Posts Tagged ‘modulation’

Mahler, Symphony No. 4, 4th movement

Monday, March 1st, 2010

First, some business.  Since Mahler’s Fifth has five movements, the two-weeks-per-movement plan of the last two months won’t work.  Since I, and many of my readers (I assume there are readers…) have Spring Break in March, the right move seems to be to spend 10 days on each of the first three movments, then fifteen days on the other two.  Three movements in March, two in April, with one day left (although I confess to not thinking about this project every day, so that isn’t entirely accurate).  Keep up with me!

To the music.  This movement is a lovely song setting.  In my reference recording, by Bernstein with Vienna, Bernstein took the indication that the voice be as child-like as possible to the extreme of assigning the part to a boy soprano.  There is an innocence gained through this, one that Bernstein used in his own Chichester Psalms to great effect.  The first time I heard this piece in performance, the Cincinnati Symphony used a grown woman rather than a child, and I don’t remember it as being any less effective.

Like the symphony, this movement begins in G major.  The form is basically strophic, and this means that there is a great deal of repetition both in the solo part and the accompaniment.  The introduction is very typical of the German lied in that it simply presents a melodic idea (in the clarinet) that is repeated as interlude and which also accompanies the solo part as a countermelody.  Like the third movement, Mahler’s harmonic language is centered around functional phrases rather than the long pedal points of some of his earlier work.  In this last Wunderhorn symphony, Mahler chooses to end with a movement that seems to suggest an earlier world.

Measure 36 and the following measures are the first appearance of material that three times will close the song sections.  Each time it ends on a different chord, but segues into material from the opening of the first movement–a somewhat unexpected tying together that brings the somewhat disparate expressions of the piece full circle.

In comparison to Mahler’s purely instrumental compositions, and especially, for example, the finale of the Second Symphony, this song setting is relatively simple, but therein lies its beauty and its charm.  Mahler’s previous use of children’s voices (again, not what is strictly called for here despite Mahler’s note about the soloist’s vocal quality) in the fifth movement of the Third Symphony is much more complex in texture and orchestration than this light, clear movement.

Only one aspect of the movement is really troubling to me, and that is Mahler’s decision to end it in a remote key–E major.  When the symphony so far has been very centered on the home key, G major, it seems very strange indeed that Mahler would end the piece elsewhere.  I have spent some time thinking of reasons for this decision, and the best I can come up with is that lowering the tonal center by a minor third has the effect of a relaxation, a release of tension in some way.  While so many popular songs in our era feature a modulation up to ramp up excitement, Mahler’s downward shift of key center may have the opposite effect.  It may also suggest that the piece, a setting of a poem depicting the heavenly life, is not really finished, just as the eternal life discussed has no end.

One strays from a purely compositional analysis here–into a realm of symbolism and implied extra-musical meaning that I have largely avoided here, but as the only vocal movement of the piece, it seems to cry out for this type of discussion.

What does one take, then, from this symphony, so unlike Mahler in so many ways?  Mahler’s compositonal technique is relatively unchanged from the previous two works–not for nothing are they grouped together.  Instead of the enormous orchestras with chorus, though, Mahler steps away, conforming to a standard symphonic plan in four movements for the first time since the First Symphony (and even that piece was not originally so).   Mahler is not the only composer to step back from gigantism–one thinks of Tchaikovsky following the bloated 1812 with the sublime Serenade in C, and of Liszt’s later works in comparison with the enormous symphonies of his middle years.  At any rate, Mahler’s orchestra is still very large by Mozart’s standards, and there are moments in the piece that are very reminiscent of the big moments in the other symphonies.  It is completely possible that my conceit of the Fourth as the “little one” is only the result of my own instrument being left out!  But there is none of the darkness here that one associates with the low brass in the earlier symphonies–the tuba of the First’s funeral march, or the trombone of the Third’s opening movement.  They simply aren’t necessary.

Onward, then, to the Fifth, a favorite of mine since I first encoutered it up close as an undergraduate!

Mahler, Symphony No. 2, Movements 3 & 4

Wednesday, October 21st, 2009

It’s been a busy time here, but I’m squeezing my thoughts on these pieces in so that I can keep on schedule.

Third movement–The name of the game here is “hypermeter,” in this case, every bar of music feeling like a beat in its own right.  The meter is 3/8, but Mahler could have written in 12/8, and the piece would have made (mostly) perfect sense.

And that “mostly” is the rub.  Because while the hypermeter generally dominates the piece and is fairly strict much of the time, there are places where Mahler steps out of the mold.  If he had chosen 12/8, in other words, there would be a few loose measures in 6/8 or 9/8 scattered through the piece.  These hypermetrical shifts tend to occur at boundary points within the piece, and are slightly more prevalent at the beginning of the movement than in the end.

