Posts Tagged ‘sequence’

Mahler–Symphony No. 4, 2nd movement

Saturday, January 30th, 2010

A day-and-a-half of snow days this week means that I can get to this a little bit ahead of schedule.

I’ve chosen to examine Mahler’s work from a purely compositional standpoint, but for a summary of Mahler’s programmatic and spiritual understandings, I would direct the reader to this excellent note by Chicago Symphony program annotator Phillip Huscher.

The tonal center of the movement is C major, but with a contstant yearning toward D, beginning with the opening material.  The overall progression of the movement, from C minor to C major, F major, twice, then to a D major section, finally ending in C again.

Like the first movement, there is a tautness, a motivic clarity that isn’t present in Mahler’s Second or Third Symphonies to the extent it is here.   There is barely a single bar in this movement that doesn’t contain motivic material introduced in the first twenty measures of the piece.  The various motives have differing roles throughout the movement–some thematic, some transitonal.

The movement begins with a horn solo that strangely emphasizes D–re in the key of the movement, and two keys removed from the tonic pitch.  There is a great deal of Mahler’s typical ambiguity between major and minor as the motives that are more thematic in nature begin to be revealed–first in the flutes, then in the strings.  If I had to type-cast the melody here, it would be moto perpetuo, in part because of the importance of the motive composed of six sixteenth-notes and that tends to run into itself. 

This reliance on motives allows Mahler to make extensive use of melodic sequences, just as in a Bach invention.  I’ve often told my students that the key to writing tonal music is to remember that there are basically two techniques–functional phrases and the sequences that connect them.  Mahler here is reinforcing my lesson.

The scordatura violin deserves a mention.  Mahler scores for it in such a way that when it is present, it is always at the orchestrational foreground.  Lesson–if you’re going to use a strange instrument, feature it.

The opening material returns in measure 110, preceded by a sequential modulation that points to the pitch D–the secondary center of the piece.  The recapitulation is largely similar to the first 100 bars, with some textural elaboration and rescoring.  At the end of this section, the sequential passage returns, and again leads to D–but this time to a large D major section.   This section seems to substitute for the C-minor section at the beginning of the piece, leading back to C major at m. 314. 

This brief C-major section leads to a coda a measure 329, substituting for the F-major music that ended the first two large sections.  What most impresses me is that the opening material here beomes the closing material.  The horn solo from the opening bars that acted as the door into this piece is now the door out.  Appropriately for a middle movement, the ending is somewhat abrupt.

Mahler Symphony No. 2, 2nd movement

Monday, October 5th, 2009

This is one of those pieces that makes my Schenkerian training pop back up… I’m not certain, but this movement seems to be a very nice example of a 5-line.  Any thoughts?  Whether this is true or not, sol plays a conspicuous role in the melodic and harmonic structure of the piece, either as pedal point through much of the movement, or as a very important point of repose for the melody.  I often find that, when in the midst of a melody, sol is easier to find than do, and many portions of this movement seem to hang around sol in a way that allows the music to spin around and around that note.

The string writing is absolute genius–my orchestration students will be studying this piece when next I teach the class.  The main landler theme is somewhat more functional in nature than much of Mahler’s writing–we usually see him building themes around a single chord.  The effect in mm. 13ff of the sustained notes helps to unfuld the theme in a very important way–it keeps it from being a mere parallel period in structure.

The change of key signature at m.39 to five sharps is a mere convenience.  Mahler means us to understand the same tonal center, but the opposite mode… A-flat major becomes G-sharp minor.  The minor-key sections are centered on long dominant pedals–more sol in the piece.  The real breaks in this emphasis on the dominant come at a very charismatic theme in the winds which is also the basis for what little developmental writing we find in this movement.

Then back to the landler of the opening, with Eb/D# as a pivot note between the two modes.  A slight variation on the opening section, but nearly identical in form.  The real meat of this movement seems to lie in the minor-key, compound meter sections of the five-part form.

Mahler seems to make a habit of drifting between major and minor triads built on the same note–here, and in the first movement, and as a motive throughout the Sixth Symphony (looking ahead to next summer).   We see this rarely in earlier composers–although I confess with not being as familiar with Lizst and Wagner as Mahler probably was. 

The second compound meter section, beginning at m. 133 is the least harmonically static music of the movement, briefly visiting B major and F# major, with even a sequence (related to Classical developmental-core technique?) a-building at m. 153ff.  I talked to my students in Forms and Analysis class today about the dangers of always seeing what we want to see in a piece… am I doing that here?

The final section, a wonderful pizzicato version of the opening landler.  Is Mahler charming us, or contrasting the pastoral mood here with a more menacing idea in the minor key sections?  Again, I can’t get over the string writing in this piece… it’s like a primer on how to write charming string textures, both with divisi and without. 

If the piece is a Schenkerian 5-line, it seems to me to descend only on the last two chords–meaning that the piece doesn’t have a coda in a traditional sense.  Yet the entire last page, from m. 285, seems to have an “after-the-ending” function.  Schenker, of course, found Mahler to be decadent, and probably would have dismissed his music out of his anti-Semitism as mere aping of earlier Austro-German greatness.  Nothing could be further from the truth.

Schedule for the rest of this piece–3rd and 4th movements until October 20, 5th movement until the 31st.

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.