Category: Melody

Harmony in Late Brahms

Harmonic wonders in Brahms’ Intermezzo Op 117 No 3 in C# Minor

#1: The key

What is so compelling about C Sharp Minor?  Perhaps it is due to the effect of certain pieces that were written in that key: the opening fugue of Beethoven’s late quartet, op 131; the 5th prelude and fugue from the first book of the Well Tempered; and, Brahms’ Intermezzo Op 117 No 3.

The spell of this key is both obvious and subtle.  Tragic but not overly so.  Deeply reflective of the human condition, but without overstatement. or wallowing.   Notes that enter this solar system of retain reveal the opposite effects of stoicism and great sympathy.

#2. The theme.

As in many of Brahms’ his late pieces, the motivic material out of which the piece is woven are themselves terse and simple.  Nothing startling in itself.  In Op 117 No. 2, just two notes, descending in a step, suffice to create the entire varied panoply of music effects heard throughout the piece.  In the case of Op 117 No. 3 it is woven out motives of three notes, rising in pitch by the steps of a scale.

Sometimes the distance between the second and third note is enlarged to three half steps.  Sometimes the middle note stands as a passing tone between the other two notes which are chord tones.  Sometimes the middle note stands as a lower neighbor note connecting two identical chord tones.  Out of these motives a long theme emerges which takes most of the entire first line of the score.

Every time the theme returns it does so in one way – invariable: exactly the same sequence of pitches (C# D# E …).  There is a growing sense of ineluctability about it, an effect that is progressively offset however by changes to the chords that set the notes of the theme.  No matter how these chords lead us away from the tonic, C# minor, all eventually leads us back to that tonic.

At the beginning the theme appears without simultaneously sounding chords.  When it appears again there are implications of triads (chords having just root, third and fifth).  At the next statement, the chords embracing the theme have become 7-chords.  And even later they have become 9-chords.  This is done is such a way that, a particular note of the theme, let us say the third note, E natural, sounds first as the third of a chord, then as the seventh of a chord, and ultimately as the 9th of the chord.  This means that the chords, rather than being built on the same root note, are built on changing root notes: a more revelatory way of enlarging upon the chords, so as to be always expanding the harmony.

We go on to trace in somewhat more detail these changes of harmony, changes that are always put held in check by the constancy of the theme notes:

– At the beginning we hear the theme as unisons, amplified by sounding in three octaves once at once, an effect made starker by the absence of vertical chords.  The harmony is there. but remains adumbrated by just the melody notes (which are sensed as chord tones and which as tones of embellishment.

– When the theme appears again at the end of measure 5, it is almost as if Brahms wants to keep the harmonic implications as Spartan as possible.  There is a hint of the tonic chord (C# minor) and a dominant chord (G# major).  The third is missing in the dominant chord, though, so we hear it as major only through the implication of the melody notes.   The effect here is one that when I played the piece today I described to myself as tragic inevitability tempered with patience and nobility.

– The next statement of the theme occurs after a Spartan interlude.  This interlude begins with an inexorable march notes of equal value (eighth notes) to which, at the end, sixteenths are added so that there is a sense of reprise of the rhythm of the main theme (which uses the rhythmic germ of sixteenth, sixteenth, eighth.   The measures of the interlude repeats, but with the magical addition of an extra voice appearing in the left hand which creates a rhythmic counterpoint to the steady eighths, but whose beauty is largely the result that these attempts at rhythmic variation are still imprisoned by the constant eighth notes.

As the theme occurs throughout the piece, it does so unaltered in terms of pitches (a series that always begins with the notes C# D# E.  However the chord that is woven around theme has expanded into a 7-chord, an F# Minor-7 chord.

The piece is in three broad parts, the first of which is brought to a close with a statement of the theme that retreats into its initial harmonic simplicity: there is a tonic chord, there is a dominant chord, but but the two are blurred together by the retention in the dominant chord of the C# from the tonic chord, an effect added to by the absence of a third in the dominant chord.  We are being reminded, though subtly, that we are in C# Minor, so that we more fully appreciate the modulation to A major in the second part.

The second section of the piece a contrapuntal and harmonic miracle brought down to earth from the celestial harmony of the spheres.  I want to hold off describing what Brahms does there until we have followed the remaining statements of the main theme which occur in part three.

