Category: Specific Pieces

Bach: The Goldberg Variations: Variation no. 11

#1  Arpeggios: Variation 11 : measure 5

In the right hand play the b2 with 2, then d3 with 3, and then, for
practice in loosening up the joints, rotate the forearm one hundred
eighty degrees, which faces the palm upwards, and turns the thumb,
which is still on the g3, upside down, then the third finger plays b3
but like the thumb, the third finger is upside down, but re-rights
itself by one hundred eighty degrees while still on the b3. at which
point the arpeggio completes itself ordinarily through the g4.

#2  Physical Glue: Variation 11 : measure 13

There are two instances of physical glue in this measure. By
physical glue I mean a physical connection between two notes in
different hands, that is not readily noticed in the score, and whose
challenge is often not experienced until it is already happening.

There is a d5 starting at the beginning of the measure in the right hand,
which is usurped by the left hand playing the same note at the sixth sixteenth of the measure, which hands the same note back to the right hand just one sixteenth later.

in the third group of sixteenths in the measure, the left hand plays
fs4, but no sooner plays it but it is usurped by the right hand playing

This suggests the creation of a separate rhythm that concerns only
repeat notes (where the hand is changed at the repeat).

rh:  .e = e__       e        s
lh:                    \s/{s} s/

By concentrating on this artificially formed rhythm composed solely of the iterations of the note d5 as it goes from right hand to left hand to right hand, and the iterations of the note fs4 as it goes from the left hand to the right hand, we have exposed the skeleton, which remains hidden under the surface of the written notes, which physocally holds the passage together.

#3 Crossing and uncrossing the hands: In the Goldberg Variations

Variation 11 : measure 1 :

Move the right hand up one octave and move the left hand down one
octave. The hands can now play their respective parts without crossing or
bunking into each other. This helps define a ‘potential’ for what the
piece should sound like were it not for sonic confusing from the
crossing voices as well as the physical confusion of the hands

When we again play it, this time as written, see if we can keep the
same amount of empty “air” between the two voices in the two hands. This air separates things physically as well as sonically. No less so than when the hands didn’t cross at all. Each hand now speaks its own pitch-shape without the other hand diverting us, or pulling our attention away from one hand to the other.

#4  “Sculpting” small groups of notes

There are only so many pitch-shapes you can get four notes, and a smaller
number when dealing with only three notes

Pitch shapes for three notes:

1  up        2   up       3
1  up        2 down   3
1  down  2   up       3
1  down  2 down   3

Pitch shapes for four notes:

up up up
up up down
up down up
up down down

down down down
down down up
down up down
down up up

Become a master of shaping each of them in its own unique way. Polish
each till it sparkles like a gem and cannot be mistaken for any of the
other shapes.

As one plays through the Goldberg Variations, in particular the more
contrapuntal sections, notice, before each group of notes, which type it
is of the types shown above, and then ‘sculpt’ its shape, like an actual
sculptor working with a mass of pliable material, till it’s clearly one of the shapes and not any of the others.  This does not happen automatically just by playing the pitches but requires an expressivity that helps display to the listener’s ear the upward and downward motion of the pitches.

Further subdivisions of the basic types can be based on whether the
motion from one note to another in a group is a step or a skip.  For
instance in Variation 9, measure 6, the last four notes in the bottom
voice (c4 d4 e4 d4) is from the point of view of pitch sculpting “up
up down”, and from the point of view of sub-type “all steps”, while
the first four notes in the next measure (cs4 a3 d4 cs4) is an example
of the basic type “down up down”, but is of the sub-type “skip skip

Although this may seem like a trivial and obvious subject, each shape and each subtype has its own aesthetic quality which can be brought out to the
listener. And there is an aesthetic quality too of saying to the listener “I’ve just finished sculpting one shape and I’m about to start sculpting another shape”.  A piece made up of an endless series of permutations of pitches, as in the Goldberg, can become a smaller, more manageable set of statements of pitch-shape types and if one wishes, subtypes.  This simplifying gives order to the overall design of the piece, and on the most intimate level.

