Why are a piano’s black keys arranged in groups of three and two?
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Amateur pianist here. A lot of people here are talking about the frequencies and stuff, which is important, but isn’t the whole story of why a piano keyboard looks like that. I will instead talk about the user interface portion of this.
To recap the frequency part in short, a long time ago, some people figured out that:
* There are 12 notes, if you go further they repeat themselves and sound nice while doing so
* Certain combinations of notes sound nice (chords) and these combinations also repeat every 12 notes
* If you mostly stuck to using only combinations of notes from a specific collection of notes, it is easier to make something that sounds nice
* In particular, one collection of notes is pretty easy to work with. This collection is called the major scale.
* The major scale is defined by a series of steps. You don’t use every note, only 7 out of the 12, and you can start anywhere and still be in a major scale as long as you follow that series of steps.
When making a keyboard instrument, you could just have a bunch of the white keys going 1-2-3-4-5-6-7-8-9-10-11-12 and repeating forever. There are several problems with this, though.
1. With wide white keys, your hands will not be big enough to play cool patterns. With narrower keys, your fingers will be so wide they tend to hit multiple notes at the same time, which does not sound great.
2. It is very hard to tell what note you are going to play before you play it because everything is a white key with no variation and no labeling.
3. There are no repeated structures in the keys that show musicians useful patterns that rely on repetition, you have to count up key by key and it is easy to lose your spot
To solve problem 1, we could convert some of the white keys to raised, out of the way black keys while keeping the white keys a reasonable width. Convert enough of the keys to black ones and you can strike a balance between being able to make chords with hands of finite width, and not accidentally hitting two notes at the same time with fingers of nonzero width.
Say we make every other second or third key black. This solves the space issue, but we still can’t tell which note is which at a glance or by touch.
Solving problems 2 and 3 at the same time, 12 is a very important number in music, so it would make sense to give the white and black keys a pattern that repeats every 12 notes (and doesn’t have any other factors) so musicians can rapidly identify what notes they are about to play, both by sight and by touch (a bit like the bump keys on a computer keyboard), and allow for easy location of “repeated” notes.
There are a number of ways we can accomplish this. 11 white then 1 black, 4 white-1 black-6 white-1 black, but remember the major scale from earlier? If we go white-black-white-black-white-white-black-white-black-white-black-white, and then repeat, all of the white keys now form a major scale, and we have a repeating pattern with no other factors. All of the other major scales (offset by a number of keys) now have a slightly understandable relationship between their relative pitch and the number of black keys they use. Thus it is now more easy to identify which collections of notes form a scale/key that sounds nice to play in.
That arrangement solves the wide hands problem and the note identifiability problem, while also presenting the musicians with a repeated pattern that makes it easier to identify what sounds nice.
There are other arrangements of white and black keys that solve these issues, but this is the one most of the world has standardized on, as anything else would make it very difficult to transfer between keyboard instruments. Drawing on a computer analogy, sure, DVORAK may be more efficient than QWERTY, but good luck getting the world to change.
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