Posts Tagged ‘counterpoint’

Mahler, Symphony No. 7, movement 1

Tuesday, July 13th, 2010

I’ve done the listening and score study this time around, but I simply am short on time this morning, so here are my big ideas, and I will leave the close reading for another time.

How long can one go as a composer before beginning to sound like oneself?  I find the opening of this movement to be similar in mood and material to parts of the first movement of the Fifth Symphony.  Mahler has been Mahler from the beginning, of course.  There are always Mahlerisms, and I have been seeking them out through the course of this exercise, but self-quotation is another matter entirely.  And again, this is not the outright recycling that composers have frequently used when time or energy ran short.  In some ways, this is the third symphony in a row that has begun with music that seems to resemble a funeral march.

A harmonic analysis reveals many “wrong way” progressions–I teach my theory students to favor the falling fifth, falling third and rising second root motions, but Mahler frequently moves in the opposite direction.  From a harmonic standpoint, sequential patterns are important here.  There are many instances of slow harmonic rhythm (and pedal point) punctuated by sequences that change chords twice in each bar.  The pedal point tendency is not new, but this use of sequence happens to an extent that seems relatively unique to this movement.

Mahler’s melodic material is highly cohesive–as usual, there is a great deal of motivic development.  At the same time, Mahler very rarely uses “simple” melody-with-accompaniment textures in this movement, which is something of a contrast with the Sixth Symphony.  Even in expository passages, melody is almost always combined with another melody, and in developmental sections, it is difficult to know what the main melodic idea is at some points.

Scoring is drastically different from the two previous pieces.  Mahler had been tending to a mixed scoring, with blending of instrumental colors, and, especially in the Sixth Symphony, most of the orchestra playing a good deal of the time.  Here, instruments seem more likely to play as sections without reinforcement from other sections, although there is still a good deal of flutes-doubling-violins to add penetration to their high register.  Instead of the eight horns customary to Mahler, there are only four, plus a tenorhorn in Bb (my assumption is that this is something like the British bore baritone I remember from my brass band days).  Color has become more of a concern for Mahler.  If memory serves from some undergraduate research into Mahler’s compositional practices, it was around this time that he rejected the piano reduction as a first draft, worried that it made his music too pianistic.  Instead, he began to work with a short score of four to five staves.  I have found this technique to be extremely helpful in creating band and orchestra pieces.

In some ways there is also a variation technique at work here.  Material presented as a funeral march reappears as a strange, wobbly dance, and then again as a triumphal fanfare.  Mahler never explicitly wrote a “theme and variations,” but he certainly appears capable of employing that strategy.

Onward then–I refer myself to my copy of the score.

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Mahler, Symphony No. 6, movement 4

Wednesday, June 30th, 2010

I will be the first to admit that I have not done my homework to the extent I would ideally like to over the past two weeks.  Perhaps I should have allotted more time to the 822 measures of this movement, but truthfully other things have got in the way.  To allow myself an extension would simply impinge on the three remaining pieces, and since by the time I am ready to write the next blog entry, we will also be on the cusp of moving, it seems better to summarize my observations and move forward today.

With this movement, it seems very difficult to get past Mahler’s symbolism–the hammer blows, the major-minor motive and the rest.  Tony Duggan, in his excellent summary of recent recordings of this piece, deals with some of the many performance issues, such as the ordering of the movements (which differs from my edition, the Dover miniature score and from many recent recordings), and the precise number of hammer blows (Mahler’s final decision appears to have been two, while my score, a reprint of the 1906 Nachfolger edition, calls for three).  He also suggests that this piece is the most classically ordered of all of Mahler’s symphonies, and I find myself tending to agree with that statement.

In an interesting way, the two hammer blows that Mahler retained seem to delineate the exposition, development and recapitulation of a sonata-allegro form, with the third (missing) blow indicating the coda.

Mahler opens this movement with an interesting texture and harmony–a German augmented-sixth chord that resolves deceptively to the tonic in m. 9, the first appearance of the major-minor motive in this movement.  The motive is presented as it appeared in the first movement, in the brass, and accompanied by timpani and drums, but with the strings offering a countermelody that contains material of motivic importance for the rest of the movement.

In m. 16, a tuba solo introduces further new material, including an octave leap.  Throughout this symphony, the octave leap has been an important element, and part of the cohesiveness of the work as a whole is Mahler’s use of the octave (and sometimes larger intervals) to create a sense of drama and pathos.  Rodney Winther teaches that small intervals build tension, while large intervals build drama, and Mahler employs both, but the drama of this movement is the aspect that wins out, I think.