#5  Variation 11: measure 1 : first half of the measure, et. al.

alternative to sculpting a sextuplet

Treat the first six notes as two groups of identically shaped three-note groups (the type of shape identified as three notes in descending steps). From the sculpting point of view, there is something to be gained by suppressing attention to the  entity of a ‘scale’ formed by 6 or 7* descending notes, and revealing  the two elegantly sculpted smaller and primal groups of three descending notes.**

#6 Conclusion

We may be stretching things to speak of sculpting a group of notes as
if we were sculpting a material object. However, if we consider what
the body of the sculptor does while sculpting and what the body of the
pianist does while playing piano, and what their intents may be, there are similarities. And it is not beyond reason to say that a motion that we would do as a sculptor, can be transformed and transported into the actions we take as pianists.  It is then up to the pianist to use their aesthetic imagination to reveal the shape thus created.

As pianists, we can imagine notes as viscous objects capable of
responding to our hands as clay to the sculptor.  In making these analogies there is always allowances for great jumps in the imagination between what we are externally doing with our body and what we feel like inwardly as to what we are doing with our body.   In this manner relevance can be gotten out of taking a group of notes and “bending”  it into the shape of a phrase.

Or working on a small group of notes until it takes a shape we are trying to gradually bring out in its sounds.  We can put it on a potter’s wheel until the shape we want develops and is eminently clear to the onlooker.  It is like taking out the notes on a lathe until we have created the proper curves of the pitch shapes.

* It is 7 notes if one includes the first note of the second half of the measure.

** If one can’t quite get the sculptural shape of the three descending notes, try singing Figaro’s aria wherein he calls attention to himself by repeating the syllables Fi-Ga-Ro, over and over on the same three descending notes.

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The Goldberg Variations: in General and in Particular When Crossing Hands

The Goldberg Variations: in general and in particular when crossing
hands.  The hands always start in a more remote position from each
other than is dictated by where the next notes are.


I held my arms in front of me, floating above the keyboard, the
forearms rotated so that the palms of the hands faced each other
across an empty horizontal space.  In that space I imagined there
being a tangible object.  The object was well defined but not quite

I imagined the feeling that my hands were two gentle but strong
clamps* on opposite ends of an object that occupied the horizontal
space between them.  I stayed aware of the imaginary object tightened
the clamps pushing inwards towards each other and that somehow the
object, with some resistance, without losing its integrity, could be
compressed along its horizontal dimension.  I gently compressed it
until my hands were the same distance from each other as the two keys
on the piano that represented in each hand the most current sixteenth
note in the piece.  One of the notes being in a voice that was in the
right hand, the other in a voice in the left hand.

I would repeat that procedure by advancing to the notes that lay on
the next sixteenth note of the piece, and so on.   The distance between
the palms and the size of the object they held was constantly changing
in size as the piece evolved in sixteenth notes.  OFten one of the two
notes was a note longer than a sixteenth, and remained in its place,
while the note in the other voice changed.  In other words, things
were constantly changing.

Regardless of the distance between the hands, when articulating the
The next pair of notes ended up being greater than, lesser than, or the
same**, their mutual distance between when articulating the current
pair of notes, I nonetheless re-expanded the distance between my hands
so that I would have to begin again by compressing the imaginary
the object between my hands until the distance between the palms
corresponded to the distance between the new pair of notes.

This technique is also surprisingly effective even at those moments and
episodes in the Goldberg when the hands cross each other.  But even
when the left hand took up a position to the right of the right hand,
as the right hand correspondingly took up a position to the left of the
left hand, the position of the arms just prior to the ‘squeezing
together’ of the imaginary object that lay between the palms, was with
uncrossed hands, the left hand being as usual to the left of the right
hand, and the right hand to the right of the left hand.  The palms
would then squeeze the imaginary object towards a point when the two
palms would converge in space even though in reality that continued in
their motions until they crossed each other.  But the procedure for
the following notes, even if it still involved crossed hands, began
from a position when the arms were not crossed but moved into a
the position that was crossed.  This was most easily forgotten if a series
of pairs of notes got further and further away from each other; the
palms should always be moved towards each other to land on the next notes

Try to avoid feeling that adjacent fingers are setting themselves down
on the keyboard one after the other.  Each finger comes from afar and
converges centrally, towards the other hand, to get to its note.

