Along with scales, arpeggios are the basic building blocks of musical material in the standard piano repertoire. Seymour Bernstein shows how arpeggios, like scales, involve fingering patterns in the left and right hands that can be reused for different keys. Thumb crossings are treacherous, particularly in the right hand where they span an interval of a fourth. Bernstein demonstrates how there needn't be a legato connection when the right-hand passes under and demonstrates exercises that can help increase fluidity for both arpeggios and scales. Again, rotation is key to properly choreograph arpeggios. As speed increases, the larger rotary motions diminish and become integrated into a fluid mechanism.

Executing octaves is a challenge for every developing pianist. Octaves are a "mold," Seymour Bernstein stresses, meaning you cannot successfully play them with disengaged, flexible fingers. To achieve the proper shape for playing octaves, the pinky and thumb must be taut – as demonstrated in Lesson 2 – while the inner fingers can assume specific positions to help with facility. Finally, playing octaves often causes the shoulders to rise, so Bernstein leaves you with sage advice: "lower your shoulders, lift your spirits."

Scales can be daunting when you are first learning them, but Seymour Bernstein breaks them down into their common elements. Every major scale has the same building blocks: two four-note "tetrachords" spaced by two whole-steps and a half-step. Another whole step is positioned between the two tetrachords so that the pattern of steps is defined as WWH W WWH – where W stands for "Whole Step" and H stand for "Half Step." Armed with this knowledge, you can build any major scale on the keyboard. To practice them, you must understand the two basic finger groupings that comprise a 7-note scale: 123 and 1234. These groupings even work on black-key scales, although you will need to begin in the middle of a grouping. Finally, Bernstein introduces the pivotal concept of rotation in choreographing scales and shows how to apply it seamlessly to these fingering groupings to increase fluidity and ease of execution.