Walking Arm

The walking arm is the up and down movement of the forearm combined with the lateral motion of that same limb. It is described as an almost invisible down-up motion of the forearm with every key that is played, for it assists in removing the burden from the fingers. The walking arm must be used with great skill and must involve the forearm only, without involving the upper arm. This movement contains a resemblance to actual walking.
For example, when the person bends the knee in walking, the foot lifts and moves the person's body to balance over the next step. Movement across is made by an up-down movement which in turn creates a lateral movement. The forearm and finger work together on this same principle. In this way, the forearm is responsive to the needs of the finger, for it will adjust upwards for the finger to move off the key and there will be a slight lift of the arm with the lift of the fingers. These adjustments of the arm up and down to black and white keys make the keyboard feel as if there is no difference in sensation between black and white keys.

The up and down movement of the forearm combined with the lateral motion of the forearm generates momentum, which enables the forearm rotation to complete its movement.
p is the symbol used to designate momentum.

1) up and down and 2) across

There is no efficient movement across the keyboard without the use of the walking arm.
The playing of the piano involves

1. vertical
2. as well as horizontal movement

(down, up, and across) . It is to be noted that, the motion in one direction must not in any way restrict the motion in the other. This can be avoided by not instigating the next action until each key is completed.

• Vertical Action
  Vertical action should feel vertical and the timing must be distinct and separate. The play to the next key must not be made until the first key is completed or else tension will result. The fingertip should hold on to the bottom of the key and not release it until all action is completed. The act of reaching or expanding begins when the action of playing a finger is over.
  Each key has a down-up motion and this sympathetic vibration must occur for each finger. It is perhaps most obvious in large skips when a big swing up and across is needed. When the walking arm is working together with the forearm rotation, the rebound factor is intrinsic and feels natural. The walking arm element helps to achieve skips in legato which are the so-called un-stretchable distances.

The "walking arm" is a specific application of coordinate motion. It describes how the arm "walks" laterally to follow the fingers, ensuring they’re always supported and never overextended. Picture walking down a path: your weight shifts smoothly from one foot to the other. Similarly, the arm shifts its weight from one finger to the next, maintaining alignment and balance. This is especially useful in passages with large intervals or shifts, preventing the hand from collapsing or the wrist from locking up.
The "walking arm" concept in piano technique, though it’s not as widely discussed as, say, arm weight or forearm rotation. It’s a term sometimes used to describe a coordinated, fluid motion of the arm that supports the fingers as they move across the keyboard, mimicking the natural, balanced weight transfer you experience when walking. The idea is to keep the arm relaxed and "behind" the fingers, guiding them smoothly from note to note, rather than letting the fingers drag the arm or having the arm remain static.
In practice, the "walking arm" involves the arm moving laterally, almost like it’s taking small "steps" in order to maintain alignment with the active finger playing each key. This helps achieve a seamless legato, prevents tension, and ensures the hand stays in an optimal position without overreaching or collapsing. It’s particularly useful for phrasing and melodic lines, where you want the sound to flow naturally, as if the arm is walking along with the music's rhythm and contour.
The concept ties into broader ideas of whole-body coordination in piano playing. For instance, some teachers compare it to how your legs shift weight effortlessly when you walk and your arm similarly transfers its support from one finger to the next. I have seen it referenced in pedagogical discussions, like those from Taubman-influenced approaches, where the arm’s role is emphasized as an active partner to the fingers, not just a passive weight.