The tuba solo is accompanied by a descending chromatic bass, which is highly typical of Mahler.  In mm. 19 and 22, the clarinets and horns have an interesting effect that I typically associate more with later composers, such as Stravinsky.  The clarinets articulate the beginning of a phrase, but the horns sustain the final note, as though the echo has a different timbre than the initial attack.  In the end, it is this sort of synthesis and blending that makes for fantastic orchestral writing, and Mahler is transcending the German orchestrational style in this instance.  A comparison with the scoring techniques used by composers of a generation earlier–Brahms, Wagner, Bruckner–reveals a much more conservative approach, with much greater use of simple block and mixed scoring techniques.  Composers of the same generation and younger, however, start to show this sort of adventurous approach to orchestration–Richard Strauss and Schoenberg, for example.  Strauss would seem to be the first of these new orchestrators to achieve notoriety–before Mahler, perhaps?

I don’t often wish that I were a trumpet player, but m. 46 has an absolutely fantastic line that makes me a little bit envious.  This is followed by another typical descent to the cadence, as the music shifts to C-minor in m. 49 for a chorale setting, first in a very dark woodwind and horn timbre, then in a lighter timbre that uses the middle, relaxed registor of the horns.  Again, Mahler is being expository here, and this material reappears later in the movement in a drastically transformed body.

From this point, the tempo and scoring become faster and fuller, and by m. 114, the written tempo is Allegro energico, the tempo of the first movement.  The martial, mechanistic feel of that movement is carried forward here in a section that, if not quotation, is at least style-copy.

In m. 182, marked pesante, the low brass state a theme that begins with a decsending octave, here on A.  This theme reappears after both of the hammer blows, and as the dark coda, which would have followed the third hammer blow in Mahler’s sometime plan for this movment. 

Measure 228 sees the harmony move from D major to D minor, with both the descending octave idea and a texture that is reminiscent of the material in the first few measures of this movement.  This portion of the piece is developmental in nature, and as it builds to the first hammer blow (m. 336) the music becomes more an more rhythmically compelx, particularly around m. 290, where Mahler juxtaposes several divisions of the beat as the music leads to a cadence in G major in m. 296.

A trend that I have detected in Mahler’s work is a growing concern with counterpoint.  Almost nowhere in this movement does Mahler use a simple “melody with accompaniment” texture.  Whether imitation or inversion or augmentation, Mahler seems to have come to a more “crafty” approach to his art.  At the same time, Mahler’s counterpoint does not adhere strictly to the traditional “rules,” and dissonance is often freely introduced without preparation.   For an example of this tendency, see mm. 302ff, wherein a two-measure motive is passed around imitatively, often with strikingly dissonant results.

I find myself shorter on time than on ideas about this piece–again, I refer myself to my notes on it.  The last three canonical symphonies remain–I am undecided about the Tenth, Das Lied von der Erde or some of the other pieces I might work with.  The Seventh, Eighth and Ninth are enormous compositions with which I am somewhat less familiar with than the first six symphonies, and come December, I will have to see where my thinking about Mahler lies.  If I have learned what I need to from this master, I may move on (to what, I am not certain).

Schedule for the Seventh will be as follows:

  • July 1-12: Movement 1
  • July 13-24: Movement 2
  • July 25-August 5: Movement 3
  • August 6-17:  Movement 4
  • August 18-31:  Movement 5

Hope to have you with me!

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Mahler, Symphony No. 5, fifth movement

Saturday, May 1st, 2010

This movement has gone, over the last weeks, from being a piece that I’ve long admired to something of an analytic enigma.  Simply put, I am at odds to determine whether this “Rondo-Finale” is best considered as a rondo, a sonata-allegro or a fugue.

First, to the title, if that can be a clue for the analyst.  Does “Rondo-Finale” suggest “rondo-as-finale” or “rondo-then-finale?”  My hearing suggests that there is indeed a rondo here, and that it is followed by a lengthy coda, so that the second possibility seems stronger.  In this case, the coda could perhaps begin in m. 581, at a key change to A-flat major, far-removed from the home key of D major.  The melodic and motivic material is related to the rondo theme (mm. 24-55), but this late harmonic move away from the home key suggests a coda.

The music up to this point is highly suggestive of rondo technique, specifically of five-part rondo with its three statements of the rondo theme with interspersed refrains.  The second refrain (beginning in m. 167, the “C” of “ABACA”) is the longest, and is heavily reliant on developmental techniques, especially exploration of remote key areas and contrapuntal recombination of motivic material.

It is, however, the first refrain (beginning at m. 56, the “B” section) that is most striking.  It suggests a four-part fugal exposition, first with a running eighth-note subject, then with various countersubjects introduced over the eighty bars of this section before the return of the rondo theme.  The second refrain can then be cast as a continuation of the fugue.  At m. 273, the original fugue subject appears in counterpoint with one of the countersubjects.  This countersubject becomes the second subject of a double fugue that dominates much of the rest of the second refrain (development).  Contrapuntal technique abounds, with the inversion of the second subject appearing in the violins at m. 457.

The final entrance of the rondo theme appears in a highly modified form at m. 497, leading not back to the beginning, then, but toward the “finale” section of the movement.

There are also intimations here of sonata-allegro, or at least something along the lines of a hybrid sonata-rondo, as found in another wonderfully contrapuntal work, the finale of Robert Schumann’s Piano Quintet, Op. 44.  The first rondo and first refrain would correspond to a sonata exposition, the second rondo and second refrain to the development, and the last refrain and “finale” to the recapitulation and coda.

It is a fascinating feature of this movement that it not only is a highly compelling piece of music, but that it also embodies these three formal procedures .

A final issue with this symphony is its harmonic plan.  The home keys of the five movements are, in order, C-sharp minor, A minor, D major, F major and D major.  Mahler uses this narrative tonality in other places.  If Mahler had in mind a major-key finale to a minor-key symphony, in the manner of Beethoven’s Fifth and Ninth Symphonies, perhaps he felt that the technical challenges involved in C-sharp major might be too much for his orchestra, given the already stiff demands of the music.  At any rate, it is also simply possible that Mahler is moving away from the single-key concept of a symphony.  The five movements appear appear to be held together from a motivic standpoint, rather than from harmonic consistency, but in a traditional sense, they are no more related than a suite of pieces extracted from an opera or ballet.  It is a testament to Mahler’s compositional technique that the piece feels completely unified without sharing a common key center.

Now on to the Sixth–four large movements, so two weeks each.

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Mahler, Symphony No. 2, First Movement

Monday, September 14th, 2009

To the next piece, then.

In some ways, the Second feels much more like Mahler than the First–a focus more on motive than on theme, on counterpoint over homophony.  As well as Mahler seems to have opened up a world in the “Titan,” in “Resurrection,” we begin in that world, as though we have lived there all along.  Where the First grew slowly out of stillness, the Second begins on the dominant pitch as well, but begins with an agitated, urgent feeling–brought on by tremolo in the strings instead of harmonics.  Instead of the gently half-floating, half-falling fourths-based line in long notes, we here get an ascending, scale based line in short note values that propels us forward into the first movement.  We are in the thick of the piece before we realize it. 

This outburst in the low strings has something in common with much of the material of the movement–it acts like many a Bach fugal subject in that it outlines an octave which will later be filled by the voice in which it appears.   Again, as in Bach, the motive undergoes a type of fortspinnung, or spinning-out.  In general, a very different treatment than much of the material in the First symphony.

Beginning in bar 18, the woodwinds enter with another octave-filling melody, this also exposing the half-plus-dotted-quarter-plus-eighth rhythm that dominates much of the melodic material of the movement. 

At the first climax of the movement, bar 38-41, we see the third crucial motive of this movement, a contrapuntal device, if such can be a motive.  Two scales are placed in contrary motion.  To any student of tonal theory or 16th-century counterpoint, this compositional device may seem completely obvious–or simply correct writing–but compared to the language of the First Symphony, Mahler’s emphasis on scalar contrary motion is a defining characteristic.  The extensive use of pedal point in the earlier work is replaced here generally by a greater contrapuntal awareness and specifically by this device.

Rehearsal 3 has the music in B major, by direct modulation, with yet another octave-filling melody.  I have been pressuring myself to be more sparing–nay, frugal–with motivic and thematic material, where Mahler seems profligate in his introduction of new themes.  However, they are often at least partly related to each other, and, additionally, to craft a movement lasting nearly half an hour (in my Bernstein-NY Phil recording), much raw material is required. 

With the material exposed, at rehearsal 4, we have a return to the opening of the piece, but, curiously, without the very first C-B-C-D-Eb.  Rather, we hear the second “lick,” following which Mahler gets more quickly to business.  The end of a group of themes, then, now followed by a transition?  Or the repeat of an “exposition?”  A major question, since I am teaching Forms and Analysis this semester, is how well, if at all, Mahler conforms to the classical forms, sonata-allegro, in particular.  I have long felt that sonata-allegro form is but one way to achieve  the exposition-development-recapitulation plan of a musical composition; for the untrained listener, the satisfaction lies less in the return of the tonic than in the restatement of the beginning in some way; a melodic affirmation that the piece has come full circle.

At m. 97, the basses give an ostinato motive that bears striking resemblance to a similar moment in the First (the first movement).  While that melody had a rising contour, this one falls.  Mahler characterized this movement as being a funeral march for the hero of the “Titan,” and here is a very specific link between the two. 

