Why is the musical scale the way it is? 12 keys: 7 major, 5 minor?

Question

Why is the musical scale the way it is? 12 keys: 7 major, 5 minor?

In: 116

Answer 1

First: why is it 12 and not 13? Because if you use notes with integer harmonics (as most instruments do) and do the math trying to determine how to subdivide an octave into equal parts, 12 is a comparatively very low dissonance number. It also allows the neat 2^(19) ≈ 3^(12) approximation, so 12 fifths is approximately 19-12=7 octaves.

Second: why the arrangement of white keys? That one is more “cultural” – probably because the circle of fifths goes F-C-G-D-A-E-B. If you use only the black keys, that’s also a pentatonic scale, but Western music usually uses 7-tone scales.