Category: Technique

How to play 3 in one hand against 2 in the other

This is a brief technical manual for coping with the rhythmic situation known as “three against two.”  One encounters this situation when one hand is subdividing a pulse into three equal parts while the other hand is subdividing the same pulse into two equal parts.

I want to break the problem down into a short series of small, doable steps.

We start by taking the two rhythms (triplet and duplet) and superimposing them one upon the other, and derive a single composite rhythm.  Once we have it in the form of a composite rhythm, there is no longer anything special required to address the coordination of one hand with the other.  Once we see 3 against 2 as a single rhythm, it looses all its strangeness, and becomes a very simple rhythm to execute.


One way to write it is: a quarter note – eighth note – eighth note – quarter note.  It does not matter if these note values are different than those in the score.  Any note values would serve the same purpose as long as their durations stand in the following comparative ratio: 2 : 1 : 1 : 2.  Half  -Quarter  – Quarter – Half, or Eighth – Sixteenth – Sixteenth – Eighth ,would do as well.

We no longer have to concern ourselves with the difference in the duration of a triplet versus a duplet.  It is all homogenized in the combined rhythm.

This, then is the composite rhythm of a 3 against 2:

|| quarter – eighth – eighth – quarter ||

|| means a bar line.  We assume the meter to be 3/4 time,

First, let us consider the situation where the 3 (or triplet) is in the right hand and the 2 (or duplet) is in the left hand.


Step 1:

|| quarter – eighth – eighth – quarter  ||

Using both hands at once, tap or play this rhythm (quarter eight eighth quarter) over and over in an endless loop*.  You can keep the hands a foot or two apart as you do this.  Each time you reach the end of the measure recycle, without a pause, to the beginning of the measure.  And continuing in this fashion, doing the measure over and over.  Do it enough times for it to feel completely natural and automatic in the hands.

What to tap on:

You can tap it on the closed fall board at two separated places, or always playing the C below middle C with the left hand and Middle C with the right hand.  Or on two drums, or on your lap, or anything else handy.

Step 2:

Repeat step 1 and add these spoken words to the notes:

|| quarter  eighth eighth quarter || quarter …. <-Play *

|| together  right   left   right”   || together … <- Say

* each note with both hands

Step 3:

Repeat step 1 and 2 with this revision.  The four notes in the composite rhythm are not all played with both hands.

(the rhythm):

|| quarter  eighth eighth  quarter  || quarter ….   || together  right   left       right       || together …

(which hand(s))

here is another description of step 3:

play the first note in both hands and say  “together”

play the second note in just the right hand and say  “right”

play the third note in just the left hand and say  “left”

play the fourth note in just the right hand and say “right”

start the pattern again with “together”

just make sure to stay with the same rhythm: quarter eighth eighth quarter.

Step 4:

4A  for the right hand:

Repeat step 3, but say only the word ‘right’ and only at those times when the right hand is due to play.

|| quarter    eighth   eighth  quarter  || quarter ….    <= play

|| right         right                     right       || right     ….    <= say

4B  for the left hand:

Repeat step 3, but say only the word ‘left’ and only at those times when the left hand is due to play.

|| quarter   eighth eighth quarter  || quarter .

|| left                          left                         || left ….     <= say

Let us now consider the situation where the 3 is in the left hand and the 2 is in the right hand.


Step 1:

Step 1 is the same as before.  Using both hands at once tap or play this rhythm (quarter eight eighth quarter) over and over in an endless loop.  At the end of each measure of 3/4 go back (without a pause) to the beginning of the measure.

Step 2:

Repeat step 1 and add these spoken words to the notes:

|| quarter    eighth eighth quarter || quarter ….   <= Play

|| together  left     right    left        || together …   <= Say this

Step 3:

Repeat step 1 and 2 with this revision.  The four notes in the composite rhythm are not all played with both hands.

|| quarter   eighth eighth quarter  || quarter ….  <= rhythm

|| both left  right left ||  both … <= which hand

here is another description of step 3:

play the    first note  in both hands  and say  “together”

play the    second note  in just the left hand    and say  left”

play the    third note     in just the right hand  and say right”

play the   fourth note    in just the left hand    and say  “left”

start the pattern again with “together”

Once again, just make sure to stay with the same rhythm: quarter-eighth-eighth-quarter.

Step 4:

4A  for the right hand:

Repeat step 3, but say only the word ‘right’ and only at those times when the right hand is due to play.

|| quarter   eighth eighth quarter  || quarter ….  <= play this rhythm

|| right                       right                      || right ….    <= say

4B  for the left hand:

Repeat step 3, but say only the word ‘left’ and only at those times when the left hand is due to play.

|| quarter   eighth eighth quarter  || quarter ….  <= play this rhythm

|| left           left                       left         || left ….     <= say

Have fun. Start slowly until the muscular and vocal habits have had a chance to set in.