One should never feel that they are simply setting adjacent fingers
down, side by side, on adjacent notes – without first drawing the
hands further apart and playing the next sixteenth note via an action
which brings the hands back towards each other.

This means that the action in the finger causing a key to sound is not
a motion that is strictly speaking downwards, since it doesn’t begin
from a static position directly above the key.  The motion of the
finger is always swept along the hypotenuse of a long skinny right
triangle.  From a physicist’s point of view, motion along a
hypotenuse can always be thought of as having a down component and a
lateral component.  It is like the path of a boat crossing a swift-flowing stream.  One does not steer directly towards the nearest point
on the opposite side of the stream, but always somewhat to a side so
as to compensate for the flow of the water.

What I am saying today seems to me to be an extension of things I have
said in the past take had the form of “never aim directly at the next
key you are playing, but overshoot it, and then settle back easily to
its location.  That this can be more accurate in the long run, instead
of betting all the money you have on getting to the goal through a
direct unwavering motion.

It is also similar to what I’ve said in the past about “damping
curves” where a series ever diminishing but accelerating motions,
first one way and then the other converges on the exact location you
have in mind on the keyboard.  I also realize that this is in
contradiction to the method I have often proposed for skipping from
one place on the keyboard to another more remote location, by using
“opposing vectors”: the current finger tries to stay on its key even
though the arm is already pulling as hard as it can towards the more
remote key; that tension builds up between the two opposing motion;
until like an overwound spring, the spring suddenly explodes, and the
hand is propelled in a single, unbroken motion, to the remote key.

* Each side was separately adjustable – not like a vice or c-clamp.

** Thus, even if the hands remained in the same place on the keyboard,
covering the same group of notes, with the five fingers of each hand,
during a series of notes, I would still oscillate the hands apart from
each other and then close up the distance between them.

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Bach: Well-Tempered Klavier: Book One: Prelude in C# Major

Note: A.B. are the initials of a student’s name

A.B.’s lesson on 2/11/18


A.B. learns a passage more by what the fingering is than what the
notes are.

He and I are in the midst of trying to change the proportion between
consciously taking notice of what note he is playing at a given moment
and consciously noticing what finger he is using to play that note.

We want to tilt the balance somewhat more in favor of knowing the
versus knowing the finger.  This in no way means that I don’t want you
to know what the finger is, only that in your present conscious state
when you are playing, you seem to be more aware of the finger you are
using the name-identity of the note the finger is playing.

I recommend in your case that you always know what note you are playing –
even if you don’t say its name, externally or internally, to yourself.


Close up the spaces between your fingers laterally until they are
gently touching.  Then open those spaces until the hand has opened up
again (still along a left-right plane).  Do these actions, back and forth
in a periodic motion.  This motion should at all times be gentle and
flowing, without, on the one hand, any abrupt changes from instant
to instant in the width of the hand from pinky to thumb, or, on the
other hand, any instants of hesitation.  It should be a continuous,
fluid motion: hand breathing open, hand breathing closed.  Perhaps
like a violinist who has been taught never to stop the bow, even for
an instant, especially when changing the direction of the bow from an up
bow to a down bow, or vice versa.

After you have practiced this periodic motion of the hands for a short
while, see if you can transfer it into the act of playing the Bach
Prelude.  As you are playing, see if you can have that continuous,
flowing, sense of your hands always being in the process of opening or
of closing.  It is a breathing action, that helps the hands conform to
the shape of the keyboard, as the distance between the currently
played piano key and the next one to be played, is constantly
changing, whether by a little or a lot.  While the sound flows
continuously, the physical distances between the notes play are
changing.  We are trying to map onto the rigidity of the keyboard the
plasticity of the distances along with the keyboard from written note to
written note.  For this to occur, it is necessary for the hand to
morph continuously from one shape into another.

Bach: Well-Tempered Klavier: Book One: Fugue in C# major:


A word about using finger substitutions, should your inclination be
to use them periodically.

Let’s start by taking an extreme case, substituting the fifth finger
for the thumb.  One way of doing this is to have the pinkie, in one
continuous motion, come directly over to where the thumb is and
replace it on the same key.

A second way is to use the pinkie to trace out lightly on the keyboard
the intermediate steps between being relatively further from the thumb
to be relatively close to the thumb.

