Posts Tagged ‘common-tone modulation’

Mahler, Symphony No. 6, third movement

Wednesday, June 16th, 2010

Eric Knechtges, a colleague at Northern Kentucky University, recently sent out a survery to university composers.  One of the questions was,  “3) Any advice for potential composition students concerning the college application process, and/or constructing a portfolio?”

Here’s my answer:

In our portfolios, I like to see three compositions which demonstrate the student’s stylistic preferences, ability to pursue a project to completion, and interest in various media.  In general, it is not necessary to include a large-ensemble piece, especially if performance recordings are available of smaller-scale works.  MIDI realizations can do more harm than good.  I would rather hear or see short-to-medium length pieces that demonstrate technical mastery of compositional skills such as motivic development, phrase and phrase group organization, variation technique, harmonic and rhythmic coherence and ability to pursue an idea to its conclusion in a fully-formed piece (with beginning, middle and end).  Submitted scores should have a professional appearance, with attention to the details and standard practices of manuscript or digital score preparation–dynamics, tempi, articulation.  There should be a clear sense that I am not looking at a “first draft,” and that significant effort has been put into revision and the “polishing” phase of work.

Perhaps these are merely my personal prejudices (particularly about making a score look good), but some of these traits are evident to me in the great music of the past.  One of these, motivic development, is the main idea behind the third movement of Mahler’s Sixth, and I want to explore that today.

When I’m teaching basic composition to my students, I always stress economy of material, because emphasizing a single motive or a small group of motives throughout a piece builds unity while also providing opportunities for variety.  Unity is essential because it makes the piece sound like itself and not like a string of melodies or harmonies.  Variety, however, is very important in most styles, because very few listeners want to hear a great deal of exact repetition.

Mahler has set this movement in the key of E-flat major, a key that is somewhat removed from the symphony’s key of A minor.  On closer inspection, though, it is the relative major of the parallel minor of the relative major of the home key (a minor to C major to C minor to E-flat major), so there is a relation here, although it’s somewhat tenuous.

The music begins with a theme, stated in the violins, that introduces much of the material with which Mahler concerns himself throughout the movement.  As Russell Mikkelson frequently states, composers are like bad poker players, because they show you their cards at the beginning of each hand.  In addition to the head-motive of this theme, with its distinctive sol-mi-sol rising and falling sixth, there are motives in the second half of the first full measure (motive a, four eighth-notes, descending by third, then by seconds) and the second half of measure 3 (motive b, a written-out “turn”).  In measure 8, the oboe presents a final important motive, motive c, a figure which alternatively rises falls and rises, with sixteenth-notes on the second half of each beat to give the impression of hesitancy.

The a motive reappears in the violin melody in m. 13, first implying a IV triad, then a borrowed iv on its repetition.  Immediately thereafter, the c motive appears in the violins and woodwinds, again as part of the melody.  In m. 16, the a motive reverses its earlier trick, outlining iv and then IV (the entire passage is constructed over a tonic pedal point).   Measures 20-27 present a fascinating woodwind accompaniment texture, based on the c motive and its inversion.  The melody is assigned to the English horn, and begins in m. 22 with an inversion of the head-motive of the first theme–a falling and rising fifth instead of the sixth from before.  The key of g minor is suggested here, but it does not last, with a return to E-flat major in the next section of music, beginning in m. 28 with a horn melody that incorporates all the important motive material so far.  In m. 31, Mahler extends the dissonant Db5 in the solo horn by two beats, requiring a 2/4 bar (m. 34) to put the next cadence on the downbeat.

There follows a chromatic passage (mm. 36-41) that appears to lead toward C major, but then at the last moment returns to E-flat.  The next passage is based solely on the motives (a and c) from the first theme, with the c motive dominating the music in mm. 42-52, with a making its appearances in mm. 45-46, again highlighting an alternating major-minor chord.  While the overt major-triad-turning-minor motive that has characterized the previous movements of the symphony does not appear in this third movement, there seem to be more sublte, buried echoes of it in this particular use of the a motive, which occurs several times.

Measures 53-56 present a fascinating common-tone modulation, where the pitch G changes from mi in E-flat major to me in E minor.  First the c motive and then the a motive introduce the “second theme,” this time in the horn.  As this theme dissolves (it never really becomes a full-fledged theme, but its certainly too long to be simply a motive), Mahler begins to expand upon the a motive–first in the clarinets by inversion and rhythmic displacement, then in the bass instruments by expanding the third into a fourth, allowing two repetitions of the motive to cover an octave (in m. 65).  In mm. 68-70, a chromatic sequence that maintains the contour of the a motive is heard against the c motive (modified) in the trumpet and oboe.

