Saturday, October 16, 2021

Augmented Reality

Although I believe I'm the inventor of AUG SIXTH DAY, that special occasion every August 6th when we *should* celebrate harmonies which exploit the interval of the augmented sixth, it still sneaks up on me every year. So I never give it the attention it deserves. Alas, on August 6, 2021, all I could find the time to do was hit re-play on this old celebration of a German Sixth Chord in a string symphony by a 12-year-old Felix Mendelssohn. 

However, as I was also spending early August prepping to teach AP Music Theory for the first time this year, thinking about that wonderful Mendelssohn passage got me thinking about the whole 4-minute Andante and all the ways the young composer uses texture, register, and harmony (with melody emerging from a combination of those three elements) to create something truly magical. I played it for my students on the first day of class, using an analytical score I created, to show them some sense of where we were heading with our study of music theory. For me, at least, there's something deeply satisfying about seeing these under-the-hood structures and hearing how they enable the music to flow, to soar, and to surprise. You can see a video demo of this score analysis at the end of this post.

I suppose my main goal that day was to introduce the concepts of harmonic reduction and Roman Numeral Analysis. Most of what happens in this Andante is fairly conventional and thus easily reduceable; even the particularly beautiful details relate closely to that framework. I wanted to show the students that all those notes the young Mendelssohn wrote have a clear, internal logic which can help us hear and understand why certain notes are so effective and affecting. In other words, I wanted to show why it's worth taking the time to study music theory!

Although I do genuinely enjoy this kind of exploration, I'll admit I don't have the kind of ear which can instantly recognize and label harmonies as they go by. But it's been satisfying to realize that after years of looking for augmented sixth chords (in part because theory students often get tripped up by the seemingly convoluted way in which these "chords" arise and are labeled), my ear does sometimes intuitively notice what's going on before I see it in a score. 

So it was that a few weeks after starting my re-exploration of Mendelssohn's augmented-sixth-based modulation in this Andante, I heard my 14-year-old cellist son play the extraordinary first movement of Brahms' first sextet at chamber music camp. (To be honest, this music was a bit over the heads of these campers musically and instrumentally, but they did a great job with the challenge, and managed to present it with confidence and a convincing overall shape.) It's music I've heard often enough, but didn't know super well, yet as the Recapitulation approached, I remembered that something special was going to happen. (Side Note: this kind of musical memory-based recognition/anticipation is one of the most satisfying things about listening to familiar music; this is surely one reason people who love classical music enjoy returning to old favorites.)

As the dramatic texture unfolded and suddenly the opening theme returned in a harmonically arresting way, it occurred to me that this sounded a lot like what happens in Mendelssohn's Andante. The two musical passages (Mendelssohn and Brahms) are different in so many ways, but that makes the analogical connection all the more meaningful. (I've been writing about my love for and fascination with analogical thinking since the blog began.) Hopefully I'll get around to writing about the Brahms sextet more in a future post as there is SO much to say, but for now just listen to the way the music moves from G-flat Major to the home key of B-flat Major. These are not closely related keys (they only share three common pitches), but Brahms uses a German Sixth chord as a sneaky way to get from one key to the next. The video below should begin at 6:35, where the cresc. is marked in the score.

The most important thing to listen for is that, in m.233, the first violin (highest instrument) goes from E-natural to F (up a half-step) at the same moment the 2nd cello (lowest instrument) goes from G-flat to F (down a half-step). G-flat and E-natural are an augmented sixth apart - not an interval that shows up if sticking to one key - and the resolution of those distant notes outward to an octave is the fundamental thing about how augmented sixth chords work. (There's something else unusual going on in this case which I'll get to in a later post.) 

Also, as we'll see/hear in the Mendelssohn, the recapitulation of the main theme occurs over a dominant pedal tone F instead of the tonic B-flat we heard at the very beginning. This adds a heightened kind of tension to the otherwise stabilizing effect created by the return of the main theme in its home key.

Now, let's back up a little. This kind of modulation technique is where I find Augmented Sixth Chords are most powerful, but they can appear in other, sometimes simpler contexts in which the chromaticism (use of pitches outside the key) is just a means of heightening the approach to a cadence. Below are two such examples from works by Haydn which crossed my path this summer. (Remember, part of my point here is to focus on augmented sixth chords which I happened to notice without looking for them.) These nicely demonstrate the simple voice-leading origins of these harmonies.

The first movement of Haydn's well-known Piano Trio in G Major, which I coached in July, begins with a graceful theme in G Major which modulates to D Major in its second phrase. The modulation is intensified by the use of chromatic passing tones between G and A in treble and B and A in the bass. The G and B occur as part of a very standard IV chord leading to a I 6/4-V-I cadence, but the insertion of G-sharp leading to A above and B-flat leading to A below creates an augmented sixth chord (in this case, a German Sixth again). All of the harmony can be heard in just the piano part, so for simplicity, I just show that, but you can hear it played below, both without and with the German Sixth.