As a specific example play c4 with your left thumb.  The pinkie at
that moment is hovering somewhere in the vicinity of f3, although it
could be lower or higher.  In this exercise be sure that the c4 sounds
continuously at all times.  During this time the pinkie starts
migrating from the f3 towards the c4, lightly brushing over the
surfaces of the intervening keys g3, a3, and b3, and vaguely noticing
the slight gaps that occur between the adjacent white notes.  As the
last step of this process, the pinkie takes possession of the c4 key and
the thumb, at that moment, or some moments afterward leaves the c4
and travels off to the right.

The second way differs from the first way and maybe more like a
sightless person reading across a page in Braille.  She makes sure she
is aware of all the bumps that are raised off a line of text on the
page, perhaps touching these bumps in a very gentle way, with just
enough pressure to be conscious of their presence.

So, while some pianists avoid finger substitutions under any
circumstances and some use them use substitutions either occasionally
or more often, those that do use substitutions should be aware that
they have a choice of ways to do it, each of which may have a certain
the advantage under the current circumstances of the piece.

Bach: Well Tempered Klavier: Book One: C Minor Prelude


Throughout the first part of this prelude, where the same note
figuration is played twice in each measure, there is a choice between
setting up the fingers of the hands to cover all the notes that will
sound in that measure, as if preparing to play a vertical chord
consisting of those notes, or at the other extreme of possibilities
keeping the hand closed and relaxed at all moments, altering the shape
of the hand at each moment to accommodate the next finger to play so
by the moment it plays it finds itself over the piano key it wants to play.

Combining this second type of procedure, with what was said above
about finger substitutions, one can, if one wishes, intermittently or
on a regular basis, let each ‘next’ finger that is about to play drift
or skim over the surface of any piano keys that intervene between
where the next is currently resting and where it needs to be a moment
later to play the next note.  This may involve a ‘gradual’ closing of
the hand or a gradual opening of the hand.  One can think of this
method as ‘filling’ in the gaps on the keyboard between consecutive
notes.  One retains, then, if desired, an ideated, virtual sensation
of where the hand is on the keyboard, a sort of ESP with regard to the
mapping where the hand is on the keyboard.


Doing the opposite to what seems intuitively appropriate.  Example one.

Sometimes A.B.’s fingers get cramped when the current configuration of
notes in a measure involves close distances, especially half steps and
whole steps.

An effective solution is to begin by spreading the hand as wide as
possible.  The fingers stretched out as far as possible one from

Then let that feeling linger in the hand when actually playing the
notes that are close together on the keyboard.  The preliminary
tension in the hand is like winding up or stretching a spring, so that
afterward, the fingers snap into position on their respective

Sometimes a similar procedure can be used in which it is the two hands
as a whole that ‘stretch’ apart, widening the distance between them,
by opening up the spaces just between the first and second fingers so
that the second fingers feel like they are stretching further and
further apart from each other as if ties together with a stiff elastic
band.  This is useful when there is a wider skip between the first and
second notes of the measure followed by notes that are in close
proximity on the keyboard


Doing the opposite to what seems intuitively appropriate.  Example two.

Measures 16 and 17:

Play the entire measure slowly using just the second finger of each
hand to sound every note.  Then repeat the same measure with the
normal fingering and in the normal tempo.  Then go on to m17 and
repeat the same process, playing it slowly with one finger from each
hand and then at regular speed with normal fingers.*

This is an example of raising the level of difficulty in a passage so
that in comparison the way it says to do it in the score seems
‘easier’ and hopefully simply ‘easy’.

* I noticed that after doing this the only thing that wasn’t quite
even was in measure 17, the fifth note, af3, going down to f3.  A
moment’s relaxation of attention and the duration of a note may be
altered to be either longer or shorter than scored. It usually happens
at the moment that the student feels like “I’ve got this; I’ll just
run out the rest of the passage on sheer momentum”.


Doing the opposite to what seems intuitively appropriate.  Example

Measure 17 of the prelude.

When you go from the fourth note to the fifth note of the measure,
switch around which hand’s which thumb plays which note.  Let the left
thumb play the b3 and let the right thumb play af3.  A.B comments it
is easier to play like this than without crossing the thumbs.
Regardless, I say, if you now go back and play it the ‘normal’ way,
the normal way will seem much easier than before.


