Posts Tagged ‘enharmonicism’

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. 2, Movements 3 & 4

Wednesday, October 21st, 2009

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

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

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

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

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

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

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

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

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

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

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

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

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

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Mahler Symphony No. 2, 2nd movement

Monday, October 5th, 2009

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

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

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

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

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

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

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

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

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

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Opus 81a

Wednesday, November 26th, 2008

Once again, the month is nearly over, and I haven’t dug into this piece nearly the way I would have liked to.  All the same… some thoughts.

Did Wagner get the idea of leitmotiv from Beethoven, or was it simply in the air?  I’m no musicologist, so someone will have to answer the question for me.  Beethoven’s Lebewohl motive in the first movement is a prototypical–just as the entire Ring cycle comes out of the descending Eb major triad, Beethoven chooses mi-re-do… what else for a Classical composer who knows that the music will end up there at some point anyway.  Yes, I still think Beethoven is a classical composer, despite the steady appearance of more and more Romantic-era traits.

Compare the two sonata forms in this piece to those in Brahms’ Op. 1.  Brahms and Beethoven are using the same harmonic concepts for the most part, but Beethoven thinks in motivic terms, while Brahms is very clearly writing themes most of the time.  Beethoven is creating an organic, living piece of music in the only way he really knows how; Brahms has chosen sonata form from several other possibilities and is putting things where they are supposed to be.

In the first movment, we seem for once to have an instance where the development section is extended, but on second inspection, the exposition and the development are in roughly equal proportions–if the repeat sign on the exposition is observed.  The form is well-balanced, too, with the inclusion of the opening Adagio.

The second movement is loads of fun–harmonically evasive, and brooding in character.  Is it a developmental core without an exposition or recapitulation?  Is there any way to see the complete sonata as one large sonata form?  There might be a paper in that.

I’m absolutely in love with the two places in the last movement (one in the exposition and one in the recapitulation) where Beethoven uses triads with roots a minor second apart.  Gb and F the first time, Cb and Bb the second time.  Both times, the passage ends with a rarity that I just taught last week in Sophomore Theory–an augmented-sixth chord that resolves to a tone that is not the root of its triad (the third in this case).  If any of my students are reading this… hint, hint… finals are coming up!  Not only that, an enharmonic passage right at the beginning of the development.  Why play in Cb when you can play in B?

On a somewhat-related note… I had time this morning to compose, and the piano piece is ready for the computer.

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