of a composer's skill because there are set rules to follow. If not followed, well one is just writing music, not a fugue.

[jesshmusic]

Can also be I - anything - I - anything etc,..

Technically this would be imitation, not a fugue. Which is also a lot of fun to write.

[Nickie Fønshauge]

Chris, take a look at Kunst der Fuge . It has a few good articles about fugues (in english) plus a wealth of fine MIDI's.

[Poolman]

You might find these notes which I wrote for a pupil useful. They don't tell you every last thing about fugue but they should keep you on the right lines. (N.B. These are the traditional rules. Composers like Bartok didn't feel bound by them. Bartok actually did run the cycle of 5ths you mention.)

Writing a Fugue

What is a fugue?
Nobody quite knows. It has been described as a texture rather than a form, but it certainly has form. The problem is that the form seems different with every fugue you examine. But all fugues have certain things in common:
1) A fugue is contrapuntal, for a fixed number of voices, or instrumental parts corresponding to but not necessarily behaving like voices, (i.e. individual melodic lines rather than melodies sticking to vocal ranges or styles.) Chords are avoided except possibly at final cadences.
2) It is based on one chief motive/melody which appears in each voice in turn. There may also be one or more subsidiary melodies.
3) At the beginning, the main theme (subject) is given out by one voice unaccompanied, then a second joins in with (virtually) the same subject, thus making two melodic strands, then a third and so on until all voices have joined in. As the organist said when he played a fugue at the end of the service “In a fugue the voices come in one by one, and the people go out one by one.”
4) Subsequent to this exposition, the subject should continue to appear in one voice or another from time to time at the composer’s discretion, always maintaining counterpoint, and developing or furthering the subject in some way.

There are few rules as such, and what few there are get broken sooner or later. Indeed some pundit once said “There is not a single correctly written fugue among Bach’s ‘Forty-eight’”. Strange when Bach is considered the greatest master of fugue! The truth is that no two of his fugues are alike because he was demonstrating which construct would suit this subject and so there is no set pattern. Some fugues use this device, others use that device, and so on according to what possibilities the subject suggests.

What all fugues have in common is the idea of an exposition introducing the voices through a subject and answer. Let’s define the “rules”:

Rules for writing an exposition
1) Create or choose a subject. It shouldn’t be too long or the fugue could get out of hand. Some subjects consist of a “head” and “tail”, i.e. two contrasting phrases probably broken by a short rest. But constant flow is OK too. Decide which voice is going to start with it. We’ll assume 4 voices SATB. Then the voices should alternate high voice, low voice etc. Viz SATB or SBTA or ATBS or ASBT or TBSA or BTAS but not STAB or BATS and so on. This is important to preserve the idea of alternating keys tonic and dominant, - or more accurately upper and lower ranges. In any case the 2nd and 4th entries will be called the Answer. This may be a straight transposition into the dominant key, in which case we have a Real Answer, or more likely the Answer will have to be modified, in which case it is a Tonal Answer. The rules in a nutshell are:
a) If the Subject starts on the Tonic note then the Answer starts on the Dominant note;
b) If the Subject starts on the Dominant then the Answer starts on the Tonic,
c) A leap (or other prominent move) in the subject from D to T or vice versa must be answered by its converse (even a little way into the subject)
d) When all this has been satisfied, the rest of the Answer is a transposition of the Subject a 5th higher/4th lower.

Examples in C major: Sub CGEDCDCB Ans GCBAGAGF#
Sub GAGCBAG Ans CDCGEDC
Sub CEGFEDC Ans GBCCBAG

The answer must be accompanied by the previous voice continuing with a new melody, and so on throughout the Exposition until all voices are going simultaneously. If the same melody is used in the “previous voice” each time the Sub/Ans appears, then this melody is called the Countersubject. It must be written in invertible counterpoint with the Subject so that it can appear both above and below it. One important point is that the first appearance of the Answer and its countersubject should stay in the Tonic key as long as possible.

2) It may be convenient to insert a new linking passage between the 2nd and 3rd entries, so as to bring the key back to the Tonic. This will be called the Codetta.

Rules for the rest of the fugue
There aren’t any, other than the implied need to present the Sub/Ans in one voice or another from time to time, preferably sharing out the entries to the various voices with an even hand. These remaining entries will modulate through related keys so we can probably talk about Middle Entries and Final Entries (Tonic). For the rest, one chooses from the following list of possible devices, as thought appropriate:

1) Episodes. These are sections which either avoid the subject and countersubject or use material freely developed from them. Their purpose is twofold: to relieve the ear from the Sub, and to achieve modulation to the key required for the next entry of the Sub.
2) Stretto (lit. “drawing together”) Virtually a canon of the Sub with itself or with the Ans. Even if it only works for part of the Sub it is worth doing. If ALL voices take part in a stretto using the complete subject, this is called a Stretto Maestrale. One good compromise is that the first three voices are unable to complete the Sub but we make the last one complete.
3) Using the Countersubject at each entry of the Sub. This is obviously a labour-saving device as well as helping unity. Sometimes a third melody can be used in the Exposition so that we have triple counterpoint; then the middle entries will show various inversions of the three tunes.
4) Melodic inversion of the Sub.
5) Augmentation and/or diminution of the sub (double or half note values).
6) Dominant Pedal near end, and or Tonic Pedal at end
7) Coda on new material or new way of looking at old.

Overall plan
Do not try to include all the above devices. A useful plan is:

Exposition Tonic (and probably Dominant) key
Episode 1 Built on fragments from Expos. And itself in double or triple counterpoint. Modulate to relative minor.
First Middle entry(s) in relative minor. One or two entries
Episode 2 New or derived. Simple 2-part work, using sequences. Modulating to Subdominant key
Second middle entry(s) in Subdom key.
Episode 3 Reworking of Episode 1 by inverting the parts. Modulating to tonic key
Final entries Tonic key mainly. Stretto if possible.
Optional short coda reaffirming tonic.

Footnote
It is not necessary for all voices to participate all the time, after the exposition. Sections in 2-part counterpoint may be appropriate for a short time. When however a voice has rested, it will draw attention to itself when it does enter, so give it the Sub or something important.

[joaz]

I just wanted to praise Poolmans masterly exposition on the art of fugue.
You make it sound such fun,it makes me want to write a few more.
Admirable clarity,I now understand why you have students Queueing round the block for your lessons.
Superb.
regards

[Jerry W.]

Terry!

Thank you for sharing this! This finally makes sense to me. I have studied fugue writing before but it never seemed to REALLY make sense. The above really helped explain things precisely.

thanks again

Jerry Wickham

[cptexas]

Wow, Terry!
That was really helpful!

I think I'll just do my fugue as a composition that's somewhat fugue-like. Maybe pull a Bartok, I don't know yet.

Thanks again!
-Chris