I would love some feedback.  For instance,

1) is this technique too complicated to follow

2) does this technique help put the 3 against 2 issue in a clearer light

3) A: didn’t help much. B: helped slightly C: made a difference

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  1. Joe – how do you feel about using a saying/ phrase to learn 3 against 2? I learned it in Sightsinging class as “Nice cup of tea” for 3 against two, where you say that as you tap. The three (nice, cup, tea) is in the right hand, and two is in the left hand (nice, of). It helps to start saying the phrase slowly in rhythm (the one you outlined)
    Then for 2 against 3, we had “Pass the butter” where two is in the left hand (Pass, but-) and three is in the right hand (Pass, the, -ter).
    Does that make sense, or is there any reason that is a bad method to use?

    Joe: It makes perfect sense. Whatever ‘works’ is a ‘good method’.

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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How one hand can help the other

Summary: Play runs evenly. Be your own teacher by having one hand help the other.

Years ago while I was playing a Mozart Concerto, I was frustrated in the first movement because I could not play evenly a scale-like run in the right hand.  The notes were not pearly.  They were not pellucid, they didn’t shine because of their evenness.

I could not seem to solve this issue myself.  I was an adult pianist, yet I felt I needed a guide, a teacher, to help me.  I needed someone to give me a model of the evenness for which I was striving; a teacher, or if not a teacher, then a conductor to follow.  I wanted something more than just a sound-model – hearing someone else play it and then trying to imitate it.

Quite by accident I took one of the fingers of my left hand (my fourth finger), and began flexing it over and over at the speed of the run, as if chiding my right hand: “why can’t you play it like this?”  Fortunately, the next thing I did was to play the right hand while making the repetitive gestures in the left hand.  All of a sudden, the right hand sounded its notes evenly.  Somehow it seemed as if the finger of the left hand was in control of the fingers of the right hand.  From the right hand’s point of view it seemed something more than just following an example.  What sort of connection had changed between my two hands?

Our body exhibits bilateral symmetry.  The center is unique but the left and right sides are mirror images (or nearly so).  When we clap our hands we take full advantage of the power one arm lends to the other when they make mirror like motions.  The center of the body acts as the mediator and connects and transmits the reinforcing motions of the arms.  Take any passage that is done by the right hand and make corresponding mirror-like gestures with the left hand.  The right hand will feel less isolated, less like it has to take care of the task all by itself.  Something is balancing it, something is making it whole.  It no longer seems awkward or happening at an extremity, “out on a limb,” as it were.

The teacher lies in yourself.

I used to say to tell my students “lessons are all about practicing.”  Everything we do at a lesson is but a model, a sample of a dialogue between the ‘teacher in you’ and the ‘pupil in you.’  Eventually you will successfully internalize both people in this dialogue.

I remembered these words when I was wiggling my left hand finger to even out my right hand fingers.  That wiggling finger had taken on the role of the ‘teacher in me’ and showing the other ‘student in me,’ my right hand, how to go about playing evenly.

It was more than just ‘moral’ support or advice being given from myself to myself.  There was a direct transference of physical energy from one side of the body to the other, each completing in space the movement of the other.

I instinctively had given the single finger in my left hand an important advantage over the right hand.  It was not cramped down onto the keyboard forced to depress certain keys.  It did not have to articulate different fingers according to a certain order.  So, it was more than a model of evenness, it was a model to the right hand of liberation, of not being constrained by which particular finger was playing which particular note at a given time.  My right hand took vicarious pleasure in what the left hand did.  Perhaps due to the “mirror” neurons in my brain, the right hand could take on the feel and internal sense of motion of the left hand, more so because of the literal connectivity of the arms through the center of the body.

Future blogs:  1. Contrary motion versus parallel motion.   2.  Parallel motion in even steps in one hand versus uneven steps in the other.


These blog entries are not ‘timely’:  they do not address issues that relate to the present news of the world.  They address perennial issues faced by most pianists when striving to excel in their playing.  I encourage you to search backwards in the blogs to find the ones that will yield the greatest benefit to you.  You are also welcome to contact me to suggest a topic that you would like to see appear on the site.

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A “crescendo” of relaxation

Illusion of a Crescendo VideoRelated Video: Illusion of a Crescendo

M. and I are working on the second (the fast) movement of the Beethoven Sonata Op 109.

She has small hands and struggles to execute the more difficult passages.  Even the span of an octave requires special effort by her. However, when she relaxes her hand, the span she is capable of between the thumb and pinkie   grows by at least several millimeters. That may be a small difference, but often is enough to determine the difference between ease and discomfort, relaxation and strain, accuracy playing the two keys and inaccuracy.

The more tension there is in the hand, the less it can freely breathe open and closed.  The hand should not remain in a fixed position any longer than it does during the day when we are not at the piano.  It is always fluid, mobile and protean, a mass ever changing in form.