When the theme next appears in its entirety is at the beginning of the third section.  The 7-chord has been expanded by a D#-9 chord (the ninth being a minor ninth above the root note).  It is as if Lear asked the of his three daughters: “what {harmony} can you say to draw a third more opulent than your sisters? Speak.”*.  Unlike Cordelia’s answer, which is most understated and matter of fact, Brahms’ answer is a 9-chord compared to the previous “sisters'” ‘5’-chords and 7-chords .

In the coda, at the penultimate entrance of the theme, the melody is accompanied by a chord whose root note is now A# which, with the other chord tones in the melody, forms an A#-half-diminished 7 chord.

At the very last, we hear the theme one more time and, as if surveying the field of a great harmonic battle which has taken place over just a single day, and which now looks deserted and barren: the original theme returning one last time accompanied by just a tonic and dominant chord, bringing the piece to rest on the C# minor chord, which, which for the first time in the piece is heard alone, complete in time and unencumbered.’

#3. The middle section of the piece

The middle of the piece deserves special analysis.  Let us start by trying to “uncover” its ‘main theme’, or at least that, which by default acts in the place of a principal voice line.  In itself it is not the most melodious of note sequences,  it is devoid of any rhythmic personality, and moves seemingly randomly from one note to another – sometimes in skips, sometimes in steps, and sometimes in capricious jumps: seeming somehow in between insipid and random.  However, this seemingly undernourished melody is is able to usher in, with each new note, a new “chapter”, a new harmonic vista, allowing us to see further and then further to the harmonic horizon, as if from higher and higher vantage points.

In its most stripped down form, which we never get to hear literally, the theme consists of the succession of the notes E F E B G# A C.  Upon this Brahms performs a series of transformations and eventually metamorphoses.

The first transformation seemingly makes things worse rather than better:  a random yanking around of the melody notes from one octave range to another.  In its base form, all the notes would sound in the octave of middle (we shall call this octave number “4”).  But this remnant of pitch stability is dislodged so that the first E sounds just in octave 4; the F simultaneously in octaves 4 and 5; the following E just in octave 5.  This is followed by B in octaves 5 and 6 simultaneously, G# in one octave only – octave 5, and the last two notes, A and C, each heard in two octaves (octaves 4 and 5).  What began as uninspired is now wonky** as well.  It is like being on a roller coaster and leaving out the parts that connect the low points and the high points.

To this Brahms adds a single bass tone, A, modestly appearing at the beginning of each measure of 2/4.  It is a first attempt at establishing a tonal center for all the meandering of the theme.

But the stability is further broken by shifting each melody note (which lasts a quarter note, or four sixteenths), to the “left” so that each note comes in a sixteenth too early, just before each beat.

So far in this analysis we see how octaves have been changed, almost capriciously, melody notes brought in ahead of time, one modest note in the bass to remind the listener of where the first beats of the measures actuakkt are.  Not a good state in which to leave things.  There is however one more step to the transformation,  Each melody note is accompanied by an voluptuous figure of four sixteenths that swoop down and then soar back up.  Somehow this makes everything else make sense to the ear.  If we examine these four note groups, by making chords out of their notes, we get this succession of triads: e-cs-e, e-b-d, e-cs-e, e-d-f, fs-d-fs, forming just by themselves, as it were, a single “thick” melody.

There are still other startling details before this section finishes***.  But it is the last one that is the most stunning.  Something that the ear believes and disbelieves at the same time.   It occurs after the second double bar, where the key signature changes back to 4 sharps.  In other words a point when we would expect either a return to the original theme, or first, some transitional passage linking the the end of the second part, the one we have just been discussing, to the beginning of the third part.  What happens instead a polyphony worthy of the forty-voice Renaissance motet “Spem in alium” by Thomas Tallis.  Little, nascent, voices, appear and then disappear into the overall harmonic firmament, each one living just for three notes, each modeled exactly on the first three notes of first statement of the theme at the beginning of the piece.   Moreover each ephemeral voice makes its appearance in such a way as to partially obscure (or perhaps “occlude” is a better word) the end of the previous one.****  This process continues in a cascading fashion working its way through an elaborate dominant-like (G#) harmony that barely succeeds in stabilizing the whole affair.   I say barely because it is intentionally destabilized  by coercing a cadence to end it based on a B Minor-7 chord.   And then, to completely throw the listener off, a similar cascade begins, seemingly without reason or preparation, tracing over the first cascade but with each note two half steps above the similarly placed note in first cascade.   The first was built around the dominant of the original tonic key of the piece.  That seems to make sense if we looking for a transition back to the original C# minor key.  The second is just ‘quasi-dominant’ in nature, but its root note is A#!   Now this unexpected A# turns out to be the dominant of D#, which is the dominant of G# which is the dominant of the original C#.  Thus it only becomes clear why this shift of two half steps had occurred between cascades when the original theme comes suddenly comes back in its full form (starting with the usual notes: cs4 ds4 e4) but this time surprisingly surrounded by a D# Major (9) chord.   This chord then transforms itself until, in a fairly short amount of time, we are clearly back in the original C# minor.  Thus the previous six measures have prepared two separate but parallel things: the longer range goal of an eventual return to the tonic key of C# Minor, and a shorter term goal of preparing the D# chordal sonority that will underlie the return to the original theme.

#4. The end of the piece

In the last two measures of the piece we have a stable, lasting C# Minor chord.  So, in the end, all is drawn back into this tonic key, which may have been at times out of mind, but which never lost its grip on the piece.  At the end there is only the solace that no matter hard we try to get away from fate, we never free our self completely from its somber embrace.  As is the case with Brahms – perhaps the greatest worker of harmony – for all the restless harmonic movement towards or away from the tonic, no note, no chord, no modulation is ever away from the tightest control of the original key.  There is never a chord, be it ever so remote from the tonic, that is not perfectly clear to the listener as to its relationship with the tonic, in spite of as many as several key regions that we would have to travel through to get to it from the tonal center of the piece.

These are just some of the harmonic and thematic wonders of Brahms’ Op. 117 No 3.

* King Lear, Act I, Scene I

** Searching google produced this definition for wonky:

– (of a thing) unsteady; shaky…                – synonyms: wobbly, unstable…                                        – not functioning correctly; faulty.

***

In measure 4 and 5 of this middle section there are two flowing voices, one in eighths, and one in sixteenths, that chime with each other in the presence of a D# followed by an F#, and a B followed by an A.   This all occurs as the ‘main’ melody settles down to rest on a long C.

In the fourth and fifth bar of the section that follows the next double bar, the simplest kind of canon is utilized, but with ranks closed, the imitative voice starting but one sixteenth after the imitated voice, but also with the imitated voice sounding a sixth lower than the imitative voice.  A simple idea structurally but one which has the effect of creating near chaos with where the principal beats are supposed lie.  The ear wants to be thrown a lifeline, and Brahms does so, but with the least clarification that will still shed some light on the situation.

****

The first such contracted theme motive is on the notes bs4 cs4 ds5, snd when the ds5 occurs, it is hidden in the middle of a triad, whose bottom note is the beginning of the next, furtive, momentarily flickering motive entrance (whose notes area4 bf bs4).

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5 Shorter Blogs on General Technique and Jazz

How to start a run (#1).       Scales can help us execute arpeggios and vice  versa (#2).    Symmetric motions in  the hands (#4)    Jazz improvisation (#4).    A deeper meaning to a group of notes (#5)

#1   How to start a run

It’s the second note that precisely defines the tempo of the run.

How quickly does a listener determine the tempo of a piece.  Not by the first note, but they can judge the tempo by hearing the first two notes.  It is the precise duration from the beginning of the first note to the beginning of the second note that is the clue.  This proves to be important for the pianist when starting a run, a scale, etc., any series of notes that are all share the same rhythmic value.  If we are careful to play the second note at exactly the right moment after the first note, then we know what precise duration to give to each of the notes follow.

#2   Using arpeggios to help play scales, and vice versa.

When I am playing a scale, and it isn’t coming out the way I want, I play instead an arpeggio starting on the tonic note of the scale.

For instance, instead of:    C D E F G A B c

I play                                          C     E     G      c

If at that point, without any time taken off in between, I play the scale again, the scale sounds more evenly and controlled.

The arpeggio in effect seems like a scale that has been sped up.  I just have to fill parenthetically the notes the arpeggio left out.

The reverse situation applies as well.  When I am playing an arpeggio, if it isn’t coming out the way I want, I play stead a scale whose tonic is implied tonic in the arpeggio.

For instance, instead of:     C  E  G  c

I play                                             C D E F G A B c

This slows down the arpeggio because I am filling in the notes between the notes of the arpeggio.  It now takes longer to get from one note of the  arpeggio to the next.  I just have be aware of the notes that I’m leaving.  Especially the interval is more than a third, as well as when I bring over thumb, or come under the thumb.

#3  Mirror motions.  The “target hand” and the “helping hand”

Symmetric motions:

The body is freest and happiest when the two bilateral side of the body (the arms in particular) are moving in opposite directions.  The physical sensation in the arm when moving away from the a central position (I.E. rightwards with the right hand, leftwards with the left hand) is different than the physical sensation in the arm when moving towards a central position (I.E. leftwards with the right hand, rightwards with the left hand).  The body is happier when the two sensations are more alike.  This is one of the reason that scales played in opposite motion in two hands seems easier than the usual practice of both hands moving rightwards, or both hands moving leftwards.

One hand helps the other: the helping hand and the “target” hand

In my playing, if I feeling awkward playing a passage or group of notes in the right hand,  In what follows the right hand is the “target” hand and the left hand is the “helping” hand.  The situation can be reversed if one is having difficulty with a passage in the left hand.

I will take the helping hand and move it in the empty space above the keyboard in a course that is a mirror image of the the directions that the right hand is going.  It goes leftwards when the target hand goes rightwards, It goes rightwards when the target hand goes leftwards.  As i said, the helping hand traces in empty space, just above the keyboard, the mirror motion of the target hand.

After doing this for a brief time, I go back to having the helping hand play the notes indicated for it in the score.  The helping hand can retain the sensations of trying to mirror the target hand even though it is restrained from doing it fully by the notes it has to play that are in the score.  But that doesn’t stop it from “trying” to start making such motions to mirror the other.  Muscles can contract as if attempting a motion in one direction even if the hand at the same time busy playing notes that go in a different direction.

#4.  Jazz improvisation

Not stopping the flow of notes every once in a while simply because you are not sure where to go to next.

During one year I had a jazz pianist come for lessons.  He thought he would gain some additional perspectives on jazz by working with a classically trained teacher.

At first I showed stuff about classical music.  It went OK.  However, then I decided that it would be more interesting to work with him while he was improvising.  My absence of technical knowledge in jazz would not prevent me from evaluating his improvisation on more general musical grounds such as sound, musicality, and motion.

I asked him to improvise for me on a standard tune.  What I noticed was that when he would begin to play a series of rapid notes, after a certain number of notes went by he paused, but then went on.  The pause to me always sounded artificial: not done for a musical reasons.  I was curious to determine whether the pause was for stylistic reasons or occurred because his fingers were momentarily ‘stumped’ as to what to do next.  It turned out to be the latter.  Ideally he would have preferred continuing the series of notes in the improvisation.

I invented a curious exercise, one that is good for classical as well as jazz pianists.    I had him wiggle his fingers rapidly in the air and simply do so without stopping.  That set up the notion that the note-stream does not ever need to stop.  The next step was to bring that finger motion to the keyboard and to play random notes.  The notes need not have any musical significance.  It was purely for him to get used to the idea that it was technically possible to generate an indefinite series of notes.  In the last stage he applied that technique to improvising on a standard melody and, every time he was on the verge of stopping because he hadn’t yet figured out the following notes, he was to use stage two and to continue playing notes they were random notes.  This opened up for him the possibility of creating a stream of fast notes at any speed, one that would last as long as he chose.

#5. A deeper meaning to a group of notes.

Sometimes it is not enough for me to play through a group of notes, just once, a part of a theme or a motive.  It is as if I am taking a cursory swipe at what I think is contained in those notes: looking especially for something that is consistent with all the notes around it.  But with repeated swipes I begin to unmask what is really going on in that group of notes.  And that something is often easily glossed-over by me to make it seem like it is just another neutral, undifferentiated part of the whole nexus of notes of which it is a part.

By the second or third time I repeat the target group of notes (usually anywhere from 2 – 8 notes), I begin to see that it has a life of its own, one that is easily submerged in the general flow of the measure.  Would I be encouraging anarchy on the part of those notes to give special care to bring out its authentic properties independently of what the rest of the surrounding passage is trying to state musically.

The answer I find is usually that bringing out the individuality of a group of notes, based on its shape, rhythm and harmonic implications, only adds, and does not detract, from the general flow of the piece; that it enriches meaning in the passage and not goes off on a tangent.

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