In everyday language, symmetry refers to the quality of being made up of exactly similar parts facing each other or around an axis. There is a sense of harmoniousness and beauty in proportion and balance that is aesthetically pleasing to us, because it reflects nature.
Symmetry can be an exact correspondence on either side of a dividing line, plane, centre or axis, or it can retain proportion and balance without being exact. A while back I wrote a blog post on an unusual way of practising that was used a lot more in the past than it appears to be today, the technique of symmetrical inversion. Since writing this, I have explored it a bit more and found a few extremely useful ways of applying it. More on this in a moment. By way of endorsement, virtuosos such as Leopold Godowsky believed very much in this way of practising, and Marc-Andre Hamelin also uses it. Listen to Mr. Hamelin talking about and demonstrating symmetrical inversion practice here, from 3:57 to 6:00.
Have you noticed that the piano keyboard is symmetrical from two places within the octave – the note D and the note A flat? Thus, if I play a D major scale ascending in my RH, using the conventional fingering 1-2-3-1-2-3-4-5, the exact mirror image can be reproduced in the LH – the same intervals, the same fingerings and finger distances, and the same pattern of black and white notes. Instead of D major, we get B flat major, starting and ending on the 3rd degree of the scale:
Similarly, the scale of A flat major, RH ascending, gives us E major descending in the LH, starting on the 3rd degree of the scale:
If I play the D major scale ascending in the LH together with the symmetrical inversion in the other hand, the RH will be playing B flat major from the 3rd degree, etc.
How it Works
Using the symmetry of the keyboard, you create an exact symmetrical version in one hand of a passage you are playing in the other. You match identical fingers and intervals and play the mirror image of the other hand simultaneously.
Famous pianist and teacher Rudolph Ganz described the technique thus:
It is my belief that symmetrically inverting any difficult technical problem will help the other hand develop equally. Experience with symmetrical practice over the years has been of considerable benefit to me and my students. How often have I listened to the whispered conversation between my two hands: “Difficult?” “Indeed!” “I’d like to try and conquer it too.” “Go ahead. Symmetrically, it is easy. Use the same fingering as mine.” Rudoph Ganz Exercises: Contemporary and Special, p. 12.
Here is the subject from Bach’s Fugue in E minor from Book 1 of the “48”, the original in the RH and the symmetrical inversion in the LH. The mirror reflection of the starting note E in the RH is C for the LH:
Let’s look at the opening of the finale of the Sonata in B flat minor, op. 35 by Chopin – a finger twister if ever there was one. To practise each hand with the inversion, you’ll need to do it twice since the original is in unison. Because the RH starts on the note F, the LH will need to start on the note B (the mirror reflection of F). Thus if the RH plays the patterns in one direction from F, the LH plays them in the opposite direction from B. Remember that we use the corresponding finger in the other hand, and when one hand plays a black key so does the other. The movements will also be symmetrical because the hands are doing the same thing. Here are both versions:
Admittedly, there is a downside to this form of practising, which may explain why it has fallen out of favour. Playing the inversion simultaneously with the right-way-up version doesn’t sound too good – to say the least! Nowadays, there is a reaction against the mechanical practice methods of the past but there is the danger of throwing out the baby with the bathwater. If you have an electronic keyboard, you could always practise like this with the sound turned down very low, in order to save your ears. Or simply practise pianissimo an octave or two higher.
There is another way of doing it where the symmetry is not exact, where you keep the general mirror design but make a counterpoint that sounds acceptable. Samuil Feinberg suggests the following RH inversion for the LH opening of Chopin’s Prelude in G:
(from The Russian Piano School, transl. and ed. Christopher Barnes. London, Kahn & Averill, p. 35.)
Why it Works
So why does this work? We know that the left hemisphere of the brain controls the RH and the right hemisphere the LH. There are connections between the identical areas in both hemispheres, which means that the nervous processes happening in one hemisphere get reproduced in the parallel areas in the other. The proprioceptive sensations in one hand help those in the other.
In addition, science has shown us that the right hemisphere of the brain deals more with spatial awareness, with greater sensitivity to motion and distance, whereas left hemisphere is responsible for linear functioning. So by practising using the symmetrical inversion tool, we can draw on the strengths of the whole brain. The two hemispheres act together to enable a sort of stereophonic knowledge. The dominant hand helps the other hand, and the benefits are enhanced tactile and intellectual memory, because again you are thinking about every single note in its context. This method is also extremely useful for solving fingering problems; your dominant hand can make a symmetrical inversion of a passage the weaker hand has to play, and you can often settle on the best fingering that way.
I don’t think this is either necessary or feasible to apply to whole works, but I do think it is extremely useful to do for awkward passages where your fingers seem to refuse to do what you want them to do in spite of more mainstream ways of practising. The Chopin Prelude (above) is a very good example.
Another application is when you might need to make an exercise out of a piece. A student was struggling with the LH in a place in Schumann’s Aufschwung (bars 5-7 in this extract).
Using 543-432 while the thumb holds its long note, the legato will need some help from the pedal. In order to play this pattern, there needs to be a small release in the wrist between the two short groups for the “3” of 543 to connect freely to the “4” of 432. In the lesson we made a quick exercise where both hands could sense how this felt, using the following pattern in symmetrical inversion. After a few minutes practising this, the LH was able to glide through the passage with the greatest of ease. Hold the thumb notes very loosely and play the quavers as smoothly as possible by keeping close to the keys with a very loose wrist.
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