Tag: Bach

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.

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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.

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One of the secrets to voice separation in Bach fugues

Summary: Have you ever felt caught up in the many notes in Bach fugues? Here is a practice technique to better understand and hear the colors, nuances, and chords with multiple voiced fugues.

Vertical Slices

The act of holding (continuing the sound of) a note while other fingers start new notes is not a passive act, it is positive act no different than pushing a note down the first time to begin sounding it.  It is more an act of re-playing than of holding.

There is a simple way of changing the sensation of holding a note to accord with this principle.  It is both an aural technique as well as a physical technique:

Literally re-play a note being held every time a note in any other voice begins to sound.   If it is a three voice fugue then, once the third voice has joined the other two, you would be playing a three-note chord each time a new note began in any of three voices.  Similarly, with four note chords, for a four voice fugue.

The process is even useful in a two voice situation,  for it calls attention to the interval that sounds between the stationary voice and moving voice.

Here is an example, using three voices.  As for the rhythm, the longer notes  are followed by an underscore (__) and are twice as long as the remainder of the notes.

highest voice:      c   d   e __   e      g    a    g     f  __

mid voice:            a__  g__   bb__    a __   d __

lowest  voice:      f__   c    d   c#    d    b    c#__ d

Using the above described procedure the passage becomes the succession of the following ten chords:

f-a-c             f-a-d          c-g-e         d-g-e        c#-bb-e

d-bf-g        b-a-a         c#-a-g       c#-d-f      d-d-f

We have in effect created a “chorale.”  I refer to this technique as doing vertical slices through a piece, so that at every moment I know what note is sounding (or continuing to sound) in what voice.

Benefits to me of using this procedure:

– There is less decay (diminuendo) in the longer sounds; the overall sound is constant in each voice.

– I become aware of simultaneous sound relationships between voices that before remained unnoticed by me.

– I hear how a single sustained sound in any voice can change character and emotional flavor two or more times before it stops sounding, simply because of the other notes that are sounding with it.

– I become far more aware of the continued presence of voices when they are intoning long notes.  My ear can now follow with greater ease the continuity of each voice separately because the voice is constantly being updated.  I don’t lose interest in a voice because it is holding a note and the sound is dying away,  and I am distracted by other notes that have started in the meantime.

– When it is time for that voice to change pitch I am clear about the connection between the pitches, because the note is still alive in my ear (or in my imagination) and I can manipulate the aesthetic character of the interval by which the voice changes pitch.

– I hear a series of chords or harmonies rather than notes.  I listen to the aural equivalent of a constantly changing kaleidoscope of colors and patterns.  Many of these chords have surprising sounds, often very dissonant and emotional, but ordinarily heard only peripherally or subliminally.  The full reality of the piece is forced upon our ear.  The sound of the piece through time is vibrant, pulsating, and alive due to change.  I don’t get detoured suddenly into just one or two voices.  I stay less with a feeling of constancy in the mood and character of the piece and more in a volatile, constantly changing reality of sound.  I don’t “summarize” anymore.  Everything is taken into account.

– The held notes are less a cause of stasis than they are the cause of constant change.

–  The hand never looses its feeling of being centered and in equilibrium.  Holding one note and having to reach for another throws nothing momentarily out of quilter.

I believe that whatever is not heard by the pianist is played haphazardly and without control.

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Practice Technique 25 : Crossing Hands (as in the Goldberg Variations)

This particular procedure is based on not treating the crossing of the hands as a special case amid the more usual case when the hands are not crossed.

Regardless of the distribution of the hands, I raise my arms up high, then let them sort of dangle* back down to the keyboard, at which point I play just the current note.

The next thing is to take the arms back up into the air.  Let them dangle back downwards (without aiming at any particular part of the keyboard) and sound the next note.

This procedure is repeated on every note.

By this process, I am eliminating all memory in the body (including in the hands and in the fingers) of where the hands and fingers were a note earlier, including what notes were played and with what fingers.

When I come to a section of the piece where the hands are to cross, there should be no internally sensed difference in the procedure.  I start, when above the keyboard, with the hands uncrossed. I “dangle” downwards as before, until I reach the keyboard, and in passing notice that the hands have exchanged sides with each other, although it seems as just as natural result of starting high up and flowing down with the arms.

This procedure is an example of a more general principal that, the taller a triangle, the smaller the subtended angle at the upper vertex.  The arm has gone up one very long, nearly vertical, side of an isosceles triangle, stops at the vertex, and starts back down the other nearly vertical side – with barely any change of direction (because the vertex angle gets smaller the triangle gets taller.

Every note of the piece (or variation) is played with a hand position that feels original and unused before.

Of course I can only practice this procedure in a very slow tempo, because of the time it takes to raise the arms up and let them down again.  But what I gain from that higher position of the arms, is the feeling in my body that every place I need to go to next always seems to lie exactly vertical down from where I am.  And a little suggestive imagination it is a feeling I can retain even when the arms are lower to the keyboard.

By coming from such a height, I also minimize the interference of the hands with the other when the hands do need to cross on the keyboard.  Whatever interference is left, it is that it occurs only during the last fraction of a second before sounding the notes.

* Why have I been using the word ‘dangle’?  It feels right seomhow.  Maybe because, while the arms are getting lowered, the feeling the entire way down to the keyboard, is that the fingers are dangling from the hand, and the forearms are dangling from the elbows. that seems to be an important part of this.  This seems to open up the possibility that things will remain in a purposefully uncertain state until the moment I sound the note, where I can benefit of the hands’ natural ability to shape themselves around an object.

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