Tag: Counterpoint (two or more voices)

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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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 28: Using Registration To Bring Out One Voice of Several In Polyphonic Situations

Taking a cue from the organists (harpsichordists too) about bringing out one voice of several, in a polyphonic situation.

On an organ, it is trivial to link one of its several keyboard to several ‘ranks’ of pipes, some which sound in different octaves.  Even a single rank of pipes (E.G. “principal”) can be set up so that if you play, for example, middle C (c4), air is sent as well to the pipes for any combination of these C-s: c2 c3 (c4) c5 c6.

If, now, the organist chooses to play a two or three voice fugue, so that one of the voices, and only that voice, sound in several octaves at once, something amazing happens.  The voice that is “on top” can loose any advantage or special-ness due to being the highest of a group of simultaneously sounding notes.   Any voice, from the lowest to the highest, can, can attain the ‘status’ of being on top.  As a learning tool, to keep focused on just single voice among several,  sounding that voice either louder than the others or in more octaves at once than the other, makes that voice go from being just one in the mixture of the voices, to one that stands out clearly.

At my lessons, I am fortunately to have two “kissing” pianos.   If a student is learning a three voice Bach fugue, I will, during a series of run-throughs, choose one among the three voices and transpose either up or down a certain number of octaves.   In this way, the bottom voice can sound like the top voice (the original top voice being now in the middle), the top voice can sound like the bottom voice (usually the second easiest voice for the student to pick out with her ears), or I can ‘liberate’ the inner voice from being imprisoned between the obvious top voice and the second most obvious bottom voice.

Sometimes I will reverse the arrangement.  I will play the piece as written, and the student has to play along with me, in one octave or more than one octave, a single voice.  The ability simply to isolate with the eye, just one voice, and follow its continuity through the entire fugue, is almost a necessary ability for the Bach player.

The most surprising thing to most students is that, even when the voices are shuffled (with or even without octave doublings) the sound of the piece is strikingly similar to the original arrangement.   Just try to do this with reversing the hands of a Beethoven Sonata.  What results rarely sounds enough like the original for the student to consider it as the same piece and not some strangely mangled version.

This means that we can conclude certain things about Bach’s “Musical Space as against Beethoven’s musical space.

The next paragraph is a bit more theoretical and can be skipped.

First a word or two about what I mean by musical space.  I believe that music is the only art which is experienced by us, in its purest form, in time alone, and not in some combination of time and space.*  This despite the many space-like things involved in playing such as the instrument we are playing, the types of movements we make in space to play that instrument, etc..  If we can legitimately use the term “space” in regard to music, then it is a highly abstract, non tangible space.   The one in which “notes” have positions on a graph relative to a time-axis and a pitch-axis.   Even a “note”, though, is already an abstract term.  It is the result holding fairly constant, during a duration of time, three perceivable parameters of sound: namely pitch, loudness, and tone quality.  One might add duration, but duration is the very fabric of conscious time.

If we accept the use of space as part of the phrase ‘musical space’, then in Bach’s musical space, voices are transparent to each other.  We do not have to try to see through the opaque surface of the highest voice in order to see (sic) the other voices.  And if the voices are on transparent layers in this space, we can order the voices in any permutation we want, and the full effect of all the voices seen through each other’s transparency will remain the same.

But if we consider Beethoven.  His musical space has different geometric (sic) properties, such that things that are possible to do in Bach’s space may not be doable in Beethoven’s space.  What is ‘on top’ tends be more opaque to the other voices than with Bach.

* This is one of the central theses in my book: “The Spectrum of the Arts” (available for free, in summary and in full text, on line at:  http://www.AJourneyThroughTheArts.com. 

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Practice Procedures: Part 9: Hearing and Bringing Out An Inner Voice

It is usually easiest for our ears to hear, and follow through time, a voice when it is “on top”, I.E. with all the other voices at a lower pitch range.  It is like the relative ease of following the line of the sopranos in a chorus.  Except in special cases, such as Bach*, the sound of the top voice acts to “block” our view (sic) of the other voices.  It is like an opaque surface hiding what is within.   The surface voice (the top voice) acts to “reflect” back to the listener its own content and resist attempts by the ear to penetrate under its surface.