In mm. 76-77, an almost Baroque-sounding descending-fifths sequence appears–extremely familiar in Common Practice styles, but realtively rare in Mahler, who simply doesn’t seem to have harmonic rhythms that move this quickly.  In the following measure (m. 78) is an early appearance (although not the first, but the first significant one) of the a motive transformed by both retrograde motion (the third at the end instead of the beginning) and the displacement of the third note up an octave, putting dramatic leaps of a seventh and a tenth into the texture.  The c and then the a motives pull the music to the next key, E major, at m. 84.

A note to my students, a spectacular example of the technique known as “horn fifths” appears in m. 85, introducing a trumpet melody that relies on the c motive.  It seems that the tendency is for the c motive to be spun out into some variation of the a motive at many points in this piece, such as in mm. 89-92.  In mm. 95-99, the c motive, and then the a motive create a monophonic modulation (based on the diminished seventh chord) to return to the main theme and the home key.

Measure 100 and the following passage suggest a recapitulation, but Mahler has other plans in mind.  The last chord in m. 114 acts as an augmented sixth chord which points to C major (an interesting use of the augmented sixth to point to a tonic function instead of the dominant, in this case to a key a minor third below the original key).  All three motives (a, b and c) appear in this C-major section, which ends in an unprepared modulation to A major  (mm. 124-145, again, down a minor third).  In this section, Mahler employs the a motive in the bass with the c motive in the horns against a violin melody that reaches higher and higher, to a C#7.  In m. 137, A major turns to A minor, without a key signature, as the oboe gives the “second theme” material. 

A slightly less abrupt key change leads to C-sharp minor in m. 146, as the full orchestra begins to enter with with climactic material based on the a motive (at first, to m. 156 or so), then on a chromatic version of the c  motive, this time in eighth notes instead of the alternating eighth-sixteenth-sixteenth-rest pattern.  By m. 160, the music has abated, leaving music in B major based on the b motive, followed by the c motive to set up an entrance of the a motive on the Neapolitan chord (C major, m. 164).  The major-minor motive is impled by the a motive in mm. 167-8, again extending the phrase by two beats, which are then rectified by the other 2/4 bar in the movement, m. 171.

The a motive takes over the texture in m. 173, as the music returns to E-flat.  Then in m. 176, the descending fifths sequence appears in a moment that is reminiscent of nearly every Hollywood love theme.  A note on the scoring here–one of the interlocking voices here is given to the 1st and 2nd violins, and the other to the violas with the oboes and clarinets, and the effect is very strong (of course, it seems to require seven woodwinds to allow the violas to balance.

The remainder of the movement is coda material, dependent mostly on the a motive and some of its modifications.  Mahler’s use of dynamics in m. 188 allows an effective color change, and there is an itneresting use of rhythmic augmentation of the a motive (with octave displacement, and modified to suggest harmonic closure) in the flute in m. 196ff.  Overall, the tautness of this piece seems to outdo everything Mahler has presented so far.  Despite the sprawling length and scoring of this symphony, the motivic clarity allows it to be highly managable in a way that hasn’t always been the case in these works.

On, then, to the highly-charged, tense finale.  I hope to be able to concentrate on aspects of compositional structure rather than any supposed autobiographical content (a study of how much of this is authentic and how much simply mythological would be very interesting; one day, I hope to tackle Henri-Louis de la Grange’s massive biography of Mahler.  Until then, my biographical understanding of these pieces comes largely from Kurt Blaukopf’s shorter work).

A final note, I’ve recently become aware of a similar project to my own, done much better, I must say, and by a composer of vastly greater experience than myself.  Anyone reading this blog should head over to YouTube to see Don Freund’s videos analyzing Book I of Bach’s Well-Tempered Clavier.  Great stuff!

Mahler–Symphony No. 4, mvt. 3

Saturday, February 20th, 2010

Since I’m a trombone player by training, and this is the only Mahler symphony that doesn’t include my instrument, I have always felt that Mahler’s Fourth was the “little” Mahler symphony, the runt of the litter.  If any of the music disproves that, it would be this movement.  There is a lightness to this music that doesn’t require three trombones and a tuba, or an entire regiment of percussionists.

After the second movment’s digression to the key of C minor, this movement is firmly rooted in the key of the symphony.  The narrative tonal scheme from the Third Symphony has been abandoned, and the piece opens in an explicit G major, with some wonderful string writing.  My Instrumentation students would do well to study how the cello is often the preferred melodic instrument in lines that would be perfectly playable by the viola.  The lower instrument simply has greater resonance and by placing the melody on the higher-pitched strings, Mahler achieves greater expressive power.  I am frustrated by most orchestration texts that include several pages of paean to the violin and then give shorter shrift to the viola, but there is something to it, I’m afraid.

