1. Learn the route before increasing the range
A formula pattern can look like a lot to remember until you separate its journey into a few clear destinations. The task is to change direction without losing the pulse or your place. Similar motion means both hands travel in the same direction; contrary motion means they travel in opposite directions. Visit Chapter 13 first if contrary motion is unfamiliar.
A common two-octave formula route inserts an outward-and-inward excursion at the midpoint of both the ascending and descending scale. The route below starts with RH C4 and LH C3. Middle C is C4. Each arrow travels one octave through the notes of C major.
| Leg | Motion | RH destination | LH destination |
|---|---|---|---|
| 1 | Together upward | C5 | C4 |
| 2 | Apart | C6 | C3 |
| 3 | Together inward | C5 | C4 |
| 4 | Together upward | C6 | C5 |
| 5 | Together downward | C5 | C4 |
| 6 | Apart | C6 | C3 |
| 7 | Together inward | C5 | C4 |
| 8 | Together downward | C4 | C3 |
Here “inward” means the hands return to their earlier spacing, not that they collide on one key. Their separation changes during the contrary-motion legs; the one-octave spacing applies to the similar-motion sections.
Give yourself a quiet tour of the destinations first: play only these landing notes, slowly and without pedal. Say “up, apart, in, up; down, apart, in, down.” Then fill in one leg at a time. The Royal Conservatory piano syllabus provides a two-octave formula-pattern reference; use the precise notation required by your teacher or syllabus when preparing an examination.
Checkpoint: you can name both hands’ next destinations before playing. Knowing only the RH route is not yet knowing the pattern.
2. Rehearse the two changes of direction
These are isolated transition studies, not a continuous engraving of the entire formula. Each bar is a separate one-octave leg. Pause at the barline, release, and reposition for the printed starting finger. The repeated tonic and fresh fingering are deliberate; do not carry these pauses into a fluent formula scale.
In the departure, RH continues upward while LH reverses. Learn the LH C–B–A–G change on its own, then include the RH C–D–E–F. At first, stop on each pair and check its position. RH changes from 5 to 1 on the repeated C5 between the printed bars.
In the return, RH continues downward while LH changes from upward to downward. LH reaches C4 with 1 and starts downward with 1. RH resets from 1 to 5 on the repeated C5. Neither study requires a clef change; ledger lines preserve the actual register.
Join only when the route is secure
For a continuous version, the shared turning tonic normally sounds once and its finger must suit the following leg. That means revising the isolated endpoint fingers, not simply deleting the repeated note from these drills. Plan that transition with your teacher before adding speed.
Transfer the route to G major only after checking every F♯ in both directions. For minor keys, choose and label the form first; melodic minor introduces a further question about which notes belong to each hand’s direction. Complete continuous major/minor formula engravings and their transition fingerings remain a later reference expansion.
Checkpoint: each direction change feels dependable. A short, secure transition is real progress; build the longer pattern from those joins.