Category: Crossing Hands

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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