The first six measures suggest, to me, a complete hyperbar, drawn out for dramatic effect.  After two “correct” hyperbars, Mahler introduces a moto perpetuo-type theme in the violins.  This is echoed in the clarinets in a six-measure hyperbar, clearly a “correct” bar with a two measure extension.  The flutes take this up for four bars, following which, at rehearsal 29, Mahler gives a two-bar “make-up” by restating some of the introductory material, and in m. 33, the initial theme returns.  In this section, uneven hyperbars seem to appear just before the return of the moto perpetuo theme. 

Measure 98 begins a long (seven measures) hyperbar, and is also a modulatory passage, albeit a strange one, to F major.  The modulation is effected by descending chromatic scales in major thirds, but is accompanied by bass notes Gb and B, suggesting a key quite remote from the goal.  Mahler approaches the F major (local) tonic again in a strange way prior to m. 125, falling to it from an A minor chord.  This is presumably because F is not the ultimate goal, only a way-station.

The use at m. 68 and m. 149 of lines that appear to quote the second movement of Mahler’s First Symphony is notable.

As we proceed through the movement, Mahler passes through Eb, then D, often repeating material heard before, usually fleshed out with countermelodies.  At m. 257, the descent ends, and Mahler moves the tonal center up to E major.  There is great music here, but not time enough to discuss it in full.  The scoring is flawless, and often seems to reinforce the hypermetrical concept of the piece.  It is difficult to understand how Mahler was able to work so masterfully with the orchestra in an age before recording, but I suppose that countless hours on the podium had acquainted him with the sounds implied by a score.

Toward the end of this movement, the hypermeter seems to become more strict, i.e., there are fewer exceptions to the rule of four-bar hyperbars.  In the final 200 bars, there is only one shift of hypermeter.

Fourth movement–Just a few observations.  In many ways, this brief setting speaks for itself.  Would it have been more appropriate to partner this movement with the last movement?  Perhaps.

The brass chorale beginning in measure 3 is stunning.  I’m fairly sure that the bassoon and contrabassoon, however, would not be able to play a true pianissimo there, although they are scored in powerful ranges.  The low Db in the contrabassoon in m. 13 is a positively religious effect that I will be listening for from now on.

My Theory III students will be studying the enharmonicism found at rehearsal 1.  The key of the pieces is Db major, and to avoid a key signature of eight flats, Mahler chooses to write in C# minor.  As far as I can telll, this is the key reason for enharmonic writing–mere convenience.  There is no surprise in this chord progression–it moves precisely as it would if the key had remained Db major.

At rehearsal 3, the music moves to the other obvious choice for a contrasting minor key.  In fact, as the relative minor, Bb minor is a more likely candidate than C# minor.  The shift, acknowledged in the key signature, to A major is a bit trickier… Bb minor would be enharmonic to A# minor, which would have a relative major of C#.  The dominant of C# is F#.  The relative major of F# minor is A.   Mahler employs a monophonic technique in the solo violin part rather than try to navigate this convoluted path in such a short movement.  He returns to Db major through C# major in a convenient enharmonic move.

My thoughts on the giant, transcendant final movement will appear at the end of the month.

Opus 110

Saturday, May 30th, 2009

Here’s the May 2009 installment of my series of posts on the Beethoven Piano Sonatas.  This month is Sonata No. 31 in A-flat, Op. 110–next month will be the last month in the cycle, which means I will need a new analysis project–let me know if you want to start one with me and dialog on the compositional aspects of pieces from the standard repertoire.  I could, of course, spend another few years going back over the Beethoven Piano Sonatas, but there is so much great music out there that I’ve never even touched, that I feel like it would be better for me to move on.  So… I haven’t decided on my next project yet, but I do have some ideas… if one or more people were interested in working through some pieces with me, I would let them have some input in the decision.  I’ve considered the Mahler symphonies, Bach’s St. Matthew Passion, Beethoven’s string quartets, Chopin’s Preludes… let me know what you think!

On to the piece:  A study in contrast this one, and highly indicative of the “official” traits of Beethoven’s late style as it has been taught to me.  I’ll dive right in.

The first movement, if not in textbook sonata form, at least seems to reference it.  I’m not Donald Tovey, who looked for sonata form in every piece he ever analyzed (the last movement of Schumann’s Piano Quintet is a Rondo with sonata aspects, not a straight sonata-allegro), but it seems reasonable to assert that Beethoven is working with thematic groups and a strong sense of motivic unity.  His use of core technique is somewhat fascinating, as it is built on a descending thirds sequence instead of the usual stepwise sequence.  I’m puzzled by the modulation to E major in what corresponds to the recapitulation.  This isn’t Beethoven opening up a window to another tonal world but rather knocking out a wall–a very unexpected place, although it makes sense that something different needs to happen where the exposition modulated to E-flat (the modulatory technique to E is an enharmonic respelling of a borrowed chord… IV becomes iv, which is vi in the new key; Beethoven gets out of that key by a fascinating use of common-tone technique and sequence).

