What does it mean to be able to write a fugue?
My theory teacher told me once in passing that she had written fugues. Later on people let me know that to write a fugue you need to be somewhat of a theory genius. Why is this so? What makes the writing of a fugue so hard and make the people that are able to write them such special theory practitioners?
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Writing a fugue is a mixture of imagination, organization, and mastery of your tools.
If you are making a drawing, keeping track of the perspective, the objects you want to appear, and just what object will obscur what other object can be done using ruler and overpainting/erasing as you go. How much time spend masters erasing obscured objects?
Fugue writing is similar, except that it's not as much objects being obscured but rather object features of similar transparect objects lining up "incidentally" in perfect patterns.
It's not as much an inborn capability as much as an acquired skill set. But once you have acquired and practiced and honed it, you may still write boring fugues or mesmerizing ones. But the latter may no longer be an academic difference.
A fugue is one of the most polyphonic musical pieces you can write. In a typical fugue there are 3 or 4 voices in play that are each treated independent melodies. While this is going on, you have to not only have to keep all the rules of counterpoint in mind for each voice and make sure the harmony always make sense, but you have a structure to keep in mind and are expected to modulate quite a bit.
A fugue always starts with what is known as an exposition where you introduce a musical idea known as the subject in one voice to start and another voice comes in with the subject in a different key known as the answer. This continues until all the voices of the piece are in then you go though several episodes which are meant to take you to different keys and are typically sequences derived from the subject. There are also several sections known as the development where the subject is restated in whatever key you modulated to.
Wikipedia has a nice article on the typical form of a fugue and what the idea of each section is and a sample analysis of a piece to help with the explanation. I will see if I can dig up an example from my theory book to help explain the form a little better.
It's hard to explain fully how much thought goes into it until you do it. You literally need to look at every note you place in every and make sure you don't have any bad counterpoint between any of the other voices and the notes and the harmony themselves are going where they need to.
Listen to a few examples and you'll start to realize what though goes into them. Here are just a few examples:
I've even wrote one recently for a composition class that you can listen to. If you are interested I can even provide a score to analyze.
I think the reason the fugue is considered a standard for demonstrating theory/composing skill is because it is very process oriented. Fugue is often described as a process rather than a form.
The standard definition of form is essential about the layout of keys and to a lesser extent themes. The hallmark of sonata form is the 'second theme group' usually in the key of the dominant or relative major and then that materials subsequent recapitulation in the tonic key. It's the layout of the keys that defines the form. You can generalize about binary form and describe it a first part that ends in a non-tonic cadence followed by a second part that ends with a tonic cadence. What happens with the thematic material within those parts/sections isn't very important regarding the formal design.
By contrast, the fugue doesn't have a set design of keys/sections, and the various procedures employed in fugal writing are specifically concern with the manipulation of the thematic material. Those procedures are very 'testable' too, meaning you can judge whether they executed correctly.
After the initial subject of a fugue is stated the procedure applied to it can include:
stating the answer either real or tonal
counterpoint lines composed to the subject and answer which can be invertible counterpoint and may recur as countersubjects
the subject can be restated and overlapped with it's restatement a procedure called stretto
various restatements of the subject can be maniplulated with inversion (play upside down), retrograde (play backwards), and rhythmic augmentation or diminution.
All of the devices above deal directly with the main subject and are testable. So: one can judge whether a countersubject is correct invertible counterpoint, one can judge if the answer is correct, or identify true/false if stretto is employed. If we return to comparison with sonata form the presence of a recapitulation is really the only testable thing. All the rest is flexible. These testable procedures provide a good genre to display knowledge of technical devices.
While not specifically fugal procedures, fugue writing will also require a solid understanding of harmony - expository tonic/dominant harmony and sequential harmony - and how to modulate through keys and form proper cadences.
The last two bullet points on the list above are where a lot of the technical skills are put on display. A stretto involving statements of the subject at multiple intervals and rhythmic points of entry and in various manipulated forms like inverted all in correct counterpoint/harmony would be considered a high point of technical display!
Sometimes these technical manipulations are not immediately discerned by the ear. You really need to read them from the score to be aware they are being employed. If a stretto involved a long-ish subject played over its inverted retrograde in augmented rhythms, it's very hard to simply hear that second, augmented part as derived from the subject. That's another important aspect of fugue as theory display: you often need to read these things from the score to be aware of them. It's sort of like music theory 'insider' knowledge of the score.
Keep in mind a fugue does not require all these tricky procedures. In fact there is something called a partimento fugue where only the entries of the of the subject/answer are notated and the other voices are improvised like in basso continuo. I suppose you could say a fugue is anything where a melodic subject is restated as an answer. Although stylistically most people would expect the answer to be harmonized in a contrapuntal style.
So, these technical procedures are what make the fugue a display of theory skills. The more of these procedures employed, the more impressive the display to those music theory insiders who can recognize them.
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