Hello everyone! Someone I know recently asked me a question about the g minor fugue from book 1 of the Well Tempered Klavier, and in answering that question, I decided to do my own analysis of the fugue. In addition to sending it to her, I have decided to post it here with some commentary. First of all, before doing any analysis, I would highly recommend listening to both the prelude and the fugue with a fresh ear and an open mind!

In doing this analysis, I have only focused on the fugue, and will therefore not be talking about the elements that the prelude and fugue share. Please do remember that these were written together for a reason, and there are certainly connections between the two pieces. Let's talk about the fugue!

Analysis of Fugue

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Please understand that I am still a student, and the information to follow is only my educated opinion

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Form

The first thing to consider (usually when listening to or reading through the piece for the first time) is the form.

For those of you who are unfamiliar with the form of a fugue, a fugue begins with an exposition. This exposition occurs while the voices are still entering. Each voice enters with a statement of the subject either in the tonic or dominant key (in some cases the answer might be in the subdominant). Often times, there will also be a countersubject (or sometimes multiple) that is stated (almost) every time the subject appears following the first entry. The countersubject usually utilizes material from the original subject. With that in mind, it is important to realize that **most of the material of the fugue comes from the original subject. **

After the exposition comes a series of episodes and middle entries.

An episode serves the purpose of developing some of the material from the subject while shifting the tonal center. An episode can be identified as a section in which there are no complete subject entries, and instead there is free counterpoint (which usually incorporates elements of the original subject).

A middle entry will contain a statement of the entire subject (and countersubject) in a variety of different keys. These entries might incorporate different ideas in accompanying the subject entry.

There will usually be several episodes and middle entries until an arrival is made back in the tonic key (for the last time). Often this final section will contain one or more statements of the subject, and will usually be a climatic point. In the case of this fugue, the subject entries overlap in what is called a stretto - meaning that one voice will enter with the subject (either fragmented or in entirety) before the other voice has finished its statement of the subject.

In the case of this fugue, there is one episode followed by several middle entries varying from B flat major to c minor. There is a brief (2 measure) episode, and then more entries ending with an entry in g minor. This entry cadences in g minor and is then followed by the third and final episode which leads to the dominant of g minor.

After this arrival on the dominant of g minor is the final section. This section sees a stretto entry of the subject in three voices. Two entries (the soprano and tenor) are complete, and one (the bass) is only the first 4 notes of the subject. The section ends with a statement of the subject by the alto, and a statement by the tenor during the final cadence.

Subject, Answer, and Countersubject

The first thing to look at when analyzing a fugue is certainly the entries of the subject and answer in the exposition. In this case, the answer is altered slightly for harmonic purposes, and therefore will be labeled a tonal answer (as opposed to a real answer). Within my analysis, I colored the subject entries blue, and the answers (in the exposition) red.

Here is the subject when it enters in the alto voice in g minor:

Here is the tonal answer when it enters in the soprano voice in d minor (the dominant):

The next thing to notice is if there is a countersubject. In this case, there is, and it is an inversion of the subject. Throughout the piece, I have labeled the countersubject in orange. Here is a picture of the counter subject, as well as a table showing which parts of the countersubject are inverted from which parts of the subject:

Segment of Subject	Inverted Segment in countersubject

Recurring Motifs

The next thing to do is look through the piece, and find any motifs which seem to be recurring. I noticed that the end of the subject was frequently used as a motif throughout the piece, and labeled it in purple to show this connection (since purple is fairly close to blue). I also noticed that the inverted version of this from the countersubject appeared frequently as well, so I labeled that in yellow to show the connection (since yellow is fairly close to orange).

I also noticed another motif that recurs several times. I labeled this in Green. I labeled the inversions of this motif in a teal.

I also noticed a motif that occurred directly twice, and three times if you counted an occurrence that was similar. I labeled this in a purplish color.

Lastly, I labeled moments that were similar in character to the first four notes of the subject (but not quite the same) using a variant of blue.

Harmonic Analysis

Within contrapuntal pieces, it is usually best to take harmony with a grain of salt, and instead look at the melodic lines. However, there were four places where I labeled harmony with roman numerals. These places were clearly strong cadences in my opinion. Just because I do not have harmony labeled in other sections does not mean there is no harmony occurring. I just think it is counter intuitive to focus on the harmony in an analysis that should focus more on the elements of melody such as counterpoint and motific ideas. Here are the four places where I labeled harmony:

The first is a cadence in the relative major of B flat major. This cadence comes at the end of an episode, and is immediately followed by an entry of the subject.

The next place is a cadence in g minor before the third episode. This cadence isn't as strong because it lands on beat three and immediately moves on, but I still considered it to be an arrival point because before it, there are many entries of the subject all leading towards the cadence, and after it, we hear the final episode.

The next section I labeled comes at the end of the final episode. I figured I would label this arrival on V because it incorporates an Italian sixth, and it is definitely an interesting harmonic decision that brings out the arrival on dominant of g minor. After this arrival, the final section begins.

The last cadence I labeled comes at the very end of the piece. It confirms the final key as g minor, and ends with a picardy third (as is customary in a minor baroque piece).

Entire Video Analysis

Here is a video of my analysis of this fugue:

Application of analysis to playing

I would also like to discuss why I find it extremely helpful to analyze a piece before playing it. Ultimately I think that the job of the performer is to understand the interconnections of the piece, and devise a strategy in their performance that will lead the audience's ear to the same connections.

For instance, when playing the countersubject, it would be extremely beneficial to try to incorporate the same articulations as are incorporated in the analagous figures (though inverted) in the subject.

These little connections are what make Bach (and many other composers) so fascinating to listen to, and the best performances (in my opinion) are the ones that highlight them!

Conclusion

Thanks for reading this! I am going to submit this to Steemit's new learning category, and I hope that this article has helped some of you! If you are confused about anything, or have any questions, please feel free to leave a comment! I have actually learned one pair of the Bach Preludes and Fugues from book 1 of the Well Tempered Klavier for school, and I hope to post a performance and analysis soon!