To understand Beethoven’s use of sequence is often to gain understanding of his medium-scale structure (and in some cases, large scale, as in the “Spring” Sonata).  In Las Cruces last week, I spoke with Fred Bugbee about NMSU’s music theory track, and eventually the conversation came around to sequences.  One reason I’ve decided to part company with my current theory textbook, Kotska & Payne’s Tonal Harmony is that their treatment of sequences simply lacks body.  The new generation of theory textbooks is much more realistic about the use of sequence in tonal music, and, truthfully, it was teaching from Clendinning & Marvin’s The Musician’s Guide to Theory and Analysis that really got across how important sequence is.  My study of Beethoven has only reinforced that.

The second movement, Allegro molto is diminutive in proportion, but as will all Beethoven’s scherzi, I am amazed at the sheer craft involved.  Every time I make the mistake of listening to a Classical or Romantic scherzo as merely a light, intermezzo sort of movement, I tend to realize that I’m not doing it justice.  With some composers, it’s an easier mistake to make than with others.  Much of Mendelssohn’s genius seems to lie in his scherzi, for example, while Dvorak has a tendency to revert to folk dances.  Nearly every time I look closely at a scherzo, however, I see a level of compositional craft that equals the outer movements.  It is as though composers were freed from the strictures of sonata-allegro or rondo (although most rondos have wonderfully original moments) and could pull out the tricks they worked on as students–canon, invertible counterpoint, rhythmic surprises, and the works.  What fun!  Beethoven doesn’t use contrapuntal tricks, but in this tiny scherzo, he gives us the most rhythmically ingenious and formally cogent plan of the piece.  Why should this tiny movement have a coda when the first movement has none?  I suspect it is more necessary here because we have heard the A-section twice, and the listener needs to have a fuller sense of closure than a simple cadence.

I could puzzle over the last movement for quite some time.  Here is Beethoven’s late-style interest in counterpoint (the fugue, complete with a second exposition in inversion), side-by-side with harmonic innovation (a common-tone diminished-seventh chord with a modulating function), and a confusion about rhythm and key signatures that simply doesn’t make sense at this point.  To wit:  for much of the piece, the key is A-flat minor, at least until the start of the fugue, but the expected seven-flat key signature never appears.  Instead, the movement begins in B-flat minor, shifts to E major and then is written in E-flat minor.  Are these key signatures simply flags of convenience?  At the same time, Beethoven indicates “Recitative,” and breaks out of the signified meter (common time).  How free is this meter?  And how, precisely, is the performer to understand the subsequent barlines?  The “Klagender Gesang” in 12/16 meter is another puzzling aspect–it is almost as though Beethoven is writing a fantasia, a written-out improvisation, at the end of which he launches into the fantastic three-voice fugue. 

Then this full-bodied G minor and G major review of earlier material–the “Klagender Gesang” in G-minor paralleling the A-flat minor section and the fugue (in inversion) in G-major (although we get only an exposition and a long episode).  At last, the retuirn (recapitulation?) of the fugue subject in the original key–part recapitulation, part coda, really. 

One more Beethoven sonata–I look forward to Ludwig’s valedictory effort in the genre.

Opus 78

Tuesday, September 30th, 2008

Well, the end of another month, and I didn’t spend as much time with my Beethoven sonata as I had hoped, but there were other musical experiences taking place.  My first-year theory students are through the “fundamentals” and we can now start to talk to each other about theory–today we discussed a definition of “tonal harmony.”  On September 21, the Harrington String Quartet came to OPSU and played a fantastic concert of Mozart, Mendelssohn and Shostakovich, and last Sunday was my first premiere in Oklahoma.  Add to that a couple of football games to eat up a Saturday or two, and finishing the horn and marimba piece, and it’s been a little busy.  But mostly good work, and I can’t complain.

But the Beethoven sonata–No. 24 in F# major, Opus 78.  I did get a chance to revisit it this afternoon, knowing that I would need to write tonight.  It really is a wonderful miniature among the giants that precede it.  I’m always amazed that Beethoven wasn’t stuck on one plan or another for his sonatas.  Myself, I tend toward the three-movement fast-slow-fast structure, so much so that in this horn and marimba piece I’ve just finished, I deliberately departed from that model–it begins in a quick tempo and ends slowly (I couldn’t resist the four-mallet tremolo at the low end of the instrument, pianissimo with soft mallets).  We’ll see what the player who commissioned it thinks.  So many of Beethoven’s earlier sonatas have that “standard” sonata cycle–like a little symphony for piano–he clearly got tired of being stuck with that.

Some things I need to work out.  My second-year theory students are studying modulation right now, and it strikes me that the development section of the first movement of Op. 78 begins in the parallel minor.  Should the parallel key be added to the list of “closely related keys?”  It certainly is easier to get to than any other key–no real pivot chord is required, only a dominant function that remains a dominant function.  Something to think about.  Similarly, in the rondo, Beethoven visits the key of (yes!) D# major, and along with it, D# minor.  Where Schubert or Chopin would have changed the key to Eb, Beethoven soldiers on through with six sharps–a real stretch for an ersatz pianist like myself.  More than ever I am in love with rondo form–the last movement of Brahms’ second symphony is what I think music will sound like in heaven.

So–here’s to next month–may I get to this writing earlier and have more intelligent things to say.  Op. 79, here I come!