raffaeleb wrote:A question for Altieri
Why does the subject in the second entry have a variation in the third note which, instead of being (Example in A: A C E results in A C D) being a way to vary?
Great question!
It is certainly not an arbitrary choice.
Traditionally, subjects that move immediately from the I to the V degree* undergo a double mutation in the answer: see, for example, fugues no. 8, 17, and 22 from volume I of Bach's CBT and no. 7 from volume II. A I-V subject is answered with V-I in the answer, so that the first two intervals are modified.
Let's look at the fugue in D# minor from vol. I (transcribed in Eb in some editions): subject D# A# B#, etc., answer A# D# F#, etc.; thus the ascending 5th and ascending 2nd of the subject become the 4th and 3rd in the answer—in short, we have what I previously defined as "double mutation."
The reason that gave rise to this custom dates back to Renaissance polyphony, in which imitation between voices did not involve a change of key from tonic to dominant (as is commonly said in scholastic fugue), but only the passage of the melody from the authentic mode to the plagal or from the plagal to the authentic, remaining obligatorily in the same mode (by mode here one means protus or Dorian, deuterus or Phrygian, tritus or Lydian, tetrardus or Mixolydian, etc.). The I-V bipolarity clearly implied the underlying mode of the piece; therefore, a motive starting with D-A (authentic protus) was not answered with A-E (Aeolian?), but with A-D (plagal protus).
This same bipolarity passed into the Baroque fugue, so that the answer, while "modulating" to the key of the dominant, does not decisively shift the tonal center toward a new tonic, but keeps the two main poles of the underlying key firmly in place, so that the "key of the dominant" touched in the answer is perceived as a momentary tonicization and not as a true modulation. I hope I have been clear enough.
Now, in the subject of the fugue workshop, in reality, the I does not move immediately to the V, but passes through the III... and here doubts arise: can the III degree be considered a simple embellishment of the I, or can it be harmonized separately?
Fugues with these characteristics are not found in the CBT; there are only some subjects in which the initial tonic is embellished by a passing note before moving to the V degree: no. 2 from vol. I, no. 1 from vol. II. Bach, in both cases, respects the criterion of double mutation in the answer.
It should also be noted what happens in fugue no. 3 of vol. II (a fugue *sui generis*, which begins with a real stretto!): the I degree goes to the III, then returns to the I and thus rises to the V; here too Bach adopts the double mutation, considering the III degree as an embellishment of the I.
But the closest Bachian example to the incipit of our workshop subject, the first that came to mind, is that of the *Musical Offering*: subject (in C minor) C-Eb-G etc., answer G-Bb-C.
And it is especially thinking of that illustrious example that my answer to the lab subject was, without thinking more than 10 seconds, E-G-A.
*Note for Cristian
If you want to avoid being misunderstood, do not use feminine numeral pronouns (THE FIFTH, THE EIGHTH, THE THIRD) when referring to the degrees of the scale, but masculine ones (THE FIFTH [degree], THE EIGHTH [degree], THE THIRD [degree]). Instead, use the feminine when referring to intervals. You will see that no more misunderstandings will arise.