The TO Motion, Explanation and Video
Let us start by analyzing the basic fingering of scales. Consider the RH, C major scale. We begin with the easiest part, which is the RH descending scale, played 5432132,1432132,1 etc. Since the thumb is below the hand, the 3 or 4 finger rolls over the thumb easily, the thumb naturally folds under those fingers, and this descending scale fingering works well. This motion is basically the TU motion; the TO descending motion is similar, but we will need to make a slight but crucial modification to this in order to make it into a true TO method, but that subtle modification will be difficult to understand until we master the TO method. Thus the difference between TU and TO for the RH descending scale is very subtle.
Now consider the RH, C major ascending scale. This is played 1231234, etc. In the TO method, the thumb is played just like the 3 and 4 fingers; i.e., it is simply raised and lowered without the sideways TU motion under the palm. Since the thumb is shorter than the other fingers, it can be brought down almost parallel to (and just behind) the passed finger without colliding with it. In order to hit the thumb on the right key, you will need to move the hand and use a slight twitch of the wrist. For scales such as the C major, both the thumb and passed finger are on white keys and will necessarily crowd each other somewhat. In order to avoid any possibility of collision, the 3 or 4 finger must be quickly moved away as the thumb comes down. This is the operation that must be practiced in order to play a smooth TO scale. In the TO method, it is not possible to hold the 3 or 4 finger down until the thumb plays, unlike the TU method, and the thumb cannot pass over these fingers. For these reasons, some people object to the name TO because it is misleading, but I have not been able to find a better name. When you first try the TO method, the scale will be uneven and there may be a “gap” when playing the thumb. The trick in learning the TO method is to reduce this "gap" so that it becomes inaudibly small. Therefore, the transition must be very quick even in a scale played slowly. As you improve, you will notice that a quick flick/rotation of the wrist/arm is helpful. Beginners usually find TO to be easier than TU, but those who learned TU for many years will find TO difficult and uneven.
The logic behind the TO method is the following. The thumb is used like any other finger. The thumb only moves up and down. This simplifies the finger motions and, in addition, the hand, arms, and elbows do not need to contort to accommodate the thumb movements. Thus the hand and arm maintain their optimum angle to the keyboard at all times and simply glide up and down with the scale. Without this simplification, technically difficult passages can become impossible, especially because you still need to add new hand motions to attain such speeds, and many of these motions are incompatible with TU. Most importantly, the movement of the thumb to its correct location is controlled mostly by the hand whereas in the TU method, it is the compound motion of the thumb and hand that determines the thumb location. Because the hand motion is smooth, the thumb is positioned more accurately than with the TU method, thus reducing missed notes and hitting of wrong notes and at the same time bestowing better tone control to the thumb. Also, the ascending scale becomes similar to the descending scale, because you always roll the fingers over for passing. This also makes it easier to play hands together since all fingers of both hands are always rolling over. Another bonus is that the thumb can now play a black key. It is this large number of simplifications, the elimination of the stress that results from the paralyzed thumb, and other advantages discussed below, that reduce the potential for mistakes and enable faster play. There are exceptions: slow, legato passages, or some scales containing black keys, etc., are executed more comfortably with a TU-like motion. Most students who had used only TU will initially have a terrible time trying to understand how anyone can play anything TO. This is the clearest indication of the harm done by not learning TO; for these students, the thumb is not "free" as explained below. We shall see that the free thumb is a very versatile finger. But don’t despair, because it turns out that most advanced TU students already know how to play TO -- they just don’t know it.
The LH is the reverse of the RH; the TO method is used for the descending scale, and the ascending scale is somewhat similar to TU. If your RH is more advanced than the LH, perform the explorations to faster TO speeds using the RH until you decide exactly what to do, then pick up that motion with the LH.
Because students without teachers have difficulty visualizing TO, we examine a video clip comparing TO and TU. I have put this video in 2 formats because each software can play only certain formats. I haven't yet learned to link to a video in HTML (so you can just click on it), so to view it, you will have to do it manually. First, open a video player such as QuickTime or Windows Media Player, then find the window where you can type in the URL of the video, usually under "File". Below are 2 URLs; one of them should work. My Media One does NOT work on either URL.
http://members.aol.com/chang8825/TOscale.mp4
http://members.aol.com/chang8825/TOscale.wmv
The video shows my RH playing two octaves TO, ascending and descending, played twice. This is then repeated using TU. To non-pianists, these may appear to be essentially the same, although the TU motion was slightly exaggerated. This illustrates why videos of piano motions are not as helpful as one might think. The TO motions ascending are basically correct. The TO motions descending has one error -- a slight bending of the nail phalange of the thumb. At these moderate speeds, this slight bending does not affect the play, but in strict TO, the thumb should remain straight for both ascending and descending play. This example illustrates the importance of learning TO as early as possible. My tendency to bend the nail phalange is the result of using only TU for many decades, before I learned TO. An important conclusion here is keep the thumb straight at all times for TO.