How to Play Formula Patterns (2 Octaves)

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In today’s episode, I wanted to discuss how to play formula patterns, which are basically an extended version of a regular scale. They’re required for piano exams starting from a Grade 2 level (RCM), and even if you aren’t doing the whole exam thing, they’re fun to play and a great brain exercise.

Let’s get to it!

How to play formula patterns

So I want to start this episode by showing you what a formula pattern looks like, because they’re kind of bizarre at first. There’s more to it than just playing a regular major scale up and then down – they have a lot more twists and turns.

Also I just want to note that we’re talking about 2 octave formula patterns today – you can do them 4 octaves as well, but they’re obviously more difficult, so we’ll save that for another day.

All right, here’s the formula pattern!

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So it’s kind of wild, right? Basically it’s a scale that alternates going parallel motion (the same direction) and contrary motion (opposite directions).

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There are a couple challenges to learning formula patterns. The first challenge is to simply memorize and comprehend the formula, which looks like this:

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Okay, so here’s how we decode this little formula pattern chart.

There are 8 blocks to this formula pattern. Each block is a 1-octave scale. Sometimes the scale will move in parallel motion, and sometimes in contrary motion. This is indicated by the arrows – if they’re headed in opposite directions (one arrow going up, one arrow going down), then it’s moving contrary. If both arrows are in the same direction, it’s moving parallel.

So say you were trying to figure out a C formula pattern. You would start by playing a C scale in parallel motion, which means both your hands are doing C, D, E, etc.

And once you hit an octave, so from C all the way to the next C, we start the second block – the right hand keeps going up, but the left hand goes back down. Then once we hit our next set of Cs, we bring the hands back in together, and so forth.

Finger patterns

Okay so you’re learning how to play formula patterns, your brain is bending, but you think you’ve internalized the pattern part of it.

The other complication in this scale variation is fingering. When your hands play a scale in the same direction (parallel), it’s actually quite challenging to use correct fingering at first, because your hands are switching fingers at different times.

In a major scale, your right hand uses this pattern:

1 2 3 1 2 3 4 5

Whereas your left hand uses this pattern:

1 2 3 4 5 1 2 3

So you can see the switches and crossings happen at different intervals. Take it extremely slow until you grasp this and can play it correctly, without just “guessing” through the fingering. It takes a little work up front, but once your fingers can do the pattern without much thought on your part, it becomes much easier to apply to other scales.

When your hands are going in opposite directions (contrary), the fingering is actually super easy. The right hand, moving up, goes like this:

1 2 3 1 2 3 4 5

And the left hand, moving down, goes like this:

1 2 3 1 2 3 4 5

They have the exact same finger pattern when they move in opposite directions. How handy!

How to play formula patterns – printout

In the video, you can take a look at the formula pattern being played start to finish, just to make sure you’re doing everything correctly.

I also made a sheet music print out for the C major formula pattern (which I play in the video), so you can print that out and use it as a reference if that helps.

Formula Pattern (C Major)


Allysia has been teaching piano in Canada for nearly a decade, and has her Grade 10 RCM certificate. She especially enjoys nerding out to music history and theory. When she’s not making videos or teaching, she’s reading, writing, and jamming in a rock band.