Expert: Marbeth - 1/30/2012

Question
QUESTION: Hello,
I am trying to work out an analysis of the ending of Bach's toccata and fugue. I'm researching the last 7 bars. I get the the harmonic degrees but i was wondering if there is a more professional explanation and analysis of this wonderful ending (especially the cadence).
Also I was wondering if there are examples of such cadences (the Suspended V going to the minor V) in earlier music before bach.
I searched the web for a complete harmonic analysis but couldn't find. If you know where I can find it please send me.
Thank you very much for your help,
Akkad Izre'el

ANSWER: I will find my score and get back to you.

The last measure is called a "Picardy third" ("tierce de Picardy").

This is when a piece in a minor key ends in the parallel major (in this case, D Major).  Parallel majors and minors have the same key letter-name but not the same key signatures (which is the case with relative major and minor keys).  Forgive me if I am telling you something you already know!
mb

---------- FOLLOW-UP ----------

QUESTION: Thank you for your reply.
The piece is in d minor and ends in d minor which isn't a picardy third but the tonic. also the last cadence is a plagal cadence (IV - I).

My question is about what happens before that in the deceptive cadence. There is a use there of the minor V which starts with a suspended V and goes to a minor V and then to VI  (Asus4 - Am  -  Bb)
the Leading of the d note to the natrual c note between the Vsus and the V is very beatifull and unique. My question is about that specific voice leading. I was wondering if there is any explanation about it and if there are examples that are earlier from Bach to that kind of voice harmonic voice leading...
Thank you agian.
Sorry for not being clear enough.

Answer
Got it now.   Sorry I was so dense!

~~

In a text-book minor key cadence, the V chord is always major because of the raised leading tone.  Generally, such a cadence is authentic (V i), as you note.

Sometimes an authentic cadence is preceded by iv:  iv V i.  In a minor key, the chord on the 4th scale degree is always minor unless an accidental appears.

Here we have a plagal cadence at the end of the fugue, as you also point out.

Bach uses a great many suspensions, sometimes chains of them…to the distress of the performer, who can be overwhelmed by finger substitutions.

~~

Moving to your question.

In the final 3 measures:
gm = iv (with A sus)
gm = iv
c#dim7 = vii°7 (incomplete dominant) = V7
dm = i

am = v (with D sus)
am = v
Bb = iv7 (incomplete subdominant minor form; C sus) = iv7….or VI
gm = iv

dm = i

Sometimes the suspended note is the ever-popular (!) non-chord tone, as in the Bb, and sometimes it conveniently fits as a 7th, as in the c#dim7.  

Taking all three final measures into consideration, structurally we have (simplified):
iv iv V7 i
v v iv7 iv
i

It appears Bach has reversed the position of iv and v in the two measures prior to the last one.

First, in the ante-penultimate measure, the dominant leads to the tonic, as we expect.  

THEN Bach leads us down the primrose path with two more dominants (penultimate measure).  We expect two more beats of dominant, meanwhile wondering why the dominant is a minor chord.

And then....instead of two more beats of the minor form of the dominant (or, better, two beats of the major form of the dominant), he chooses two beats of the subdominant (iv7 iv).  

Finally, we get to i.

Above all this, he has the suspensions!

~~

As to explanation, I have no idea.  I wouldn't guess puckishness (at reversing the positions of iv and v in the penultimate and ante-penultimate measures).  I would suggest Bach-ishness!  A great master!

~~

As to previous iterations of this idea in earlier composers, I am sorry that I do not know that, either, though you might find examples in other pieces by Bach.  I would look in the preludes and fugues, organ trio sonatas, Brandenburg concerti, the concerti for two or more keyboards, and large church works (as opposed to the chorale preludes, cantatas, suites, or viola da gamba sonatas).

I have chosen incomplete iv7 over VI because I like the parallelism of incomplete chords (in the ante-penultimate and penultimate measures).  As you know, many times different people interpret notes as different chords altogether.  I justify this with the note about parallelism of incomplete chords (functioning as V7 and iv7).

If you mean (and I think you do) VI (C is a non-chord tone & result of sus.) preceded by v, I think this is not so uncommon.

If you mean VI resolving to iv, I think this is uncommon and perhaps even unique to this Bach's oeuvre.  

Have I answered your question yet?!
mb