Mahler has structured this opening section in very clear phrases with very clear cadences, which is not always his habit.  In m. 37, after an imperfect authentic cadence on the home key, there is a long extension and transition to the next key.  Mahler signals that the section is nearly over in the same way that Bach often did, by introducing the subdominant.  In this instance, it sounds oddly fresh, even though every first-year music theory student knows that the subdominant (or IV chord) is not at all a rare bird.  It’s just that Mahler has done an effective job of holding it in reserve and now (m. 47), lands on it in a significant way.

The transitional passage that follows is masterful.  The pizzicato bass line from the first few measures gives continuity while the horns and oboe sound the notes that pivot us into the new key, e minor.  Mahler’s use of musical material is tightly controlled–even though he introduces new themes here, they are built over a structure that is related to the accompaniment of the G-major section.    One also can’t help but admire the way that, for Mahler, the orchestra itself is an instrument, rather than being a collection of instruments.  A great example is the dovetailing of the melody in m. 66 from oboe to the first violins.  Those three overlapping notes allow a smooth transition of timbre–more like a pianist coloring notes by managing flow of wrist and hand than an organist pulling stops.  Throughout this passage, the oboe and violins seem to be doing this trading off–the effect is like an impossible instrument.

One instrument that is used sparingly in this movement is the bass clarinet.  I’m intrigued by Mahler’s approach to this instrument in all of his music, but in a twenty-minute movement (by Bernstein’s baton), there are barely ten notes, all within the texture.  Mahler calls for the third clarinetist to “double” on bass, but many of the changes seem very quick for that.

The e-minor moment doesn’t last long–it is developmental in nature and doesn’t have the cleanly defined phrase structure of the G-major section, and in fact shortly (by measure 91) lands on a pedal D to prepare for the G-major material which follows.  The sense of contrast, though, in tempo, scoring, tonality and formal construction is crucial to building a movement of this size and scope. 

Measures 97-99 again show a transition in melodic responsbility that struck me first as an interesting heterophonic approach to changing orchestral color, but on closer inspection reveal that Mahler is using canonic technique, a relatively rare tool for him and for his era.

The next G-major section, beginning in m. 107, is, according to Mahler’s score, a variation.  It is developmental in nature, but also shares constructive elements with the first section in that it is composed of discrete phrases with clear cadences.  Mahler indicates a faster tempo, and so we move quickly through this section, which isn’t as developmental as it might be–perhaps because there is more of a tonal plan reminiscent of rondo form, where the tonic key returns several times rather than a rounded binary in which the tonic is always the goal of the music.  Strangely enough, the tonic is not the ultimate goal!

Orchestrationally, mm. 179-191 are fascinating.  A trio between oboe, English horn (another instrument used sparingly here in this movement) and horn moves between key centers, implying (but not comfirming) g-minor.  A fantastic color follows this trio as four flutes in their weakest register take on the melody for a moment before passing it on to the cellos, reinforcing the crucial intervals.

A conductor from years ago used to state that small intervals create tension, but large intervals create drama.  To that, I would add another function, suggested in Peter Schubert’s book on 16th-century counterpoint–a leap establishes a musical space which steps must then fill in.  In this instance (mm. 188-190), the flutes emphasize these space-defining leaps and the cellos fill them in without assistance.

The goal of this transition has been C-sharp-minor, and on arriving there, Mahler writes a passage that could have come directly from the music of Jean Sibelius–mm. 195 to 200–but immediately after, he is back to Mahler.   C-sharp-minor morphs to one of Mahler’s major-minor moments in mm. 214-221, this time on F-sharp.  This would seem to be yet another common-tone modulation, as the ambiguity of chord quality allows the pitch F-sharp to become the aural focus.  Mahler takes advantage of this by shifting F-sharps role from fa to ti, and making it the leading-tone of the home key, G major.

Here begins a truly fascinating passage from a compositional standpoint.  To be successful, any slow movement must build to some sort of climax that instead of quiet and mediative is full-bodied, energetic and provides the necessary contrast to make a complete statement.  For Mozart, the technique was often the Romanza structure, as in the D-minor Piano Concerto or the Grand Partita serenade.  For Beethoven and Brahms, the technique is often rhythmic diminution combined with fugato, as in the Eroica symphony or the Brahms’ Second Symphony. 

Mahler approaches this moment through the dance, by reference to folk and popular idioms.  A 3/4 version of the opening theme morphs into a landler in m. 237.  This landler becomes a polka in m. 263, barely before we have understood the first dance.  Very quickly, this polka comes off the rails with the instruction to bump the tempo up another notch in m. 278, where the dance seems to lose control completely. 

Measure 283 is a return to the opening material, and this section would seem to suggest a calm recapitulation that will cadence nicely in the home key, buy Mahler has two more surpises in store.

The first is an ending to this abbreviated G-major section (suggestive again of rondo form) that moves toward a tonic note of E, just as it did the first time.  The music should be wrapping up, but clearly Mahler is on his way out again.  Instead of e-minor, however, in m. 315 there is an explosion in E-major, the fullest, strongest texture of the symphony so far.  The brass are in full force, and take the lead.  G-major to E-major is a remote modulation, and the E-major section leads (with a note from the bass clarinet darkening the texture wonderfully in mm. 330-331) to C major, the subdominant.  

From here, it should be a quick move to a cadence on the home key.  The dominant, D, appears, but when the music moves to G major, in m. 340, we realize that D isn’t the dominant, but a temporary tonic.  G feels like a subdominant, then, which means that the movement can’t be over.  Over the last few bars, though, there is no move to a dominant-seventh on D and G-major has appeared for the last time in this movment.  Mahler ends the movement on a dominant chord, a half cadence.  A peek ahead to the last movement reveals that it, too, is in G-major and begins on the tonic chord.  The last two movements are, thus, inseparable.  The third movement is incomplete without the fourth, and the fourth movement has a twenty-minute introduction.

Symphony No. 1, 2nd movement

Saturday, July 25th, 2009

I’ve long felt that a hallmark of the German symphonic tradition, beginning with Haydn and Mozart, is a degree of equality between the wind and string sections of the orchestra.  I cannot imagine writing an orchestral piece of any size that doesn’t exploit this split of the orchestra into two relatively equal (in terms of power) groupings.  It isn’t that Austro-German composers never use mixed scoring, it’s just that they seem to prefer block approaches.  This is quite apparent in in Mahler’s second movement here, which fills the role of the scherzo and trio.

The first presentation of the melody (A major), after a rollicking string introduction, is in the winds accompanied by strings.  After a transition, the melody appears a second time in the strings, with the winds as accompaniment.  A second theme then, first in the dominant (E major), then in D major.  The infamous Mahler instruction, “Schalltrichter auf!” makes its appearance.  It makes the oboes and clarinets raucous, and the horns, although stopped (gestopft) more cutting. 

In m. 56 we see a two-sixteenths-eighth rhythm against triplets–again, the roughness that results is part of the charm of this movement.

Rehearsal 11, m. 108 brings the scherzo back to the original key with an interesting “winding down” effect, as though Mahler were imitating a wind-up record player, though I wonder if he had heard such a thing.  Direct repetition, with slight changes in scoring, and then we come to the Trio, in F major, by a common tone modulation (do in A becomes mi in F).

The trio theme is derived from the scherzo theme.  Again, the wonderful economy of material we heard in the first movement.  Then through G major to C major, and a second common-tone modulation to return to the home key (mi in C becomes sol in A). 

The return of the trio material demonstrates, I think, Mahler’s reason for using seven horns in this piece.  If strings and woodwinds constitute two roughly equal groupings, seven horns bring into the realm of possibility a third group, and we see it here at rehearsal 26, where the scherzo melody returns in the horns instead of the woodwinds.  This recapitulation is dominated by the massed horn sound that creates thrilling moments whenever it appears.

The heavy brass is still not used in an independent way, as a massed choir, but does provide a fourth group that could balance the other three; later composers (led by Mahler) would find that percussion could provide a fifth such group.

As is typical of the late Romantics, the return of the Scherzo is shorter than its first appearance, but more intense, mostly through scoring.

What can this movement tell us about larger forms?  It is one of the shortest in Mahler’s symphonies, and built mostly through repetition of swathes of material, not through development–on the whole, quite typical of the designs of minuets, and later scherzi, in German music.  The transition back to the tonic in the first scherzo is wonderful–we can all learn from its simplicity, its humor, its effectiveness.  Building a form not through outright repetition but by changing scoring is a useful device, one I have used.

The introduction of the horns as a “third section” is intriguing as well.  I find that I tend more toward block scoring than mixed in my own writing as well, but it seems more appropriate in the context of this dance movement than it did in the first movement, which is much more developmental in nature.  Does anyone know if Mahler is the first composer to call for massed horns in a symphony?  We see eight horns (if you include the Wagner tubas) in Wagner, of course… but in symphonic writing?