# Why are a piano’s black keys arranged in groups of three and two?

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Why are a piano’s black keys arranged in groups of three and two?

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The older I get the more elegant it appears. There’s some deep symmetry that arises from this. The most easily seen is that you have (in every octave)

W B W B W

B W B W B

With a tritone separating them (F and B).

The white keys all together make C major or A minor, all the black keys are flats/sharps. So they mark the increments in those scales and can be used to visualize the increments in the other keys.

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Sound waves can have different frequencies, and this pretty much correlates to pitch. Higher pitch has higher frequency. But you can have a sound is between the standard notes. So sound frequencies can be anything, the ones that are notes can be thought of a ladder. You can’t stand between two rungs, only on one.

How they’re spaced involves some math into music theory, so let’s jump ahead to the chromatic scale. This is a twelve-note scale https://en.wikipedia.org/wiki/Chromatic_scale https://en.wikipedia.org/wiki/Diatonic_and_chromatic goes into more depth of scales that are a subset, for example a C major scale.

An instrument like the violin or trombone can make pitches between the notes. For a violin, you can put your finger at any point, not just the frets like on a guitar. With a piano you’re not changing the length of the string, you’re sounding a separate set of strings.

You could arrange a piano keyboard with one row of the same color key, one per tone on the chromatic scale, but then you’d need to keep track of what size steps to make for your major and minor scales: Do you skip a key or not to go up or down one full note? For chords, what shape do you need to make with your fingers?

Among other things, having a repeating pattern means you can locate a given note by its place in the pattern.

I’m going to add a simpler reply, just to put a finer point on the great explanation already given. A Cliff notes version, since this is ELI5.

1. The smallest distance between notes in Western music is the half step. And two half steps put together make a whole step.
2. We like to arrange the notes that we will use in writing music into a linear array, called a scale. It’s like you’re going to draw with crayons, but instead of using all 64 in the box, you choose 7 colors for your picture.
3. Now, here’s the weird part. You know how you expect a staircase to be all even sizes? It would be weird if every now and then the staircase had a short step here and there. Well, Western music is weird in that way. We have been trained by hundreds of years of music history to like a scale that is uneven. A major scale is mostly whole steps, but there is a half step between notes 3 and 4, and also between 7 and 8 (And 8 is just a repetition of the first note, just to make it feel complete and like we came home, or finished the story. A staircase like that would look weird, right? But that’s what sounds good to us.
4. The C major scale is the easiest to see this with. It’s just the white keys, CDEFGAB[C]. I bracketed the last one, because it’s not a new unique note, it just makes the scale feel finished. C to D has a black key between them, so that’s a whole step. Same for D to E. But E to F, there’s that half step. Then all whole steps until B to C, which has no black key between, so it’s a half step. Minor scales put the half steps in different places, but it still is an uneven array of notes.

So scales are uneven, which is weird and not symmetrical, but that’s what sounds good to us. Playing other scales uses different notes, but that arrangement of distances stays the same. Why do we like it? Some say it is because that’s the kind of music you hear your whole life, some have even said it’s hardwired in the brain.

Interestingly, a lot of musical items are uneven, or don’t make sense to a non-musician (“Hey, why are all the doorways in your house different heights?”) And if you try to change something that’s uneven (like a major chord) into something that is…. more logical? Symmetrical? It often sounds weird or unsettling [such as an Augmented triad].

And of course, this is Western music. If you live in India or Asia, there might be other systems that I’m just not qualified to talk about. In Western music, the study of non-Western music is called ethnomusicology.