If we want to switch our awareness to what another voice is doing through time, the obvious solution is to temporarily put that voice on top of the original top voice.  This involves nothing more than transposing upwards the desired inner voice the (minimum) number of octaves that place it into a pitch range that is higher than the printed top voice.  Then, the “accident of birth” that had placed the former “highest voice” in its privileged position on top is superseded by a simple readjustment in pitch.  The inner voice now sounds like the top voice, and we can more easily hear its individual shape and melodic features, as well as how the other voices relate to ‘it’.  When we shift back to the normal pitch arrangement of the voices, that distinctness of the voice in question can be still to a certain extent noted.  Its “top-ness” may be more of an aesthetic quality or condition than a predetermined aural fact.

When you have a second pianist at a second piano, the latter can transpose one of the inner voices into several octaves at once, similar to what an organist does when adding a 16, 4, and 2 foot pipe too the standard 8 foot pipe.  This has an effect on the ear similar to softening all the other voices and playing the target voice loudly.  This helps explain why polyphony on an organ can sound so well blended (or homogenized) that each voice can be found in each octave, and it is more difficult to discern the contrapuntal relations between the voices.  No voice ever gets totally free of the other voices, but is closed in on the top and the bottom.

* in Bach’s case, usually each voice is transparent to all the others.  Being on top has just a temporary advantage.

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Techniques for the pianist with Smaller Hands: Part One: Substitution


Let us say, as an example, that the left hand wants to play three ascending pitches, an A, then an F# and lastly a D.  The effect desired is one of legato.

A substitution seems warranted on the F# in the case of the smaller hand.

In discussing the general principle of finger substitution while on a single note, we will not emphasize the action of fingers individually, one of which would act to replace the other on the key surface.

Instead we will focus on the entire hand, or more specifically, the five fingers of the hand.   We first note that the five fingers of the hand can choose to align themselves on one horizontal plane.  Furthermore the fingers can all be touching one another horizontally by eliminating any spaces between adjacent fingers.  The result is that we create a continuous, unbroken mass of flesh running from the thumb to the pinkie.

The lowest note of three, the A, we play with the pinkie.  We create the onset of the sound of the middle pitch, the F#, with the second finger.  At this point the process of substitution begins, first by closing up the spaces among the adjacent fingers in order to produce a single solid object.  In this case, the fifth, fourth and third fingers in particular close up  rightwards and the space between the third and second fingers disappears too.

Now that we have a solid unit formed by four fingers, the interesting part of the process begins.  With the F# still sounding, and without the pedal doing anything to insure that it will continue sounding, we take the relatively smooth lower, horizontal surface formed by the fusion of the four fingers, and move it, as a whole, as if one object incapable of being subdivided, from the left towards the right, guided by the action of the arm.

What will occur, if we look at it in slow motion, is that the second finger, which started out as the only finger on the F#, finds itself starting to share space on the F# key with the third finger, until the third finger alone is in contact with the E key.  Without any interruption in the continuousness of the process, the third finger starts sharing the surface of the F# key with the fourth finger, until the fourth finger alone is in contact with the F# key.   As the object is solid and not in several parts, the sound will continue without re-attacking it.

At this point this one object, made of all the fingers, has moved sufficiently to the right.  For the fourth finger is now situated, passively, on the F# key.  And most pianists, even those with smaller hands, would find it convenient to move from F# to D using the fourth and first fingers.   The stability of the fourth finger on the F# is just a facet of the stability of the hand as a whole, without any extra pressure needing to be applied by the fourth finger itself.

Just to stress the point one more time, our perception while doing this overall process is not one of moving separate finger segments, one finger to the next, because the fingers during this process no longer exist separately.  They are fused together (webbed together if you like ducks) into a ‘part’ of the anatomy of the body that is experienced from within us as single and undivided.  We have simply moved the surface of that undivided part of the body right relative to the keyboard.  If a higher pitch precedes a lower pitch, then the same sort of movement would be, just as easily as before, from right to left.

The final stage in the process is to have the thumb to move rightwards to the D, which involves, if we limit it to the perspective of the fingers, to a gradual opening of the space between the first and second fingers.

A concluding general observation.  Often the lack of fluency sound-wise in a connection between notes comes from trying to think of the physical connection as a single event in time, rather than as a process in time which, though there is no change in the sound yet, there are a series of successive steps blending one into the other.

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