# Analysis of Bach's fugue BWV 846 in C major (WTC I)

by José Rodríguez Alvira

This fugue in C major, the first fugue from the first book of Bach's Well-Tempered Clavier, presents several interesting aspects:

• The exposition presents the voices in the unusual order of subject - answer - answer - subject.
• After the exposition Bach present numerous stretti without any interruption.
• The only measures where the subject is not present are measure 23 and the two last measures of the fugue.

Some authors propose various numerological symbolism. The 14 notes long subject is said to be related to Bach's name:

B = 2, A = 1, C = 3, H = 8
2 + 1 + 3 + 8 = 14

It is also said that the subject appears exactly 24 times in this fugue representing the 24 fugues in the first book of the Well-Tempered Clavier. But as you will see in our analysis, there are only 22 complete subjects. To be able to get to the total of 24 subjects you need to include two incomplete presentations of the subject. The 1st incomplete appearance is in measure 14:

As you can see, the 4 last notes are missing. Yet, this voice enters in a stretto, so you really hear it as a subject entrance even if the 4 last notes are missing.

The 2nd incomplete appearance is in measure 15. In this measure only the first 7 notes are presented:

In the 3rd incomplete appearance in measure 20, we only hear the first 3 notes (although you may find some relations between the sixteenth notes in the next measure with the 32ths notes of the subject):

It is up to you to decide...

Follows the complete analysis of the fugue. We have numbered the subject and answers appearance. Incomplete appearances, appear in green color: