Posts Tagged ‘counterpoint’

Harmony

Thursday, June 23rd, 2016

Yet another post in response to a question from my student Cooper Wood, who sent a text message yesterday asking, in part, how I work with harmony, and how I structure chords.  Early on in my lessons at Ohio State, Donald Harris put a similar question to me, and I don’t quite remember my answer–I’m not sure that I was able to answer him at that point, so here, twelve years later, is an attempt.

I have often thought of composers falling into three groups–harmonic, melodic, and rhythmic.  Beethoven and I are rhythmic composers, and for us, if the rhythm is correct, the harmony and melody will fall into place around it through the application of motivic constructions and a sense of when the harmony needs to change.  It is not that a rhythmic composer ignores harmony but that the musical meaning isn’t concentrated there.  As interesting as Beethoven’s harmonic language can be, there is no equivalent to the Tristan chord in his work.

Two things I don’t do, at least not regularly:  I don’t consider my work from a functional/tonal perspective, at least not during the writing of it, and I don’t simply sit at the piano and let my fingers fall where they may, to see what kinds of chords come out.  That is to say, I rarely think of chords in either sense–neither as units functioning in some system nor as groups of notes played simultaneously.

Here, then, are some of the ways that I think about harmony:

Thickness of texture: Is this a moment in the piece where a more complex, richer sound is required? This makes harmony into a timbral decision, where there is a continuum, something like this:

Single line—Octave doubling—Non-octave doubling—Two or more parallel intervals—Voice-leading—Clusters

My 2010 Piano Sonata displays almost all of these at some point.

Scale and Mode: While I rarely explicitly choose a specific scale or mode, melodically, my music often behaves in modal ways, and I feel that introducing an accidental is a change in harmony.  On the small scale, this may happen quickly.  I notice a distinct preference in my music for flats over sharps, and my feeling about accidentals is that they point, so I am frequently choosing notes that point down a half-step.  My trombone concerto Homo sapiens trombonensis (2005) includes examples of this sort of thinking.

Consonance and Dissonance: I spent several years before graduate school trying to come to terms with my personal approach to dissonance, as nothing, at least to my thinking at the time, says more about a composer than his or her use of harmonic language.  I still hold to Vincent Persichetti’s idea, laid out in Twentieth-Century Harmony, that the degree of dissonance is something that a composer must tightly control.  So, in my work, I tend to make harmonic decisions based on how consonant or dissonant a passage needs to be, adding notes when appropriate, and thinning out the texture when necessary.  For me, chord constructive is an additive conception.

Organum: William Russo’s book Composing Music was at one time a standard title on the shelves at Barnes & Noble, and though I never bought the book, I certainly read large chunks in comfortable chairs.  One idea that stuck with me is what he calls organum–doubling a line at a parallel interval to increase the complexity of the timbre.  A key feature of my style for at least the past ten years has been melodic doubling in sevenths, usually minor sevenths, although sometimes following the diatonic scale.  Much of my piano music uses these parallel sevenths, beginning with 2008’s Starry Wanderers.

Set Class: In some of my works, I have, early on in the process, discovered a set that appeals to me, and based the work on that to one degree or another.  This is usually an outgrowth of my work with motive, and in some ways, the set becomes a harmonic motive.  In my most recent work for solo piano, The Rainbow’s Daughter, I found myself drawn to the set [0236] during the composing of the first movement, “Polychrome’s Prism.”  Its two thirds (which I wrote as two sixths) slide easily into a minor triad, giving the sense of refraction that I wanted to suggest.  In the subsequent movements, I found that I could turn [0236] just as easily into an augmented, diminished, or major triad, and the structure of what is one of my most harmonically-conceived pieces became clear.

Counterpoint: I often attempt to combine melodies, resulting in harmonic structures.  My training in 16th-century counterpoint (begun with Dan Trueman in music theory at CCM, and continued in self-study, most significantly in Schubert’s Modal Counterpoint: Renaissance Style, which I used as a teaching text) and in 18th-century counterpoint (with Jan Radzynski at Ohio State), had the desired effect–it gave me a sense of the possibilities of the ars combinatoria and as a result, I think about the direction of each voice in a composition, with the resulting variety of rhythmic and melodic direction.  I don’t, however, generally include canon, fugato, or strictly fugal sections in my work.  I don’t find that these techniques provide sufficient reward for the effort involved.

Layering: In place of imitative counterpoint, I often choose a layered approach, in which small, repeated melodic/rhythmic units either build a texture through successive entrances or appear simultaneously.  I used this extensively in my 2010 band piece Moriarty’s Necktie, and the idea of adding a layer is never far from my mind, although this rarely results in a simple melody+figuration texture.

So–I don’t know that I have answered the question put to me now by both my teacher and my student, but these are some of the things that I think about as I work.  For Cooper, I hope this helps.  For Don, just know that I am still working on that answer for you.

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The Middle

Tuesday, February 5th, 2013

My last post described some things that I learned from another art form, woodcarving, through my father and his teacher, Spirit Williams.  Here’s another in the same vein, purely by chance, mind you.

I firmly believe that other art forms have a great deal to tell us about composing, which means that if I have a chance to chat up an artist during a plane ride, I’m going to take it. Last Spring, I met Kiersi Burkhart on a plane from somewhere to somewhere (I think it involved Denver, a city where I one day hope to see more than the airport and the hotel where the airline sends me when my flight is screwed up). She writes young adult novels, and also a blog. This post showed up the other day, about how to help the middle of a novel.   Her five suggestions have me thinking about the middle of pieces, so here are my thoughts about Kiersi’s thoughts and how they might relate to composing.

1. Raise the stakes. This “tip” gets thrown around a lot, and for a long time I wasn’t really sure how one could implement such broad-sided advice.

The easiest way I’ve found is to first work out what your characters’ goals are (both small and large), and then determine: what are the consequences of your characters not achieving those goals? Now make them even more dire. Life and death. Death and destruction. Whatever you can do to make the repercussions of your characters’ not achieving their goals worse, do it.

I think the best way to raise the stakes in a musical composition is to move beyond your starting material in some way.  I’m not suggesting that you string together theme after theme after theme (although it worked occasionally for Mozart), but if you’ve focused on one melodic idea up until this point, say, a third of the way in to the composition, it’s time for some contrast.  This new material should relate to earlier portions of the piece in some way–a similar harmonic framework, or a motivic relationship–but there is a need for variety as well.

Another way to raise the stakes might be to employ a change in texture–if things have been very homophonic up to now, it’s time for some counterpoint; if you’ve been writing lots of interwoven lines, it’s time to pare the texture down.  All kinds of great things can happen in the middle of pieces–the classical approach to creating a movement has a middle that is much more loosely-constructed than the beginning, and even in the middle of a Bach fugue, we can go long stretches without either a cadence or the fugal subject, just riffing on little ideas that have come up.  Speaking of riffing, think of the structure of a bebop jazz performance, with its tightly-constructed presentations of the head at the beginning and end and the loosely-constructed solos in the middle.

2. Lower the low points. The best part of middles is when it seems all hope is lost–that there is no possible way your character can achieve his purpose.

Remember in Star Wars: The Empire Strikes Back, when Han Solo gets trapped in carbonite? Even worse, he’s shipped off with a bounty hunter to see Jabba the Hut, and our heroes are too busy trying to save Luke to chase him down.

At this moment in the story, we (the audience) feel somewhat defeated, like there’s no possible way Han can be rescued from his terrible fate. And in Return of the Jedi, this situation only gets worse when Leia is enslaved by Jabba.

Find that low point in your story (make one, if it’s not there already) and then make it worse. While you’re beating your hero into the ground, beat harder. Did something go wrong in his heist plan? Find three other things to go wrong, too. And it’ll be really satisfying to your audience when your clever protagonist manages to worm her way out of this ridiculous bind.

I think what Kiersi is getting at here is dramatic tension–the middle is the place where we really aren’t sure how things are going to work out, and as such, it has the possibility of being the most exciting part of a piece of music.  Certainly, as a composer, I often view my pieces this way when they are in process: there comes a point when I know what the rest of the piece is going to look like, and I know that I will be able to finish it.  Composing the middle, though, can be frustrating for exactly that reason–I don’t know how I’m going to get out of the situation in which I’ve placed myself.  There’s a famous moment in the first movement of Beethoven’s Eroica where the texture devolves into these dissonant, repeated chords, as though Beethoven threw up his hands, smacked the piano keyboard, and wrote down the results.  Beethoven takes this almost-mistake and slowly winds his way out, with a diminuendo and resolutions of dissonant notes that leads back to the main theme–the beginning of the ending.  In my own Piano Sonata, about three-quarters of the way through, the relatively-complex rhythms and texture dissolve into a single line, notated in stemless noteheads, a moment of repose for performer and audience, and a summation of what has come so far in the piece, and preparation for some of the breathless material that lies ahead in the push to the climax.

3. Up the conflict. Are your characters friends, lovers, or comrades in arms? Are they getting along, smooching, snuggling and heisting in perfect harmony?

This is the primary way in which I find middles sag: the character relationships stale. Either they are at peace with one another for too long, or they’re at odds without any moments of relief.

Cause some conflict. Stir up some drama. But be wary of falling into common conflict traps: misunderstandings that would be easy to resolve, unlikely coincidences, or blowing up a small issue into a big one (this is my biggest complaint with romantic sub-plots).

Use inherent character flaws to guide your conflicts. Is one of your characters prideful? Have that pride lead her to hurt the other character in a way that seems irreparable.

Again, we have to turn to Beethoven, who can’t seem to write a middle section of a symphony movement without a fugato (and who was imitated by countless others).  As Kiersi mentions, though, it’s easy to fall into some common traps, and fugato is one of them (why does Brahms turn every movement of Ein Deutsches Requiem into a fugue?  I submit that it may have been youthful inexperience).  Unless your piece has been somewhat contrapuntal up to now, throwing a fugue in seems kind of desperate (Berlioz writes scathingly about this practice in his orchestration treatise).  But the beauty of fugue is that it does have that “cool” factor, and it’s critical to find something to do with your materials that propels the piece forward.  Look for the same kinds of rhythmic intensification that fugue can provide–change the position of motives within the bar, let them happen sooner, and closer together.  Foil the listener’s expectations about when things will happen: sooner (more drama), later (more tension).

4. Comic relief. I might be the only writer with this particular problem, but I have a hunch that I’m not. Why so serious? If things are getting intense in your middle–as it probably should–be cognizant of how your reader is feeling. In the middle of drama and conflict, give your reader the occasional break.

The break doesn’t always have to be comic. Let your characters have moments of tenderness or insight into one another. In a romance, let passion momentarily override conflict (leading to more conflict, of course). In a thriller, let your protagonist feel victory–short-lived victory. A good middle is a combination of low and high points, leading up to your dramatic finale.

This can be hard to remember, but great music can be funny, not just serious.  Whether it’s Bach’s quodlibet in the Goldberg Variations with its use of street songs (not funny to us, but probably hysterical to Bach), or the trio of the Scherzo in Persichetti’s Symphony for Band, where a little group of instruments, pulled along by a muted trombone, plays a little march that sounds like it would go with a Dr. Seuss story, there is humor in good music.  A composer is a human being, and being human means being both tragic and comic.  Some composers do this better than others: think of the burlesque version of the march from Shostakovich’s Seventh Symphony that shows up in Bartok’s Concerto for Orchestra.  I’m sure that Shostakovich laughed the first time he heard it, because his own music is filled with irony and parody as well.

That said, it’s easier to plant comic relief in a dramatic work–the Papageno subplot in Mozart’s The Magic Flute, for example, and of course the dark humor of the graveyard scene in Hamlet that adds levity while staying on topic–the downstairs view of the goings on at Elsinor, perhaps.  Kiersi also suggests that intimate moments in the middle provide a break–it works in music, too, as in the piano-cello duet in the second movement of John Corigliano’s Symphony No. 1–intimate not only in texture but in meaning as well.

5. Escalate tension. A good climax is the tip of the highest peak of your story arc. Leading up to that peak are your second, third, and fourth-highest peaks.

I suggest doing this with “post-outlining”: now that you know all the plot points of your story (all the “ups” and “downs,”) organize them in order of severity. Your lowest lows and your highest highs should come near the end, leading up to your finale.

This is especially important when revealing important plot information. You don’t want to save all of your high-value cards and staggering reveals for the very end; drop some of your big bombs (but not your biggest bomb) during that sagging middle section, then escalate leading up to that super mondo finale–and hopefully leave your readers panting.

This suggestion may or may not apply to a given situation–sometimes the beginning of the end of a piece of music is a moment where tension is released–the recapitulation of a sonata-form movement, for example, or the beginning of the “Simple Gifts” variations in Copland’s Appalachian Spring.  The ending of a piece is inevitable once it begins, and layering coda upon coda (in the way Tchaikovsky does in his Fifth Symphony, for example) doesn’t move the beginning of the ending anywhere closer to being the middle.  In good music there is a crucial difference between music of the beginning, music of the middle, and music of the end.  Some great middle moments, though–the trombone chorale in the last movement of Mahler’s Resurrection Symphony comes to mind–are the last moment of calm, an eye in the hurricane.  The birdsong section of the slow movement of Dvorak’s New World Symphony is a change of character that builds into a critical statement of the motto theme of the symphony before the return of the main theme for the movement.  It would behoove all of us to study the Romanza movements that Mozart frequently uses in his later piano concerti–the quick middle Sturm und Drang sections like the one in K.466 are the uber-middle–the middle part of the middle movement of the three-movement structure.  The formal considerations of music are somewhat different than those of the novel, of course, because of the way that repetition is a critical component of good composition, but the dramatic concerns are similar.

Ralph Vaughan Williams is said to have said what every composer (and author) knows: something to the effect that starting a piece is easy, but getting to the end is hard.  This is the difference between being a tunesmith and being a composer:  a song is all theme, but a composer has to be able to take themes (or the equivalent) and connect them in meaningful ways, constructing the musical equivalent of a novel.

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Mahler, Symphony No. 9, movement 3

Friday, December 17th, 2010

This “Rondo-Burleske” is yet another intriguing, tightly-wrought movement that reveals its secrets somewhat reluctantly but in fullness.  A six-measure introduction reveals most of the motivic material for the movement, beginning with a three-note figure announced by the trumpet.  This is answered by a five-note, arch-shaped cell played in octaves by the strings.  The three-note motive returns in the horns, with a three-note rising response in the low winds and woodwinds.  After a measure’s silence (m. 5), the introduction ends with a repetition of the final motive in the winds and brass.

What has really happened in the first six measures is a halting, hesitant version of the rondo theme for this movement.  The material presented appears again and again throughout the movement, beginning with the first presentation of the melodic idea for the movement in full, confident form.  The melody of the first six bars becomes a full-fledged Mahlerian rondo theme, rollicking and surging forward in two-measure segments until the end of the phrase in m. 22.  The initial three-note motive is the primary melodic material.  The next passage, mm. 23-43, is somewhat more conventional in nature, but Mahler’s scoring renders it a contrapuntal wonder, with the melody shared between first and second violins.  This segment is essentially developmental in function and leads to a return of the first phrase, now varied in rhythm and texture, in m. 44.

At m. 51ff, the melody is again divided between first and second violins, and I have to wonder at the implications for the seating of these sections–are the violins to be separated for a stereophonic effect, or placed together for a unified sound?   The overriding segmentation into two-bar ideas is maintained through this pertion of music as well.

A passage of fantastic string writing follows beginning in m. 66.  A sequential passage breaks the two-bar hypermeter, in preparation for an imitative passage between strings and horns.  The section breaks down to a notated key change (to D minor) preceded by conventional material presented in single-bar segments.  The material continues to be halting, lurching forward from statement to statement.  In m. 97, a fascinating coloration of the melody in the violins occurs as the flutes play off-beats.  This leads to a transition to the first episode of the rondo form.

The episode, beginning in m. 109, begins in F major, and subsitutes 2/4 for cut time, with the instruction “L’istesso tempo.”  The mood is significantly more relaxed than the refrain, with the lurching  feel left behind.  This material has an emphasis on root motion by thirds, initially descending, but later ascending.  It is somewhat ironic, that in a harmonic system based on thirds, Mahler’s root motion by thirds seems to undermine the tonal system.  The hypermeter here seems to suggest four-bar measures rather than the two-bar measures of the refrain, although with less regularity than before, with some three-bar measures making their appearance.  This episode ends with no transition in m. 180 when the refrain again bursts forth.

This second appearance of the refrain is rhythmically modified, in that triplets are substituted for the eighth-note figures of the opening.  The overall melodic structure is similar, as the hypermetric structure with its two-bar cells.

At m. 209, a motive I will refer to as the “chorale” makes its first appearance (it will later be presented by the brass in chorale style, but for now, it is more or less a countersubject in a fugato treatment of the refrain melody).  The first downbeat of the refrain melody is also the first beat of the chorale, as in m. 209, where it appears in the trombones, which continue the refrain while the clarinets enter with the remainder of the chorale.

After this fugato version of the refrain, the first episode reappears in m. 262.  In a Classical seven-part rondo, the first episode wouldn’t reappear until the end of the movement, as the next-to-last part of the form.  Instead of the original F major, the episode is now in A major.

Another interesting aspect of this movement is Mahler’s extensive use of enharmonicism, particularly in this repeated episode.  This allows rapid changes of harmony between remote areas, of course, but also conflicts with the nature of the orchestral instruments, which do not treat enharmonic pitches equivalently in the way that the piano does.

The next statement of the refrain begins in m. 311 and lasts 35 measures, in a typical truncation of refrain material.  Less typical, however, is the manner in which the chorale melody begins to dominate this section, even in its determination of the medium-scale formal structure, which appears in nine-bar phrases.

In m. 347, a written key change to D major sets up the culminating presentation of the chorale, in the brass, which introduces a third episode.  This is based on new motivic material, resembling a simple turn.  This “slow” episode continues to build until m. 421.  Which leads to a transitional section with a very interesting alternation of material from the refrain and the “slow” episode.  The refrain returns in m. 522 with the melody appearing in the trombones.

In m. 617, at the marking “Piu stretto,” the first of two codas begins, in the Romantic tendency to extend after-the-ending material.  The first coda, and the second, which begins in m. 641, both are restatements of the refrain melody at faster tempi.  The movement lurches to its conclusion.

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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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