Measure 18 into measure 19.  An example of both “physical glue” and
“sonic glue”*

Notice the two times you play f3 in the left hand in the first of those two
measures.  Now notice that when you go over the bar line it is the
same f3 again that reappears, but this time played by the right hand.
Try to string these three f’s into its own little melody despite any
intervening notes.  This will make it easier for the right thumb to
find its way down to f3 at the beginning of m19.

* physical glue is taking physical notice of the connection between
two or more notes that are not sounded in direct succession (one and
immediately the next), and/or taking physical notice of the connection
between two notes that lie one in one hand and the other in the other
hand.  There is also what I call sonic glue where it is the attention
of the ear and not the muscles that are brought to bear on either non
consecutive notes or notes moving from one hand to another.


Adapting from measure 19 to measure 20.

Making something more difficult than it has to be in order to make it
seem easier.

Play the first of these measures in the octave it is written, but as
you cross the barline, abruptly switch to playing the notes an octave
higher than written.  In this way, you have added to the difficulty of
having to change from one chord to another, that of having to change
octave as well.  If you now again limit both measures to the same
octave range, just having to change the chord seems easier to do on
its own.

In general, the process of exaggerating the difficulty of a passage is
often a better strategy than simply trying to cope with the difficulty
at the level it is presented to you.  For after having made it more
difficult, the primary feeling, when going back to the original level
of difficulty, is one of abatement and movement towards ease.


Adapting from measure 19 to measure 20.  Another device.

Start playing in measure 19, but as you cross the bar line into
measure 20, play the first two notes of each hand simultaneously and
hold them out.  Then play through both measures normally.


Adapting from measure 19 to measure 20.  A third device.

At the beginning of measure 20, play and hold the first notes of the
measure (a2 in the left hand and fs3 in the right hand).  Then
leisurely go to the second notes (ef3–c4).  Now try from the previous
measure, normally.


Measure 37: starting on the third beat

Shifting the balance in awareness between what finger one is using to
play the note and what the note is that is being played by the finger.

I asked A.B. to play all the notes with just the third fingers of each
hand. By using just one finger for all the notes, in both hands, we are
drawing attention away from what fingers one is using to what notes
are being played.


Measure 37 into 38.

Notice the difference in the width of the triad e3-g3-bf3 at the end of
m37 and the triad af3-c4-f4 at the beginning of m38.  Your hand seems
to be unaware that the second triad covers a bit wider span of notes
on the keyboard.  This should be recognized in addition to the fact
that the notes in the second triad are mostly located higher than those
of the first triad.

After that the right hand can become a little more closed (rather than
opened) for the tetrad d4 f4 af4 c5


Measure 19 into 20.

Exact Timing of Events in Consciousness

Your left hand has just played c3 at the end of measure 19, and it
seems to me when observing your hand that you are now trying to move
your left hand already to ef3 (the second note of m20) before actually
settling down to play the af2 (the first note of m20).  Make sure you
play that first note before dealing with the ef3.  Go to the A=flat first.


Measure 30 (the jump in the right hand at the beginning of the

Start by playing the first note in the right hand (d4) followed by the
second note in the left hand (b3).  Think more of the downwards pitch
motion of d4 to b3 than the upwards motion from d4 to g5.  Instead of
most of your thought going to move the right hand up to the g5, give
thought to something moving downwards to balance out the motions of
the hand.  Let the b3 be the anchor for the g5, rather than trying to
calculate the distance from d4 to g5.


Measure 1.

The hidden terrain of the keyboard.

A.B. happens to be resting his second finger of the right hand on fs4
when he plays the first note of the measure, c5.

In Ken Burns’ series on the Civil War, instead of following the
overall course of a battle, we sometimes experience it through the eyes of just
one soldier.  I said: your second finger has to take a very
circuitous or ‘scenic’ route from fs4 to ef4 (the second note of the
measure and the first note that the second finger will play.  This
route involves the second finger climbing down from one “mountain peak” in the form of a black key (fs), roaming silently through a
valley of some white keys, and then climbing up a second peak (ef4).
It’s OK, just perhaps a little more challenging, terrain wise than if
the second finger was initially resting on a white note.

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