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

Question

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

In: 44

Answer 1

Western music scales basically boil down to the mathematical coincidence that:

2^(7)=128 ≈ (3/2)^(12)≈129.7

This gives us the circle of fifths, 12 semitones in an octave, and scales with 7 notes per octave. Then, the most evenly spaced way to take 7 steps to go 12 semitones is 2+2+1+2+2+2+1 which is a major scale. Making the skipped 5 notes black gives the groups of 2 and 3 you see on keyboard instruments.