Thermodynamics of Piano Playing

An important field of mathematics is the study of large numbers. Even when single events of a particular type are not predictable, large numbers of such events often behave according to strict laws. Although the energies of individual molecules of water in a glass may differ considerably, the temperature of the water can stay very constant and can be measured with high accuracy. Does piano playing have an analogous situation that would allow us to apply the laws of large numbers and thereby draw some useful conclusions?

Piano playing is a complex process because of a large number of variables that enter into the production of music. The study of large numbers is accomplished by counting the "number of states" of a system. The grand total of meaningful states so counted might be called the "canonical ensemble", a meaningful assembly that sings together a tune that we can decipher. Believe it or not, "canonical ensemble" (see Statistical Mechanics by Kerson Huang, Wily, 1963, P. 75) is legitimate thermodynamic terminology! Therefore, all we need to do is to calculate the canonical ensemble, and when finished, we simply apply the known mathematical rules of large systems (i.e., thermodynamics) and voila! We are done!

The variables in question here are clearly the different motions of the human body, especially those parts important in playing the piano. Our job is to count all the ways in which the body can be moved in playing the piano; this is clearly a very large number; the question is, is it large enough for a meaningful canonical ensemble?

Since no one has ever attempted to calculate this canonical ensemble, we are exploring new territory here, and I will attempt only a very approximate estimate. The beauty of canonical ensembles is that, in the end, if the calculations are correct (a legitimate concern for something this new), the method used to arrive at it is usually immaterial -- you always arrive at the same answers. We calculate the ensemble by listing all the relevant variables, and counting the total parameter space of these variables. So here we go.

Let's start with the fingers. Fingers can move up and down, sideways, and be curled or straight (three variables). Say there are 10 measurably different positions for each variable (parameter space = 10); counting only the number of 10s, we have 4 so far, including the fact that we have 10 fingers. There are actually many more variables (such as rotating the fingers around each finger axis) and more than 10 measurable parameters per variable, but we are counting only those states that can be reasonably used to play the piano, for a given piece of music. The reason for this restriction is that we will be using the results of these calculations for comparing how two persons play the same piece, or how one person would play it twice in a row. This will become clearer later on.

Now the palms can be raised or lowered, flexed sideways, and rotated around the axis of the forearm. That's 3 more 10s for a total of 7. The forearm can be raised or lowered, and swung sideways; new total is 9. The upper arm can be swung forward-backwards, or sideways; new total is 11. The body can be moved forwards-backwards, and sideways: new total is 13. Then there are the variables of force, speed, and acceleration, for a total of at least 16. Thus the total parameter space of a pianist has many more than 10(exp)16 states (one followed by 16 zeros!). The actual number for a given piece of music is many orders of magnitude larger because of the above calculation is only for one note and a typical piece of music contains thousands or tens of thousands of notes. The final parameter space is therefore about 10(exp)20. This is approaching the ensemble space for molecules; for example, one cc of water has 10(exp)23 molecules, each with several degrees of freedom of motion and many possible energy states. Since thermodynamics applies to volumes of water very much smaller than 0.0001 cc, the canonical ensemble of the pianist is pretty close to thermodynamic conditions.

If the canonical ensemble of the pianist is nearly thermodynamic in nature, what conclusion can we draw? The most important result is that any single point in this phase space is totally irrelevant, because the chances of your reproducing this particular point is essentially zero. From this result, we can draw some immediate conclusions:

First Law of Pianodynamics: no two persons can play the same piece of music in exactly the same way. A corollary to this first law is that the same person, playing the same piece of music twice, will never play it exactly the same way.

So what? Well, what this means is that the notion that listening to someone play might decrease your creativity by your imitating that artist is not a viable idea, since it is never possible to imitate exactly. It really supports the school of thought which claims that listening to good artists play cannot hurt. Each pianist is a unique artist, and no one will ever reproduce her/is music. The corollary provides a scientific explanation for the difference between listening to a recording (which reproduces a performance exactly) and listening to a live performance, which can never be reproduced (except as a recording).

Second Law of Pianodynamics: we can never completely control every aspect of how we play a given piece.

This law is useful for understanding how we can unconsciously pick up bad habits, and how, when we perform, the music takes on its own life and in some ways, goes out of our own control. The powerful laws of pianodynamics take over in these cases and it is useful to know our limitations and to know the sources of our difficulties in order to control them as much as possible. It is a truly humbling thought, to realize that after a long, hard practice we could have picked up any number of bad habits without ever even suspecting it. This may in fact provide the explanation of why it is so beneficial to play slowly on the last run-through during practice. By playing slowly and accurately, you are greatly narrowing the ensemble space, and excluding the "bad" ones that are far away from the "correct" space of motions. If this procedure does indeed eliminate bad habits, and is cumulative from practice session to practice session, then it could produce a huge difference in the rate at which you acquire technique in the long run.