Thursday, February 21, 2013

The Anatomy of a Bach Chorale

After chewing over that University of Melbourne study on consonance and pitch in a few posts, I think it would be interesting to dig into consonance, dissonance and harmony from a musical point of view, rather than a scientific point of view. Thanks, by the way, to my commentor Joel for making an excellent contribution to figuring out what was going on in that study.

I have mentioned a couple of times a book that has been in print for nearly 250 years: a collection of Bach chorales put together by various people including Bach's son, C. P. E. Bach. I was just looking at it and learned that the original sources for almost half of these 371 chorales have been lost! I hadn't known that before. Just how much of Bach's music have we lost? Between his death in 1750 and the explosion of Bach performance and appreciation in the last three-quarters of the 19th century, quite a bit apparently.

In any case, what I want to do is take a Bach chorale and look at it closely to see just why Bach is so respected as the master of harmony. Luckily a suitable chorale is available on YouTube with the score. Here is "Aus tiefer Not schrei ich zu Dir" (Out of deep distress I cry to you), the concluding chorale from the cantata, BWV 38:

In the collection of Bach chorales, this one is titled "Aus tiefer Not", but you will notice that the text actually sung here is "Ob bei uns ist der Sünden viel". Bach used the text of the first part of Luther's chorale for the opening movement, and the text of the second part for the concluding chorale. Here is the first section:

It is actually clearer in the YouTube clip! Let's just walk through what Bach is doing here. The key is A minor, which has no sharps or flats. We see added sharps because in minor keys, in order to create a leading tone, we need to raise the seventh note of the scale--in this case G becomes G#. There are two short phrases in this first section. Each one ends with a held note, shown by the fermata sign (the curvy thing with a dot). This is where the singers take a breath. The two most important harmonies in a piece in A minor are the tonic triad, ACE and the dominant: EG#B. As you can see, both phrases end on the dominant. We don't get a cadence on the tonic until the second section.

Bach does something very radical at the very beginning here: he begins, not only with the dominant, but with a dominant 7th. This chord is spelled EG#BD. The D is the seventh. But the D is put in the lowest voice, the bass. When the bass note is a note other than the root of the chord (A is the root of an A chord, E is the root of an E chord, etc.), the chord is said to be "in inversion". This was a discovery (theory?) of Rameau in his famous book on harmony published in the 1720s. If E is in the bass, the chord is in "root position" if G#, then first inversion, if B, then second inversion and if D is in the bass, third inversion. The interesting thing about 7th chords in last inversion is that, since the seventh is in the bass and sevenths have to resolve down (one of those rules), then a dominant chord in last inversion pretty much always has to go to a tonic chord in first inversion. If you have a look, you will see that yes, that is exactly what happens. Then we have another dominant chord, this time in second inversion and then a tonic in root position. This is how Bach gets this strong descending bass line: D C B A. Next is a little hint of G major, but at the last instant, the harmony swerves back to the dominant of A minor. And that's the first phrase! Tricky to put into words. The great strength of music notation is that it records all this very efficiently. The second phrase begins with a strong dominant to tonic, both in root position, then wanders into C major for a bit before, again, closing with the dominant of A minor. Now it would be good to go back and listen to this first section again, trying to hear some of this.

Not counting the repeat, this first section is only about 20 seconds of music. Can you hear how strong the 'flavour' of the first chord is? How that bass note has to resolve somewhere? Bach does  much more radical things than this, of course, but this is a good sample of what goes on in a Bach chorale.

Each voice is independent and sings well. The bass line is nearly as important as the soprano melody on top and even the middle voices, the alto and tenor, are enjoyable.

The exercise of taking a simple melody, like the top line here, and writing the other three voices or "harmonizing" the melody, is one that every music student spends quite a bit of time learning how to do. This kind of smooth, flowing harmony, with occasional pungent harmonic tension, is a lot harder to write than it sounds!

So that's a little 20 second insight into Bach's harmony... If you want to listen to the whole cantata, of which this is the last movement, here it is:


Anonymous said...

Hi. I am just embarking on an analysis of Bach Chorales and your analysis and audio was really helpful. Thank you.

Bryan Townsend said...

You're welcome! One down, only 370 to go.

Farcry C. Zuke said...
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Farcry C. Zuke said...
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Farcry C. Zuke said...

Hi Bryan,

I am wondering if you would be willing to talk about your opinions on the penultimate measure of this chorale. What do you see the Gminor chord as? I am thinking that Bach was hinting at A Phrygian here, since the melody is in E Phrygian. There is sort of this Aminor/E Phrygian battle going on in the harmony of this piece. I am curious to hear your thoughts. Also, if the last cadence is a half cadence in A minor, where was the pivot from C major back to A minor?


Bryan Townsend said...

Delighted to talk harmony with a fellow composer, Farcry. Welcome to the Music Salon. This is quite an unusual chorale and perhaps I should have picked a more conventional one for this post. But here goes. One unusual aspect is how much the chorale avoids a perfect authentic cadence in the tonic. Out of five cadences, one ending each phrase of the chorale, only one, the third and central cadence, is on the tonic, A minor. The first cadence, the one I talk about in the post, is from F major to E major or, in the key of A minor, it is a VI - V or a half cadence. The next cadence is also a half cadence, but this time from iv to V. The third cadence is the only PAC, V - I. The next phrase tonicizes G and ends with a V7 - I cadence in G major. The next and final cadence in the chorale is another half cadence i - V. And that's it! The Bach chorales contain an amazing amount of unusual harmonic practices, which is probably why composers still study them. You were asking about the penultimate measure. Here are the chords: FAC (VI), CEG (III), BbGD (vii6), ADF (iv6/4). Yes, the G minor in first inversion is very problematic to analyze harmonically.To answer your last question first, I think the pivot back to A minor is clearly in the antepenultimate measure, signaled by the G#. Yes, I agree about the Phrygian interpretation. I usually look to the voice-leading to answer problematic questions about harmony. The Bb is acting in a Phyrgian--or Neapolitan--relationship with the tonic A. In that sense it is a chromatic coloration that adds to the intensity of the setting. A standard Neapolitan 6th chord in that place would not have been usual, though using it to prepare a iv chord instead of a V is odd. The standard Neapolitan would have been BbDF, which wouldn't lead so interestingly to the iv chord.

Hope that makes sense?

Bryan Townsend said...

Sorry, I meant to say that a standard Neapolitan 6th chord in that place would not have been UNusual!

Farcry C. Zuke said...

Hey Bryan,

Here is my analysis of this chorale. I really love the ambiguities of Bach in this one.

Bryan Townsend said...

Farcry, please accept my humble apologies for not taking up your comment and responding yet. I am extremely interested in your analysis, but a few things have prevented me getting to it. I will as soon as I can!!

Farcry C. Zuke said...

Oh, no worries! I mainly talk about the harmonic oddities in this chorale and the ambiguities that this Phrygian melody creates. You may find them interesting!

Bryan Townsend said...

Oh yes, I most certainly will. But I realised as soon as I started reading, that I would have to devote my full concentration and the last week has just been too scattered.

NeilW said...

I'm studying Bach chorales really closely to recover that feeling. For me modern music has things to teach, but I want to go back to the tonal instability of the masters.