A few measures earlier is the motive of the scales by contrary motion, appearing here in a transitional passage, but more often used in the run-up to a climactic moment.  The hero descends to the grave, and ascends to heaven simultaneously.  As Oscar Hammerstein wrote, “passions that thrill…are the passions that kill.”  Schopenauer, Wagner, Mahler, and fifty years later, Broadway.

Rehearsal 8, measure 129, gives a subsidiary motive, again filling an octave, but, rarely for this piece, from the top down instead of from the bottom up.   It feels a borrowing from Wagner’s Ring.  It creates a particularly Wagnerian moment later in the piece (before rehearsal 23, in a “recapitultion” or coda–I’m not sure which). 

The first (and only) time I heard this piece in concert, I was startled by Mahler’s use of doubled English horn and bass clarinet (m. 151ff), and have since stolen that scoring in my own piece for orchestra, Five Rhythmic Etudes.  What I did not remember is the return of the same material for trumpet and trombone, (mm. 262ff).  Again, one is struck by repetition.  A few years later, Schoenberg would attempt to banish repetition from his work, and we have been living to an extent under this stricture ever since (his one-act opera Erwartung contains almost no motivic repetition in more than forty-five minutes of music).  Is a large-scale work such as this dependent on repetition to be successful?  It is everywhere–on the beat level, the measure level, the phrase level and the sectional level, both exact and varied.

On a related matter, I’m fascinated by Mahler’s “preview technique.”  In the First Symphony, a large swath of the first movement reappears in the finale.  I’m fairly sure that the first movement is not previewing the last movement.  But in m. 270 of the present movement, the horns give a chorale melody that reappears nearly half an hour later in the finale.  It leads here to one of the very characteristic (in both rhythm and melody) themes of the first movement, where in the finale, it leads to the key melody of that movement.  This is not simply a compositional technique–mark that there is none of the craft here of a Bach contrapunctus–but rather a psychological device and a feeling of having been given a taste of things to come, a look into the ultimate direction of the piece, and since the subject of the first movement is death, and the subject of the last is, unabashedly, resurrection, we are here meant to understand that even in death there is life.

Measure 329 sees a final eruption of the opening material–more fully-scored, more determined than ever.  This leads to what feels like a recapitulation, and the major-key theme–first heard at rehearsal 3 in E major, now in A major (the key relation hearkens to sonata-allegro)–almost evaporates into the end of the movement.   Beginning in measure 384, Mahler introduces a shifting major-minor feeling that brings to mind the key motive of the Sixth Symphony–the instrumental piece most associated with death in Mahler’s catalog.  The piece could have ended with a whimper on a major note, but this rocking back and forth allows the funeral march to fade into the distance.  Are we left standing at the hero’s grave?  The music unravels amid reminders of the material it was made of, last tastes of the world we knew.

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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.

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Opus 106

Monday, April 13th, 2009

I am way behind on this, I know, but it is time to say something about “Hammerklavier” and move on.

But where to begin?  As a piano operator, I can’t even begin to touch this piece, and as a musician, I’m not sure where I land, to be frank.

It is simply bigger, fuller, greater, and deeper than any music I have ever tried to bring to life.  As a trombonist, I play an instrument with a distinct lack of serious music by great composers, and with the possible exception of the concert by Christopher Rouse, I would say that there isn’t anything that even comes close to this piece.  As an ensemble musician, my experience of a piece is very different from that of a soloist, or even of a clarinetist or violinist.  Yes, I’ve played a Brahms symphony, but I had to sit and listen to the first three movements before playing a single note.  And the conductor was in charge.  And of course, I conduct, but it has never been my privelege to lead any of the band music that begins to approach the level of this sonata–I’m thinking of Colgrass’ Winds of Nagaul or Husa’s Music for Prague.

So my encounter with Opus 106 has been somewhat stunning.  Of course I have listened to and studied epic music before, but to imagine the range of expression and technique required here of a single musician brings to the fore to an even greater degree the scope of this piece.

Beethoven has been percussive before.  He has been formally extensive before.  He has been contrapuntal before.  He has waxed philosophically before in slow movements.  But here, every measure seems endowed with a depth, a seriousness–this is truly what people mean by “late Beethoven.”  There is no orchestration to distract from the absoluteness of the music in piano writing–there is only music, on this very imperfect instrument where notes decay too quickly and half a composer’s energy is given to making them last longer.

If I tried to name specifics, this post would be pages long.  I could spend the next year working out this piece, but it is time to move on–to three more titanic pieces!

I’m still looking for suggestions for what to study next… lately I’ve thought about Bach’s St. Matthew Passion, as well as continuing to ponder the Mahler symphonies.

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