In a case likes this, it's almost silly to think of the sonority as a chord - the main point is the voice-leading created by the chromatic passing tones, but they do add an extra oomph to the cadential approach. (For the students I was coaching, I pointed this out as a rationale for leaning on those notes just a bit.) You can hear and see this passage both with German Sixth removed and then as written in this little demo video:

In my most recent blog post, I wrote about a Haydn quartet movement with which I'd fallen in love. My focus there was on a more unique cadential approach in the opening phrase, but that simple theme also includes a passage quite close in character to the trio excerpt shown above. In this case, the music is in C Major and approaching a cadence in C, so the destination for first violin and cello again is the 5th scale degree (G) which anchors the I 6/4 chord. 

Again, you can hear and see this passage both with German Sixth removed and then as written in this little demo video:

Both Haydn examples of Augmented Sixth Chords are German Sixths because of the addition of one more chromatic note (F-natural in the trio and E-flat in the quartet), but the basic idea of intensifying the connection between the very conventional IV and I 6/4 is easy to see, and again, it would be tempting simply to call these chromatic passing tones and not even bother to attach a fancy name to the sonorities.*

In the Mendelssohn and Brahms examples, the German Sixth is used much more dramatically as a means of modulation which initiates a harmonically suspended recapitulation. In each case, the music has ended up in the distant "flat 6th" of the tonic key (A-flat in Mendelssohn's C Major and G-flat in Brahms' B-flat Major) as the music has reached a low ebb. Both composers then add an augmented 6th above that flat 6 - that means the addition of a sharp 4 - to push back to the I 6/4 chord of the home key which features a 5 in the bass. Flat 6 goes down to 5, while Sharp 4 goes up to 5. Whereas the two Haydn examples had the German Sixth pass quickly mid-phrase into a concluding cadence with no change of key, Mendelssohn and Brahms use the German Sixth to push us into a new key and a new (returning) phrase. 

Technically, the new phrase - recognized as such because of the return of the main theme - becomes an extension of a longer cadential motion, so it's also a continuation of the distant key music that led into the Recap. (We generally think of a phrase ending as being defined by a cadence; here, the new phrase arrives mid-cadence.) We definitely hear the melody as beginning something new, but because the German Sixth naturally progresses to an unstable I 6/4 chord, the main theme begins over the fifth scale degree (Dominant) instead of the first (Tonic). This sleight of hand propels the music forward until the cadence in the home key is finally reached. Mendelssohn's cadence back in C Major happens as expected after eight bars. Brahms somehow manages to evade a cadence back in the home key of B-flat for a full 36 bars! Listen here starting at 10:38 until we finally get our resolution in the tonic over a minute later at 11:45. 

There is so much more that could be said about each of these works, and I will devote future posts to a "running diary" account of all the little details that I love. (I already have thirty virtual sticky notes on my 3-page Mendelssohn score.) In the meantime, here is a draft of a scrolling score I've prepared for the Mendelssohn. It has a few special features:

  • I've included a basic (hopefully correct) Roman numeral analysis below the score which shows the modulations to G Major and A-flat Major and return back to C. The German Sixth chord occurs exactly halfway through in m. 42. (more on these proportions in a post to come)
  • A reduction of the harmonies to two staves below. Although register shifts play a big role in how Mendelssohn's music takes shape, I chose to set up this 4-voice reduction to emphasize where common tones occur between chords. Thus, you'll find that this reduction does not correspond exactly to where the pitches occur among the parts. (more on these registral shifts in a post to come)
  • Perhaps most unusually, the recording I use is the one of my then 12-year old daughter's chamber orchestra playing this in a concert ten years ago. Though far from perfect, there are many elements (including my daughter's participation, of course) which make this my favorite recording I've found of this transcendent music. (This is my favorite professional recording.)

* Just to give Haydn his due, he does sometimes use Augmented Sixth chords in more dramatic structural ways as well. The suspenseful introduction to his "Oxford" Symphony ends with strings repeating the notes of a German sixth multiple times before the music resolves to the V7 chord of the tonic G major as the Allegro begins. In this case, Haydn does not resolve the Augmented Sixth in the usual way: while the bass E-flat does go down to D, the C-sharp which ought to resolve up to D moves down to C-natural instead. However, the effect is similar, and as with the Mendelssohn and Brahms examples described above, the fact that the cadence doesn't really end until four bars later makes this a most unusual opening for a symphonic main theme. You can see/hear all of this starting at 1:15 here

P.S. If you're interested in more different contextual uses of Augmented Sixth chords, the Beethoven and Schumann examples I posted way back on the inaugural Aug 6th Day in 2012 are quite tasty as well.

No comments: