Complex counterpoint in Bach
Some of the most complex wonders of Bach’s counterpoint, such as the F minor Sinfonia or the first movement of the B minor flute sonata, result from a procedure that is structurally, surprisingly simple.
There are three voices in the Sinfonia and three in the flute sonata (two in the keyboard and one in the flute). At the same time, there are several distinct motives present, any one of which can appear in one voice or another at any time. There are often three different motives appearing simultaneously in the three voices.
This suggests a creative procedure similar to making a mosaic. In a mosaic, there may be only several differently shaped pieces, or tesserae. From these few pieces, the entire structure of the work is created.
Though there is great variety in the sound of the piece, the parts making it up at any one moment are just one of the severally shaped pieces of the mosaic.
The counterpoint is most effective when these basic pieces are as different from each other as is possible. The F Minor Sinfonia is the perfect example of this. There are just three motives: one is a series of slow, chromatically descending quarter notes; the second is a series of three eighth notes, a movement up of a third and then down of a second; the last is faster, moving motive in sixteenths and thirty seconds. Bach creates an entire universe, aesthetically full and complete, with these three motives that each take up abode in one voice and then another. What genius!
While artists may follow the procedure of “separating” the voices in their playing, sometimes the greatest separation effect comes from following a single motive as it migrates from voice to another. I first discovered this principle in the five voice fugue in C-sharp minor in Book One, especially after the eighth notes begin.
Quality distinguished from quantity
Quantity versus quality, the immeasurable versus the measurable.
Non-typically, Irving has chosen to start work on a piece by Debussy.
This affords an opportunity to revise his customary way of approaching a new piece.
Part One: Keeping score on the number of wrong notes.
Usually, when Irving begins a practicing session, he measures his improvement in direct proportion to the increasing percentage of right notes that he plays and the decreasing number of errors.
This means he is devoting his conscious effort to ‘measurable’ quantities (the pitches of notes) rather than other things that are, in contrast to quantities, best termed qualities that are evoked in his playing.
How do we sidestep his “pointillistic” application of correct notes to the piece?
The first step was a bit drastic. I asked him to leave the right pedal down until a large group of notes were all swimming around in a common and confusing sounding tonal pool.
We then refined this so the notes that were thrown in the pool were only those that were chord-tones according to the current harmony. By doing this, a chord was being gradually built up, one note at a time, until all the notes of the chord were sounding together.
Now came the leap of musical imagination together with a slight derailing of the forward arrow of time. “The sound of this chord-cluster in its entirety,” I said, “should be in your imagination from the moment you play the first sound of the group that is going to form the chord at the end of the process. It is like a magical pedal that not only combines the sounds left in the wake of each sound, but can also summon up the presence of the sounds that remain to be heard.”
Once this effect is achieved with regularity, the next step is to re-create that feeling at will, with or without relying on the literal application of the pedal.
Part Two: Some other the desirable ‘qualities’ to evoke in the Debussy.
One note then the next:
A new note doesn’t always ‘eclipse’ an old note. The new note should not be opaque, in time, to the memory of the previous note. Let each note blend into the next, yielding its essence as an inheritance to the next note.
Melodies should seem to leave thick ‘trails’ behind their advancing wave front in time. The combined presence of their notes persists in time. Even without the pedal, the melody should sound in the imagination as if it were sounding in a perfect echo chamber; each part of the melody is inseparably bound to the overall shape of that melody.
Even in the early stages of reading a new piece, the pianist sometimes should try to play a passage in the intended final tempo. Otherwise the pianist who is interested primarily in right notes will automatically exclude from his consciousness the unique musical qualities of the piece that will animate and give life to the performance that will only become manifest in the piece’s proper tempo. Make the piece yield up its secrets before all the notes are learned.
Quality is so fundamentally different than quantity that the notes, if they are merely correct, eclipse the ability to modulate and shape sound, create tonal imagery, and release – as a flower giving off an aroma – all that is non-quantitative and miraculous about the piece and its sound.
Tempo can be used generally as a tool with which to experiment for evoking the qualities inherent in a piece. Playing a passage in its final tempo* sooner rather than later in the learning process, including wrong notes, will bring us to a realization of the indefinable aesthetic essence of the passage, rather than repeating the passage over and over in a gradually increasing tempo. The downside of approaching the final tempo gradually and incrementally is that the desired tempo may never actually be reached. Why? Because the successful execution, in the final tempo, depends as much on a clear musical vision of the aesthetic qualities of the piece as it does on physical technique. We need the qualities of the piece to guide and lead the notes into yielding their musical essence that transcends the actual identity of the pitches.
* whether this final tempo is slower or faster than the initial practice tempo
Coaching an instrumentalist for an orchestra audition
In today’s incarnation, “Irving” is a bassoonist rather than a pianist. He is about to audition for a local orchestra. The required excerpt for the audition is the opening of the second movement of Scheherazade.
I listened to him play the solo through. The notes were there, but overall it lacked a sense of the presence in his imagination of the other instruments playing at the same time, and the effect that would have on how he sounded the passage.
He had played the same solo a year or so earlier in an orchestra. So I asked him “what instruments were accompanying you during the solo?”
He thought about and said “the woodwinds?”
I said, “No, it is actually four solo double basses.”*
He played the solo again, but this time I played on the piano the chords played by the four double basses. This caused a sudden change in his playing. One thing that happened was that he fine-tuned both the pitch and the feeling of his notes to better fit in with the chords. In tonal music, no note has a single, abstract, or ideal pitch. It varies in small amounts to best fit in with the harmonic context in the form of the chord that is sounding at that moment. Each chord in turn has a certain feeling, which if recognized and felt fine tunes the timbre or tone quality of the bassoonist’s note.
No longer was his playing an island to itself, it had a broader context. The trick, I said, is to make these modulations to the sounds even when you are playing by yourself without the other instruments, which can only be heard in your head. The person auditioning you is listening to see whether this broader musical context shines through the notes that you play.
“How do I do this,” he asked?
Let’s start with knowing when in the solo the chord in the basses changes. He didn’t know. I said: let’s play through it again, this time listening specifically for the changes in the chords. It shouldn’t be too difficult to do because, based on how he had played the passage when I played the chords at the piano, he was already subconsciously responding to them.
Next I asked him if the first chord in the basses seemed to last a surprisingly long time before changing. If so, what beneficial effect did that harmonic inflexibility have on the effect of the solo? He said that it made the bassoon solo seem more “frozen and static.” I agreed.
Was he, I asked, aware that this first chord contained only root notes and fifths and lacked the third of the chord, the note that which would determine whether the chord was a major chord or minor chord. It was incumbent on the bassoonist to make that choice clear to the listener, and to be especially aware of when the bassoon made up for the deficit of the third by momentarily playing the third himself.
Later in the session I wanted to demonstrate, in a more general way, how the ‘color’ of a note depends on the chord to which it belongs. And how this color could change, depending on whether he was playing the root, third, fifth or seventh of the chord.
I had him hold a single note for as long as he could, while I surrounded his chord with first one chord then another. I started with the three major chords and the three minor chords that contained the note he was holding. Then I went on to seven-chords that contained his note. Then I gradually shifted to chords that didn’t contain his note, which therefore caused his note to be dissonant – but always dissonant in a specific enough way to create a definite and peculiar color to the dissonance.
Though he held the bassoon’s pitch relatively constant, he instinctively changed the timbre and the intonation to reflect the way his note fit (or did not fit) in the chord.
* albeit an odd orchestration, but an inspired choice given the shape and mood of the solo.
Bach’s counterpoint – who’s on “top”?
The amazing thing about Bach’s counterpoint is that the musical meaning of a piece does not change if you transpose one or more voices to different octaves or simply rearrange the order of the voices from highest to lowest. The voice that is originally on top does not have to be on top for the counterpoint to have the same effect. It is as if each voice in a Bach fugue is transparent to all the others. No voice, regardless of its pitch range, is opaque in that it blocks or occludes any other voice. The voices shine through each other. Figuratively speaking, every voice is on top.
Being the top voice loses its automatic prominence to the ear. All of them, in effect, are on top, or none of them are.* You can think of it either way.
It is a mistake to concentrate our attention when playing on the top voice, or to whichever voice currently “has the theme.”
Of almost no other composer is this true. In a Beethoven sonata, for instance, only rarely can you move the right hand notes into the bass and the left hand notes into the treble and have a result that ‘works’ as well musically, that aesthetically resembles the un-switched version. In Beethoven, depending on which octave a note sounds in, it creates an impression of sound that is different than the same note sounding in a different octave. Each octave range has its own sound-personality.
One of the ways of determining the unique properties of the musical space of a great composer is to experiment subjecting the piece to certain specific types of distortions and then noting the results sound-wise. One such attempt at distortion is the rearrangement of the voices described above. Here are some others:
– how much can you change the tempo of the piece without distorting the meaning of the piece or its character?
– how much can you change the rhythm of the melody without changing the essence of a melody?
– how much of the essence of the music is changed by changing the instrument or instruments playing it?
– to what extent will the integrity of the piece be ruined by starting to switch around parts (what comes first, what comes second, etc.)?
The answers to these questions will be obvious to the ear, and will vary from one composer to another. They reveal to us what some of the basic, “geometric” properties of that composer’s “musical space” are.
These experiments are similar to those in the mathematical subject of topology, where a common question is to ask how much one can distort a shape and still have it retain certain basic properties.
*This is why Bach’s fugues for organ work as fugues even though it is often the case that each voice sounds in several octaves at once because of linking an eight foot stop with a four foot stop and/or a sixteen foot stop. The same applies to Bach on a harpsichord when ‘couplers’ are used to cause a note to sound in more than one octave at once though we are only pushing down one key.
Rubato. How to make the piece “breathe”
P. is an adult student who is playing Brahms. She asked me, “How do I make my playing sound like the recordings of it I enjoy?”
“I know there is flexibility in the performer’s playing. I sense it, I ‘hear’ it. It sounds so natural and obvious, yet I don’t know how to reproduce it when I am playing the piece. I can’t make it sound as musical. Why?”
My answer: “Welcome to the wonderful world of rubato!”
The following was my attempt to “teach” rubato.
First, I said that I thought the way by which she evaluated her success at playing a piece was ‘measured’, and in inverse proportion, by the number of mistakes.
P: “Shouldn’t I know all the notes solidly before I start playing around with them musically?”
Me: “To develop rubato, you may need to change some long term habits. Don’t evaluate your success by right or wrong notes. And don’t wait until you know the notes of the piece before you add musicality as if it were an added ingredient. It’s the other way around: you learn the notes more quickly if you play musically if, for no other reason, than you come to understand more quickly why the composer the chose the notes that he chose.”
Michelangelo said that he could envision the finished shape of his sculpture when he was looking at the untouched block of marble, from which the sculpture was to be carved. He would then cut away the material of what in retrospect would be the “negative space” surrounding the inner form, until the positive space of the inner form was revealed.
His first cuts of the chisel were probably rough and not meant to be specific. Your first experiments at rubato can also be rough and random. Pick a spot in the piece, any spot, and try speeding up or slowing down the next group of notes. As the sculptress of the musical phrase, you then ask yourself, did this change, did this bending of the steady tempo into a curve, make the piece sound better? Did the change make the music make more sense to the ear? If not, pick a different random spot and try to distort it again with a change of speed lasting a group of notes. It will not take much experimentation to discover the proper places and degrees of “bending” in the phrase.
In the above analogy, the un-hewn block of marble stands for the piece played with correct notes but without rubato. The final form of the marble is what results from the rubato.
A “planar” (and “plainer”) version of the Venus de Milo would be far less inviting to the eye than the curvaceous form we see in the Louvre. A musical phrase is an elastic thing, it stretches and contracts. It is a living thing that constantly breathes in and out.
The violin bow must distend the linear shape of the violin string before it will ring true to its pitch. Harmony is always the result of a reconciliation of conflicts.
In the following more geometric analogy a base, or unvarying tempo, is like the x-axis of a graph: an unvarying straight, horizontal line.
The application of rubato creates a curve that is sometimes above the x-axis and sometimes below. If the y-coordinates of this curve are summed up over an entire cycle or phrase then, the positives added to the negatives, in a true rubato, will result in the values canceling each other out by the end of the phrase. This leaves us arithmetically a net value of zero, but at the expense of loosing any aesthetic shape.
This balancing out can happen in many ways. Only rarely will the speed-ings up (positive y values) and the slow-ings down (negative y values) exhibit the same values as each other, although this can happen in principle. More likely there will be an unequal division of the musical phrase through time in terms of when accelerando is taking place and when a ritard is taking place.
Here is one of many possibilities: a few large positive y values (a few notes dramatically speeding up) can be balanced out by a large number of small negative y values (a greater number of notes slowing down but little by little).
The result of this final balancing out by the end of the phrase is that the next phrase tends to begin at the same time on the clock that it would have begun if the phrase had been played without rubato, but in a steady tempo. But in the interim instead of a static phrase we have one that exhibits a dynamic equilibrium of opposing forces.
P’s first attempts at rubato resulted in her playing a measure or two in one steady tempo followed by another phrase at a different, but still steady, tempo. Rubato probes more deeply into the evolving phrase. The changes occur more frequently and dramatically. Slight ritards and accelerandos may not always be enough to carve out a shape to a phrase.
A last word about “emotion.”
P. said, “I try to feel the emotion in the Brahms but it doesn’t seem to emerge. ”
Joe: “You don’t put emotion “in,” the emotion comes “out” as a byproduct of the bending and shaping of the phrase. Then the phrase resonates with emotion, both pianist and listener experiencing it for the first time. When properly shaped the phrase ‘rings’ like a bell when struck.”