The best playing results when the hand is capable of both taking and loosing any shape or span.  It should remain in its momentary shape without any tension or clinging to that shape, then be able to change to a different shape a moment later without having to overcome any inertia. There should be no resistance to change when it occurs due to any sort of clinging to the previous shape.

Let us say we are playing a series of diatonic triads going up the C Major scale.  It is incorrect to assume that the hand can exactly maintain the same shape for throughout.  Watch closely and you will see that the lateral angle in the wrist, and even in the fingers, is constantly changing.  That the angles in the shoulder and elbow are also changing.  If we freeze the hand as we play the triads, while the first triad may feel comfortable, each subsequent triad will feel more and more awkward.  Sometimes, though, it takes close attention to the changing muscular sensations of our body to notice this change as it occurs.

A crescendo of relaxation:

If, as is often the case, we are unaware of growing tension as we are playing, the only antidote is relaxing over and over as we proceed.  Though we may feel as relaxed now as we were a few measures ago, the chances are good that we are not.  It may seem to us that each time we relax during the piece we are getting more relaxed than we have been any time prior in the piece, but in reality it takes this ‘crescendo’ of renewed acts of relaxing to offset a less conscious drift in the other direction.

Often, when a student is playing a piece, and sees that a more difficult part of the piece is coming over the time-horizon, she will tend to do two things: get louder and get tenser.  It is as much an emotional reaction to worry and fear than a simple physical reaction to cope with the anticipated physical difficulty.  The paradox, of course, is that the less tense the playing mechanism remains, the easier it will be to play the upcoming passage, regardless of its difficulty.

Odd as it may sound, the best physical state while playing is the one that most resembles a quiet state of not doing anything at all.  Often we exaggerate the difference between the former and the latter, and do “too much” in order to play.

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  1. It reminds me of a dancer who stays in a “momentary shape” and also “ever changing in form”. What a lovely image to compare a pianist to a dancer, the expression emerging from the physical into the ethereal in a similar way but heightened with addition of sound.

  2. What is the best way to practice this state of ‘not doing anything at all’ while practicing? Are there any specific techniques you have for that?

    1. Part of the answer is doing the least physical effort that is nonetheless adequate to producing desirable results. It is separating the degree of effort from the degree of the desired result. There was a medieval philosopher, William of Ockham, who in essence said: if there are various ways of solving a problem or achieving a certain result, and some of the ways are complicated and some are much simpler, choose a simpler one – choose the simplest one possible. Ockham himself said: do not multiply entities unnecessarily. Of course, for most people, his way of describing his idea about keeping things simple is not expressed at all simply.

      Another way I think about this is like this:

      When people are singing or playing “in the groove” they often describe the experience as:

      I wasn’t conscious of trying to do anything. Or, it was as if I was listening to singing rather than singing. Or, the sounds flow of their own accord; the notes seem to flow out without prompting; the music is speaking through me; I am only the transmitting mechanism; I feel like everything is under the control of the music; my ego and
      physical intents have little to do with it. All notes, all sounds, come from silence. Silence precedes them, silence surrounds them, silence follows them. They materialize out of the ether and vanish in press of time. Time itself is an artifact that allows us to tell the story one piece at a time, though in the essence it is not yet words, yet all the words are there somehow in a womb; a single pregnant mass.

Melodies in octaves – balance of sound between the octaves

Summary: How to ‘de-muddify’ notes in octaves

For me, one of the most difficult sonic tasks at the piano is to balance two notes if they are exactly one octave apart.  If a melody sounds in two octaves at once, it is usually at this distance of one octave.   In spite of all my attempts, the resulting sound is not a clear blending, but contains elements of diffuseness and mutual interference.  I never have considered this sound acceptable.

Interestingly, this problem disappears if I separate the two notes by exactly two octaves.  The way the overtones of the two notes combine in this case creates a pristine and crystalline acoustical effect, noticeably different than the muddiness of the single octave.  For organists it is the same as the difference of combining the principal 8 foot and 2 foot stops as against the 8 and 4 foot stops.

There are three things that I can do to help clarify the sound in the cases where the composer does have a melody in notes one octave apart.  How to de-muddify:

1. Have the duration of the notes in the lower octave be slightly shorter than those in the upper octave. This will overcome the natural tendency for lower pitches to seem to move more slowly than higher pitches. There will be a barely detectable silence in the sound from the lower octave at end of each of its notes, before the next notes of the melody begin simultaneously.

2. I can play around with the relative loudness of the two notes. Depending on the musical context, there will be cases when the lower notes can be slightly louder than the upper, and other cases when the opposite seems best. This is like “orchestrating” the given passage.

3. Consider the note an octave higher as being simply the first overtone of the lower note. In this way we can hear the upper note as being already contained in the lower note.

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