Question: I’m starting to learn Bach’s Fugue in D major from Book 1 of the Well-Tempered Clavier. I’ve read your extremely useful article, How to Learn a Fugue, and I have started to practice the fugue accordingly.

My question is related to the structure of the fugue (of this particular fugue as well as of fugues in general), which is not clear to me. Could you help me analyzing it? I looked for the separate article on fugal structure that you referred to in your lesson about learning a fugue, but I couldn’t find it.

Thank you for your help in advance – I’m looking forward to reading your article!

– Marcell

Albert’s reply: While fugues can get as complex as the final movement of Beethoven’s “Hammerklavier” Sonata for piano or his Grosse Fuge (Great Fugue) for string quartet, all fugues have fundamental elements in common. As a quintessential Baroque fugue, Bach’s D major fugue from Book 1 of the Well-Tempered Clavier will make for suitable illustration of how to analyze a fugue.

The first element is the fugue subject. In a conventional (Baroque) fugue, the subject is first stated by itself:

Incidentally, this subject is an example of double dotting or overdotting. The subject should not be performed literally as written:

Rather, the held notes should be held even longer, and the subsequent sixteenth notes should be played more like 32nd notes:

Next, the subject meets with an answer in measure 2, which is a statement of the subject in a new voice:

In a Baroque fugue, the answer can be either real or tonal.

A real answer is an exact transposition of the subject to the dominant. If any of the intervals is not identical to its corresponding interval in the subject (i.e., if any interval has been changed in any way), the answer is tonal.

In the case of the D major fugue, the answer is real, since each interval is exactly the same.

The introduction of all voices forms the exposition of the fugue (not to be confused with a sonata form exposition). All voices need to be introduced with a statement of the subject one after another, although they need not come in any particular order. In this fugue, Bach introduces the voices in order from low to high.

Here are the third and fourth entries, in measures 4 and 5:

Notice how the entries during the fugal exposition alternate between tonic (D) and dominant (A)?

The D major Fugue has no countersubject. When the second voice enters, the first voice plays new material. If this material becomes thematic (i.e., if it continues to be used), then it is the fugue’s countersubject.

Measure 3 does not have an entry of the subject, and upon first glance it seems to consist entirely of new material. However, if you look (and listen!) closely you’ll discover that Bach augments part of the subject by lengthening its rhythmic value, in this case turning 32nd notes into sixteenths. (Doing the opposite, reducing the rhythmic values, is called diminution.) Here are measures 2 and 3; the subject fragment and its augmentation are marked with brackets:

Measure 6 starts the first development (or developmental episode), with two false entries in the tenor:

A false entry occurs whenever a statement of a subject is left unfinished. The subject is stated in full in the bass and soprano voices in measures 7 and 8, respectively. There is a cadence to measure 9, which then starts the next developmental episode.

In addition to two false entries in the bass, measures 9 and 10 contain new episodic material:

The episodic material is derived from the fragment of the subject, and augmented as in measure 3. The purpose of the episode is to modulate to a new key, in this case the subdominant, G.

Measures 11 through 17 contain a stretto. In a stretto, entries of the subject overlap, meaning another subject starts before the previous one completes. Most stretti do not state each subject fully. This stretto is nearly a stretto maestrale, in which each subject appears in full. Here are measures 11 and 12:

Measure 16 ends with a cadence to E minor, which is reached on the downbeat of measure 17. Measure 17 thus starts the next section of the fugue, which is a third development, stretching to measure 22. This section (mm. 17–22) recycles material and techniques heard earlier – false entries, stretti and the episodic material found in measures 3 and 9.

Now the fugue reaches the tonic, D major, with a powerful cadence ending on the downbeat of measure 23. Measures 23 to the end thus form the coda. The coda simply brings the fugue to a conclusion, freely revisiting thematic fragments and reinforcing the home key.